partykit/0000755000176200001440000000000014723366102012125 5ustar liggesuserspartykit/tests/0000755000176200001440000000000014723350653013273 5ustar liggesuserspartykit/tests/regtest-party-random.R0000644000176200001440000000131214172230000017460 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) ## packages library("partykit") library("rpart") ## data-generating process dgp <- function(n) data.frame(y = gl(4, n), x1 = rnorm(4 * n), x2 = rnorm(4 * n)) ## rpart check learn <- dgp(100) fit <- as.party(rpart(y ~ ., data = learn)) test <- dgp(100000) system.time(id <- fitted_node(node_party(fit), test)) system.time(yhat <- predict_party(fit, id = id, newdata = test)) ### predictions in info slots tmp <- data.frame(x = rnorm(100)) pfit <- party(node = partynode(1L, split = partysplit(1L, breaks = 0), kids = list(partynode(2L, info = -0.5), partynode(3L, info = 0.5))), data = tmp) pfit p <- predict(pfit, newdata = tmp) p table(p, sign(tmp$x)) partykit/tests/regtest-honesty.R0000644000176200001440000000251714254064505016564 0ustar liggesusers library("partykit") n <- 100 x <- runif(n) y <- rnorm(n, mean = sin(x), sd = .1) s <- gl(4, n / 4) set.seed(29) ### estimate with honesty cf_ss <- cforest(y ~ x, strata = s, ntree = 5, mtry = 1, perturb = list(replace = FALSE, fraction = c(.5, .5))) ### sample used for tree induction stopifnot(sum(tapply(cf_ss$weights[[1]], s, sum)) == n / 2) ### sample used for parameter estimation stopifnot(sum(tapply(cf_ss$honest_weights[[1]], s, sum)) == n / 2) p <- predict(cf_ss) set.seed(29) ### w/o honesty cf_ss2 <- cforest(y ~ x, strata = s, ntree = 5, mtry = 1, perturb = list(replace = FALSE, fraction = .5)) stopifnot(sum(tapply(cf_ss2$weights[[1]], s, sum)) == n / 2) # random diffs also on other platforms #if (.Platform$OS.type != "windows") # stopifnot(all.equal(cf_ss$nodes, cf_ss2$nodes)) stopifnot(all.equal(cf_ss$weights, cf_ss2$weights)) stopifnot(all.equal(predict(cf_ss, type = "node"), predict(cf_ss2, type = "node"))) tmp <- cf_ss2 tmp$weights <- lapply(tmp$weights, function(x) 1L - x) pp <- predict(tmp) stopifnot(all.equal(p, pp)) ### bootstrap ignores honesty cf_bs <- cforest(y ~ x, strata = s, ntree = 5, perturb = list(replace = TRUE, fraction = c(.5, .5))) stopifnot(sum(tapply(cf_bs$weights[[1]], s, sum)) == n) stopifnot(is.null(cf_bs$honest_weights)) partykit/tests/regtest-ctree.Rout.save0000644000176200001440000000551314172230000017641 0ustar liggesusers R version 4.0.3 (2020-10-10) -- "Bunny-Wunnies Freak Out" Copyright (C) 2020 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > ## package > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > > ## iris data > data("iris", package = "datasets") > irisct <- ctree(Species ~ ., data = iris) > print(irisct) Model formula: Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width Fitted party: [1] root | [2] Petal.Length <= 1.9: setosa (n = 50, err = 0.0%) | [3] Petal.Length > 1.9 | | [4] Petal.Width <= 1.7 | | | [5] Petal.Length <= 4.8: versicolor (n = 46, err = 2.2%) | | | [6] Petal.Length > 4.8: versicolor (n = 8, err = 50.0%) | | [7] Petal.Width > 1.7: virginica (n = 46, err = 2.2%) Number of inner nodes: 3 Number of terminal nodes: 4 > table(fit = predict(irisct), true = iris$Species) true fit setosa versicolor virginica setosa 50 0 0 versicolor 0 49 5 virginica 0 1 45 > > ## airquality data > data("airquality", package = "datasets") > airq <- subset(airquality, !is.na(Ozone)) > airqct <- ctree(Ozone ~ ., data = airq) > print(airqct) Model formula: Ozone ~ Solar.R + Wind + Temp + Month + Day Fitted party: [1] root | [2] Temp <= 82 | | [3] Wind <= 6.9: 55.600 (n = 10, err = 21946.4) | | [4] Wind > 6.9 | | | [5] Temp <= 77: 18.479 (n = 48, err = 3956.0) | | | [6] Temp > 77: 31.143 (n = 21, err = 4620.6) | [7] Temp > 82 | | [8] Wind <= 10.3: 81.633 (n = 30, err = 15119.0) | | [9] Wind > 10.3: 48.714 (n = 7, err = 1183.4) Number of inner nodes: 4 Number of terminal nodes: 5 > sum((airq$Ozone - predict(airqct))^2) [1] 46825.35 > > ### split in one variable only: Temp is selected freely in the root node > ### but none of the other variables is allowed deeper in the tree > airqct1 <- ctree(Ozone ~ ., data = airq, + control = ctree_control(maxvar = 1L)) > psplitids <- unique(do.call("c", + nodeapply(node_party(airqct1), + ids = nodeids(node_party(airqct1)), + FUN = function(x) split_node(x)$varid))) > stopifnot(length(psplitids) == 1L) > > proc.time() user system elapsed 0.987 0.037 1.013 partykit/tests/bugfixes.R0000644000176200001440000014404014723337715015241 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) set.seed(290875) datLB <- structure(list(Site = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 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3L, 1L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 2L, 3L, 3L, 1L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 3L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 2L, 3L, 3L, 1L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 3L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 2L, 3L, 3L, 1L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 3L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 2L, 3L, 3L, 1L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 2L, 1L, 1L, 2L), .Label = c("10000U", "5000U", "Placebo" ), class = "factor"), Age = c(65L, 70L, 64L, 59L, 76L, 59L, 72L, 40L, 52L, 47L, 57L, 47L, 70L, 49L, 59L, 64L, 45L, 66L, 49L, 54L, 47L, 31L, 53L, 61L, 40L, 67L, 54L, 41L, 66L, 68L, 41L, 77L, 41L, 56L, 46L, 46L, 47L, 35L, 58L, 62L, 73L, 52L, 53L, 69L, 55L, 52L, 51L, 56L, 65L, 35L, 43L, 61L, 43L, 64L, 57L, 60L, 44L, 41L, 51L, 57L, 42L, 48L, 57L, 39L, 67L, 39L, 69L, 54L, 67L, 58L, 72L, 65L, 68L, 75L, 26L, 36L, 72L, 54L, 64L, 39L, 54L, 48L, 83L, 74L, 41L, 65L, 79L, 63L, 63L, 34L, 42L, 57L, 68L, 51L, 51L, 61L, 42L, 73L, 57L, 59L, 57L, 68L, 55L, 46L, 79L, 43L, 50L, 39L, 57L, 65L, 70L, 64L, 59L, 76L, 59L, 72L, 40L, 52L, 47L, 57L, 47L, 70L, 49L, 59L, 64L, 45L, 66L, 49L, 54L, 47L, 31L, 53L, 61L, 40L, 67L, 54L, 41L, 66L, 68L, 41L, 77L, 41L, 56L, 46L, 46L, 47L, 35L, 58L, 62L, 73L, 52L, 53L, 69L, 55L, 52L, 51L, 56L, 65L, 35L, 43L, 61L, 43L, 64L, 57L, 60L, 44L, 41L, 51L, 57L, 42L, 48L, 57L, 39L, 67L, 39L, 69L, 54L, 67L, 58L, 72L, 65L, 68L, 75L, 26L, 36L, 72L, 54L, 64L, 39L, 54L, 48L, 83L, 74L, 41L, 65L, 79L, 63L, 63L, 34L, 42L, 57L, 68L, 51L, 51L, 61L, 42L, 73L, 57L, 59L, 57L, 68L, 55L, 46L, 79L, 43L, 50L, 39L, 57L, 65L, 70L, 64L, 59L, 76L, 59L, 72L, 40L, 52L, 47L, 57L, 47L, 70L, 49L, 59L, 64L, 45L, 66L, 49L, 54L, 47L, 31L, 53L, 61L, 40L, 67L, 54L, 41L, 66L, 68L, 41L, 77L, 41L, 56L, 46L, 46L, 47L, 35L, 58L, 62L, 73L, 52L, 53L, 69L, 55L, 52L, 51L, 56L, 65L, 35L, 43L, 61L, 43L, 64L, 57L, 60L, 44L, 41L, 51L, 57L, 42L, 48L, 57L, 39L, 67L, 39L, 69L, 54L, 67L, 58L, 72L, 65L, 68L, 75L, 26L, 36L, 72L, 54L, 64L, 39L, 54L, 48L, 83L, 74L, 41L, 65L, 79L, 63L, 63L, 34L, 42L, 57L, 68L, 51L, 51L, 61L, 42L, 73L, 57L, 59L, 57L, 68L, 55L, 46L, 79L, 43L, 50L, 39L, 57L, 65L, 70L, 64L, 59L, 76L, 59L, 72L, 40L, 52L, 47L, 57L, 47L, 70L, 49L, 59L, 64L, 45L, 66L, 49L, 54L, 47L, 31L, 53L, 61L, 40L, 67L, 54L, 41L, 66L, 68L, 41L, 77L, 41L, 56L, 46L, 46L, 47L, 35L, 58L, 62L, 73L, 52L, 53L, 69L, 55L, 52L, 51L, 56L, 65L, 35L, 43L, 61L, 43L, 64L, 57L, 60L, 44L, 41L, 51L, 57L, 42L, 48L, 57L, 39L, 67L, 39L, 69L, 54L, 67L, 58L, 72L, 65L, 68L, 75L, 26L, 36L, 72L, 54L, 64L, 39L, 54L, 48L, 83L, 74L, 41L, 65L, 79L, 63L, 63L, 34L, 42L, 57L, 68L, 51L, 51L, 61L, 42L, 73L, 57L, 59L, 57L, 68L, 55L, 46L, 79L, 43L, 50L, 39L, 57L, 65L, 70L, 64L, 59L, 76L, 59L, 72L, 40L, 52L, 47L, 57L, 47L, 70L, 49L, 59L, 64L, 45L, 66L, 49L, 54L, 47L, 31L, 53L, 61L, 40L, 67L, 54L, 41L, 66L, 68L, 41L, 77L, 41L, 56L, 46L, 46L, 47L, 35L, 58L, 62L, 73L, 52L, 53L, 69L, 55L, 52L, 51L, 56L, 65L, 35L, 43L, 61L, 43L, 64L, 57L, 60L, 44L, 41L, 51L, 57L, 42L, 48L, 57L, 39L, 67L, 39L, 69L, 54L, 67L, 58L, 72L, 65L, 68L, 75L, 26L, 36L, 72L, 54L, 64L, 39L, 54L, 48L, 83L, 74L, 41L, 65L, 79L, 63L, 63L, 34L, 42L, 57L, 68L, 51L, 51L, 61L, 42L, 73L, 57L, 59L, 57L, 68L, 55L, 46L, 79L, 43L, 50L, 39L, 57L), W0 = c(32L, 60L, 44L, 53L, 53L, 49L, 42L, 34L, 41L, 27L, 48L, 34L, 49L, 46L, 56L, 59L, 62L, 50L, 42L, 53L, 67L, 44L, 65L, 56L, 30L, 47L, 50L, 34L, 39L, 43L, 46L, 52L, 38L, 33L, 28L, 34L, 39L, 29L, 52L, 52L, 54L, 52L, 47L, 44L, 42L, 42L, 44L, 60L, 60L, 50L, 38L, 44L, 54L, 54L, 56L, 51L, 53L, 36L, 59L, 49L, 50L, 46L, 55L, 46L, 34L, 57L, 41L, 49L, 42L, 31L, 50L, 35L, 38L, 53L, 42L, 53L, 46L, 50L, 43L, 46L, 41L, 33L, 36L, 33L, 37L, 24L, 42L, 30L, 42L, 49L, 58L, 26L, 37L, 40L, 33L, 41L, 46L, 40L, 40L, 61L, 35L, 58L, 49L, 52L, 45L, 67L, 57L, 63L, 53L, 32L, 60L, 44L, 53L, 53L, 49L, 42L, 34L, 41L, 27L, 48L, 34L, 49L, 46L, 56L, 59L, 62L, 50L, 42L, 53L, 67L, 44L, 65L, 56L, 30L, 47L, 50L, 34L, 39L, 43L, 46L, 52L, 38L, 33L, 28L, 34L, 39L, 29L, 52L, 52L, 54L, 52L, 47L, 44L, 42L, 42L, 44L, 60L, 60L, 50L, 38L, 44L, 54L, 54L, 56L, 51L, 53L, 36L, 59L, 49L, 50L, 46L, 55L, 46L, 34L, 57L, 41L, 49L, 42L, 31L, 50L, 35L, 38L, 53L, 42L, 53L, 46L, 50L, 43L, 46L, 41L, 33L, 36L, 33L, 37L, 24L, 42L, 30L, 42L, 49L, 58L, 26L, 37L, 40L, 33L, 41L, 46L, 40L, 40L, 61L, 35L, 58L, 49L, 52L, 45L, 67L, 57L, 63L, 53L, 32L, 60L, 44L, 53L, 53L, 49L, 42L, 34L, 41L, 27L, 48L, 34L, 49L, 46L, 56L, 59L, 62L, 50L, 42L, 53L, 67L, 44L, 65L, 56L, 30L, 47L, 50L, 34L, 39L, 43L, 46L, 52L, 38L, 33L, 28L, 34L, 39L, 29L, 52L, 52L, 54L, 52L, 47L, 44L, 42L, 42L, 44L, 60L, 60L, 50L, 38L, 44L, 54L, 54L, 56L, 51L, 53L, 36L, 59L, 49L, 50L, 46L, 55L, 46L, 34L, 57L, 41L, 49L, 42L, 31L, 50L, 35L, 38L, 53L, 42L, 53L, 46L, 50L, 43L, 46L, 41L, 33L, 36L, 33L, 37L, 24L, 42L, 30L, 42L, 49L, 58L, 26L, 37L, 40L, 33L, 41L, 46L, 40L, 40L, 61L, 35L, 58L, 49L, 52L, 45L, 67L, 57L, 63L, 53L, 32L, 60L, 44L, 53L, 53L, 49L, 42L, 34L, 41L, 27L, 48L, 34L, 49L, 46L, 56L, 59L, 62L, 50L, 42L, 53L, 67L, 44L, 65L, 56L, 30L, 47L, 50L, 34L, 39L, 43L, 46L, 52L, 38L, 33L, 28L, 34L, 39L, 29L, 52L, 52L, 54L, 52L, 47L, 44L, 42L, 42L, 44L, 60L, 60L, 50L, 38L, 44L, 54L, 54L, 56L, 51L, 53L, 36L, 59L, 49L, 50L, 46L, 55L, 46L, 34L, 57L, 41L, 49L, 42L, 31L, 50L, 35L, 38L, 53L, 42L, 53L, 46L, 50L, 43L, 46L, 41L, 33L, 36L, 33L, 37L, 24L, 42L, 30L, 42L, 49L, 58L, 26L, 37L, 40L, 33L, 41L, 46L, 40L, 40L, 61L, 35L, 58L, 49L, 52L, 45L, 67L, 57L, 63L, 53L, 32L, 60L, 44L, 53L, 53L, 49L, 42L, 34L, 41L, 27L, 48L, 34L, 49L, 46L, 56L, 59L, 62L, 50L, 42L, 53L, 67L, 44L, 65L, 56L, 30L, 47L, 50L, 34L, 39L, 43L, 46L, 52L, 38L, 33L, 28L, 34L, 39L, 29L, 52L, 52L, 54L, 52L, 47L, 44L, 42L, 42L, 44L, 60L, 60L, 50L, 38L, 44L, 54L, 54L, 56L, 51L, 53L, 36L, 59L, 49L, 50L, 46L, 55L, 46L, 34L, 57L, 41L, 49L, 42L, 31L, 50L, 35L, 38L, 53L, 42L, 53L, 46L, 50L, 43L, 46L, 41L, 33L, 36L, 33L, 37L, 24L, 42L, 30L, 42L, 49L, 58L, 26L, 37L, 40L, 33L, 41L, 46L, 40L, 40L, 61L, 35L, 58L, 49L, 52L, 45L, 67L, 57L, 63L, 53L), Fem = c(1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L), Week = c(2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L), Total = c(30L, 26L, 20L, 61L, 35L, 34L, 32L, 33L, 32L, 10L, 41L, 19L, 47L, 35L, 44L, 48L, 60L, 53L, 42L, 56L, 64L, 40L, 58L, 54L, 33L, NA, 43L, 29L, 41L, 31L, 26L, 44L, 19L, 38L, 16L, 23L, 37L, 42L, 55L, 30L, 52L, 44L, 45L, 34L, 39L, 14L, 34L, 57L, 53L, 50L, 27L, NA, 53L, 32L, 55L, 50L, 56L, 29L, 53L, 50L, 38L, 48L, 34L, 44L, 31L, 48L, 40L, 25L, 30L, 18L, 27L, 24L, 25L, 40L, 48L, 45L, 47L, 42L, 24L, 39L, 30L, 27L, 15L, 32L, NA, 29L, 23L, 22L, 46L, 25L, 46L, 26L, NA, 24L, 10L, 50L, NA, 28L, 16L, 52L, 21L, 38L, 45L, 46L, 46L, 63L, NA, 51L, 38L, 24L, 27L, 23L, 64L, 48L, 43L, 32L, 21L, 34L, 31L, 32L, 21L, 44L, 45L, 48L, 56L, 60L, 52L, 43L, 52L, 65L, 32L, 55L, 52L, 25L, 54L, 51L, 27L, 33L, 29L, 29L, 47L, 20L, 40L, 11L, 16L, 39L, 35L, 51L, 43L, 52L, 33L, 41L, 29L, 38L, 9L, 32L, 53L, 55L, NA, 16L, 46L, 51L, 40L, 44L, 50L, 47L, 24L, 45L, 48L, 42L, 46L, 26L, 47L, 25L, 50L, 42L, 30L, 40L, 23L, 43L, 34L, 21L, 38L, 26L, 52L, 45L, 52L, 17L, 25L, 44L, 25L, 16L, 31L, NA, 18L, 30L, 21L, 41L, 30L, 46L, 27L, 23L, 25L, 13L, 22L, 41L, 29L, 18L, 61L, 29L, 50L, 36L, 36L, 33L, 71L, 36L, 46L, NA, 37L, 41L, 26L, 62L, 49L, 48L, 43L, 27L, 35L, 32L, 35L, 24L, 48L, 49L, 54L, 55L, 64L, 57L, 33L, 54L, 64L, 36L, NA, 48L, 29L, 43L, 46L, 21L, 39L, 28L, 33L, 50L, 27L, 48L, 7L, 15L, 39L, 24L, 52L, 45L, 54L, 54L, 45L, 28L, 47L, 9L, 35L, 52L, 62L, 46L, 19L, 26L, 56L, 52L, 50L, 56L, 53L, 32L, 44L, 56L, 43L, 57L, 40L, 50L, NA, 50L, 38L, 41L, 43L, 26L, 32L, 28L, 33L, 44L, 37L, 51L, 45L, 60L, 37L, 15L, 46L, 30L, 17L, 27L, NA, 20L, 36L, 25L, 43L, 49L, 50L, 22L, 18L, 37L, 16L, 28L, 41L, 30L, 25L, 68L, 30L, 53L, NA, NA, 44L, 66L, 23L, 50L, 33L, 39L, 65L, 35L, NA, 41L, 48L, 42L, 32L, 37L, 6L, 57L, 28L, 44L, 53L, 49L, 57L, 67L, 61L, 37L, 55L, 62L, 42L, 56L, 52L, 32L, 46L, 49L, 22L, 37L, 33L, 45L, 50L, 29L, 49L, 13L, 17L, 45L, 29L, 54L, 47L, 51L, 46L, 43L, 35L, 39L, 16L, 54L, 53L, 67L, 50L, 23L, 30L, 39L, 42L, 53L, 59L, 51L, 45L, 50L, 49L, 42L, 57L, 49L, 46L, NA, 50L, 50L, 41L, 36L, 33L, 40L, 34L, 42L, 47L, 37L, 52L, 50L, 54L, 36L, 21L, 46L, 28L, 22L, 49L, NA, 25L, 41L, 26L, 49L, 55L, 56L, 38L, 34L, NA, 32L, 34L, 58L, 37L, 33L, 59L, 35L, 47L, 40L, 45L, 46L, 68L, NA, 50L, 36L, 36L, 67L, 35L, NA, 51L, 51L, 46L, 38L, 36L, 14L, 51L, 28L, 44L, 56L, 60L, 58L, 66L, 54L, 43L, 51L, 64L, 43L, 60L, 53L, 32L, 50L, 53L, 22L, 37L, 38L, 56L, 49L, 32L, 44L, 21L, 29L, 43L, 42L, 57L, 46L, 57L, 47L, 41L, 41L, 39L, 33L, 53L, 58L, NA, 57L, 26L, 34L, 9L, 47L, 52L, 53L, 51L, 36L, 48L, 57L, 46L, 49L, 47L, 51L, NA, 49L, 56L, 31L, 45L, 41L, 47L, 28L, 53L, 53L, 43L, 53L, 52L, 59L, 38L, 25L, 44L, 30L, 41L, 60L, NA, 41L, 43L, 33L, 54L, 58L, 60L, 35L, 36L, 38L, 16L, 36L, 53L, 44L, 48L, 71L, 48L, 59L, 52L, 54L, 48L, 71L, 52L, 54L, 51L)), .Names = c("Site", "ID", "Treat", "Age", "W0", "Fem", "Week", "Total"), class = "data.frame", row.names = c(NA, -545L)) library("partykit") library("rpart") fac <- c(1,3,6) for(j in 1:length(fac)) datLB[,fac[j]] <- as.factor(datLB[,fac[j]]) dat <- subset(datLB,Week==16) dat <- na.omit(dat) fit <- rpart(Total ~ Site + Treat + Age + W0, method = "anova", data = dat) f <- as.party(fit) plot(f,tp_args = list(id = FALSE)) f[10]$node$split ### factors with empty levels in learning sample if (require("mlbench")) { data("Vowel", package = "mlbench") ct <- ctree(V2 ~ V1, data = Vowel[1:200,]) ### only levels 1:4 in V1 try(p1 <- predict(ct, newdata = Vowel)) ### 14 levels in V1 } ### deal with empty levels for teststat = "quad" by ### removing elements of the teststatistic with zero variance ### reported by Wei-Yin Loh tdata <- structure(list(ytrain = structure(c(3L, 7L, 3L, 2L, 1L, 6L, 2L, 1L, 1L, 2L, 1L, 2L, 3L, 3L, 2L, 1L, 2L, 6L, 2L, 4L, 6L, 1L, 2L, 3L, 7L, 6L, 4L, 6L, 2L, 2L, 1L, 2L, 6L, 1L, 7L, 1L, 3L, 6L, 2L, 1L, 7L, 2L, 7L, 2L, 3L, 2L, 1L, 1L, 3L, 1L, 6L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 6L, 6L, 7L, 2L, 2L, 2L, 2L, 2L, 1L, 3L, 6L, 5L, 1L, 1L, 4L, 7L, 2L, 3L, 3L, 3L, 1L, 8L, 1L, 6L, 2L, 8L, 3L, 4L, 6L, 2L, 7L, 3L, 6L, 6L, 1L, 1L, 2L, 6L, 3L, 3L, 1L, 2L, 3L, 1L, 2L, 7L, 2L, 3L, 6L, 2L, 5L, 2L, 2L, 2L, 1L, 3L, 3L, 7L, 3L, 2L, 3L, 3L, 1L, 6L, 1L, 1L, 1L, 7L, 1L, 3L, 7L, 6L, 1L, 3L, 3L, 6L, 4L, 2L, 3L, 2L, 8L, 3L, 4L, 2L, 2L, 2L, 3L, 2L, 2L, 2L, 3L, 4L, 6L, 4L, 8L, 2L, 2L, 3L, 3L, 2L, 3L, 6L, 2L, 1L, 2L, 2L, 7L, 2L, 1L, 1L, 7L, 2L, 7L, 6L, 6L, 6L), .Label = c("0", "1", "2", "3", "4", "5", "6", "7"), class = "factor"), landmass = c(5L, 3L, 4L, 6L, 3L, 4L, 1L, 2L, 2L, 6L, 3L, 1L, 5L, 5L, 1L, 3L, 1L, 4L, 1L, 5L, 4L, 2L, 1L, 5L, 3L, 4L, 5L, 4L, 4L, 1L, 4L, 1L, 4L, 2L, 5L, 2L, 4L, 4L, 6L, 1L, 1L, 3L, 3L, 3L, 4L, 1L, 1L, 2L, 4L, 1L, 4L, 4L, 3L, 2L, 6L, 3L, 3L, 2L, 4L, 4L, 3L, 3L, 3L, 3L, 1L, 6L, 1L, 4L, 4L, 2L, 1L, 1L, 5L, 3L, 3L, 6L, 5L, 5L, 3L, 5L, 3L, 4L, 1L, 5L, 5L, 5L, 4L, 6L, 5L, 5L, 4L, 4L, 3L, 3L, 4L, 4L, 5L, 5L, 3L, 6L, 4L, 1L, 6L, 5L, 1L, 4L, 4L, 6L, 5L, 3L, 1L, 6L, 1L, 4L, 4L, 5L, 5L, 3L, 5L, 5L, 2L, 6L, 2L, 2L, 6L, 3L, 1L, 5L, 3L, 4L, 4L, 5L, 4L, 4L, 5L, 6L, 4L, 4L, 5L, 5L, 5L, 1L, 1L, 1L, 4L, 2L, 3L, 3L, 5L, 5L, 4L, 5L, 4L, 6L, 2L, 4L, 5L, 1L, 5L, 4L, 3L, 2L, 1L, 1L, 5L, 6L, 3L, 2L, 5L, 6L, 3L, 4L, 4L, 4L), zone = c(1L, 1L, 1L, 3L, 1L, 2L, 4L, 3L, 3L, 2L, 1L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 1L, 2L, 3L, 4L, 1L, 1L, 4L, 1L, 2L, 1L, 4L, 4L, 4L, 1L, 3L, 1L, 4L, 2L, 2L, 3L, 4L, 4L, 1L, 1L, 1L, 1L, 4L, 4L, 3L, 1L, 4L, 1L, 1L, 4L, 3L, 2L, 1L, 1L, 4L, 2L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 2L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 4L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 2L, 2L, 1L, 1L, 4L, 2L, 4L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 4L, 2L, 3L, 3L, 1L, 1L, 4L, 1L, 1L, 2L, 1L, 1L, 4L, 4L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 4L, 1L, 1L, 4L, 1L, 1L, 4L, 3L, 4L, 4L, 1L, 2L, 1L, 4L, 1L, 3L, 1L, 2L, 2L, 2L), area = c(648L, 29L, 2388L, 0L, 0L, 1247L, 0L, 2777L, 2777L, 7690L, 84L, 19L, 1L, 143L, 0L, 31L, 23L, 113L, 0L, 47L, 600L, 8512L, 0L, 6L, 111L, 274L, 678L, 28L, 474L, 9976L, 4L, 0L, 623L, 757L, 9561L, 1139L, 2L, 342L, 0L, 51L, 115L, 9L, 128L, 43L, 22L, 0L, 49L, 284L, 1001L, 21L, 28L, 1222L, 1L, 12L, 18L, 337L, 547L, 91L, 268L, 10L, 108L, 249L, 0L, 132L, 0L, 0L, 109L, 246L, 36L, 215L, 28L, 112L, 1L, 93L, 103L, 1904L, 1648L, 435L, 70L, 21L, 301L, 323L, 11L, 372L, 98L, 181L, 583L, 0L, 236L, 10L, 30L, 111L, 0L, 3L, 587L, 118L, 333L, 0L, 0L, 0L, 1031L, 1973L, 1L, 1566L, 0L, 447L, 783L, 0L, 140L, 41L, 0L, 268L, 128L, 1267L, 925L, 121L, 195L, 324L, 212L, 804L, 76L, 463L, 407L, 1285L, 300L, 313L, 9L, 11L, 237L, 26L, 0L, 2150L, 196L, 72L, 1L, 30L, 637L, 1221L, 99L, 288L, 66L, 0L, 0L, 0L, 2506L, 63L, 450L, 41L, 185L, 36L, 945L, 514L, 57L, 1L, 5L, 164L, 781L, 0L, 84L, 236L, 245L, 178L, 0L, 9363L, 22402L, 15L, 0L, 912L, 333L, 3L, 256L, 905L, 753L, 391L), population = c(16L, 3L, 20L, 0L, 0L, 7L, 0L, 28L, 28L, 15L, 8L, 0L, 0L, 90L, 0L, 10L, 0L, 3L, 0L, 1L, 1L, 119L, 0L, 0L, 9L, 7L, 35L, 4L, 8L, 24L, 0L, 0L, 2L, 11L, 1008L, 28L, 0L, 2L, 0L, 2L, 10L, 1L, 15L, 5L, 0L, 0L, 6L, 8L, 47L, 5L, 0L, 31L, 0L, 0L, 1L, 5L, 54L, 0L, 1L, 1L, 17L, 61L, 0L, 10L, 0L, 0L, 8L, 6L, 1L, 1L, 6L, 4L, 5L, 11L, 0L, 157L, 39L, 14L, 3L, 4L, 57L, 7L, 2L, 118L, 2L, 6L, 17L, 0L, 3L, 3L, 1L, 1L, 0L, 0L, 9L, 6L, 13L, 0L, 0L, 0L, 2L, 77L, 0L, 2L, 0L, 20L, 12L, 0L, 16L, 14L, 0L, 2L, 3L, 5L, 56L, 18L, 9L, 4L, 1L, 84L, 2L, 3L, 3L, 14L, 48L, 36L, 3L, 0L, 22L, 5L, 0L, 9L, 6L, 3L, 3L, 0L, 5L, 29L, 39L, 2L, 15L, 0L, 0L, 0L, 20L, 0L, 8L, 6L, 10L, 18L, 18L, 49L, 2L, 0L, 1L, 7L, 45L, 0L, 1L, 13L, 56L, 3L, 0L, 231L, 274L, 0L, 0L, 15L, 60L, 0L, 22L, 28L, 6L, 8L), language = structure(c(10L, 6L, 8L, 1L, 6L, 10L, 1L, 2L, 2L, 1L, 4L, 1L, 8L, 6L, 1L, 6L, 1L, 3L, 1L, 10L, 10L, 6L, 1L, 10L, 5L, 3L, 10L, 10L, 3L, 1L, 6L, 1L, 10L, 2L, 7L, 2L, 3L, 10L, 1L, 2L, 2L, 6L, 5L, 6L, 3L, 1L, 2L, 2L, 8L, 2L, 10L, 10L, 6L, 1L, 1L, 9L, 3L, 3L, 10L, 1L, 4L, 4L, 1L, 6L, 1L, 1L, 2L, 3L, 6L, 1L, 3L, 2L, 7L, 9L, 6L, 10L, 6L, 8L, 1L, 10L, 6L, 3L, 1L, 9L, 8L, 10L, 10L, 1L, 10L, 8L, 10L, 10L, 4L, 4L, 10L, 10L, 10L, 10L, 10L, 10L, 8L, 2L, 10L, 10L, 1L, 8L, 10L, 10L, 10L, 6L, 6L, 1L, 2L, 3L, 10L, 10L, 8L, 6L, 8L, 6L, 2L, 1L, 2L, 2L, 10L, 5L, 2L, 8L, 6L, 10L, 6L, 8L, 3L, 1L, 7L, 1L, 10L, 6L, 10L, 8L, 10L, 1L, 1L, 1L, 8L, 6L, 6L, 4L, 8L, 7L, 10L, 10L, 3L, 10L, 1L, 8L, 9L, 1L, 8L, 10L, 1L, 2L, 1L, 1L, 5L, 6L, 6L, 2L, 10L, 1L, 6L, 10L, 10L, 10L), .Label = c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10"), class = "factor"), bars = c(0L, 0L, 2L, 0L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 2L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 1L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 2L, 0L, 0L, 3L, 0L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 3L, 0L, 0L, 0L, 0L, 3L, 3L, 0L, 0L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 5L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 3L, 0L), stripes = c(3L, 0L, 0L, 0L, 0L, 2L, 1L, 3L, 3L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 5L, 0L, 0L, 0L, 3L, 2L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 2L, 0L, 3L, 0L, 0L, 0L, 5L, 5L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 3L, 3L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 5L, 3L, 3L, 1L, 9L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 3L, 0L, 3L, 0L, 2L, 3L, 3L, 0L, 2L, 0L, 0L, 0L, 0L, 3L, 0L, 5L, 0L, 3L, 2L, 0L, 11L, 2L, 3L, 2L, 3L, 14L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 5L, 3L, 0L, 3L, 1L, 0L, 3L, 3L, 0L, 5L, 3L, 0L, 2L, 0L, 0L, 0L, 3L, 0L, 0L, 2L, 5L, 0L, 0L, 0L, 3L, 0L, 0L, 3L, 2L, 0L, 0L, 3L, 0L, 3L, 0L, 0L, 0L, 0L, 3L, 5L, 0L, 0L, 3L, 0L, 0L, 5L, 5L, 0L, 0L, 0L, 0L, 0L, 3L, 6L, 0L, 9L, 0L, 13L, 0L, 0L, 0L, 3L, 0L, 0L, 3L, 0L, 0L, 7L), colours = c(5L, 3L, 3L, 5L, 3L, 3L, 3L, 2L, 3L, 3L, 2L, 3L, 2L, 2L, 3L, 3L, 8L, 2L, 6L, 4L, 3L, 4L, 6L, 4L, 5L, 3L, 3L, 3L, 3L, 2L, 5L, 6L, 5L, 3L, 2L, 3L, 2L, 3L, 4L, 3L, 3L, 3L, 3L, 2L, 4L, 6L, 3L, 3L, 4L, 2L, 4L, 3L, 3L, 6L, 7L, 2L, 3L, 3L, 3L, 4L, 3L, 3L, 3L, 2L, 3L, 7L, 2L, 3L, 4L, 5L, 2L, 2L, 6L, 3L, 3L, 2L, 3L, 4L, 3L, 2L, 3L, 3L, 3L, 2L, 4L, 2L, 4L, 4L, 3L, 4L, 4L, 3L, 3L, 3L, 3L, 3L, 4L, 3L, 3L, 3L, 2L, 4L, 2L, 3L, 7L, 2L, 5L, 3L, 3L, 3L, 3L, 3L, 2L, 3L, 2L, 3L, 4L, 3L, 3L, 2L, 3L, 4L, 6L, 2L, 4L, 2L, 3L, 2L, 7L, 4L, 4L, 2L, 3L, 3L, 2L, 4L, 2L, 5L, 4L, 4L, 4L, 5L, 4L, 4L, 4L, 4L, 2L, 2L, 4L, 3L, 4L, 3L, 4L, 2L, 3L, 2L, 2L, 6L, 4L, 5L, 3L, 3L, 6L, 3L, 2L, 4L, 4L, 7L, 2L, 3L, 4L, 4L, 4L, 5L), red = c(1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), green = c(1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L), blue = c(0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L), gold = c(1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L), white = c(1L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 1L), black = c(1L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L), orange = c(0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L), mainhue = structure(c(5L, 7L, 5L, 2L, 4L, 7L, 8L, 2L, 2L, 2L, 7L, 2L, 7L, 5L, 2L, 4L, 2L, 5L, 7L, 6L, 2L, 5L, 2L, 4L, 7L, 7L, 7L, 7L, 4L, 7L, 4L, 2L, 4L, 7L, 7L, 4L, 5L, 7L, 2L, 2L, 2L, 8L, 8L, 7L, 2L, 5L, 2L, 4L, 1L, 2L, 5L, 5L, 8L, 2L, 2L, 8L, 8L, 8L, 5L, 7L, 4L, 1L, 8L, 2L, 4L, 2L, 2L, 4L, 4L, 5L, 1L, 2L, 2L, 7L, 2L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 5L, 8L, 1L, 7L, 7L, 7L, 7L, 7L, 2L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 2L, 5L, 5L, 2L, 7L, 2L, 7L, 4L, 2L, 3L, 7L, 8L, 2L, 2L, 6L, 5L, 2L, 7L, 7L, 7L, 5L, 7L, 1L, 7L, 7L, 2L, 8L, 7L, 3L, 7L, 7L, 5L, 5L, 5L, 5L, 8L, 5L, 2L, 6L, 8L, 7L, 4L, 5L, 2L, 5L, 7L, 7L, 2L, 7L, 7L, 7L, 5L, 7L, 5L, 7L, 7L, 7L, 7L, 2L, 5L, 4L, 7L, 8L, 8L, 8L, 7L, 7L, 4L, 7L, 7L, 7L, 7L, 5L, 5L, 5L), .Label = c("black", "blue", "brown", "gold", "green", "orange", "red", "white"), class = "factor"), circles = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 4L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L), crosses = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 2L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), saltires = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), quarters = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 4L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L), sunstars = c(1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 6L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 22L, 0L, 0L, 1L, 1L, 14L, 3L, 1L, 0L, 1L, 4L, 1L, 1L, 5L, 0L, 4L, 1L, 15L, 0L, 1L, 0L, 0L, 0L, 1L, 10L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 7L, 0L, 0L, 0L, 1L, 0L, 0L, 5L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 4L, 1L, 0L, 1L, 1L, 1L, 2L, 0L, 6L, 4L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 2L, 5L, 1L, 0L, 4L, 0L, 1L, 0L, 2L, 0L, 2L, 0L, 1L, 0L, 5L, 5L, 1L, 0L, 0L, 1L, 0L, 2L, 0L, 0L, 0L, 1L, 0L, 0L, 2L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 50L, 1L, 0L, 0L, 7L, 1L, 5L, 1L, 0L, 0L, 1L), crescent = c(0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), triangle = c(0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L), icon = c(1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L), animate = c(0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L), text = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), topleft = structure(c(1L, 6L, 4L, 2L, 2L, 6L, 7L, 2L, 2L, 7L, 6L, 2L, 7L, 4L, 2L, 1L, 6L, 4L, 7L, 5L, 2L, 4L, 7L, 7L, 7L, 6L, 2L, 7L, 4L, 6L, 6L, 7L, 2L, 2L, 6L, 3L, 4L, 6L, 7L, 2L, 2L, 7L, 7L, 6L, 7L, 4L, 2L, 3L, 6L, 2L, 4L, 4L, 7L, 7L, 7L, 7L, 2L, 2L, 4L, 6L, 1L, 1L, 7L, 2L, 6L, 6L, 2L, 6L, 6L, 1L, 1L, 2L, 7L, 6L, 2L, 6L, 4L, 6L, 4L, 2L, 4L, 6L, 3L, 7L, 1L, 6L, 1L, 6L, 6L, 6L, 4L, 2L, 2L, 6L, 7L, 1L, 2L, 6L, 7L, 2L, 4L, 4L, 2L, 6L, 7L, 6L, 4L, 2L, 2L, 6L, 7L, 7L, 2L, 5L, 4L, 2L, 6L, 6L, 6L, 7L, 7L, 6L, 6L, 6L, 2L, 7L, 6L, 7L, 2L, 6L, 4L, 4L, 4L, 4L, 6L, 2L, 2L, 5L, 7L, 6L, 3L, 4L, 2L, 2L, 6L, 4L, 2L, 6L, 6L, 2L, 4L, 6L, 6L, 7L, 7L, 6L, 6L, 7L, 6L, 1L, 7L, 7L, 7L, 2L, 6L, 1L, 3L, 3L, 6L, 2L, 2L, 4L, 4L, 4L), .Label = c("black", "blue", "gold", "green", "orange", "red", "white"), class = "factor"), botright = structure(c(5L, 7L, 8L, 7L, 7L, 1L, 2L, 2L, 2L, 2L, 7L, 2L, 7L, 5L, 2L, 7L, 7L, 5L, 7L, 7L, 2L, 5L, 2L, 4L, 7L, 5L, 7L, 8L, 4L, 7L, 5L, 2L, 4L, 7L, 7L, 7L, 5L, 7L, 2L, 2L, 2L, 8L, 7L, 7L, 5L, 5L, 2L, 7L, 1L, 2L, 7L, 7L, 8L, 2L, 2L, 8L, 7L, 7L, 2L, 5L, 4L, 4L, 7L, 2L, 7L, 7L, 2L, 5L, 5L, 5L, 7L, 2L, 2L, 5L, 2L, 8L, 7L, 1L, 6L, 2L, 7L, 5L, 4L, 8L, 5L, 7L, 5L, 2L, 7L, 7L, 2L, 7L, 7L, 2L, 5L, 5L, 8L, 7L, 7L, 2L, 5L, 7L, 2L, 7L, 2L, 7L, 4L, 2L, 2L, 2L, 8L, 2L, 2L, 5L, 5L, 2L, 1L, 7L, 5L, 5L, 8L, 1L, 2L, 7L, 7L, 7L, 7L, 3L, 7L, 5L, 5L, 5L, 7L, 2L, 8L, 5L, 2L, 2L, 8L, 1L, 4L, 7L, 2L, 5L, 1L, 5L, 2L, 7L, 1L, 7L, 2L, 7L, 5L, 7L, 8L, 7L, 7L, 2L, 1L, 7L, 7L, 8L, 8L, 7L, 7L, 5L, 8L, 7L, 7L, 7L, 7L, 5L, 3L, 5L), .Label = c("black", "blue", "brown", "gold", "green", "orange", "red", "white"), class = "factor")), .Names = c("ytrain", "landmass", "zone", "area", "population", "language", "bars", "stripes", "colours", "red", "green", "blue", "gold", "white", "black", "orange", "mainhue", "circles", "crosses", "saltires", "quarters", "sunstars", "crescent", "triangle", "icon", "animate", "text", "topleft", "botright"), row.names = c(NA, -174L), class = "data.frame") tdata$language <- factor(tdata$language) tdata$ytrain <- factor(tdata$ytrain) ### was: error model <- ctree(ytrain ~ ., data = tdata, control = ctree_control(testtype = "Univariate", splitstat = "maximum")) if (require("coin")) { ### check against coin (independence_test automatically ### removes empty levels) p <- info_node(node_party(model))$criterion["p.value",] p[is.na(p)] <- 0 p2 <- sapply(names(p), function(n) pvalue(independence_test(ytrain ~ ., data = tdata[, c("ytrain", n)], teststat = "quad"))) stopifnot(max(abs(p - p2)) < sqrt(.Machine$double.eps)) p <- info_node(node_party(model[2]))$criterion["p.value",] p[is.na(p)] <- 0 p2 <- sapply(names(p), function(n) pvalue(independence_test(ytrain ~ ., data = tdata[tdata$language != "8", c("ytrain", n)], teststat = "quad"))) stopifnot(max(abs(p - p2)) < sqrt(.Machine$double.eps)) p <- info_node(node_party(model[3]))$criterion["p.value",] p[is.na(p)] <- 0 p2 <- sapply(names(p), function(n) pvalue(independence_test(ytrain ~ ., data = tdata[!(tdata$language %in% c("2", "4", "8")), c("ytrain", n)], teststat = "quad"))) stopifnot(max(abs(p - p2)) < sqrt(.Machine$double.eps)) } ### check coersion of constparties to simpleparties ### containing terminal nodes without corresponding observations ## create party data("WeatherPlay", package = "partykit") py <- party( partynode(1L, split = partysplit(1L, index = 1:3), kids = list( partynode(2L, split = partysplit(3L, breaks = 75), kids = list( partynode(3L, info = "yes"), partynode(4L, info = "no"))), partynode(5L, split = partysplit(3L, breaks = 20), kids = list( partynode(6L, info = "no"), partynode(7L, info = "yes"))), partynode(8L, split = partysplit(4L, index = 1:2), kids = list( partynode(9L, info = "yes"), partynode(10L, info = "no"))))), WeatherPlay) names(py) <- LETTERS[nodeids(py)] pn <- node_party(py) cp <- party(pn, data = WeatherPlay, fitted = data.frame( "(fitted)" = fitted_node(pn, data = WeatherPlay), "(response)" = WeatherPlay$play, check.names = FALSE), terms = terms(play ~ ., data = WeatherPlay), ) print(cp) cp <- as.constparty(cp) nd <- data.frame(outlook = factor("overcast", levels = levels(WeatherPlay$outlook)), humidity = 10, temperature = 10, windy = "yes") try(predict(cp, type = "node", newdata = nd)) try(predict(cp, type = "response", newdata = nd)) as.simpleparty(cp) print(cp) ### scores y <- gl(3, 10, ordered = TRUE) x <- rnorm(length(y)) x <- ordered(cut(x, 3)) d <- data.frame(y = y, x = x) ### partykit with scores ct11 <- partykit::ctree(y ~ x, data = d) ct12 <- partykit::ctree(y ~ x, data = d, scores = list(y = c(1, 4, 5))) ct13 <- partykit::ctree(y ~ x, data = d, scores = list(y = c(1, 4, 5), x = c(1, 5, 6))) ### party with scores ct21 <- party::ctree(y ~ x, data = d) ct22 <- party::ctree(y ~ x, data = d, scores = list(y = c(1, 4, 5))) ct23 <- party::ctree(y ~ x, data = d, scores = list(y = c(1, 4, 5), x = c(1, 5, 6))) stopifnot(all.equal(ct11$node$info$p.value, 1 - ct21@tree$criterion$criterion, check.attr = FALSE)) stopifnot(all.equal(ct12$node$info$p.value, 1 - ct22@tree$criterion$criterion, check.attr = FALSE)) stopifnot(all.equal(ct13$node$info$p.value, 1 - ct23@tree$criterion$criterion, check.attr = FALSE)) ### ytrafo y <- runif(100, max = 3) x <- rnorm(length(y)) d <- data.frame(y = y, x = x) ### partykit with scores ct11 <- partykit::ctree(y ~ x, data = d) ct12 <- partykit::ctree(y ~ x, data = d, ytrafo = list(y = sqrt)) ### party with scores ct21 <- party::ctree(y ~ x, data = d) f <- function(data) coin::trafo(data, numeric_trafo = sqrt) ct22 <- party::ctree(y ~ x, data = d, ytrafo = f) stopifnot(all.equal(ct11$node$info$p.value, 1 - ct21@tree$criterion$criterion, check.attr = FALSE)) stopifnot(all.equal(ct12$node$info$p.value, 1 - ct22@tree$criterion$criterion, check.attr = FALSE)) ### spotted by Peter Philip Stephensen (DREAM) ### splits x >= max(x) where possible in partykit::ctree nAge <- 30 d <- data.frame(Age=rep(1:nAge,2),y=c(rep(1,nAge),rep(0,nAge)), n = rep(0,2*nAge)) ntot <- 100 alpha <- .5 d[d$y==1,]$n = floor(ntot * alpha * d[d$y==1,]$Age / nAge) d[d$y==0,]$n = ntot - d[d$y==1,]$n d$n <- as.integer(d$n) ctrl <- partykit::ctree_control(maxdepth=3, minbucket = min(d$n) + 1) tree <- partykit::ctree(y ~ Age, weights=n, data=d, control=ctrl) ## IGNORE_RDIFF_BEGIN tree ## IGNORE_RDIFF_END (w1 <- predict(tree, type = "node")) (ct <- ctree(dist + I(dist^2) ~ speed, data = cars)) predict(ct) ### nodeapply was not the same for permutations of ids ### spotted by Heidi Seibold airq <- subset(airquality, !is.na(Ozone)) airct <- ctree(Ozone ~ ., data = airq) n1 <- nodeapply(airct, ids = c(3, 5, 6), function(x) x$info$nobs) n2 <- nodeapply(airct, ids = c(6, 3, 5), function(x) x$info$nobs) stopifnot(all.equal(n1[names(n2)], n2)) ### pruning got "fitted" wrong, spotted by Jason Parker data("Titanic") titan <- as.data.frame(Titanic) (tree <- ctree(Survived ~ Class + Sex + Age, data = titan, weights = Freq)) ### prune off nodes 5-12 and check if the other nodes are not affected nodeprune(tree, 4) ### subsetting removed weights from fitted, by Jon Peck t1 <- ctree(Survived ~Age+Sex+Class, data=Titanic, weights=Freq, maxdepth = 1) tita <- as.data.frame(Titanic) t2 <- ctree(Survived ~Age+Sex+Class, data=tita[rep(1:nrow(tita), tita$Freq),], maxdepth = 1) # all the same t1 t1[1] t2 t2[1] ### this gave a warning "ME is not a factor" if (require("TH.data")) { data("mammoexp", package = "TH.data") a <- cforest(ME ~ PB + SYMPT, data = mammoexp, ntree = 5) print(predict(a, newdata=mammoexp[1:3,])) } ### pruning didn't work properly mt <- lmtree(dist ~ speed, data = cars) mt2 <- nodeprune(mt, 2) stopifnot(all(mt2$fitted[["(fitted)"]] %in% c(2, 3))) ### a <- rep('N',87) a[77] <- 'Y' b <- rep(FALSE, 87) b[c(7,10,11,33,56,77)] <- TRUE d <- rep(1,87) d[c(29,38,40,42,65,77)] <- 0 dfb <- data.frame(a = as.factor(a), b = as.factor(b), d = as.factor(d)) tr <- ctree(a ~ ., data = dfb, control = ctree_control(minsplit = 10,minbucket = 5, maxsurrogate = 2, alpha = 0.05)) tNodes <- node_party(tr) ### this creates a tie on purpose and "d" should be selected ### this check fails on M1mac nodeInfo <- info_node(tNodes) nodeInfo$criterion #stopifnot(names(nodeInfo$p.value) == "d") #stopifnot(split_node(tNodes)$varid == 3) ### reported by John Ogawa, 2020-12-11 class(dfb$a) <- c("Hansi", "factor") tr2 <- ctree(a ~ ., data = dfb, control = ctree_control(minsplit = 10,minbucket = 5, maxsurrogate = 2, alpha = 0.05)) stopifnot(isTRUE(all.equal(tr, tr2, check.attributes = FALSE))) partykit/tests/regtest-split.Rout.save0000644000176200001440000001171614172230001017675 0ustar liggesusers R version 3.5.0 (2018-04-23) -- "Joy in Playing" Copyright (C) 2018 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > set.seed(1) > > dat <- data.frame(v1 = as.double(1:100)) > > sv1 <- partysplit(as.integer(1), breaks = as.double(50)) > character_split(sv1, dat) $name [1] "v1" $levels [1] "<= 50" "> 50" > stopifnot(all(kidids_split(sv1, dat) == ((dat$v1 > 50) + 1))) > > sv1 <- partysplit(as.integer(1), breaks = as.double(50), + index = as.integer(c(2, 1))) > character_split(sv1, dat) $name [1] "v1" $levels [1] "> 50" "<= 50" > stopifnot(all(kidids_split(sv1, dat) == ((dat$v1 <= 50) + 1))) > > sv1 <- partysplit(as.integer(1), breaks = as.double(50), right = FALSE) > character_split(sv1, dat) $name [1] "v1" $levels [1] "< 50" ">= 50" > stopifnot(all(kidids_split(sv1, dat) == ((dat$v1 >= 50) + 1))) > > sv1 <- partysplit(as.integer(1), breaks = as.double(50), + index = as.integer(c(2, 1)), right = FALSE) > character_split(sv1, dat) $name [1] "v1" $levels [1] ">= 50" "< 50" > stopifnot(all(kidids_split(sv1, dat) == ((dat$v1 < 50) + 1))) > > sv1 <- partysplit(as.integer(1), breaks = as.double(c(25, 75))) > character_split(sv1, dat) $name [1] "v1" $levels [1] "(-Inf,25]" "(25,75]" "(75, Inf]" > stopifnot(all(kidids_split(sv1, dat) == + as.integer(cut(dat$v1, c(-Inf, 25, 75, Inf))))) > > sv1 <- partysplit(as.integer(1), breaks = as.double(c(25, 75)), right = FALSE) > character_split(sv1, dat) $name [1] "v1" $levels [1] "[-Inf,25)" "[25,75)" "[75, Inf)" > stopifnot(all(kidids_split(sv1, dat) == + as.integer(cut(dat$v1, c(-Inf, c(25, 75), Inf), right = FALSE)))) > > sv1 <- partysplit(as.integer(1), breaks = as.double(c(25, 75)), + index = as.integer(3:1), right = FALSE) > character_split(sv1, dat) $name [1] "v1" $levels [1] "[75, Inf)" "[25,75)" "[-Inf,25)" > stopifnot(all(kidids_split(sv1, dat) == + (3:1)[as.integer(cut(dat$v1, c(-Inf, c(25, 75), Inf), right = FALSE))])) > > > dat$v2 <- gl(4, 25) > > sv2 <- partysplit(as.integer(2), index = as.integer(c(1, 2, 1, 2))) > character_split(sv2, dat) $name [1] "v2" $levels [1] "1, 3" "2, 4" > kidids_split(sv2, dat) [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 [38] 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [75] 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 > > sv2 <- partysplit(as.integer(2), breaks = as.integer(c(1, 3))) > character_split(sv2, dat) $name [1] "v2" $levels [1] "1" "2, 3" "4" > kidids_split(sv2, dat) [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 [38] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [75] 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 > > > dat <- data.frame(x = gl(3, 30, labels = LETTERS[1:3]), y = rnorm(90), + z = gl(9, 10, labels = LETTERS[1:9], ordered = TRUE)) > csp <- partysplit(as.integer(1), index = as.integer(c(1, 2, 1))) > kidids_split(csp, dat) [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 [39] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [77] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 > #kidids_node(list(csp), dat) > > nsp <- partysplit(as.integer(2), breaks = c(-1, 0, 1), index = as.integer(c(1, 2, 1, 3))) > kidids_split(nsp, dat) [1] 2 1 2 3 1 2 1 1 1 2 3 1 2 1 3 2 2 1 1 1 1 1 1 1 1 2 2 1 2 1 3 2 1 2 1 2 2 2 [39] 3 1 2 2 1 1 2 2 1 1 2 1 1 2 1 1 3 3 2 1 1 2 3 2 1 1 2 1 1 3 1 3 1 2 1 2 1 1 [77] 2 1 1 2 2 2 3 1 1 1 3 2 1 1 > > osp <- partysplit(as.integer(3), breaks = as.integer(c(3, 6)), index = as.integer(c(2, 1, 2))) > kidids_split(osp, dat) [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 [39] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 [77] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 > > nadat <- dat > nadat$x[1:10] <- NA > nadat$y[11:20] <- NA > #kidids_node(list(csp, nsp, osp), nadat) > > character_split(csp, dat) $name [1] "x" $levels [1] "A, C" "B" > character_split(nsp, dat) $name [1] "y" $levels [1] "(-Inf,-1] | (0,1]" "(-1,0]" "(1, Inf]" > character_split(osp, dat) $name [1] "z" $levels [1] "D, E, F" "A, B, C, G, H, I" > > > proc.time() user system elapsed 1.056 0.061 1.101 partykit/tests/regtest-ctree.R0000644000176200001440000000155714172230000016160 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) ## package library("partykit") ## iris data data("iris", package = "datasets") irisct <- ctree(Species ~ ., data = iris) print(irisct) table(fit = predict(irisct), true = iris$Species) ## airquality data data("airquality", package = "datasets") airq <- subset(airquality, !is.na(Ozone)) airqct <- ctree(Ozone ~ ., data = airq) print(airqct) sum((airq$Ozone - predict(airqct))^2) ### split in one variable only: Temp is selected freely in the root node ### but none of the other variables is allowed deeper in the tree airqct1 <- ctree(Ozone ~ ., data = airq, control = ctree_control(maxvar = 1L)) psplitids <- unique(do.call("c", nodeapply(node_party(airqct1), ids = nodeids(node_party(airqct1)), FUN = function(x) split_node(x)$varid))) stopifnot(length(psplitids) == 1L) partykit/tests/regtest-MIA.R0000644000176200001440000000226114172230001015456 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) library("partykit") set.seed(29) n <- 100 x <- 1:n/n y <- rnorm(n, mean = (x < .5) + 1) xna <- x xna[xna < .2] <- NA d <- data.frame(x = x, y = y) dna <- data.frame(x = xna, y = y) (t1 <- ctree(y ~ x, data = d)) (t2 <- ctree(y ~ x, data = dna)) (t3 <- ctree(y ~ x, data = dna, control = ctree_control(MIA = TRUE))) predict(t1, type = "node")[is.na(xna)] predict(t2, type = "node")[is.na(xna)] predict(t3, type = "node")[is.na(xna)] xna <- x xna[xna > .8] <- NA d <- data.frame(x = x, y = y) dna <- data.frame(x = xna, y = y) (t1 <- ctree(y ~ x, data = d)) (t2 <- ctree(y ~ x, data = dna)) (t3 <- ctree(y ~ x, data = dna, control = ctree_control(MIA = TRUE))) (n1 <- predict(t1, type = "node")) (n2 <- predict(t2, type = "node")) (n3 <- predict(t3, type = "node")) table(n1, n2) table(n1, n3) d$x <- as.factor(cut(d$x, breaks = 0:5 / 5)) dna$x <- as.factor(cut(dna$x, breaks = 0:5 / 5)) (t1 <- ctree(y ~ x, data = d)) (t2 <- ctree(y ~ x, data = dna)) (t3 <- ctree(y ~ x, data = dna, control = ctree_control(MIA = TRUE))) (n1 <- predict(t1, type = "node")) (n2 <- predict(t2, type = "node")) (n3 <- predict(t3, type = "node")) table(n1, n2) table(n1, n3) partykit/tests/regtest-node.R0000644000176200001440000000105214172230001015772 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) library("partykit") set.seed(1) mysplit <- function(x) partysplit(1L, breaks = as.double(x)) x <- vector(mode = "list", length = 5) x[[1]] <- list(id = 1L, split = mysplit(1 / 3), kids = 2:3, info = "one") x[[2]] <- list(id = 2L, info = "two") x[[3]] <- list(id = 3L, split = mysplit(2 / 3), kids = 4:5, info = "three") x[[4]] <- list(id = 4L, info = "four") x[[5]] <- list(id = 5L, info = "five") rx <- as.partynode(x) stopifnot(identical(as.list(rx), x)) dat <- data.frame(x = runif(100)) kidids_node(rx, dat) partykit/tests/constparty.R0000644000176200001440000002662314172230001015613 0ustar liggesusers### R code from vignette source 'constparty.Rnw' ### test here after removal of RWeka dependent code ################################################### ### code chunk number 1: setup ################################################### options(width = 70) library("partykit") set.seed(290875) ################################################### ### code chunk number 2: Titanic ################################################### data("Titanic", package = "datasets") ttnc <- as.data.frame(Titanic) ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] names(ttnc)[2] <- "Gender" ################################################### ### code chunk number 3: rpart ################################################### library("rpart") (rp <- rpart(Survived ~ ., data = ttnc, model = TRUE)) ################################################### ### code chunk number 4: rpart-party ################################################### (party_rp <- as.party(rp)) ################################################### ### code chunk number 5: rpart-plot-orig ################################################### plot(rp) text(rp) ################################################### ### code chunk number 6: rpart-plot ################################################### plot(party_rp) ################################################### ### code chunk number 7: rpart-pred ################################################### all.equal(predict(rp), predict(party_rp, type = "prob"), check.attributes = FALSE) ################################################### ### code chunk number 8: rpart-fitted ################################################### str(fitted(party_rp)) ################################################### ### code chunk number 9: rpart-prob ################################################### prop.table(do.call("table", fitted(party_rp)), 1) ################################################### ### code chunk number 10: J48 ################################################### #if (require("RWeka")) { # j48 <- J48(Survived ~ ., data = ttnc) #} else { # j48 <- rpart(Survived ~ ., data = ttnc) #} #print(j48) # # #################################################### #### code chunk number 11: J48-party #################################################### #(party_j48 <- as.party(j48)) # # #################################################### #### code chunk number 12: J48-plot #################################################### #plot(party_j48) # # #################################################### #### code chunk number 13: J48-pred #################################################### #all.equal(predict(j48, type = "prob"), predict(party_j48, type = "prob"), # check.attributes = FALSE) ################################################### ### code chunk number 14: PMML-Titantic ################################################### ttnc_pmml <- file.path(system.file("pmml", package = "partykit"), "ttnc.pmml") (ttnc_quest <- pmmlTreeModel(ttnc_pmml)) ################################################### ### code chunk number 15: PMML-Titanic-plot1 ################################################### plot(ttnc_quest) ################################################### ### code chunk number 16: ttnc2-reorder ################################################### ttnc2 <- ttnc[, names(ttnc_quest$data)] for(n in names(ttnc2)) { if(is.factor(ttnc2[[n]])) ttnc2[[n]] <- factor( ttnc2[[n]], levels = levels(ttnc_quest$data[[n]])) } ################################################### ### code chunk number 17: PMML-Titanic-augmentation ################################################### ttnc_quest2 <- party(ttnc_quest$node, data = ttnc2, fitted = data.frame( "(fitted)" = predict(ttnc_quest, ttnc2, type = "node"), "(response)" = ttnc2$Survived, check.names = FALSE), terms = terms(Survived ~ ., data = ttnc2) ) ttnc_quest2 <- as.constparty(ttnc_quest2) ################################################### ### code chunk number 18: PMML-Titanic-plot2 ################################################### plot(ttnc_quest2) ################################################### ### code chunk number 19: PMML-write ################################################### library("pmml") tfile <- tempfile() write(toString(pmml(rp)), file = tfile) ################################################### ### code chunk number 20: PMML-read ################################################### (party_pmml <- pmmlTreeModel(tfile)) all.equal(predict(party_rp, newdata = ttnc, type = "prob"), predict(party_pmml, newdata = ttnc, type = "prob"), check.attributes = FALSE) ################################################### ### code chunk number 21: mytree-1 ################################################### findsplit <- function(response, data, weights, alpha = 0.01) { ## extract response values from data y <- factor(rep(data[[response]], weights)) ## perform chi-squared test of y vs. x mychisqtest <- function(x) { x <- factor(x) if(length(levels(x)) < 2) return(NA) ct <- suppressWarnings(chisq.test(table(y, x), correct = FALSE)) pchisq(ct$statistic, ct$parameter, log = TRUE, lower.tail = FALSE) } xselect <- which(names(data) != response) logp <- sapply(xselect, function(i) mychisqtest(rep(data[[i]], weights))) names(logp) <- names(data)[xselect] ## Bonferroni-adjusted p-value small enough? if(all(is.na(logp))) return(NULL) minp <- exp(min(logp, na.rm = TRUE)) minp <- 1 - (1 - minp)^sum(!is.na(logp)) if(minp > alpha) return(NULL) ## for selected variable, search for split minimizing p-value xselect <- xselect[which.min(logp)] x <- rep(data[[xselect]], weights) ## set up all possible splits in two kid nodes lev <- levels(x[drop = TRUE]) if(length(lev) == 2) { splitpoint <- lev[1] } else { comb <- do.call("c", lapply(1:(length(lev) - 2), function(x) combn(lev, x, simplify = FALSE))) xlogp <- sapply(comb, function(q) mychisqtest(x %in% q)) splitpoint <- comb[[which.min(xlogp)]] } ## split into two groups (setting groups that do not occur to NA) splitindex <- !(levels(data[[xselect]]) %in% splitpoint) splitindex[!(levels(data[[xselect]]) %in% lev)] <- NA_integer_ splitindex <- splitindex - min(splitindex, na.rm = TRUE) + 1L ## return split as partysplit object return(partysplit(varid = as.integer(xselect), index = splitindex, info = list(p.value = 1 - (1 - exp(logp))^sum(!is.na(logp))))) } ################################################### ### code chunk number 22: mytree-2 ################################################### growtree <- function(id = 1L, response, data, weights, minbucket = 30) { ## for less than 30 observations stop here if (sum(weights) < minbucket) return(partynode(id = id)) ## find best split sp <- findsplit(response, data, weights) ## no split found, stop here if (is.null(sp)) return(partynode(id = id)) ## actually split the data kidids <- kidids_split(sp, data = data) ## set up all daugther nodes kids <- vector(mode = "list", length = max(kidids, na.rm = TRUE)) for (kidid in 1:length(kids)) { ## select observations for current node w <- weights w[kidids != kidid] <- 0 ## get next node id if (kidid > 1) { myid <- max(nodeids(kids[[kidid - 1]])) } else { myid <- id } ## start recursion on this daugther node kids[[kidid]] <- growtree(id = as.integer(myid + 1), response, data, w) } ## return nodes return(partynode(id = as.integer(id), split = sp, kids = kids, info = list(p.value = min(info_split(sp)$p.value, na.rm = TRUE)))) } ################################################### ### code chunk number 23: mytree-3 ################################################### mytree <- function(formula, data, weights = NULL) { ## name of the response variable response <- all.vars(formula)[1] ## data without missing values, response comes last data <- data[complete.cases(data), c(all.vars(formula)[-1], response)] ## data is factors only stopifnot(all(sapply(data, is.factor))) if (is.null(weights)) weights <- rep(1L, nrow(data)) ## weights are case weights, i.e., integers stopifnot(length(weights) == nrow(data) & max(abs(weights - floor(weights))) < .Machine$double.eps) ## grow tree nodes <- growtree(id = 1L, response, data, weights) ## compute terminal node number for each observation fitted <- fitted_node(nodes, data = data) ## return rich constparty object ret <- party(nodes, data = data, fitted = data.frame("(fitted)" = fitted, "(response)" = data[[response]], "(weights)" = weights, check.names = FALSE), terms = terms(formula)) as.constparty(ret) } ################################################### ### code chunk number 24: mytree-4 ################################################### (myttnc <- mytree(Survived ~ Class + Age + Gender, data = ttnc)) ################################################### ### code chunk number 25: mytree-5 ################################################### plot(myttnc) ################################################### ### code chunk number 26: mytree-pval ################################################### nid <- nodeids(myttnc) iid <- nid[!(nid %in% nodeids(myttnc, terminal = TRUE))] (pval <- unlist(nodeapply(myttnc, ids = iid, FUN = function(n) info_node(n)$p.value))) ################################################### ### code chunk number 27: mytree-nodeprune ################################################### myttnc2 <- nodeprune(myttnc, ids = iid[pval > 1e-5]) ################################################### ### code chunk number 28: mytree-nodeprune-plot ################################################### plot(myttnc2) ################################################### ### code chunk number 29: mytree-glm ################################################### logLik(glm(Survived ~ Class + Age + Gender, data = ttnc, family = binomial())) ################################################### ### code chunk number 30: mytree-bs ################################################### bs <- rmultinom(25, nrow(ttnc), rep(1, nrow(ttnc)) / nrow(ttnc)) ################################################### ### code chunk number 31: mytree-ll ################################################### bloglik <- function(prob, weights) sum(weights * dbinom(ttnc$Survived == "Yes", size = 1, prob[,"Yes"], log = TRUE)) ################################################### ### code chunk number 32: mytree-bsll ################################################### f <- function(w) { tr <- mytree(Survived ~ Class + Age + Gender, data = ttnc, weights = w) bloglik(predict(tr, newdata = ttnc, type = "prob"), as.numeric(w == 0)) } apply(bs, 2, f) ################################################### ### code chunk number 33: mytree-node ################################################### nttnc <- expand.grid(Class = levels(ttnc$Class), Gender = levels(ttnc$Gender), Age = levels(ttnc$Age)) nttnc ################################################### ### code chunk number 34: mytree-prob ################################################### predict(myttnc, newdata = nttnc, type = "node") predict(myttnc, newdata = nttnc, type = "response") predict(myttnc, newdata = nttnc, type = "prob") ################################################### ### code chunk number 35: mytree-FUN ################################################### predict(myttnc, newdata = nttnc, FUN = function(y, w) rank(table(rep(y, w)))) partykit/tests/regtest-node.Rout.save0000644000176200001440000000310214172230001017455 0ustar liggesusers R version 3.5.0 (2018-04-23) -- "Joy in Playing" Copyright (C) 2018 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > set.seed(1) > > mysplit <- function(x) partysplit(1L, breaks = as.double(x)) > x <- vector(mode = "list", length = 5) > x[[1]] <- list(id = 1L, split = mysplit(1 / 3), kids = 2:3, info = "one") > x[[2]] <- list(id = 2L, info = "two") > x[[3]] <- list(id = 3L, split = mysplit(2 / 3), kids = 4:5, info = "three") > x[[4]] <- list(id = 4L, info = "four") > x[[5]] <- list(id = 5L, info = "five") > > rx <- as.partynode(x) > stopifnot(identical(as.list(rx), x)) > > dat <- data.frame(x = runif(100)) > kidids_node(rx, dat) [1] 1 2 2 2 1 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 1 2 1 1 2 1 2 2 2 2 2 2 1 2 2 2 [38] 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 1 1 1 2 2 2 2 1 2 1 2 1 2 2 1 2 2 2 2 2 [75] 2 2 2 2 2 2 2 2 2 1 2 1 2 1 1 1 1 1 2 2 2 2 2 2 2 2 > > proc.time() user system elapsed 1.643 0.115 1.727 partykit/tests/regtest-split.R0000644000176200001440000000461314172230001016206 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) library("partykit") set.seed(1) dat <- data.frame(v1 = as.double(1:100)) sv1 <- partysplit(as.integer(1), breaks = as.double(50)) character_split(sv1, dat) stopifnot(all(kidids_split(sv1, dat) == ((dat$v1 > 50) + 1))) sv1 <- partysplit(as.integer(1), breaks = as.double(50), index = as.integer(c(2, 1))) character_split(sv1, dat) stopifnot(all(kidids_split(sv1, dat) == ((dat$v1 <= 50) + 1))) sv1 <- partysplit(as.integer(1), breaks = as.double(50), right = FALSE) character_split(sv1, dat) stopifnot(all(kidids_split(sv1, dat) == ((dat$v1 >= 50) + 1))) sv1 <- partysplit(as.integer(1), breaks = as.double(50), index = as.integer(c(2, 1)), right = FALSE) character_split(sv1, dat) stopifnot(all(kidids_split(sv1, dat) == ((dat$v1 < 50) + 1))) sv1 <- partysplit(as.integer(1), breaks = as.double(c(25, 75))) character_split(sv1, dat) stopifnot(all(kidids_split(sv1, dat) == as.integer(cut(dat$v1, c(-Inf, 25, 75, Inf))))) sv1 <- partysplit(as.integer(1), breaks = as.double(c(25, 75)), right = FALSE) character_split(sv1, dat) stopifnot(all(kidids_split(sv1, dat) == as.integer(cut(dat$v1, c(-Inf, c(25, 75), Inf), right = FALSE)))) sv1 <- partysplit(as.integer(1), breaks = as.double(c(25, 75)), index = as.integer(3:1), right = FALSE) character_split(sv1, dat) stopifnot(all(kidids_split(sv1, dat) == (3:1)[as.integer(cut(dat$v1, c(-Inf, c(25, 75), Inf), right = FALSE))])) dat$v2 <- gl(4, 25) sv2 <- partysplit(as.integer(2), index = as.integer(c(1, 2, 1, 2))) character_split(sv2, dat) kidids_split(sv2, dat) sv2 <- partysplit(as.integer(2), breaks = as.integer(c(1, 3))) character_split(sv2, dat) kidids_split(sv2, dat) dat <- data.frame(x = gl(3, 30, labels = LETTERS[1:3]), y = rnorm(90), z = gl(9, 10, labels = LETTERS[1:9], ordered = TRUE)) csp <- partysplit(as.integer(1), index = as.integer(c(1, 2, 1))) kidids_split(csp, dat) #kidids_node(list(csp), dat) nsp <- partysplit(as.integer(2), breaks = c(-1, 0, 1), index = as.integer(c(1, 2, 1, 3))) kidids_split(nsp, dat) osp <- partysplit(as.integer(3), breaks = as.integer(c(3, 6)), index = as.integer(c(2, 1, 2))) kidids_split(osp, dat) nadat <- dat nadat$x[1:10] <- NA nadat$y[11:20] <- NA #kidids_node(list(csp, nsp, osp), nadat) character_split(csp, dat) character_split(nsp, dat) character_split(osp, dat) partykit/tests/regtest-glmtree.R0000644000176200001440000000761514172230001016517 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) library("partykit") set.seed(29) n <- 1000 x <- runif(n) z <- runif(n) y <- rnorm(n, mean = x * c(-1, 1)[(z > 0.7) + 1], sd = 3) z_noise <- factor(sample(1:3, size = n, replace = TRUE)) d <- data.frame(y = y, x = x, z = z, z_noise = z_noise) fmla <- as.formula("y ~ x | z + z_noise") fmly <- gaussian() fit <- partykit:::glmfit # versions of the data d1 <- d d1$z <- signif(d1$z, digits = 1) k <- 20 zs_noise <- matrix(rnorm(n*k), nrow = n) colnames(zs_noise) <- paste0("z_noise_", 1:k) d2 <- cbind(d, zs_noise) fmla2 <- as.formula(paste("y ~ x | z + z_noise +", paste0("z_noise_", 1:k, collapse = " + "))) d3 <- d2 d3$z <- factor(sample(1:3, size = n, replace = TRUE, prob = c(0.1, 0.5, 0.4))) d3$y <- rnorm(n, mean = x * c(-1, 1)[(d3$z == 2) + 1], sd = 3) ## check weights w <- rep(1, n) w[1:10] <- 2 (mw1 <- glmtree(formula = fmla, data = d, weights = w)) (mw2 <- glmtree(formula = fmla, data = d, weights = w, caseweights = FALSE)) ## check dfsplit (mmfluc2 <- mob(formula = fmla, data = d, fit = partykit:::glmfit)) (mmfluc3 <- glmtree(formula = fmla, data = d)) (mmfluc3_dfsplit <- glmtree(formula = fmla, data = d, dfsplit = 10)) ## check tests if (require("strucchange")) print(sctest(mmfluc3, node = 1)) # does not yet work x <- mmfluc3 (tst3 <- nodeapply(x, ids = nodeids(x), function(n) n$info$criterion)) ## check logLik and AIC logLik(mmfluc2) logLik(mmfluc3) logLik(mmfluc3_dfsplit) logLik(glm(y ~ x, data = d)) AIC(mmfluc3) AIC(mmfluc3_dfsplit) ## check pruning pr2 <- prune.modelparty(mmfluc2) AIC(mmfluc2) AIC(pr2) mmfluc_dfsplit3 <- glmtree(formula = fmla, data = d, alpha = 0.5, dfsplit = 3) mmfluc_dfsplit4 <- glmtree(formula = fmla, data = d, alpha = 0.5, dfsplit = 4) pr_dfsplit3 <- prune.modelparty(mmfluc_dfsplit3) pr_dfsplit4 <- prune.modelparty(mmfluc_dfsplit4) AIC(mmfluc_dfsplit3) AIC(mmfluc_dfsplit4) AIC(pr_dfsplit3) AIC(pr_dfsplit4) width(mmfluc_dfsplit3) width(mmfluc_dfsplit4) width(pr_dfsplit3) width(pr_dfsplit4) ## check inner and terminal options <- list(NULL, "object", "estfun", c("object", "estfun")) arguments <- list("inner", "terminal", c("inner", "terminal")) for (o in options) { print(o) x <- glmtree(formula = fmla, data = d, inner = o) str(nodeapply(x, ids = nodeids(x), function(n) n$info[c("object", "estfun")]), 2) } for (o in options) { print(o) x <- glmtree(formula = fmla, data = d, terminal = o) str(nodeapply(x, ids = nodeids(x), function(n) n$info[c("object", "estfun")]), 2) } ## check model m_mt <- glmtree(formula = fmla, data = d, model = TRUE) m_mf <- glmtree(formula = fmla, data = d, model = FALSE) dim(m_mt$data) dim(m_mf$data) ## check multiway (m_mult <- glmtree(formula = fmla2, data = d3, catsplit = "multiway", minsize = 80)) ## check parm fmla_p <- as.formula("y ~ x + z_noise + z_noise_1 | z + z_noise_2") (m_interc <- glmtree(formula = fmla_p, data = d2, parm = 1)) (m_p3 <- glmtree(formula = fmla_p, data = d2, parm = 3)) ## check trim (m_tt <- glmtree(formula = fmla, data = d, trim = 0.2)) (m_tf <- glmtree(formula = fmla, data = d, trim = 300, minsize = 300)) ## check breakties m_bt <- glmtree(formula = fmla, data = d1, breakties = TRUE) m_df <- glmtree(formula = fmla, data = d1, breakties = FALSE) all.equal(m_bt, m_df, check.environment = FALSE) unclass(m_bt)$node$info$criterion unclass(m_df)$node$info$criterion ### example from mob vignette data("PimaIndiansDiabetes", package = "mlbench") logit <- function(y, x, start = NULL, weights = NULL, offset = NULL, ...) { glm(y ~ 0 + x, family = binomial, start = start, ...) } pid_formula <- diabetes ~ glucose | pregnant + pressure + triceps + insulin + mass + pedigree + age pid_tree <- mob(pid_formula, data = PimaIndiansDiabetes, fit = logit) pid_tree nodeapply(pid_tree, ids = nodeids(pid_tree), function(n) n$info$criterion) partykit/tests/regtest-weights.Rout.save0000644000176200001440000001170614172230001020213 0ustar liggesusers R version 3.5.0 (2018-04-23) -- "Joy in Playing" Copyright (C) 2018 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > > > ## artificial data --------------------------------------------------------------------------------- > set.seed(0) > d <- data.frame(x = seq(-1, 1, length.out = 1000), z = factor(rep(0:1, 500))) > d$y <- 0 + 1 * d$x + rnorm(nrow(d)) > d$w <- rep(1:4, nrow(d)/4) > dd <- d[rep(1:nrow(d), d$w), ] > > > ## convenience function: likelihood ratio test ----------------------------------------------------- > lrtest <- function(data, ...) { + lr <- -2 * (logLik(lm(y ~ x, data = data, ...)) - logLik(lm(y ~ x * z, data = data, ...))) + matrix( + c(lr, pchisq(lr, df = 2, lower.tail = FALSE)), + dimnames = list(c("statistic", "p.value"), "z") + ) + } > > > ## lm: case weights -------------------------------------------------------------------------------- > > ## weighted and explicitly expanded data should match exactly > lm1 <- lmtree(y ~ x | z, data = d, weights = w, maxdepth = 2) > lm2 <- lmtree(y ~ x | z, data = dd, maxdepth = 2) > all.equal(sctest.modelparty(lm1), sctest.modelparty(lm2)) [1] TRUE > > ## LR test should be similar (albeit not identical) > all.equal(sctest.modelparty(lm1), lrtest(dd), tol = 0.05) [1] TRUE > > > ## lm: proportionality weights --------------------------------------------------------------------- > > ## LR test should be similar > lm3 <- lmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, caseweights = FALSE) > all.equal(sctest.modelparty(lm3), lrtest(d, weights = d$w), tol = 0.05) [1] TRUE > > ## constant factor should not change results > lm3x <- lmtree(y ~ x | z, data = d, weights = 2 * w, maxdepth = 2, caseweights = FALSE) > all.equal(sctest.modelparty(lm3), sctest.modelparty(lm3x)) [1] TRUE > > > ## glm: case weights ------------------------------------------------------------------------------- > > ## for glm different vcov are available > glm1o <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, vcov = "opg") > glm2o <- glmtree(y ~ x | z, data = dd, maxdepth = 2, vcov = "opg") > all.equal(sctest.modelparty(glm1o), sctest.modelparty(glm1o)) [1] TRUE > > glm1i <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, vcov = "info") > glm2i <- glmtree(y ~ x | z, data = dd, maxdepth = 2, vcov = "info") > all.equal(sctest.modelparty(glm1i), sctest.modelparty(glm2i)) [1] TRUE > > glm1s <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, vcov = "sandwich") > glm2s <- glmtree(y ~ x | z, data = dd, maxdepth = 2, vcov = "sandwich") > all.equal(sctest.modelparty(glm1s), sctest.modelparty(glm2s)) [1] TRUE > > ## different vcov should yield similar (albeit not identical) statistics > all.equal(sctest.modelparty(glm1o), sctest.modelparty(glm1i), tol = 0.05) [1] TRUE > all.equal(sctest.modelparty(glm1o), sctest.modelparty(glm1s), tol = 0.05) [1] TRUE > > ## LR test should be similar > all.equal(sctest.modelparty(glm1o), lrtest(dd), tol = 0.05) [1] TRUE > > > ## glm: proportionality weights -------------------------------------------------------------------- > > ## different test versions should be similar > glmFo <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, caseweights = FALSE, vcov = "opg") > glmFi <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, caseweights = FALSE, vcov = "info") > glmFs <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, caseweights = FALSE, vcov = "sandwich") > > all.equal(sctest.modelparty(glmFo), sctest.modelparty(glmFi), tol = 0.05) [1] TRUE > all.equal(sctest.modelparty(glmFo), sctest.modelparty(glmFs), tol = 0.05) [1] TRUE > all.equal(sctest.modelparty(glmFo), lrtest(d, weights = d$w), tol = 0.05) [1] TRUE > > ## constant factor should not change results > glmFxo <- glmtree(y ~ x | z, data = d, weights = 2 * w, maxdepth = 2, caseweights = FALSE, vcov = "opg") > glmFxi <- glmtree(y ~ x | z, data = d, weights = 2 * w, maxdepth = 2, caseweights = FALSE, vcov = "info") > glmFxs <- glmtree(y ~ x | z, data = d, weights = 2 * w, maxdepth = 2, caseweights = FALSE, vcov = "sandwich") > > all.equal(sctest.modelparty(glmFo), sctest.modelparty(glmFxo)) [1] TRUE > all.equal(sctest.modelparty(glmFi), sctest.modelparty(glmFxi)) [1] TRUE > all.equal(sctest.modelparty(glmFs), sctest.modelparty(glmFxs)) [1] TRUE > > proc.time() user system elapsed 1.457 0.072 1.516 partykit/tests/regtest-nmax.Rout.save0000644000176200001440000000366314172230001017507 0ustar liggesusers R version 3.5.0 (2018-04-23) -- "Joy in Playing" Copyright (C) 2018 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > > set.seed(29) > n <- 1000 > z <- runif(n) > y <- rnorm(n, mean = c(-1, 1)[(z > 0.5) + 1], sd = 3) > d <- data.frame(y = y, y2 = factor(y > median(y)), + z = z) > > c1 <- ctree(y2 ~ z, data = d, control = ctree_control(nmax = Inf, alpha = .5)) > c2 <- ctree(y2 ~ z, data = d, control = ctree_control(nmax = 25, alpha = .5)) > c3 <- ctree(y2 ~ z, data = d, control = ctree_control(nmax = nrow(d), alpha = .5)) > c4 <- ctree(y2 ~ z, data = d, control = ctree_control(nmax = 100, alpha = .5)) > > all.equal(predict(c1, type = "node"), predict(c3, type = "node")) [1] TRUE > > p1 <- predict(c1, type = "prob") > p2 <- predict(c2, type = "prob") > p3 <- predict(c3, type = "prob") > p4 <- predict(c4, type = "prob") > > ### binomial log-lik > sum(log(p1[cbind(1:nrow(d), unclass(d$y2))])) [1] -675.3508 > sum(log(p2[cbind(1:nrow(d), unclass(d$y2))])) [1] -676.0943 > sum(log(p3[cbind(1:nrow(d), unclass(d$y2))])) [1] -675.3508 > sum(log(p4[cbind(1:nrow(d), unclass(d$y2))])) [1] -676.0943 > > c1 <- ctree(y ~ z, data = d, control = ctree_control(nmax = c("yx" = Inf, "z" = 25), alpha = .5)) > > proc.time() user system elapsed 1.517 0.125 1.622 partykit/tests/regtest-nmax.R0000644000176200001440000000203314172230001016010 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) library("partykit") set.seed(29) n <- 1000 z <- runif(n) y <- rnorm(n, mean = c(-1, 1)[(z > 0.5) + 1], sd = 3) d <- data.frame(y = y, y2 = factor(y > median(y)), z = z) c1 <- ctree(y2 ~ z, data = d, control = ctree_control(nmax = Inf, alpha = .5)) c2 <- ctree(y2 ~ z, data = d, control = ctree_control(nmax = 25, alpha = .5)) c3 <- ctree(y2 ~ z, data = d, control = ctree_control(nmax = nrow(d), alpha = .5)) c4 <- ctree(y2 ~ z, data = d, control = ctree_control(nmax = 100, alpha = .5)) all.equal(predict(c1, type = "node"), predict(c3, type = "node")) p1 <- predict(c1, type = "prob") p2 <- predict(c2, type = "prob") p3 <- predict(c3, type = "prob") p4 <- predict(c4, type = "prob") ### binomial log-lik sum(log(p1[cbind(1:nrow(d), unclass(d$y2))])) sum(log(p2[cbind(1:nrow(d), unclass(d$y2))])) sum(log(p3[cbind(1:nrow(d), unclass(d$y2))])) sum(log(p4[cbind(1:nrow(d), unclass(d$y2))])) c1 <- ctree(y ~ z, data = d, control = ctree_control(nmax = c("yx" = Inf, "z" = 25), alpha = .5)) partykit/tests/bugfixes.Rout.save0000644000176200001440000016644514723340205016727 0ustar liggesusers R version 4.4.2 (2024-10-31) -- "Pile of Leaves" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > set.seed(290875) > > datLB <- + structure(list(Site = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, + 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, + 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, + 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, + 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, + 9L, 9L, 9L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, + 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, + 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, + 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, + 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, + 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, + 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, + 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, + 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 1L, 1L, 1L, + 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, + 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, + 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, + 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, + 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 1L, 1L, 1L, 1L, 1L, 1L, + 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, + 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, + 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, + 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, + 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, + 9L, 9L, 9L, 9L, 9L, 9L, 9L), ID = c(1.1, 2.1, 3.1, 4.1, 5.1, + 6.1, 7.1, 8.1, 9.1, 10.1, 11.1, 12.1, 1.2, 2.2, 3.2, 4.2, 5.2, + 6.2, 7.2, 8.2, 9.2, 10.2, 11.2, 12.2, 13.2, 14.2, 1.3, 2.3, 3.3, + 4.3, 5.3, 6.3, 7.3, 8.3, 9.3, 10.3, 11.3, 12.3, 1.4, 2.4, 3.4, + 4.4, 5.4, 6.4, 7.4, 8.4, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 1.6, 2.6, + 3.6, 4.6, 5.6, 6.6, 7.6, 8.6, 9.6, 10.6, 11.6, 12.6, 13.6, 14.6, + 15.6, 1.7, 2.7, 3.7, 4.7, 5.7, 6.7, 7.7, 8.7, 9.7, 10.7, 11.7, + 12.7, 1.8, 2.8, 3.8, 4.8, 5.8, 6.8, 7.8, 8.8, 9.8, 10.8, 11.8, + 12.8, 13.8, 14.8, 15.8, 16.8, 17.8, 18.8, 19.8, 1.9, 2.9, 3.9, + 4.9, 5.9, 6.9, 7.9, 8.9, 9.9, 10.9, 11.9, 1.1, 2.1, 3.1, 4.1, + 5.1, 6.1, 7.1, 8.1, 9.1, 10.1, 11.1, 12.1, 1.2, 2.2, 3.2, 4.2, + 5.2, 6.2, 7.2, 8.2, 9.2, 10.2, 11.2, 12.2, 13.2, 14.2, 1.3, 2.3, + 3.3, 4.3, 5.3, 6.3, 7.3, 8.3, 9.3, 10.3, 11.3, 12.3, 1.4, 2.4, + 3.4, 4.4, 5.4, 6.4, 7.4, 8.4, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 1.6, + 2.6, 3.6, 4.6, 5.6, 6.6, 7.6, 8.6, 9.6, 10.6, 11.6, 12.6, 13.6, + 14.6, 15.6, 1.7, 2.7, 3.7, 4.7, 5.7, 6.7, 7.7, 8.7, 9.7, 10.7, + 11.7, 12.7, 1.8, 2.8, 3.8, 4.8, 5.8, 6.8, 7.8, 8.8, 9.8, 10.8, + 11.8, 12.8, 13.8, 14.8, 15.8, 16.8, 17.8, 18.8, 19.8, 1.9, 2.9, + 3.9, 4.9, 5.9, 6.9, 7.9, 8.9, 9.9, 10.9, 11.9, 1.1, 2.1, 3.1, + 4.1, 5.1, 6.1, 7.1, 8.1, 9.1, 10.1, 11.1, 12.1, 1.2, 2.2, 3.2, + 4.2, 5.2, 6.2, 7.2, 8.2, 9.2, 10.2, 11.2, 12.2, 13.2, 14.2, 1.3, + 2.3, 3.3, 4.3, 5.3, 6.3, 7.3, 8.3, 9.3, 10.3, 11.3, 12.3, 1.4, + 2.4, 3.4, 4.4, 5.4, 6.4, 7.4, 8.4, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, + 1.6, 2.6, 3.6, 4.6, 5.6, 6.6, 7.6, 8.6, 9.6, 10.6, 11.6, 12.6, + 13.6, 14.6, 15.6, 1.7, 2.7, 3.7, 4.7, 5.7, 6.7, 7.7, 8.7, 9.7, + 10.7, 11.7, 12.7, 1.8, 2.8, 3.8, 4.8, 5.8, 6.8, 7.8, 8.8, 9.8, + 10.8, 11.8, 12.8, 13.8, 14.8, 15.8, 16.8, 17.8, 18.8, 19.8, 1.9, + 2.9, 3.9, 4.9, 5.9, 6.9, 7.9, 8.9, 9.9, 10.9, 11.9, 1.1, 2.1, + 3.1, 4.1, 5.1, 6.1, 7.1, 8.1, 9.1, 10.1, 11.1, 12.1, 1.2, 2.2, + 3.2, 4.2, 5.2, 6.2, 7.2, 8.2, 9.2, 10.2, 11.2, 12.2, 13.2, 14.2, + 1.3, 2.3, 3.3, 4.3, 5.3, 6.3, 7.3, 8.3, 9.3, 10.3, 11.3, 12.3, + 1.4, 2.4, 3.4, 4.4, 5.4, 6.4, 7.4, 8.4, 1.5, 2.5, 3.5, 4.5, 5.5, + 6.5, 1.6, 2.6, 3.6, 4.6, 5.6, 6.6, 7.6, 8.6, 9.6, 10.6, 11.6, + 12.6, 13.6, 14.6, 15.6, 1.7, 2.7, 3.7, 4.7, 5.7, 6.7, 7.7, 8.7, + 9.7, 10.7, 11.7, 12.7, 1.8, 2.8, 3.8, 4.8, 5.8, 6.8, 7.8, 8.8, + 9.8, 10.8, 11.8, 12.8, 13.8, 14.8, 15.8, 16.8, 17.8, 18.8, 19.8, + 1.9, 2.9, 3.9, 4.9, 5.9, 6.9, 7.9, 8.9, 9.9, 10.9, 11.9, 1.1, + 2.1, 3.1, 4.1, 5.1, 6.1, 7.1, 8.1, 9.1, 10.1, 11.1, 12.1, 1.2, + 2.2, 3.2, 4.2, 5.2, 6.2, 7.2, 8.2, 9.2, 10.2, 11.2, 12.2, 13.2, + 14.2, 1.3, 2.3, 3.3, 4.3, 5.3, 6.3, 7.3, 8.3, 9.3, 10.3, 11.3, + 12.3, 1.4, 2.4, 3.4, 4.4, 5.4, 6.4, 7.4, 8.4, 1.5, 2.5, 3.5, + 4.5, 5.5, 6.5, 1.6, 2.6, 3.6, 4.6, 5.6, 6.6, 7.6, 8.6, 9.6, 10.6, + 11.6, 12.6, 13.6, 14.6, 15.6, 1.7, 2.7, 3.7, 4.7, 5.7, 6.7, 7.7, + 8.7, 9.7, 10.7, 11.7, 12.7, 1.8, 2.8, 3.8, 4.8, 5.8, 6.8, 7.8, + 8.8, 9.8, 10.8, 11.8, 12.8, 13.8, 14.8, 15.8, 16.8, 17.8, 18.8, + 19.8, 1.9, 2.9, 3.9, 4.9, 5.9, 6.9, 7.9, 8.9, 9.9, 10.9, 11.9 + ), Treat = structure(c(2L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 2L, 3L, + 1L, 3L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 3L, 2L, + 1L, 3L, 2L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, + 3L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 3L, 3L, 1L, 2L, 2L, 1L, 3L, + 2L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, + 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 2L, 3L, 3L, 1L, + 2L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 2L, + 1L, 1L, 2L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 3L, + 2L, 1L, 2L, 1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 3L, 2L, 1L, 3L, 2L, + 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 3L, 2L, 3L, + 1L, 1L, 3L, 2L, 1L, 2L, 3L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 3L, 1L, + 3L, 1L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, + 3L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, 2L, 3L, 3L, 1L, 2L, 3L, 2L, + 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 2L, 1L, 1L, 2L, + 2L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, + 1L, 3L, 1L, 3L, 2L, 3L, 1L, 2L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, + 1L, 3L, 2L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, + 2L, 1L, 2L, 3L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, + 1L, 2L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, + 1L, 2L, 2L, 1L, 3L, 1L, 2L, 3L, 3L, 1L, 2L, 3L, 2L, 1L, 2L, 1L, + 3L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, + 3L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, + 3L, 2L, 3L, 1L, 2L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 3L, 2L, + 1L, 3L, 2L, 3L, 2L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, + 3L, 3L, 1L, 2L, 2L, 1L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 3L, + 2L, 3L, 1L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, + 1L, 3L, 1L, 2L, 3L, 3L, 1L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, + 3L, 2L, 3L, 2L, 1L, 3L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 3L, 1L, 1L, + 2L, 3L, 2L, 3L, 1L, 3L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 2L, 3L, + 1L, 2L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, + 3L, 2L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 2L, 3L, 3L, 1L, + 2L, 2L, 1L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 1L, 2L, 3L, 2L, 3L, 1L, + 3L, 1L, 2L, 1L, 3L, 2L, 1L, 3L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 1L, + 2L, 3L, 3L, 1L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 1L, 3L, 2L, 3L, + 2L, 1L, 3L, 2L, 1L, 1L, 2L), .Label = c("10000U", "5000U", "Placebo" + ), class = "factor"), Age = c(65L, 70L, 64L, 59L, 76L, 59L, 72L, + 40L, 52L, 47L, 57L, 47L, 70L, 49L, 59L, 64L, 45L, 66L, 49L, 54L, + 47L, 31L, 53L, 61L, 40L, 67L, 54L, 41L, 66L, 68L, 41L, 77L, 41L, + 56L, 46L, 46L, 47L, 35L, 58L, 62L, 73L, 52L, 53L, 69L, 55L, 52L, + 51L, 56L, 65L, 35L, 43L, 61L, 43L, 64L, 57L, 60L, 44L, 41L, 51L, + 57L, 42L, 48L, 57L, 39L, 67L, 39L, 69L, 54L, 67L, 58L, 72L, 65L, + 68L, 75L, 26L, 36L, 72L, 54L, 64L, 39L, 54L, 48L, 83L, 74L, 41L, + 65L, 79L, 63L, 63L, 34L, 42L, 57L, 68L, 51L, 51L, 61L, 42L, 73L, + 57L, 59L, 57L, 68L, 55L, 46L, 79L, 43L, 50L, 39L, 57L, 65L, 70L, + 64L, 59L, 76L, 59L, 72L, 40L, 52L, 47L, 57L, 47L, 70L, 49L, 59L, + 64L, 45L, 66L, 49L, 54L, 47L, 31L, 53L, 61L, 40L, 67L, 54L, 41L, + 66L, 68L, 41L, 77L, 41L, 56L, 46L, 46L, 47L, 35L, 58L, 62L, 73L, + 52L, 53L, 69L, 55L, 52L, 51L, 56L, 65L, 35L, 43L, 61L, 43L, 64L, + 57L, 60L, 44L, 41L, 51L, 57L, 42L, 48L, 57L, 39L, 67L, 39L, 69L, + 54L, 67L, 58L, 72L, 65L, 68L, 75L, 26L, 36L, 72L, 54L, 64L, 39L, + 54L, 48L, 83L, 74L, 41L, 65L, 79L, 63L, 63L, 34L, 42L, 57L, 68L, + 51L, 51L, 61L, 42L, 73L, 57L, 59L, 57L, 68L, 55L, 46L, 79L, 43L, + 50L, 39L, 57L, 65L, 70L, 64L, 59L, 76L, 59L, 72L, 40L, 52L, 47L, + 57L, 47L, 70L, 49L, 59L, 64L, 45L, 66L, 49L, 54L, 47L, 31L, 53L, + 61L, 40L, 67L, 54L, 41L, 66L, 68L, 41L, 77L, 41L, 56L, 46L, 46L, + 47L, 35L, 58L, 62L, 73L, 52L, 53L, 69L, 55L, 52L, 51L, 56L, 65L, + 35L, 43L, 61L, 43L, 64L, 57L, 60L, 44L, 41L, 51L, 57L, 42L, 48L, + 57L, 39L, 67L, 39L, 69L, 54L, 67L, 58L, 72L, 65L, 68L, 75L, 26L, + 36L, 72L, 54L, 64L, 39L, 54L, 48L, 83L, 74L, 41L, 65L, 79L, 63L, + 63L, 34L, 42L, 57L, 68L, 51L, 51L, 61L, 42L, 73L, 57L, 59L, 57L, + 68L, 55L, 46L, 79L, 43L, 50L, 39L, 57L, 65L, 70L, 64L, 59L, 76L, + 59L, 72L, 40L, 52L, 47L, 57L, 47L, 70L, 49L, 59L, 64L, 45L, 66L, + 49L, 54L, 47L, 31L, 53L, 61L, 40L, 67L, 54L, 41L, 66L, 68L, 41L, + 77L, 41L, 56L, 46L, 46L, 47L, 35L, 58L, 62L, 73L, 52L, 53L, 69L, + 55L, 52L, 51L, 56L, 65L, 35L, 43L, 61L, 43L, 64L, 57L, 60L, 44L, + 41L, 51L, 57L, 42L, 48L, 57L, 39L, 67L, 39L, 69L, 54L, 67L, 58L, + 72L, 65L, 68L, 75L, 26L, 36L, 72L, 54L, 64L, 39L, 54L, 48L, 83L, + 74L, 41L, 65L, 79L, 63L, 63L, 34L, 42L, 57L, 68L, 51L, 51L, 61L, + 42L, 73L, 57L, 59L, 57L, 68L, 55L, 46L, 79L, 43L, 50L, 39L, 57L, + 65L, 70L, 64L, 59L, 76L, 59L, 72L, 40L, 52L, 47L, 57L, 47L, 70L, + 49L, 59L, 64L, 45L, 66L, 49L, 54L, 47L, 31L, 53L, 61L, 40L, 67L, + 54L, 41L, 66L, 68L, 41L, 77L, 41L, 56L, 46L, 46L, 47L, 35L, 58L, + 62L, 73L, 52L, 53L, 69L, 55L, 52L, 51L, 56L, 65L, 35L, 43L, 61L, + 43L, 64L, 57L, 60L, 44L, 41L, 51L, 57L, 42L, 48L, 57L, 39L, 67L, + 39L, 69L, 54L, 67L, 58L, 72L, 65L, 68L, 75L, 26L, 36L, 72L, 54L, + 64L, 39L, 54L, 48L, 83L, 74L, 41L, 65L, 79L, 63L, 63L, 34L, 42L, + 57L, 68L, 51L, 51L, 61L, 42L, 73L, 57L, 59L, 57L, 68L, 55L, 46L, + 79L, 43L, 50L, 39L, 57L), W0 = c(32L, 60L, 44L, 53L, 53L, 49L, + 42L, 34L, 41L, 27L, 48L, 34L, 49L, 46L, 56L, 59L, 62L, 50L, 42L, + 53L, 67L, 44L, 65L, 56L, 30L, 47L, 50L, 34L, 39L, 43L, 46L, 52L, + 38L, 33L, 28L, 34L, 39L, 29L, 52L, 52L, 54L, 52L, 47L, 44L, 42L, + 42L, 44L, 60L, 60L, 50L, 38L, 44L, 54L, 54L, 56L, 51L, 53L, 36L, + 59L, 49L, 50L, 46L, 55L, 46L, 34L, 57L, 41L, 49L, 42L, 31L, 50L, + 35L, 38L, 53L, 42L, 53L, 46L, 50L, 43L, 46L, 41L, 33L, 36L, 33L, + 37L, 24L, 42L, 30L, 42L, 49L, 58L, 26L, 37L, 40L, 33L, 41L, 46L, + 40L, 40L, 61L, 35L, 58L, 49L, 52L, 45L, 67L, 57L, 63L, 53L, 32L, + 60L, 44L, 53L, 53L, 49L, 42L, 34L, 41L, 27L, 48L, 34L, 49L, 46L, + 56L, 59L, 62L, 50L, 42L, 53L, 67L, 44L, 65L, 56L, 30L, 47L, 50L, + 34L, 39L, 43L, 46L, 52L, 38L, 33L, 28L, 34L, 39L, 29L, 52L, 52L, + 54L, 52L, 47L, 44L, 42L, 42L, 44L, 60L, 60L, 50L, 38L, 44L, 54L, + 54L, 56L, 51L, 53L, 36L, 59L, 49L, 50L, 46L, 55L, 46L, 34L, 57L, + 41L, 49L, 42L, 31L, 50L, 35L, 38L, 53L, 42L, 53L, 46L, 50L, 43L, + 46L, 41L, 33L, 36L, 33L, 37L, 24L, 42L, 30L, 42L, 49L, 58L, 26L, + 37L, 40L, 33L, 41L, 46L, 40L, 40L, 61L, 35L, 58L, 49L, 52L, 45L, + 67L, 57L, 63L, 53L, 32L, 60L, 44L, 53L, 53L, 49L, 42L, 34L, 41L, + 27L, 48L, 34L, 49L, 46L, 56L, 59L, 62L, 50L, 42L, 53L, 67L, 44L, + 65L, 56L, 30L, 47L, 50L, 34L, 39L, 43L, 46L, 52L, 38L, 33L, 28L, + 34L, 39L, 29L, 52L, 52L, 54L, 52L, 47L, 44L, 42L, 42L, 44L, 60L, + 60L, 50L, 38L, 44L, 54L, 54L, 56L, 51L, 53L, 36L, 59L, 49L, 50L, + 46L, 55L, 46L, 34L, 57L, 41L, 49L, 42L, 31L, 50L, 35L, 38L, 53L, + 42L, 53L, 46L, 50L, 43L, 46L, 41L, 33L, 36L, 33L, 37L, 24L, 42L, + 30L, 42L, 49L, 58L, 26L, 37L, 40L, 33L, 41L, 46L, 40L, 40L, 61L, + 35L, 58L, 49L, 52L, 45L, 67L, 57L, 63L, 53L, 32L, 60L, 44L, 53L, + 53L, 49L, 42L, 34L, 41L, 27L, 48L, 34L, 49L, 46L, 56L, 59L, 62L, + 50L, 42L, 53L, 67L, 44L, 65L, 56L, 30L, 47L, 50L, 34L, 39L, 43L, + 46L, 52L, 38L, 33L, 28L, 34L, 39L, 29L, 52L, 52L, 54L, 52L, 47L, + 44L, 42L, 42L, 44L, 60L, 60L, 50L, 38L, 44L, 54L, 54L, 56L, 51L, + 53L, 36L, 59L, 49L, 50L, 46L, 55L, 46L, 34L, 57L, 41L, 49L, 42L, + 31L, 50L, 35L, 38L, 53L, 42L, 53L, 46L, 50L, 43L, 46L, 41L, 33L, + 36L, 33L, 37L, 24L, 42L, 30L, 42L, 49L, 58L, 26L, 37L, 40L, 33L, + 41L, 46L, 40L, 40L, 61L, 35L, 58L, 49L, 52L, 45L, 67L, 57L, 63L, + 53L, 32L, 60L, 44L, 53L, 53L, 49L, 42L, 34L, 41L, 27L, 48L, 34L, + 49L, 46L, 56L, 59L, 62L, 50L, 42L, 53L, 67L, 44L, 65L, 56L, 30L, + 47L, 50L, 34L, 39L, 43L, 46L, 52L, 38L, 33L, 28L, 34L, 39L, 29L, + 52L, 52L, 54L, 52L, 47L, 44L, 42L, 42L, 44L, 60L, 60L, 50L, 38L, + 44L, 54L, 54L, 56L, 51L, 53L, 36L, 59L, 49L, 50L, 46L, 55L, 46L, + 34L, 57L, 41L, 49L, 42L, 31L, 50L, 35L, 38L, 53L, 42L, 53L, 46L, + 50L, 43L, 46L, 41L, 33L, 36L, 33L, 37L, 24L, 42L, 30L, 42L, 49L, + 58L, 26L, 37L, 40L, 33L, 41L, 46L, 40L, 40L, 61L, 35L, 58L, 49L, + 52L, 45L, 67L, 57L, 63L, 53L), Fem = c(1L, 1L, 1L, 1L, 1L, 1L, + 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, + 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, + 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, + 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, + 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, + 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, + 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, + 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, + 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, + 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, + 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, + 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, + 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, + 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, + 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, + 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, + 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, + 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, + 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, + 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, + 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, + 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, + 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, + 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, + 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, + 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, + 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, + 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, + 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, + 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, + 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, + 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, + 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L), Week = c(2L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, + 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 4L, 4L, 4L, 4L, 4L, + 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, + 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, + 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, + 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, + 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, + 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, + 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, + 8L, 8L, 8L, 8L, 8L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, + 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, + 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, + 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, + 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, + 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, + 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, + 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, + 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 16L, 16L, 16L, 16L, + 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, + 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, + 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, + 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, + 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, + 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, + 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, + 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, + 16L), Total = c(30L, 26L, 20L, 61L, 35L, 34L, 32L, 33L, 32L, + 10L, 41L, 19L, 47L, 35L, 44L, 48L, 60L, 53L, 42L, 56L, 64L, 40L, + 58L, 54L, 33L, NA, 43L, 29L, 41L, 31L, 26L, 44L, 19L, 38L, 16L, + 23L, 37L, 42L, 55L, 30L, 52L, 44L, 45L, 34L, 39L, 14L, 34L, 57L, + 53L, 50L, 27L, NA, 53L, 32L, 55L, 50L, 56L, 29L, 53L, 50L, 38L, + 48L, 34L, 44L, 31L, 48L, 40L, 25L, 30L, 18L, 27L, 24L, 25L, 40L, + 48L, 45L, 47L, 42L, 24L, 39L, 30L, 27L, 15L, 32L, NA, 29L, 23L, + 22L, 46L, 25L, 46L, 26L, NA, 24L, 10L, 50L, NA, 28L, 16L, 52L, + 21L, 38L, 45L, 46L, 46L, 63L, NA, 51L, 38L, 24L, 27L, 23L, 64L, + 48L, 43L, 32L, 21L, 34L, 31L, 32L, 21L, 44L, 45L, 48L, 56L, 60L, + 52L, 43L, 52L, 65L, 32L, 55L, 52L, 25L, 54L, 51L, 27L, 33L, 29L, + 29L, 47L, 20L, 40L, 11L, 16L, 39L, 35L, 51L, 43L, 52L, 33L, 41L, + 29L, 38L, 9L, 32L, 53L, 55L, NA, 16L, 46L, 51L, 40L, 44L, 50L, + 47L, 24L, 45L, 48L, 42L, 46L, 26L, 47L, 25L, 50L, 42L, 30L, 40L, + 23L, 43L, 34L, 21L, 38L, 26L, 52L, 45L, 52L, 17L, 25L, 44L, 25L, + 16L, 31L, NA, 18L, 30L, 21L, 41L, 30L, 46L, 27L, 23L, 25L, 13L, + 22L, 41L, 29L, 18L, 61L, 29L, 50L, 36L, 36L, 33L, 71L, 36L, 46L, + NA, 37L, 41L, 26L, 62L, 49L, 48L, 43L, 27L, 35L, 32L, 35L, 24L, + 48L, 49L, 54L, 55L, 64L, 57L, 33L, 54L, 64L, 36L, NA, 48L, 29L, + 43L, 46L, 21L, 39L, 28L, 33L, 50L, 27L, 48L, 7L, 15L, 39L, 24L, + 52L, 45L, 54L, 54L, 45L, 28L, 47L, 9L, 35L, 52L, 62L, 46L, 19L, + 26L, 56L, 52L, 50L, 56L, 53L, 32L, 44L, 56L, 43L, 57L, 40L, 50L, + NA, 50L, 38L, 41L, 43L, 26L, 32L, 28L, 33L, 44L, 37L, 51L, 45L, + 60L, 37L, 15L, 46L, 30L, 17L, 27L, NA, 20L, 36L, 25L, 43L, 49L, + 50L, 22L, 18L, 37L, 16L, 28L, 41L, 30L, 25L, 68L, 30L, 53L, NA, + NA, 44L, 66L, 23L, 50L, 33L, 39L, 65L, 35L, NA, 41L, 48L, 42L, + 32L, 37L, 6L, 57L, 28L, 44L, 53L, 49L, 57L, 67L, 61L, 37L, 55L, + 62L, 42L, 56L, 52L, 32L, 46L, 49L, 22L, 37L, 33L, 45L, 50L, 29L, + 49L, 13L, 17L, 45L, 29L, 54L, 47L, 51L, 46L, 43L, 35L, 39L, 16L, + 54L, 53L, 67L, 50L, 23L, 30L, 39L, 42L, 53L, 59L, 51L, 45L, 50L, + 49L, 42L, 57L, 49L, 46L, NA, 50L, 50L, 41L, 36L, 33L, 40L, 34L, + 42L, 47L, 37L, 52L, 50L, 54L, 36L, 21L, 46L, 28L, 22L, 49L, NA, + 25L, 41L, 26L, 49L, 55L, 56L, 38L, 34L, NA, 32L, 34L, 58L, 37L, + 33L, 59L, 35L, 47L, 40L, 45L, 46L, 68L, NA, 50L, 36L, 36L, 67L, + 35L, NA, 51L, 51L, 46L, 38L, 36L, 14L, 51L, 28L, 44L, 56L, 60L, + 58L, 66L, 54L, 43L, 51L, 64L, 43L, 60L, 53L, 32L, 50L, 53L, 22L, + 37L, 38L, 56L, 49L, 32L, 44L, 21L, 29L, 43L, 42L, 57L, 46L, 57L, + 47L, 41L, 41L, 39L, 33L, 53L, 58L, NA, 57L, 26L, 34L, 9L, 47L, + 52L, 53L, 51L, 36L, 48L, 57L, 46L, 49L, 47L, 51L, NA, 49L, 56L, + 31L, 45L, 41L, 47L, 28L, 53L, 53L, 43L, 53L, 52L, 59L, 38L, 25L, + 44L, 30L, 41L, 60L, NA, 41L, 43L, 33L, 54L, 58L, 60L, 35L, 36L, + 38L, 16L, 36L, 53L, 44L, 48L, 71L, 48L, 59L, 52L, 54L, 48L, 71L, + 52L, 54L, 51L)), .Names = c("Site", "ID", "Treat", "Age", "W0", + "Fem", "Week", "Total"), class = "data.frame", row.names = c(NA, + -545L)) > > > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > library("rpart") > > fac <- c(1,3,6) > for(j in 1:length(fac)) datLB[,fac[j]] <- as.factor(datLB[,fac[j]]) > dat <- subset(datLB,Week==16) > dat <- na.omit(dat) > fit <- rpart(Total ~ Site + Treat + Age + W0, + method = "anova", data = dat) > f <- as.party(fit) > plot(f,tp_args = list(id = FALSE)) > f[10]$node$split $varid [1] 3 $breaks NULL $index [1] 2 2 1 $right [1] TRUE $prob [1] 0 1 $info NULL attr(,"class") [1] "partysplit" > > ### factors with empty levels in learning sample > if (require("mlbench")) { + data("Vowel", package = "mlbench") + ct <- ctree(V2 ~ V1, data = Vowel[1:200,]) ### only levels 1:4 in V1 + try(p1 <- predict(ct, newdata = Vowel)) ### 14 levels in V1 + } Loading required package: mlbench Error in model.frame.default(delete.response(object$terms), newdata, xlev = xlev) : factor V1 has new levels 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 > > ### deal with empty levels for teststat = "quad" by > ### removing elements of the teststatistic with zero variance > ### reported by Wei-Yin Loh > tdata <- + structure(list(ytrain = structure(c(3L, 7L, 3L, 2L, 1L, 6L, 2L, + 1L, 1L, 2L, 1L, 2L, 3L, 3L, 2L, 1L, 2L, 6L, 2L, 4L, 6L, 1L, 2L, + 3L, 7L, 6L, 4L, 6L, 2L, 2L, 1L, 2L, 6L, 1L, 7L, 1L, 3L, 6L, 2L, + 1L, 7L, 2L, 7L, 2L, 3L, 2L, 1L, 1L, 3L, 1L, 6L, 2L, 2L, 2L, 2L, + 2L, 1L, 1L, 6L, 6L, 7L, 2L, 2L, 2L, 2L, 2L, 1L, 3L, 6L, 5L, 1L, + 1L, 4L, 7L, 2L, 3L, 3L, 3L, 1L, 8L, 1L, 6L, 2L, 8L, 3L, 4L, 6L, + 2L, 7L, 3L, 6L, 6L, 1L, 1L, 2L, 6L, 3L, 3L, 1L, 2L, 3L, 1L, 2L, + 7L, 2L, 3L, 6L, 2L, 5L, 2L, 2L, 2L, 1L, 3L, 3L, 7L, 3L, 2L, 3L, + 3L, 1L, 6L, 1L, 1L, 1L, 7L, 1L, 3L, 7L, 6L, 1L, 3L, 3L, 6L, 4L, + 2L, 3L, 2L, 8L, 3L, 4L, 2L, 2L, 2L, 3L, 2L, 2L, 2L, 3L, 4L, 6L, + 4L, 8L, 2L, 2L, 3L, 3L, 2L, 3L, 6L, 2L, 1L, 2L, 2L, 7L, 2L, 1L, + 1L, 7L, 2L, 7L, 6L, 6L, 6L), .Label = c("0", "1", "2", "3", "4", + "5", "6", "7"), class = "factor"), landmass = c(5L, 3L, 4L, 6L, + 3L, 4L, 1L, 2L, 2L, 6L, 3L, 1L, 5L, 5L, 1L, 3L, 1L, 4L, 1L, 5L, + 4L, 2L, 1L, 5L, 3L, 4L, 5L, 4L, 4L, 1L, 4L, 1L, 4L, 2L, 5L, 2L, + 4L, 4L, 6L, 1L, 1L, 3L, 3L, 3L, 4L, 1L, 1L, 2L, 4L, 1L, 4L, 4L, + 3L, 2L, 6L, 3L, 3L, 2L, 4L, 4L, 3L, 3L, 3L, 3L, 1L, 6L, 1L, 4L, + 4L, 2L, 1L, 1L, 5L, 3L, 3L, 6L, 5L, 5L, 3L, 5L, 3L, 4L, 1L, 5L, + 5L, 5L, 4L, 6L, 5L, 5L, 4L, 4L, 3L, 3L, 4L, 4L, 5L, 5L, 3L, 6L, + 4L, 1L, 6L, 5L, 1L, 4L, 4L, 6L, 5L, 3L, 1L, 6L, 1L, 4L, 4L, 5L, + 5L, 3L, 5L, 5L, 2L, 6L, 2L, 2L, 6L, 3L, 1L, 5L, 3L, 4L, 4L, 5L, + 4L, 4L, 5L, 6L, 4L, 4L, 5L, 5L, 5L, 1L, 1L, 1L, 4L, 2L, 3L, 3L, + 5L, 5L, 4L, 5L, 4L, 6L, 2L, 4L, 5L, 1L, 5L, 4L, 3L, 2L, 1L, 1L, + 5L, 6L, 3L, 2L, 5L, 6L, 3L, 4L, 4L, 4L), zone = c(1L, 1L, 1L, + 3L, 1L, 2L, 4L, 3L, 3L, 2L, 1L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, + 1L, 2L, 3L, 4L, 1L, 1L, 4L, 1L, 2L, 1L, 4L, 4L, 4L, 1L, 3L, 1L, + 4L, 2L, 2L, 3L, 4L, 4L, 1L, 1L, 1L, 1L, 4L, 4L, 3L, 1L, 4L, 1L, + 1L, 4L, 3L, 2L, 1L, 1L, 4L, 2L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, + 4L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 2L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, + 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 4L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, + 1L, 4L, 4L, 1L, 1L, 4L, 4L, 2L, 2L, 1L, 1L, 4L, 2L, 4L, 1L, 1L, + 1L, 1L, 1L, 1L, 1L, 4L, 2L, 3L, 3L, 1L, 1L, 4L, 1L, 1L, 2L, 1L, + 1L, 4L, 4L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, + 1L, 1L, 1L, 2L, 1L, 1L, 2L, 4L, 1L, 1L, 4L, 1L, 1L, 4L, 3L, 4L, + 4L, 1L, 2L, 1L, 4L, 1L, 3L, 1L, 2L, 2L, 2L), area = c(648L, 29L, + 2388L, 0L, 0L, 1247L, 0L, 2777L, 2777L, 7690L, 84L, 19L, 1L, + 143L, 0L, 31L, 23L, 113L, 0L, 47L, 600L, 8512L, 0L, 6L, 111L, + 274L, 678L, 28L, 474L, 9976L, 4L, 0L, 623L, 757L, 9561L, 1139L, + 2L, 342L, 0L, 51L, 115L, 9L, 128L, 43L, 22L, 0L, 49L, 284L, 1001L, + 21L, 28L, 1222L, 1L, 12L, 18L, 337L, 547L, 91L, 268L, 10L, 108L, + 249L, 0L, 132L, 0L, 0L, 109L, 246L, 36L, 215L, 28L, 112L, 1L, + 93L, 103L, 1904L, 1648L, 435L, 70L, 21L, 301L, 323L, 11L, 372L, + 98L, 181L, 583L, 0L, 236L, 10L, 30L, 111L, 0L, 3L, 587L, 118L, + 333L, 0L, 0L, 0L, 1031L, 1973L, 1L, 1566L, 0L, 447L, 783L, 0L, + 140L, 41L, 0L, 268L, 128L, 1267L, 925L, 121L, 195L, 324L, 212L, + 804L, 76L, 463L, 407L, 1285L, 300L, 313L, 9L, 11L, 237L, 26L, + 0L, 2150L, 196L, 72L, 1L, 30L, 637L, 1221L, 99L, 288L, 66L, 0L, + 0L, 0L, 2506L, 63L, 450L, 41L, 185L, 36L, 945L, 514L, 57L, 1L, + 5L, 164L, 781L, 0L, 84L, 236L, 245L, 178L, 0L, 9363L, 22402L, + 15L, 0L, 912L, 333L, 3L, 256L, 905L, 753L, 391L), population = c(16L, + 3L, 20L, 0L, 0L, 7L, 0L, 28L, 28L, 15L, 8L, 0L, 0L, 90L, 0L, + 10L, 0L, 3L, 0L, 1L, 1L, 119L, 0L, 0L, 9L, 7L, 35L, 4L, 8L, 24L, + 0L, 0L, 2L, 11L, 1008L, 28L, 0L, 2L, 0L, 2L, 10L, 1L, 15L, 5L, + 0L, 0L, 6L, 8L, 47L, 5L, 0L, 31L, 0L, 0L, 1L, 5L, 54L, 0L, 1L, + 1L, 17L, 61L, 0L, 10L, 0L, 0L, 8L, 6L, 1L, 1L, 6L, 4L, 5L, 11L, + 0L, 157L, 39L, 14L, 3L, 4L, 57L, 7L, 2L, 118L, 2L, 6L, 17L, 0L, + 3L, 3L, 1L, 1L, 0L, 0L, 9L, 6L, 13L, 0L, 0L, 0L, 2L, 77L, 0L, + 2L, 0L, 20L, 12L, 0L, 16L, 14L, 0L, 2L, 3L, 5L, 56L, 18L, 9L, + 4L, 1L, 84L, 2L, 3L, 3L, 14L, 48L, 36L, 3L, 0L, 22L, 5L, 0L, + 9L, 6L, 3L, 3L, 0L, 5L, 29L, 39L, 2L, 15L, 0L, 0L, 0L, 20L, 0L, + 8L, 6L, 10L, 18L, 18L, 49L, 2L, 0L, 1L, 7L, 45L, 0L, 1L, 13L, + 56L, 3L, 0L, 231L, 274L, 0L, 0L, 15L, 60L, 0L, 22L, 28L, 6L, + 8L), language = structure(c(10L, 6L, 8L, 1L, 6L, 10L, 1L, 2L, + 2L, 1L, 4L, 1L, 8L, 6L, 1L, 6L, 1L, 3L, 1L, 10L, 10L, 6L, 1L, + 10L, 5L, 3L, 10L, 10L, 3L, 1L, 6L, 1L, 10L, 2L, 7L, 2L, 3L, 10L, + 1L, 2L, 2L, 6L, 5L, 6L, 3L, 1L, 2L, 2L, 8L, 2L, 10L, 10L, 6L, + 1L, 1L, 9L, 3L, 3L, 10L, 1L, 4L, 4L, 1L, 6L, 1L, 1L, 2L, 3L, + 6L, 1L, 3L, 2L, 7L, 9L, 6L, 10L, 6L, 8L, 1L, 10L, 6L, 3L, 1L, + 9L, 8L, 10L, 10L, 1L, 10L, 8L, 10L, 10L, 4L, 4L, 10L, 10L, 10L, + 10L, 10L, 10L, 8L, 2L, 10L, 10L, 1L, 8L, 10L, 10L, 10L, 6L, 6L, + 1L, 2L, 3L, 10L, 10L, 8L, 6L, 8L, 6L, 2L, 1L, 2L, 2L, 10L, 5L, + 2L, 8L, 6L, 10L, 6L, 8L, 3L, 1L, 7L, 1L, 10L, 6L, 10L, 8L, 10L, + 1L, 1L, 1L, 8L, 6L, 6L, 4L, 8L, 7L, 10L, 10L, 3L, 10L, 1L, 8L, + 9L, 1L, 8L, 10L, 1L, 2L, 1L, 1L, 5L, 6L, 6L, 2L, 10L, 1L, 6L, + 10L, 10L, 10L), .Label = c("1", "2", "3", "4", "5", "6", "7", + "8", "9", "10"), class = "factor"), bars = c(0L, 0L, 2L, 0L, + 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 2L, 1L, 0L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, + 1L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 3L, 3L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 2L, 0L, + 0L, 3L, 0L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, + 0L, 0L, 0L, 1L, 0L, 0L, 0L, 3L, 0L, 0L, 0L, 0L, 3L, 3L, 0L, 0L, + 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 5L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 3L, 0L), stripes = c(3L, 0L, + 0L, 0L, 0L, 2L, 1L, 3L, 3L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, 2L, 0L, + 0L, 0L, 5L, 0L, 0L, 0L, 3L, 2L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 2L, + 0L, 3L, 0L, 0L, 0L, 5L, 5L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 3L, + 3L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 5L, 3L, 3L, 1L, 9L, 0L, 0L, + 0L, 0L, 2L, 0L, 0L, 3L, 0L, 3L, 0L, 2L, 3L, 3L, 0L, 2L, 0L, 0L, + 0L, 0L, 3L, 0L, 5L, 0L, 3L, 2L, 0L, 11L, 2L, 3L, 2L, 3L, 14L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 5L, 3L, 0L, 3L, 1L, 0L, 3L, + 3L, 0L, 5L, 3L, 0L, 2L, 0L, 0L, 0L, 3L, 0L, 0L, 2L, 5L, 0L, 0L, + 0L, 3L, 0L, 0L, 3L, 2L, 0L, 0L, 3L, 0L, 3L, 0L, 0L, 0L, 0L, 3L, + 5L, 0L, 0L, 3L, 0L, 0L, 5L, 5L, 0L, 0L, 0L, 0L, 0L, 3L, 6L, 0L, + 9L, 0L, 13L, 0L, 0L, 0L, 3L, 0L, 0L, 3L, 0L, 0L, 7L), colours = c(5L, + 3L, 3L, 5L, 3L, 3L, 3L, 2L, 3L, 3L, 2L, 3L, 2L, 2L, 3L, 3L, 8L, + 2L, 6L, 4L, 3L, 4L, 6L, 4L, 5L, 3L, 3L, 3L, 3L, 2L, 5L, 6L, 5L, + 3L, 2L, 3L, 2L, 3L, 4L, 3L, 3L, 3L, 3L, 2L, 4L, 6L, 3L, 3L, 4L, + 2L, 4L, 3L, 3L, 6L, 7L, 2L, 3L, 3L, 3L, 4L, 3L, 3L, 3L, 2L, 3L, + 7L, 2L, 3L, 4L, 5L, 2L, 2L, 6L, 3L, 3L, 2L, 3L, 4L, 3L, 2L, 3L, + 3L, 3L, 2L, 4L, 2L, 4L, 4L, 3L, 4L, 4L, 3L, 3L, 3L, 3L, 3L, 4L, + 3L, 3L, 3L, 2L, 4L, 2L, 3L, 7L, 2L, 5L, 3L, 3L, 3L, 3L, 3L, 2L, + 3L, 2L, 3L, 4L, 3L, 3L, 2L, 3L, 4L, 6L, 2L, 4L, 2L, 3L, 2L, 7L, + 4L, 4L, 2L, 3L, 3L, 2L, 4L, 2L, 5L, 4L, 4L, 4L, 5L, 4L, 4L, 4L, + 4L, 2L, 2L, 4L, 3L, 4L, 3L, 4L, 2L, 3L, 2L, 2L, 6L, 4L, 5L, 3L, + 3L, 6L, 3L, 2L, 4L, 4L, 7L, 2L, 3L, 4L, 4L, 4L, 5L), red = c(1L, + 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, + 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, + 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, + 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, + 0L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, + 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, + 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), green = c(1L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, + 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, + 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, + 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, + 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, + 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, + 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, + 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, + 1L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, + 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L), blue = c(0L, + 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, + 0L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, + 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, + 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, + 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, + 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, + 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, + 0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, + 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, + 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L), gold = c(1L, + 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, + 0L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, + 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, + 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, + 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, + 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, + 1L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, + 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, + 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L), white = c(1L, + 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, + 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, + 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, + 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, + 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, + 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, + 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, + 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 1L), black = c(1L, + 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, + 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, + 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, + 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L), orange = c(0L, + 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, + 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, + 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L), mainhue = structure(c(5L, + 7L, 5L, 2L, 4L, 7L, 8L, 2L, 2L, 2L, 7L, 2L, 7L, 5L, 2L, 4L, 2L, + 5L, 7L, 6L, 2L, 5L, 2L, 4L, 7L, 7L, 7L, 7L, 4L, 7L, 4L, 2L, 4L, + 7L, 7L, 4L, 5L, 7L, 2L, 2L, 2L, 8L, 8L, 7L, 2L, 5L, 2L, 4L, 1L, + 2L, 5L, 5L, 8L, 2L, 2L, 8L, 8L, 8L, 5L, 7L, 4L, 1L, 8L, 2L, 4L, + 2L, 2L, 4L, 4L, 5L, 1L, 2L, 2L, 7L, 2L, 7L, 7L, 7L, 8L, 8L, 8L, + 8L, 5L, 8L, 1L, 7L, 7L, 7L, 7L, 7L, 2L, 7L, 7L, 7L, 7L, 7L, 7L, + 7L, 7L, 2L, 5L, 5L, 2L, 7L, 2L, 7L, 4L, 2L, 3L, 7L, 8L, 2L, 2L, + 6L, 5L, 2L, 7L, 7L, 7L, 5L, 7L, 1L, 7L, 7L, 2L, 8L, 7L, 3L, 7L, + 7L, 5L, 5L, 5L, 5L, 8L, 5L, 2L, 6L, 8L, 7L, 4L, 5L, 2L, 5L, 7L, + 7L, 2L, 7L, 7L, 7L, 5L, 7L, 5L, 7L, 7L, 7L, 7L, 2L, 5L, 4L, 7L, + 8L, 8L, 8L, 7L, 7L, 4L, 7L, 7L, 7L, 7L, 5L, 5L, 5L), .Label = c("black", + "blue", "brown", "gold", "green", "orange", "red", "white"), class = "factor"), + circles = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 1L, 0L, 0L, 1L, 0L, 1L, 4L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, + 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, + 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L), crosses = c(0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, + 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 2L, 1L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, + 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, + 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), saltires = c(0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, + 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L), quarters = c(0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, + 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, + 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 4L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, + 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, + 0L, 0L, 0L, 0L), sunstars = c(1L, 1L, 1L, 0L, 0L, 1L, 0L, + 0L, 1L, 6L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 22L, + 0L, 0L, 1L, 1L, 14L, 3L, 1L, 0L, 1L, 4L, 1L, 1L, 5L, 0L, + 4L, 1L, 15L, 0L, 1L, 0L, 0L, 0L, 1L, 10L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 7L, + 0L, 0L, 0L, 1L, 0L, 0L, 5L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 1L, + 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 1L, 1L, 0L, 0L, 1L, 1L, 0L, 4L, 1L, 0L, 1L, 1L, 1L, 2L, 0L, + 6L, 4L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 2L, 5L, 1L, 0L, 4L, + 0L, 1L, 0L, 2L, 0L, 2L, 0L, 1L, 0L, 5L, 5L, 1L, 0L, 0L, 1L, + 0L, 2L, 0L, 0L, 0L, 1L, 0L, 0L, 2L, 1L, 0L, 0L, 1L, 0L, 0L, + 1L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 50L, 1L, 0L, 0L, 7L, 1L, + 5L, 1L, 0L, 0L, 1L), crescent = c(0L, 0L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, + 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L), triangle = c(0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, + 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L), icon = c(1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, + 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, + 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, + 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, + 1L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, + 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, + 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L), animate = c(0L, + 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, + 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, + 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, + 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L), text = c(0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, + 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, + 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, + 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, + 0L, 0L, 0L, 0L, 0L), topleft = structure(c(1L, 6L, 4L, 2L, + 2L, 6L, 7L, 2L, 2L, 7L, 6L, 2L, 7L, 4L, 2L, 1L, 6L, 4L, 7L, + 5L, 2L, 4L, 7L, 7L, 7L, 6L, 2L, 7L, 4L, 6L, 6L, 7L, 2L, 2L, + 6L, 3L, 4L, 6L, 7L, 2L, 2L, 7L, 7L, 6L, 7L, 4L, 2L, 3L, 6L, + 2L, 4L, 4L, 7L, 7L, 7L, 7L, 2L, 2L, 4L, 6L, 1L, 1L, 7L, 2L, + 6L, 6L, 2L, 6L, 6L, 1L, 1L, 2L, 7L, 6L, 2L, 6L, 4L, 6L, 4L, + 2L, 4L, 6L, 3L, 7L, 1L, 6L, 1L, 6L, 6L, 6L, 4L, 2L, 2L, 6L, + 7L, 1L, 2L, 6L, 7L, 2L, 4L, 4L, 2L, 6L, 7L, 6L, 4L, 2L, 2L, + 6L, 7L, 7L, 2L, 5L, 4L, 2L, 6L, 6L, 6L, 7L, 7L, 6L, 6L, 6L, + 2L, 7L, 6L, 7L, 2L, 6L, 4L, 4L, 4L, 4L, 6L, 2L, 2L, 5L, 7L, + 6L, 3L, 4L, 2L, 2L, 6L, 4L, 2L, 6L, 6L, 2L, 4L, 6L, 6L, 7L, + 7L, 6L, 6L, 7L, 6L, 1L, 7L, 7L, 7L, 2L, 6L, 1L, 3L, 3L, 6L, + 2L, 2L, 4L, 4L, 4L), .Label = c("black", "blue", "gold", + "green", "orange", "red", "white"), class = "factor"), botright = structure(c(5L, + 7L, 8L, 7L, 7L, 1L, 2L, 2L, 2L, 2L, 7L, 2L, 7L, 5L, 2L, 7L, + 7L, 5L, 7L, 7L, 2L, 5L, 2L, 4L, 7L, 5L, 7L, 8L, 4L, 7L, 5L, + 2L, 4L, 7L, 7L, 7L, 5L, 7L, 2L, 2L, 2L, 8L, 7L, 7L, 5L, 5L, + 2L, 7L, 1L, 2L, 7L, 7L, 8L, 2L, 2L, 8L, 7L, 7L, 2L, 5L, 4L, + 4L, 7L, 2L, 7L, 7L, 2L, 5L, 5L, 5L, 7L, 2L, 2L, 5L, 2L, 8L, + 7L, 1L, 6L, 2L, 7L, 5L, 4L, 8L, 5L, 7L, 5L, 2L, 7L, 7L, 2L, + 7L, 7L, 2L, 5L, 5L, 8L, 7L, 7L, 2L, 5L, 7L, 2L, 7L, 2L, 7L, + 4L, 2L, 2L, 2L, 8L, 2L, 2L, 5L, 5L, 2L, 1L, 7L, 5L, 5L, 8L, + 1L, 2L, 7L, 7L, 7L, 7L, 3L, 7L, 5L, 5L, 5L, 7L, 2L, 8L, 5L, + 2L, 2L, 8L, 1L, 4L, 7L, 2L, 5L, 1L, 5L, 2L, 7L, 1L, 7L, 2L, + 7L, 5L, 7L, 8L, 7L, 7L, 2L, 1L, 7L, 7L, 8L, 8L, 7L, 7L, 5L, + 8L, 7L, 7L, 7L, 7L, 5L, 3L, 5L), .Label = c("black", "blue", + "brown", "gold", "green", "orange", "red", "white"), class = "factor")), .Names = c("ytrain", + "landmass", "zone", "area", "population", "language", "bars", + "stripes", "colours", "red", "green", "blue", "gold", "white", + "black", "orange", "mainhue", "circles", "crosses", "saltires", + "quarters", "sunstars", "crescent", "triangle", "icon", "animate", + "text", "topleft", "botright"), row.names = c(NA, -174L), class = "data.frame") > tdata$language <- factor(tdata$language) > tdata$ytrain <- factor(tdata$ytrain) > > ### was: error > model <- ctree(ytrain ~ ., data = tdata, + control = ctree_control(testtype = "Univariate", splitstat = "maximum")) > > if (require("coin")) { + ### check against coin (independence_test automatically + ### removes empty levels) + p <- info_node(node_party(model))$criterion["p.value",] + p[is.na(p)] <- 0 + p2 <- sapply(names(p), function(n) + pvalue(independence_test(ytrain ~ ., + data = tdata[, c("ytrain", n)], teststat = "quad"))) + stopifnot(max(abs(p - p2)) < sqrt(.Machine$double.eps)) + + p <- info_node(node_party(model[2]))$criterion["p.value",] + p[is.na(p)] <- 0 + p2 <- sapply(names(p), function(n) + pvalue(independence_test(ytrain ~ ., + data = tdata[tdata$language != "8", c("ytrain", n)], + teststat = "quad"))) + stopifnot(max(abs(p - p2)) < sqrt(.Machine$double.eps)) + + p <- info_node(node_party(model[3]))$criterion["p.value",] + p[is.na(p)] <- 0 + p2 <- sapply(names(p), function(n) + pvalue(independence_test(ytrain ~ ., + data = tdata[!(tdata$language %in% c("2", "4", "8")), + c("ytrain", n)], + teststat = "quad"))) + stopifnot(max(abs(p - p2)) < sqrt(.Machine$double.eps)) + } Loading required package: coin Loading required package: survival > > ### check coersion of constparties to simpleparties > ### containing terminal nodes without corresponding observations > ## create party > data("WeatherPlay", package = "partykit") > py <- party( + partynode(1L, + split = partysplit(1L, index = 1:3), + kids = list( + partynode(2L, + split = partysplit(3L, breaks = 75), + kids = list( + partynode(3L, info = "yes"), + partynode(4L, info = "no"))), + partynode(5L, + split = partysplit(3L, breaks = 20), + kids = list( + partynode(6L, info = "no"), + partynode(7L, info = "yes"))), + partynode(8L, + split = partysplit(4L, index = 1:2), + kids = list( + partynode(9L, info = "yes"), + partynode(10L, info = "no"))))), + WeatherPlay) > names(py) <- LETTERS[nodeids(py)] > > pn <- node_party(py) > cp <- party(pn, + data = WeatherPlay, + fitted = data.frame( + "(fitted)" = fitted_node(pn, data = WeatherPlay), + "(response)" = WeatherPlay$play, + check.names = FALSE), + terms = terms(play ~ ., data = WeatherPlay), + ) > print(cp) [1] root | [2] outlook in sunny | | [3] humidity <= 75: yes | | [4] humidity > 75: no | [5] outlook in overcast | | [6] humidity <= 20: no | | [7] humidity > 20: yes | [8] outlook in rainy | | [9] windy in false: yes | | [10] windy in true: no > cp <- as.constparty(cp) > > nd <- data.frame(outlook = factor("overcast", levels = levels(WeatherPlay$outlook)), + humidity = 10, temperature = 10, windy = "yes") > try(predict(cp, type = "node", newdata = nd)) Error in model.frame.default(delete.response(object$terms), newdata, xlev = xlev) : factor windy has new level yes > try(predict(cp, type = "response", newdata = nd)) Error in model.frame.default(delete.response(object$terms), newdata, xlev = xlev) : factor windy has new level yes > as.simpleparty(cp) Model formula: play ~ outlook + temperature + humidity + windy Fitted party: [1] root | [2] outlook in sunny | | [3] humidity <= 75: yes (n = 2, err = 0.0%) | | [4] humidity > 75: no (n = 3, err = 0.0%) | [5] outlook in overcast | | [6] humidity <= 20: NA (n = 0, err = NA) | | [7] humidity > 20: yes (n = 4, err = 0.0%) | [8] outlook in rainy | | [9] windy in false: yes (n = 3, err = 0.0%) | | [10] windy in true: no (n = 2, err = 0.0%) Number of inner nodes: 4 Number of terminal nodes: 6 > print(cp) Model formula: play ~ outlook + temperature + humidity + windy Fitted party: [1] root | [2] outlook in sunny | | [3] humidity <= 75: yes (n = 2, err = 0.0%) | | [4] humidity > 75: no (n = 3, err = 0.0%) | [5] outlook in overcast | | [6] humidity <= 20: NA (n = 0, err = NA) | | [7] humidity > 20: yes (n = 4, err = 0.0%) | [8] outlook in rainy | | [9] windy in false: yes (n = 3, err = 0.0%) | | [10] windy in true: no (n = 2, err = 0.0%) Number of inner nodes: 4 Number of terminal nodes: 6 > > ### scores > y <- gl(3, 10, ordered = TRUE) > x <- rnorm(length(y)) > x <- ordered(cut(x, 3)) > d <- data.frame(y = y, x = x) > > ### partykit with scores > ct11 <- partykit::ctree(y ~ x, data = d) > ct12 <- partykit::ctree(y ~ x, data = d, + scores = list(y = c(1, 4, 5))) > ct13 <- partykit::ctree(y ~ x, data = d, + scores = list(y = c(1, 4, 5), x = c(1, 5, 6))) > > ### party with scores > ct21 <- party::ctree(y ~ x, data = d) > ct22 <- party::ctree(y ~ x, data = d, + scores = list(y = c(1, 4, 5))) > ct23 <- party::ctree(y ~ x, data = d, + scores = list(y = c(1, 4, 5), x = c(1, 5, 6))) > > stopifnot(all.equal(ct11$node$info$p.value, + 1 - ct21@tree$criterion$criterion, check.attr = FALSE)) > stopifnot(all.equal(ct12$node$info$p.value, + 1 - ct22@tree$criterion$criterion, check.attr = FALSE)) > stopifnot(all.equal(ct13$node$info$p.value, + 1 - ct23@tree$criterion$criterion, check.attr = FALSE)) > > ### ytrafo > y <- runif(100, max = 3) > x <- rnorm(length(y)) > d <- data.frame(y = y, x = x) > > ### partykit with scores > ct11 <- partykit::ctree(y ~ x, data = d) > ct12 <- partykit::ctree(y ~ x, data = d, + ytrafo = list(y = sqrt)) > > ### party with scores > ct21 <- party::ctree(y ~ x, data = d) > f <- function(data) coin::trafo(data, numeric_trafo = sqrt) > ct22 <- party::ctree(y ~ x, data = d, + ytrafo = f) > > stopifnot(all.equal(ct11$node$info$p.value, + 1 - ct21@tree$criterion$criterion, check.attr = FALSE)) > stopifnot(all.equal(ct12$node$info$p.value, + 1 - ct22@tree$criterion$criterion, check.attr = FALSE)) > > > ### spotted by Peter Philip Stephensen (DREAM) > ### splits x >= max(x) where possible in partykit::ctree > nAge <- 30 > d <- data.frame(Age=rep(1:nAge,2),y=c(rep(1,nAge),rep(0,nAge)), + n = rep(0,2*nAge)) > ntot <- 100 > alpha <- .5 > d[d$y==1,]$n = floor(ntot * alpha * d[d$y==1,]$Age / nAge) > d[d$y==0,]$n = ntot - d[d$y==1,]$n > d$n <- as.integer(d$n) > ctrl <- partykit::ctree_control(maxdepth=3, minbucket = min(d$n) + 1) > tree <- partykit::ctree(y ~ Age, weights=n, data=d, control=ctrl) > ## IGNORE_RDIFF_BEGIN > tree Model formula: y ~ Age Fitted party: [1] root | [2] Age <= 15 | | [3] Age <= 7 | | | [4] Age <= 4: 0.038 (n = 400, err = 14.4) | | | [5] Age > 4: 0.097 (n = 300, err = 26.2) | | [6] Age > 7 | | | [7] Age <= 11: 0.155 (n = 400, err = 52.4) | | | [8] Age > 11: 0.222 (n = 400, err = 69.2) | [9] Age > 15 | | [10] Age <= 22: 0.313 (n = 700, err = 150.5) | | [11] Age > 22 | | | [12] Age <= 26: 0.405 (n = 400, err = 96.4) | | | [13] Age > 26: 0.472 (n = 400, err = 99.7) Number of inner nodes: 6 Number of terminal nodes: 7 > ## IGNORE_RDIFF_END > > (w1 <- predict(tree, type = "node")) 4 4 4 4 5 5 5 7 7 7 7 8 8 8 8 10 10 10 10 10 10 10 12 12 12 12 4 4 4 4 5 5 5 7 7 7 7 8 8 8 8 10 10 10 10 10 10 10 12 12 12 12 13 13 13 13 4 4 4 4 5 5 5 7 7 7 7 8 8 8 8 10 10 10 10 10 10 10 13 13 13 13 4 4 4 4 5 5 5 7 7 7 7 8 8 8 8 10 10 10 10 10 10 10 12 12 12 12 13 13 13 13 12 12 12 12 13 13 13 13 > > (ct <- ctree(dist + I(dist^2) ~ speed, data = cars)) Model formula: ~dist + I(dist^2) + speed Fitted party: [1] root | [2] speed <= 12: * | [3] speed > 12 | | [4] speed <= 20: * | | [5] speed > 20: * Number of inner nodes: 2 Number of terminal nodes: 3 > predict(ct) dist I(dist^2) 1 18.20000 409.6667 2 18.20000 409.6667 3 18.20000 409.6667 4 18.20000 409.6667 5 18.20000 409.6667 6 18.20000 409.6667 7 18.20000 409.6667 8 18.20000 409.6667 9 18.20000 409.6667 10 18.20000 409.6667 11 18.20000 409.6667 12 18.20000 409.6667 13 18.20000 409.6667 14 18.20000 409.6667 15 18.20000 409.6667 16 46.28571 2423.1429 17 46.28571 2423.1429 18 46.28571 2423.1429 19 46.28571 2423.1429 20 46.28571 2423.1429 21 46.28571 2423.1429 22 46.28571 2423.1429 23 46.28571 2423.1429 24 46.28571 2423.1429 25 46.28571 2423.1429 26 46.28571 2423.1429 27 46.28571 2423.1429 28 46.28571 2423.1429 29 46.28571 2423.1429 30 46.28571 2423.1429 31 46.28571 2423.1429 32 46.28571 2423.1429 33 46.28571 2423.1429 34 46.28571 2423.1429 35 46.28571 2423.1429 36 46.28571 2423.1429 37 46.28571 2423.1429 38 46.28571 2423.1429 39 46.28571 2423.1429 40 46.28571 2423.1429 41 46.28571 2423.1429 42 46.28571 2423.1429 43 46.28571 2423.1429 44 82.85714 7272.8571 45 82.85714 7272.8571 46 82.85714 7272.8571 47 82.85714 7272.8571 48 82.85714 7272.8571 49 82.85714 7272.8571 50 82.85714 7272.8571 > > ### nodeapply was not the same for permutations of ids > ### spotted by Heidi Seibold > airq <- subset(airquality, !is.na(Ozone)) > airct <- ctree(Ozone ~ ., data = airq) > n1 <- nodeapply(airct, ids = c(3, 5, 6), function(x) x$info$nobs) > n2 <- nodeapply(airct, ids = c(6, 3, 5), function(x) x$info$nobs) > stopifnot(all.equal(n1[names(n2)], n2)) > > ### pruning got "fitted" wrong, spotted by Jason Parker > data("Titanic") > titan <- as.data.frame(Titanic) > (tree <- ctree(Survived ~ Class + Sex + Age, data = titan, weights = Freq)) Model formula: Survived ~ Class + Sex + Age Fitted party: [1] root | [2] Sex in Male | | [3] Class in 1st: No (n = 180, err = 34.4%) | | [4] Class in 2nd, 3rd, Crew | | | [5] Age in Child | | | | [6] Class in 2nd: Yes (n = 11, err = 0.0%) | | | | [7] Class in 3rd: No (n = 48, err = 27.1%) | | | [8] Age in Adult | | | | [9] Class in 2nd, 3rd | | | | | [10] Class in 2nd: No (n = 168, err = 8.3%) | | | | | [11] Class in 3rd: No (n = 462, err = 16.2%) | | | | [12] Class in Crew: No (n = 862, err = 22.3%) | [13] Sex in Female | | [14] Class in 1st, 2nd, Crew | | | [15] Class in 1st: Yes (n = 145, err = 2.8%) | | | [16] Class in 2nd, Crew: Yes (n = 129, err = 12.4%) | | [17] Class in 3rd: No (n = 196, err = 45.9%) Number of inner nodes: 8 Number of terminal nodes: 9 > ### prune off nodes 5-12 and check if the other nodes are not affected > nodeprune(tree, 4) Model formula: Survived ~ Class + Sex + Age Fitted party: [1] root | [2] Sex in Male | | [3] Class in 1st: No (n = 180, err = 34.4%) | | [4] Class in 2nd, 3rd, Crew: No (n = 1551, err = 19.7%) | [5] Sex in Female | | [6] Class in 1st, 2nd, Crew | | | [7] Class in 1st: Yes (n = 145, err = 2.8%) | | | [8] Class in 2nd, Crew: Yes (n = 129, err = 12.4%) | | [9] Class in 3rd: No (n = 196, err = 45.9%) Number of inner nodes: 4 Number of terminal nodes: 5 > > ### subsetting removed weights from fitted, by Jon Peck > t1 <- ctree(Survived ~Age+Sex+Class, data=Titanic, weights=Freq, maxdepth = 1) > tita <- as.data.frame(Titanic) > t2 <- ctree(Survived ~Age+Sex+Class, data=tita[rep(1:nrow(tita), tita$Freq),], maxdepth = 1) > # all the same > t1 Model formula: Survived ~ Age + Sex + Class Fitted party: [1] root | [2] Sex in Male: No (n = 1731, err = 21.2%) | [3] Sex in Female: Yes (n = 470, err = 26.8%) Number of inner nodes: 1 Number of terminal nodes: 2 > t1[1] Model formula: Survived ~ Age + Sex + Class Fitted party: [1] root | [2] Sex in Male: No (n = 1731, err = 21.2%) | [3] Sex in Female: Yes (n = 470, err = 26.8%) Number of inner nodes: 1 Number of terminal nodes: 2 > t2 Model formula: Survived ~ Age + Sex + Class Fitted party: [1] root | [2] Sex in Male: No (n = 1731, err = 21.2%) | [3] Sex in Female: Yes (n = 470, err = 26.8%) Number of inner nodes: 1 Number of terminal nodes: 2 > t2[1] Model formula: Survived ~ Age + Sex + Class Fitted party: [1] root | [2] Sex in Male: No (n = 1731, err = 21.2%) | [3] Sex in Female: Yes (n = 470, err = 26.8%) Number of inner nodes: 1 Number of terminal nodes: 2 > > ### this gave a warning "ME is not a factor" > if (require("TH.data")) { + data("mammoexp", package = "TH.data") + a <- cforest(ME ~ PB + SYMPT, data = mammoexp, ntree = 5) + print(predict(a, newdata=mammoexp[1:3,])) + } Loading required package: TH.data Loading required package: MASS Attaching package: 'TH.data' The following object is masked from 'package:MASS': geyser 1 2 3 Never Never Never Levels: Never < Within a Year < Over a Year > > ### pruning didn't work properly > mt <- lmtree(dist ~ speed, data = cars) > mt2 <- nodeprune(mt, 2) > stopifnot(all(mt2$fitted[["(fitted)"]] %in% c(2, 3))) > > ### > a <- rep('N',87) > a[77] <- 'Y' > b <- rep(FALSE, 87) > b[c(7,10,11,33,56,77)] <- TRUE > d <- rep(1,87) > d[c(29,38,40,42,65,77)] <- 0 > dfb <- data.frame(a = as.factor(a), b = as.factor(b), d = as.factor(d)) > tr <- ctree(a ~ ., data = dfb, control = ctree_control(minsplit = 10,minbucket = 5, + maxsurrogate = 2, alpha = 0.05)) > tNodes <- node_party(tr) > ### this creates a tie on purpose and "d" should be selected > ### this check fails on M1mac > nodeInfo <- info_node(tNodes) > nodeInfo$criterion b d statistic 13.5000000000 13.5000000000 p.value 0.0004770700 0.0004770700 criterion -0.0001771838 -0.0001771838 > #stopifnot(names(nodeInfo$p.value) == "d") > #stopifnot(split_node(tNodes)$varid == 3) > > ### reported by John Ogawa, 2020-12-11 > class(dfb$a) <- c("Hansi", "factor") > tr2 <- ctree(a ~ ., data = dfb, control = ctree_control(minsplit = 10,minbucket = 5, + maxsurrogate = 2, alpha = 0.05)) > stopifnot(isTRUE(all.equal(tr, tr2, check.attributes = FALSE))) > > proc.time() user system elapsed 1.438 0.071 1.511 partykit/tests/regtest-weights.R0000644000176200001440000000755614172230001016536 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) library("partykit") ## artificial data --------------------------------------------------------------------------------- set.seed(0) d <- data.frame(x = seq(-1, 1, length.out = 1000), z = factor(rep(0:1, 500))) d$y <- 0 + 1 * d$x + rnorm(nrow(d)) d$w <- rep(1:4, nrow(d)/4) dd <- d[rep(1:nrow(d), d$w), ] ## convenience function: likelihood ratio test ----------------------------------------------------- lrtest <- function(data, ...) { lr <- -2 * (logLik(lm(y ~ x, data = data, ...)) - logLik(lm(y ~ x * z, data = data, ...))) matrix( c(lr, pchisq(lr, df = 2, lower.tail = FALSE)), dimnames = list(c("statistic", "p.value"), "z") ) } ## lm: case weights -------------------------------------------------------------------------------- ## weighted and explicitly expanded data should match exactly lm1 <- lmtree(y ~ x | z, data = d, weights = w, maxdepth = 2) lm2 <- lmtree(y ~ x | z, data = dd, maxdepth = 2) all.equal(sctest.modelparty(lm1), sctest.modelparty(lm2)) ## LR test should be similar (albeit not identical) all.equal(sctest.modelparty(lm1), lrtest(dd), tol = 0.05) ## lm: proportionality weights --------------------------------------------------------------------- ## LR test should be similar lm3 <- lmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, caseweights = FALSE) all.equal(sctest.modelparty(lm3), lrtest(d, weights = d$w), tol = 0.05) ## constant factor should not change results lm3x <- lmtree(y ~ x | z, data = d, weights = 2 * w, maxdepth = 2, caseweights = FALSE) all.equal(sctest.modelparty(lm3), sctest.modelparty(lm3x)) ## glm: case weights ------------------------------------------------------------------------------- ## for glm different vcov are available glm1o <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, vcov = "opg") glm2o <- glmtree(y ~ x | z, data = dd, maxdepth = 2, vcov = "opg") all.equal(sctest.modelparty(glm1o), sctest.modelparty(glm1o)) glm1i <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, vcov = "info") glm2i <- glmtree(y ~ x | z, data = dd, maxdepth = 2, vcov = "info") all.equal(sctest.modelparty(glm1i), sctest.modelparty(glm2i)) glm1s <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, vcov = "sandwich") glm2s <- glmtree(y ~ x | z, data = dd, maxdepth = 2, vcov = "sandwich") all.equal(sctest.modelparty(glm1s), sctest.modelparty(glm2s)) ## different vcov should yield similar (albeit not identical) statistics all.equal(sctest.modelparty(glm1o), sctest.modelparty(glm1i), tol = 0.05) all.equal(sctest.modelparty(glm1o), sctest.modelparty(glm1s), tol = 0.05) ## LR test should be similar all.equal(sctest.modelparty(glm1o), lrtest(dd), tol = 0.05) ## glm: proportionality weights -------------------------------------------------------------------- ## different test versions should be similar glmFo <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, caseweights = FALSE, vcov = "opg") glmFi <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, caseweights = FALSE, vcov = "info") glmFs <- glmtree(y ~ x | z, data = d, weights = w, maxdepth = 2, caseweights = FALSE, vcov = "sandwich") all.equal(sctest.modelparty(glmFo), sctest.modelparty(glmFi), tol = 0.05) all.equal(sctest.modelparty(glmFo), sctest.modelparty(glmFs), tol = 0.05) all.equal(sctest.modelparty(glmFo), lrtest(d, weights = d$w), tol = 0.05) ## constant factor should not change results glmFxo <- glmtree(y ~ x | z, data = d, weights = 2 * w, maxdepth = 2, caseweights = FALSE, vcov = "opg") glmFxi <- glmtree(y ~ x | z, data = d, weights = 2 * w, maxdepth = 2, caseweights = FALSE, vcov = "info") glmFxs <- glmtree(y ~ x | z, data = d, weights = 2 * w, maxdepth = 2, caseweights = FALSE, vcov = "sandwich") all.equal(sctest.modelparty(glmFo), sctest.modelparty(glmFxo)) all.equal(sctest.modelparty(glmFi), sctest.modelparty(glmFxi)) all.equal(sctest.modelparty(glmFs), sctest.modelparty(glmFxs)) partykit/tests/regtest-cforest.Rout.save0000644000176200001440000002270514172230001020207 0ustar liggesusers R version 3.5.2 (2018-12-20) -- "Eggshell Igloo" Copyright (C) 2018 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > stopifnot(require("party")) Loading required package: party Loading required package: modeltools Loading required package: stats4 Loading required package: strucchange Loading required package: zoo Attaching package: 'zoo' The following objects are masked from 'package:base': as.Date, as.Date.numeric Loading required package: sandwich Attaching package: 'party' The following objects are masked from 'package:partykit': cforest, ctree, ctree_control, edge_simple, mob, mob_control, node_barplot, node_bivplot, node_boxplot, node_inner, node_surv, node_terminal, varimp > set.seed(29) > > ### regression > airq <- airquality[complete.cases(airquality),] > > mtry <- ncol(airq) - 1L > ntree <- 25 > > cf_partykit <- partykit::cforest(Ozone ~ ., data = airq, + ntree = ntree, mtry = mtry) > > w <- do.call("cbind", cf_partykit$weights) > > cf_party <- party::cforest(Ozone ~ ., data = airq, + control = party::cforest_unbiased(ntree = ntree, mtry = mtry), + weights = w) > > p_partykit <- predict(cf_partykit) > p_party <- predict(cf_party) > > stopifnot(max(abs(p_partykit - p_party)) < sqrt(.Machine$double.eps)) > > prettytree(cf_party@ensemble[[1]], inames = names(airq)[-1]) 1) Wind <= 5.7; criterion = 1, statistic = 30.75 2)* weights = 0 1) Wind > 5.7 3) Temp <= 84; criterion = 1, statistic = 30.238 4) Temp <= 77; criterion = 0.999, statistic = 10.471 5) Wind <= 9.2; criterion = 0.895, statistic = 2.632 6)* weights = 0 5) Wind > 9.2 7) Solar.R <= 112; criterion = 0.907, statistic = 2.823 8)* weights = 0 7) Solar.R > 112 9)* weights = 0 4) Temp > 77 10) Day <= 13; criterion = 0.981, statistic = 5.479 11)* weights = 0 10) Day > 13 12)* weights = 0 3) Temp > 84 13)* weights = 0 > party(cf_partykit$nodes[[1]], data = model.frame(cf_partykit)) [1] root | [2] Wind <= 5.7: * | [3] Wind > 5.7 | | [4] Temp <= 84 | | | [5] Temp <= 77 | | | | [6] Wind <= 9.2: * | | | | [7] Wind > 9.2 | | | | | [8] Solar.R <= 112: * | | | | | [9] Solar.R > 112: * | | | [10] Temp > 77 | | | | [11] Day <= 13: * | | | | [12] Day > 13: * | | [13] Temp > 84: * > > v_party <- do.call("rbind", lapply(1:5, function(i) party::varimp(cf_party))) > > v_partykit <- do.call("rbind", lapply(1:5, function(i) partykit::varimp(cf_partykit))) > > summary(v_party) Solar.R Wind Temp Month Min. :22.87 Min. :146.3 Min. :760.9 Min. :0.5159 1st Qu.:25.06 1st Qu.:152.8 1st Qu.:784.3 1st Qu.:0.5236 Median :26.11 Median :176.0 Median :806.2 Median :0.6119 Mean :26.90 Mean :171.9 Mean :813.8 Mean :0.7391 3rd Qu.:26.26 3rd Qu.:189.3 3rd Qu.:841.5 3rd Qu.:0.9886 Max. :34.18 Max. :195.1 Max. :875.9 Max. :1.0556 Day Min. :2.051 1st Qu.:2.512 Median :2.689 Mean :3.409 3rd Qu.:3.487 Max. :6.304 > summary(v_partykit) Solar.R Wind Temp Month Min. :23.35 Min. :161.7 Min. :760.8 Min. :-2.446 1st Qu.:24.81 1st Qu.:190.1 1st Qu.:763.4 1st Qu.: 2.983 Median :26.93 Median :199.4 Median :768.7 Median : 3.440 Mean :29.65 Mean :195.5 Mean :777.1 Mean : 2.662 3rd Qu.:31.46 3rd Qu.:205.0 3rd Qu.:769.2 3rd Qu.: 4.575 Max. :41.69 Max. :221.5 Max. :823.4 Max. : 4.757 Day Min. :-1.1396 1st Qu.:-0.4362 Median :24.3535 Mean :17.7578 3rd Qu.:31.8914 Max. :34.1200 > > party::varimp(cf_party, conditional = TRUE) Solar.R Wind Temp Month Day 16.7190604 100.7812597 534.9587763 -0.2538655 4.4848324 > partykit::varimp(cf_partykit, conditional = TRUE) Solar.R Wind Temp Month Day 27.520179 144.897612 476.407961 0.308407 -0.655686 > > > ### classification > set.seed(29) > mtry <- ncol(iris) - 1L > ntree <- 25 > > cf_partykit <- partykit::cforest(Species ~ ., data = iris, + ntree = ntree, mtry = mtry) > > w <- do.call("cbind", cf_partykit$weights) > > cf_party <- party::cforest(Species ~ ., data = iris, + control = party::cforest_unbiased(ntree = ntree, mtry = mtry), + weights = w) > > p_partykit <- predict(cf_partykit, type = "prob") > p_party <- do.call("rbind", treeresponse(cf_party)) > > stopifnot(max(abs(unclass(p_partykit) - unclass(p_party))) < sqrt(.Machine$double.eps)) > > prettytree(cf_party@ensemble[[1]], inames = names(iris)[-5]) 1) Petal.Length <= 1.9; criterion = 1, statistic = 86.933 2)* weights = 0 1) Petal.Length > 1.9 3) Petal.Width <= 1.6; criterion = 1, statistic = 42.075 4) Sepal.Width <= 2.5; criterion = 0.931, statistic = 3.316 5)* weights = 0 4) Sepal.Width > 2.5 6)* weights = 0 3) Petal.Width > 1.6 7) Petal.Length <= 5.1; criterion = 0.774, statistic = 1.466 8)* weights = 0 7) Petal.Length > 5.1 9)* weights = 0 > party(cf_partykit$nodes[[1]], data = model.frame(cf_partykit)) [1] root | [2] Petal.Length <= 1.9: * | [3] Petal.Length > 1.9 | | [4] Petal.Width <= 1.6 | | | [5] Sepal.Width <= 2.5: * | | | [6] Sepal.Width > 2.5: * | | [7] Petal.Width > 1.6 | | | [8] Petal.Length <= 5.1: * | | | [9] Petal.Length > 5.1: * > > v_party <- do.call("rbind", lapply(1:5, function(i) party::varimp(cf_party))) > > v_partykit <- do.call("rbind", lapply(1:5, function(i) + partykit::varimp(cf_partykit, risk = "mis"))) > > summary(v_party) Sepal.Length Sepal.Width Petal.Length Petal.Width Min. :0 Min. :0 Min. :0.3786 Min. :0.3014 1st Qu.:0 1st Qu.:0 1st Qu.:0.3807 1st Qu.:0.3029 Median :0 Median :0 Median :0.4000 Median :0.3050 Mean :0 Mean :0 Mean :0.3941 Mean :0.3111 3rd Qu.:0 3rd Qu.:0 3rd Qu.:0.4036 3rd Qu.:0.3121 Max. :0 Max. :0 Max. :0.4079 Max. :0.3343 > summary(v_partykit) Sepal.Width Petal.Length Petal.Width Min. :0 Min. :0.3869 Min. :0.2971 1st Qu.:0 1st Qu.:0.3921 1st Qu.:0.3036 Median :0 Median :0.3966 Median :0.3057 Mean :0 Mean :0.3952 Mean :0.3117 3rd Qu.:0 3rd Qu.:0.4003 3rd Qu.:0.3179 Max. :0 Max. :0.4003 Max. :0.3343 > > party::varimp(cf_party, conditional = TRUE) Sepal.Length Sepal.Width Petal.Length Petal.Width 0.0000000 0.0000000 0.2778571 0.1014286 > partykit::varimp(cf_partykit, risk = "misclass", conditional = TRUE) Sepal.Width Petal.Length Petal.Width 0.0000000 0.2782738 0.1171429 > > ### mean aggregation > set.seed(29) > > ### fit forest > cf <- partykit::cforest(dist ~ speed, data = cars, ntree = 100) > > ### prediction; scale = TRUE introduced in 1.2-1 > pr <- predict(cf, newdata = cars[1,,drop = FALSE], type = "response", scale = TRUE) > ### this is equivalent to > w <- predict(cf, newdata = cars[1,,drop = FALSE], type = "weights") > stopifnot(isTRUE(all.equal(pr, sum(w * cars$dist) / sum(w), + check.attributes = FALSE))) > > ### check if this is the same as mean aggregation > > ### compute terminal node IDs for first obs > nd1 <- predict(cf, newdata = cars[1,,drop = FALSE], type = "node") > ### compute terminal nide IDs for all obs > nd <- predict(cf, newdata = cars, type = "node") > ### random forests weighs > lw <- cf$weights > > ### compute mean predictions for each tree > ### and extract mean for terminal node containing > ### first observation > np <- vector(mode = "list", length = length(lw)) > m <- numeric(length(lw)) > > for (i in 1:length(lw)) { + np[[i]] <- tapply(lw[[i]] * cars$dist, nd[[i]], sum) / + tapply(lw[[i]], nd[[i]], sum) + m[i] <- np[[i]][as.character(nd1[i])] + } > > stopifnot(isTRUE(all.equal(mean(m), sum(w * cars$dist) / sum(w)))) > > ### check parallel variable importance (make this reproducible) > if(.Platform$OS.type == "unix") { + RNGkind("L'Ecuyer-CMRG") + v1 <- partykit::varimp(cf_partykit, risk = "misclass", conditional = TRUE, cores = 2) + v2 <- partykit::varimp(cf_partykit, risk = "misclass", conditional = TRUE, cores = 2) + stopifnot(all.equal(v1, v2)) + } > > ### check weights argument > cf_partykit <- partykit::cforest(Species ~ ., data = iris, + ntree = ntree, mtry = 4) > w <- do.call("cbind", cf_partykit$weights) > cf_2 <- partykit::cforest(Species ~ ., data = iris, + ntree = ntree, mtry = 4, weights = w) > stopifnot(max(abs(predict(cf_2, type = "prob") - + predict(cf_partykit, type = "prob"))) < sqrt(.Machine$double.eps)) > > > proc.time() user system elapsed 5.245 0.192 5.095 partykit/tests/regtest-lmtree.R0000644000176200001440000000110414172230000016332 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) library("partykit") set.seed(29) n <- 1000 x <- runif(n) z <- runif(n) y <- rnorm(n, mean = x * c(-1, 1)[(z > 0.7) + 1], sd = 3) z_noise <- factor(sample(1:3, size = n, replace = TRUE)) d <- data.frame(y = y, x = x, z = z, z_noise = z_noise) fmla <- as.formula("y ~ x | z + z_noise") (m_mob <- mob(formula = fmla, data = d, fit = partykit:::lmfit)) (m_lm2 <- lmtree(formula = fmla, data = d)) mods <- nodeapply(m_lm2, ids = nodeids(m_lm2, terminal = TRUE), function(x) x$info$object) sum(sapply(mods, function(x) sum(x$residuals^2))) partykit/tests/regtest-glmtree.Rout.save0000644000176200001440000003554614172230000020207 0ustar liggesusers R version 4.0.3 (2020-10-10) -- "Bunny-Wunnies Freak Out" Copyright (C) 2020 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > > set.seed(29) > n <- 1000 > x <- runif(n) > z <- runif(n) > y <- rnorm(n, mean = x * c(-1, 1)[(z > 0.7) + 1], sd = 3) > z_noise <- factor(sample(1:3, size = n, replace = TRUE)) > d <- data.frame(y = y, x = x, z = z, z_noise = z_noise) > > > fmla <- as.formula("y ~ x | z + z_noise") > fmly <- gaussian() > fit <- partykit:::glmfit > > # versions of the data > d1 <- d > d1$z <- signif(d1$z, digits = 1) > > k <- 20 > zs_noise <- matrix(rnorm(n*k), nrow = n) > colnames(zs_noise) <- paste0("z_noise_", 1:k) > d2 <- cbind(d, zs_noise) > fmla2 <- as.formula(paste("y ~ x | z + z_noise +", + paste0("z_noise_", 1:k, collapse = " + "))) > > > d3 <- d2 > d3$z <- factor(sample(1:3, size = n, replace = TRUE, prob = c(0.1, 0.5, 0.4))) > d3$y <- rnorm(n, mean = x * c(-1, 1)[(d3$z == 2) + 1], sd = 3) > > ## check weights > w <- rep(1, n) > w[1:10] <- 2 > (mw1 <- glmtree(formula = fmla, data = d, weights = w)) Generalized linear model tree (family: gaussian) Model formula: y ~ x | z + z_noise Fitted party: [1] root | [2] z <= 0.70311: n = 706 | (Intercept) x | -0.1447422 -0.8138701 | [3] z > 0.70311: n = 304 | (Intercept) x | 0.07006626 0.73278593 Number of inner nodes: 1 Number of terminal nodes: 2 Number of parameters per node: 2 Objective function (negative log-likelihood): 2551.48 > (mw2 <- glmtree(formula = fmla, data = d, weights = w, caseweights = FALSE)) Generalized linear model tree (family: gaussian) Model formula: y ~ x | z + z_noise Fitted party: [1] root | [2] z <= 0.70311: n = 704 | (Intercept) x | -0.1447422 -0.8138701 | [3] z > 0.70311: n = 296 | (Intercept) x | 0.07006626 0.73278593 Number of inner nodes: 1 Number of terminal nodes: 2 Number of parameters per node: 2 Objective function (negative log-likelihood): 2551.48 > > > > ## check dfsplit > (mmfluc2 <- mob(formula = fmla, data = d, fit = partykit:::glmfit)) Model-based recursive partitioning (partykit:::glmfit) Model formula: y ~ x | z + z_noise Fitted party: [1] root | [2] z <= 0.70311: n = 704 | (Intercept) x | -0.1619978 -0.7896293 | [3] z > 0.70311: n = 296 | (Intercept) x | 0.08683535 0.65598287 Number of inner nodes: 1 Number of terminal nodes: 2 Number of parameters per node: 2 Objective function: 2551.673 > (mmfluc3 <- glmtree(formula = fmla, data = d)) Generalized linear model tree (family: gaussian) Model formula: y ~ x | z + z_noise Fitted party: [1] root | [2] z <= 0.70311: n = 704 | (Intercept) x | -0.1619978 -0.7896293 | [3] z > 0.70311: n = 296 | (Intercept) x | 0.08683535 0.65598287 Number of inner nodes: 1 Number of terminal nodes: 2 Number of parameters per node: 2 Objective function (negative log-likelihood): 2551.673 > (mmfluc3_dfsplit <- glmtree(formula = fmla, data = d, dfsplit = 10)) Generalized linear model tree (family: gaussian) Model formula: y ~ x | z + z_noise Fitted party: [1] root | [2] z <= 0.70311: n = 704 | (Intercept) x | -0.1619978 -0.7896293 | [3] z > 0.70311: n = 296 | (Intercept) x | 0.08683535 0.65598287 Number of inner nodes: 1 Number of terminal nodes: 2 Number of parameters per node: 2 Objective function (negative log-likelihood): 2551.673 > > > ## check tests > if (require("strucchange")) + print(sctest(mmfluc3, node = 1)) # does not yet work Loading required package: strucchange Loading required package: zoo Attaching package: 'zoo' The following objects are masked from 'package:base': as.Date, as.Date.numeric Loading required package: sandwich z z_noise statistic 2.292499e+01 0.6165335 p.value 7.780038e-04 0.9984952 > > x <- mmfluc3 > (tst3 <- nodeapply(x, ids = nodeids(x), function(n) n$info$criterion)) $`1` NULL $`2` NULL $`3` NULL > > > > > ## check logLik and AIC > logLik(mmfluc2) 'log Lik.' -2551.673 (df=7) > logLik(mmfluc3) 'log Lik.' -2551.673 (df=7) > logLik(mmfluc3_dfsplit) 'log Lik.' -2551.673 (df=16) > logLik(glm(y ~ x, data = d)) 'log Lik.' -2563.694 (df=3) > > AIC(mmfluc3) [1] 5117.347 > AIC(mmfluc3_dfsplit) [1] 5135.347 > > ## check pruning > pr2 <- prune.modelparty(mmfluc2) > AIC(mmfluc2) [1] 5117.347 > AIC(pr2) [1] 5117.347 > > mmfluc_dfsplit3 <- glmtree(formula = fmla, data = d, alpha = 0.5, dfsplit = 3) > mmfluc_dfsplit4 <- glmtree(formula = fmla, data = d, alpha = 0.5, dfsplit = 4) > pr_dfsplit3 <- prune.modelparty(mmfluc_dfsplit3) > pr_dfsplit4 <- prune.modelparty(mmfluc_dfsplit4) > AIC(mmfluc_dfsplit3) [1] 5142.774 > AIC(mmfluc_dfsplit4) [1] 5156.774 > AIC(pr_dfsplit3) [1] 5142.774 > AIC(pr_dfsplit4) [1] 5124.456 > > width(mmfluc_dfsplit3) [1] 8 > width(mmfluc_dfsplit4) [1] 8 > width(pr_dfsplit3) [1] 8 > width(pr_dfsplit4) [1] 3 > > ## check inner and terminal > options <- list(NULL, + "object", + "estfun", + c("object", "estfun")) > > arguments <- list("inner", + "terminal", + c("inner", "terminal")) > > > for (o in options) { + print(o) + x <- glmtree(formula = fmla, data = d, inner = o) + str(nodeapply(x, ids = nodeids(x), function(n) n$info[c("object", "estfun")]), 2) + } NULL List of 3 $ 1:List of 2 ..$ NA: NULL ..$ NA: NULL $ 2:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL $ 3:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL [1] "object" List of 3 $ 1:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL $ 2:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL $ 3:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL [1] "estfun" List of 3 $ 1:List of 2 ..$ NA : NULL ..$ estfun: num [1:1000, 1:2] -0.1375 -0.0583 -0.0553 0.1043 -0.0744 ... .. ..- attr(*, "dimnames")=List of 2 $ 2:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL $ 3:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL [1] "object" "estfun" List of 3 $ 1:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ estfun: num [1:1000, 1:2] -0.1375 -0.0583 -0.0553 0.1043 -0.0744 ... .. ..- attr(*, "dimnames")=List of 2 $ 2:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL $ 3:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL > > for (o in options) { + print(o) + x <- glmtree(formula = fmla, data = d, terminal = o) + str(nodeapply(x, ids = nodeids(x), function(n) n$info[c("object", "estfun")]), 2) + } NULL List of 3 $ 1:List of 2 ..$ NA: NULL ..$ NA: NULL $ 2:List of 2 ..$ NA: NULL ..$ NA: NULL $ 3:List of 2 ..$ NA: NULL ..$ NA: NULL [1] "object" List of 3 $ 1:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL $ 2:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL $ 3:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ NA : NULL [1] "estfun" List of 3 $ 1:List of 2 ..$ NA : NULL ..$ estfun: num [1:1000, 1:2] -0.1375 -0.0583 -0.0553 0.1043 -0.0744 ... .. ..- attr(*, "dimnames")=List of 2 $ 2:List of 2 ..$ NA : NULL ..$ estfun: num [1:704, 1:2] -0.1291 0.5104 -0.0603 -0.1868 -0.0981 ... .. ..- attr(*, "dimnames")=List of 2 $ 3:List of 2 ..$ NA : NULL ..$ estfun: num [1:296, 1:2] -0.1053 -0.0877 0.0544 -0.1581 0.43 ... .. ..- attr(*, "dimnames")=List of 2 [1] "object" "estfun" List of 3 $ 1:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ estfun: num [1:1000, 1:2] -0.1375 -0.0583 -0.0553 0.1043 -0.0744 ... .. ..- attr(*, "dimnames")=List of 2 $ 2:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ estfun: num [1:704, 1:2] -0.1291 0.5104 -0.0603 -0.1868 -0.0981 ... .. ..- attr(*, "dimnames")=List of 2 $ 3:List of 2 ..$ object:List of 24 .. ..- attr(*, "class")= chr [1:2] "glm" "lm" ..$ estfun: num [1:296, 1:2] -0.1053 -0.0877 0.0544 -0.1581 0.43 ... .. ..- attr(*, "dimnames")=List of 2 > > > ## check model > m_mt <- glmtree(formula = fmla, data = d, model = TRUE) > m_mf <- glmtree(formula = fmla, data = d, model = FALSE) > > dim(m_mt$data) [1] 1000 4 > dim(m_mf$data) [1] 0 4 > > > ## check multiway > (m_mult <- glmtree(formula = fmla2, data = d3, catsplit = "multiway", minsize = 80)) Generalized linear model tree (family: gaussian) Model formula: y ~ x | z + z_noise + z_noise_1 + z_noise_2 + z_noise_3 + z_noise_4 + z_noise_5 + z_noise_6 + z_noise_7 + z_noise_8 + z_noise_9 + z_noise_10 + z_noise_11 + z_noise_12 + z_noise_13 + z_noise_14 + z_noise_15 + z_noise_16 + z_noise_17 + z_noise_18 + z_noise_19 + z_noise_20 Fitted party: [1] root | [2] z in 1: n = 76 | (Intercept) x | 0.9859847 -3.2600047 | [3] z in 2: n = 537 | (Intercept) x | -0.06970187 1.12305074 | [4] z in 3: n = 387 | (Intercept) x | 0.3824392 -1.8337151 Number of inner nodes: 1 Number of terminal nodes: 3 Number of parameters per node: 2 Objective function (negative log-likelihood): 2511.927 > > > ## check parm > fmla_p <- as.formula("y ~ x + z_noise + z_noise_1 | z + z_noise_2") > (m_interc <- glmtree(formula = fmla_p, data = d2, parm = 1)) Generalized linear model tree (family: gaussian) Model formula: y ~ x + z_noise + z_noise_1 | z + z_noise_2 Fitted party: [1] root | [2] z <= 0.65035: n = 644 | (Intercept) x z_noise2 z_noise3 z_noise_1 | -0.05585503 -1.01257554 0.34044520 -0.16384987 0.24197601 | [3] z > 0.65035: n = 356 | (Intercept) x z_noise2 z_noise3 z_noise_1 | 0.06411865 0.78733976 -0.67811149 -0.14240432 -0.01239154 Number of inner nodes: 1 Number of terminal nodes: 2 Number of parameters per node: 5 Objective function (negative log-likelihood): 2548.32 > > (m_p3 <- glmtree(formula = fmla_p, data = d2, parm = 3)) Generalized linear model tree (family: gaussian) Model formula: y ~ x + z_noise + z_noise_1 | z + z_noise_2 Fitted party: [1] root: n = 1000 (Intercept) x z_noise2 z_noise3 z_noise_1 -0.058855295 -0.340314311 -0.008404682 -0.109839080 0.154798281 Number of inner nodes: 0 Number of terminal nodes: 1 Number of parameters per node: 5 Objective function (negative log-likelihood): 2562.32 > > > ## check trim > (m_tt <- glmtree(formula = fmla, data = d, trim = 0.2)) Generalized linear model tree (family: gaussian) Model formula: y ~ x | z + z_noise Fitted party: [1] root | [2] z <= 0.70311: n = 704 | (Intercept) x | -0.1619978 -0.7896293 | [3] z > 0.70311: n = 296 | (Intercept) x | 0.08683535 0.65598287 Number of inner nodes: 1 Number of terminal nodes: 2 Number of parameters per node: 2 Objective function (negative log-likelihood): 2551.673 > > (m_tf <- glmtree(formula = fmla, data = d, trim = 300, minsize = 300)) Generalized linear model tree (family: gaussian) Model formula: y ~ x | z + z_noise Fitted party: [1] root | [2] z <= 0.6892: n = 691 | (Intercept) x | -0.1778199 -0.7692901 | [3] z > 0.6892: n = 309 | (Intercept) x | 0.1065746 0.5562243 Number of inner nodes: 1 Number of terminal nodes: 2 Number of parameters per node: 2 Objective function (negative log-likelihood): 2552.12 > > > > ## check breakties > m_bt <- glmtree(formula = fmla, data = d1, breakties = TRUE) > m_df <- glmtree(formula = fmla, data = d1, breakties = FALSE) > > all.equal(m_bt, m_df, check.environment = FALSE) [1] "Component \"node\": Component \"kids\": Component 1: Component 5: Component 6: Mean relative difference: 0.1237503" [2] "Component \"node\": Component \"kids\": Component 2: Component 5: Component 5: Mean relative difference: 0.1746109" [3] "Component \"node\": Component \"kids\": Component 2: Component 5: Component 6: Mean relative difference: 0.0443985" [4] "Component \"node\": Component \"info\": Component \"p.value\": Mean relative difference: 1.100407" [5] "Component \"node\": Component \"info\": Component \"test\": Mean relative difference: 0.07721086" [6] "Component \"info\": Component \"call\": target, current do not match when deparsed" [7] "Component \"info\": Component \"control\": Component \"breakties\": 1 element mismatch" > > unclass(m_bt)$node$info$criterion NULL > unclass(m_df)$node$info$criterion NULL > > > ### example from mob vignette > data("PimaIndiansDiabetes", package = "mlbench") > > logit <- function(y, x, start = NULL, weights = NULL, offset = NULL, ...) { + glm(y ~ 0 + x, family = binomial, start = start, ...) + } > > pid_formula <- diabetes ~ glucose | pregnant + pressure + triceps + + insulin + mass + pedigree + age > > pid_tree <- mob(pid_formula, data = PimaIndiansDiabetes, fit = logit) > pid_tree Model-based recursive partitioning (logit) Model formula: diabetes ~ glucose | pregnant + pressure + triceps + insulin + mass + pedigree + age Fitted party: [1] root | [2] mass <= 26.3: n = 167 | x(Intercept) xglucose | -9.95150963 0.05870786 | [3] mass > 26.3 | | [4] age <= 30: n = 304 | | x(Intercept) xglucose | | -6.70558554 0.04683748 | | [5] age > 30: n = 297 | | x(Intercept) xglucose | | -2.77095386 0.02353582 Number of inner nodes: 2 Number of terminal nodes: 3 Number of parameters per node: 2 Objective function: 355.4578 > nodeapply(pid_tree, ids = nodeids(pid_tree), function(n) n$info$criterion) $`1` NULL $`2` NULL $`3` NULL $`4` NULL $`5` NULL > > > > > proc.time() user system elapsed 20.340 0.056 20.394 partykit/tests/regtest-MIA.Rout.save0000644000176200001440000001536514172230001017154 0ustar liggesusers R version 3.5.0 (2018-04-23) -- "Joy in Playing" Copyright (C) 2018 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. 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Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > set.seed(29) > > n <- 100 > x <- 1:n/n > y <- rnorm(n, mean = (x < .5) + 1) > xna <- x > xna[xna < .2] <- NA > d <- data.frame(x = x, y = y) > dna <- data.frame(x = xna, y = y) > > (t1 <- ctree(y ~ x, data = d)) Model formula: y ~ x Fitted party: [1] root | [2] x <= 0.5: 1.998 (n = 50, err = 52.5) | [3] x > 0.5: 0.743 (n = 50, err = 45.6) Number of inner nodes: 1 Number of terminal nodes: 2 > (t2 <- ctree(y ~ x, data = dna)) Model formula: y ~ x Fitted party: [1] root | [2] x <= 0.5: 2.070 (n = 37, err = 40.2) | [3] x > 0.5: 0.960 (n = 63, err = 68.5) Number of inner nodes: 1 Number of terminal nodes: 2 > (t3 <- ctree(y ~ x, data = dna, control = ctree_control(MIA = TRUE))) Model formula: y ~ x Fitted party: [1] root | [2] x <= 0.5: 1.998 (n = 50, err = 52.5) | [3] x > 0.5: 0.743 (n = 50, err = 45.6) Number of inner nodes: 1 Number of terminal nodes: 2 > > predict(t1, type = "node")[is.na(xna)] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 > predict(t2, type = "node")[is.na(xna)] 3 3 3 2 3 2 2 3 3 2 3 3 3 2 3 3 3 3 2 3 3 3 2 3 2 2 3 3 2 3 3 3 2 3 3 3 3 2 > predict(t3, type = "node")[is.na(xna)] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 > > xna <- x > xna[xna > .8] <- NA > d <- data.frame(x = x, y = y) > dna <- data.frame(x = xna, y = y) > > (t1 <- ctree(y ~ x, data = d)) Model formula: y ~ x Fitted party: [1] root | [2] x <= 0.5: 1.998 (n = 50, err = 52.5) | [3] x > 0.5: 0.743 (n = 50, err = 45.6) Number of inner nodes: 1 Number of terminal nodes: 2 > (t2 <- ctree(y ~ x, data = dna)) Model formula: y ~ x Fitted party: [1] root | [2] x <= 0.5: 1.864 (n = 61, err = 65.5) | [3] x > 0.5 | | [4] x <= 0.73: 0.755 (n = 29, err = 18.9) | | [5] x > 0.73: 0.150 (n = 10, err = 12.4) Number of inner nodes: 2 Number of terminal nodes: 3 > (t3 <- ctree(y ~ x, data = dna, control = ctree_control(MIA = TRUE))) Model formula: y ~ x Fitted party: [1] root | [2] x <= 0.5: 1.998 (n = 50, err = 52.5) | [3] x > 0.5 | | [4] x <= 0.73: 0.928 (n = 43, err = 31.9) | | [5] x > 0.73: -0.396 (n = 7, err = 3.1) Number of inner nodes: 2 Number of terminal nodes: 3 > > (n1 <- predict(t1, type = "node")) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 > (n2 <- predict(t2, type = "node")) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 4 2 2 5 4 4 4 2 2 5 4 2 4 2 2 2 5 2 2 2 4 2 2 5 4 4 4 2 2 5 4 2 4 2 2 2 5 2 2 2 > (n3 <- predict(t3, type = "node")) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 > table(n1, n2) n2 n1 2 4 5 2 50 0 0 3 11 29 10 > table(n1, n3) n3 n1 2 4 5 2 50 0 0 3 0 43 7 > > d$x <- as.factor(cut(d$x, breaks = 0:5 / 5)) > dna$x <- as.factor(cut(dna$x, breaks = 0:5 / 5)) > > (t1 <- ctree(y ~ x, data = d)) Model formula: y ~ x Fitted party: [1] root | [2] x in (0,0.2], (0.2,0.4], (0.4,0.6]: 1.808 (n = 60, err = 68.1) | [3] x in (0.6,0.8], (0.8,1]: 0.714 (n = 40, err = 40.6) Number of inner nodes: 1 Number of terminal nodes: 2 > (t2 <- ctree(y ~ x, data = dna)) Model formula: y ~ x Fitted party: [1] root | [2] x in (0,0.2], (0.2,0.4], (0.4,0.6]: 1.651 (n = 75, err = 89.0) | [3] x in (0.6,0.8]: 0.529 (n = 25, err = 24.8) Number of inner nodes: 1 Number of terminal nodes: 2 > (t3 <- ctree(y ~ x, data = dna, control = ctree_control(MIA = TRUE))) Model formula: y ~ x Fitted party: [1] root | [2] x in (0.6,0.8]: 0.714 (n = 40, err = 40.6) | [3] x in (0,0.2], (0.2,0.4], (0.4,0.6]: 1.808 (n = 60, err = 68.1) Number of inner nodes: 1 Number of terminal nodes: 2 > > (n1 <- predict(t1, type = "node")) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 > (n2 <- predict(t2, type = "node")) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 3 2 2 3 2 2 2 2 3 2 2 2 2 3 3 2 2 2 2 2 3 2 2 3 2 2 2 2 3 2 2 2 2 3 > (n3 <- predict(t3, type = "node")) 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 > table(n1, n2) n2 n1 2 3 2 60 0 3 15 25 > table(n1, n3) n3 n1 2 3 2 0 60 3 40 0 > > proc.time() user system elapsed 1.267 0.068 1.320 partykit/tests/regtest-party.Rout.save0000644000176200001440000012631214646205614017722 0ustar liggesusers R version 4.4.1 (2024-06-14) -- "Race for Your Life" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > suppressWarnings(RNGversion("3.5.2")) > > ## load package and fix seed > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > set.seed(1) > > ## rpart: kyphosis data > library("rpart") > data("kyphosis", package = "rpart") > fit <- rpart(Kyphosis ~ Age + Number + Start, data = kyphosis) > pfit <- as.party(fit) > all(predict(pfit, newdata = kyphosis, type = "node") == fit$where) [1] TRUE > > ## J48: iris data > if (require("RWeka")) { + data("iris", package = "datasets") + itree <- J48(Species ~ ., data = iris) + pitree <- as.party(itree) + stopifnot(all(predict(pitree) == predict(pitree, newdata = iris[, 3:4]))) + + print(all.equal(predict(itree, type = "prob", newdata = iris), + predict(pitree, type = "prob", newdata = iris))) + print(all.equal(predict(itree, newdata = iris), + predict(pitree, newdata = iris))) + + ## rpart/J48: GlaucomaM data + data("GlaucomaM", package = "TH.data") + w <- runif(nrow(GlaucomaM)) + fit <- rpart(Class ~ ., data = GlaucomaM, weights = w) + pfit <- as.party(fit) + print(all(predict(pfit, type = "node") == fit$where)) + tmp <- GlaucomaM[sample(1:nrow(GlaucomaM), 100),] + print(all.equal(predict(fit, type = "prob", newdata = tmp), predict(pfit, type = "prob", newdata = tmp))) + print(all.equal(predict(fit, type = "class", newdata = tmp), predict(pfit, newdata = tmp))) + itree <- J48(Class ~ ., data = GlaucomaM) + pitree <- as.party(itree) + print(all.equal(predict(itree, newdata = tmp, type = "prob"), predict(pitree, newdata = tmp, type = "prob"))) + } Loading required package: RWeka [1] TRUE [1] "names for current but not for target" [1] TRUE [1] TRUE [1] TRUE [1] TRUE > > ## rpart: airquality data > data("airquality") > aq <- subset(airquality, !is.na(Ozone)) > w <- runif(nrow(aq), max = 3) > aqr <- rpart(Ozone ~ ., data = aq, weights = w) > aqp <- as.party(aqr) > tmp <- subset(airquality, is.na(Ozone)) > all.equal(predict(aqr, newdata = tmp), predict(aqp, newdata = tmp)) [1] TRUE > > ## rpart: GBSG2 data > data("GBSG2", package = "TH.data") > library("survival") > fit <- rpart(Surv(time, cens) ~ ., data = GBSG2) > pfit <- as.party(fit) > pfit$fitted (fitted) (response) 1 6 1814 2 8 2018 3 8 712 4 8 1807 5 6 772 6 11 448 7 3 2172+ 8 5 2161+ 9 11 471 10 10 2014+ 11 10 577 12 10 184 13 5 1840+ 14 6 1842+ 15 5 1821+ 16 5 1371 17 8 707 18 5 1743+ 19 5 1781+ 20 8 865 21 6 1684 22 5 1701+ 23 6 1701+ 24 6 1693+ 25 11 379 26 5 1105 27 6 548 28 8 1296 29 6 1483+ 30 6 1570+ 31 6 1469+ 32 6 1472+ 33 5 1342+ 34 6 1349+ 35 8 1162 36 6 1342+ 37 11 797 38 8 1232+ 39 6 1230+ 40 8 1205+ 41 8 1090+ 42 8 1095+ 43 6 449 44 6 972+ 45 6 825+ 46 6 2438+ 47 6 2233+ 48 11 286 49 8 1861+ 50 8 1080 51 6 1521 52 6 1693+ 53 6 1528 54 10 169 55 8 272 56 6 731 57 8 2059+ 58 8 1853+ 59 10 1854+ 60 8 1645+ 61 11 544 62 8 1666+ 63 6 353 64 8 1791+ 65 6 1685+ 66 3 191 67 10 370 68 8 173 69 11 242 70 6 420 71 8 438 72 6 1624+ 73 10 1036 74 11 359 75 8 171 76 11 959 77 6 1351+ 78 10 486 79 11 525 80 5 762 81 10 175 82 3 1195+ 83 10 338 84 8 1125+ 85 8 916+ 86 6 972+ 87 3 867+ 88 10 249 89 11 281 90 6 758+ 91 11 377 92 6 1976+ 93 5 2539+ 94 6 2467+ 95 5 876 96 5 2132+ 97 11 426 98 5 554 99 8 1246 100 5 1926+ 101 11 1207 102 8 1852+ 103 8 1174 104 8 1250+ 105 6 530 106 10 1502+ 107 5 1364+ 108 8 1170 109 6 1729+ 110 5 1642+ 111 5 1218 112 3 1358+ 113 11 360 114 5 550 115 8 857+ 116 8 768+ 117 6 858+ 118 6 770+ 119 10 679 120 6 1164 121 6 350 122 6 578 123 6 1460 124 6 1434+ 125 6 1763 126 6 889 127 11 357 128 8 547 129 5 1722+ 130 6 2372+ 131 6 2030 132 5 1002 133 3 1280 134 8 338 135 6 533 136 6 168+ 137 5 1169+ 138 5 1675 139 6 1862+ 140 5 629+ 141 10 1167+ 142 6 495 143 5 967+ 144 5 1720+ 145 6 598 146 11 392 147 3 1502+ 148 6 229+ 149 8 310+ 150 5 1296+ 151 10 488+ 152 3 942+ 153 8 570+ 154 10 1177+ 155 8 1113+ 156 8 288 157 6 723+ 158 11 403 159 10 1225 160 8 338 161 8 1337 162 6 1420 163 8 2048+ 164 8 600 165 5 1765+ 166 8 491 167 10 305 168 6 1582+ 169 8 1771+ 170 8 960 171 10 571 172 8 675+ 173 5 285 174 8 1472+ 175 5 1279 176 6 148+ 177 6 1863+ 178 5 1933+ 179 10 358 180 5 734+ 181 6 2372 182 6 2563+ 183 5 2372+ 184 6 1989 185 8 2015 186 6 1956+ 187 8 945 188 6 2153+ 189 6 838 190 8 113 191 6 1833+ 192 8 1722+ 193 8 241 194 5 1352 195 8 1702+ 196 8 1222+ 197 6 1089+ 198 3 1243+ 199 8 579 200 8 1043 201 6 2234+ 202 5 2297+ 203 6 2014+ 204 6 518 205 6 940+ 206 6 766+ 207 11 251 208 6 1959+ 209 3 1897+ 210 11 160 211 5 970+ 212 5 892+ 213 5 753+ 214 8 348 215 10 275 216 5 1329 217 6 1193 218 10 698 219 10 436 220 6 552 221 6 564 222 6 2239+ 223 5 2237+ 224 6 529 225 3 1820+ 226 6 1756+ 227 11 515 228 11 272 229 6 891 230 6 1356+ 231 10 1352+ 232 6 1077+ 233 6 675 234 10 855+ 235 6 740+ 236 6 2551+ 237 8 754 238 8 819 239 10 1280 240 5 2388+ 241 5 2296+ 242 6 1884+ 243 6 1059 244 8 859+ 245 6 1109+ 246 6 1192 247 8 1806 248 11 500 249 10 1589 250 10 1463 251 6 1826+ 252 8 1231+ 253 5 1117+ 254 8 836 255 6 1222+ 256 8 663+ 257 10 722 258 5 322+ 259 6 1150 260 10 446 261 10 1855+ 262 10 238 263 6 1838+ 264 11 1826+ 265 6 1093 266 3 2051+ 267 10 370 268 5 861 269 10 1587 270 6 552 271 3 2353+ 272 8 2471+ 273 8 893 274 5 2093 275 10 2612+ 276 8 956 277 10 1637+ 278 5 2456+ 279 8 2227+ 280 6 1601 281 6 1841+ 282 8 2177+ 283 6 2052+ 284 11 973+ 285 3 2156+ 286 8 1499+ 287 3 2030+ 288 8 573 289 5 1666+ 290 8 1979+ 291 8 1786+ 292 8 1847+ 293 5 2009+ 294 5 1926+ 295 3 1490+ 296 11 233 297 8 1240+ 298 3 1751+ 299 8 1878+ 300 5 1171+ 301 10 1751+ 302 6 1756+ 303 8 714 304 8 1505+ 305 8 776 306 6 1443+ 307 3 1317+ 308 6 870+ 309 11 859 310 6 223 311 6 1212+ 312 5 1119+ 313 8 740+ 314 8 1062+ 315 5 8+ 316 6 936+ 317 8 740+ 318 10 632 319 5 1760+ 320 6 1013+ 321 10 779+ 322 10 375 323 8 1323+ 324 5 1233+ 325 5 986+ 326 10 650+ 327 10 628+ 328 6 1866+ 329 8 491 330 6 1918 331 10 72 332 10 1140 333 8 799 334 6 1105 335 5 548 336 11 227 337 6 1838+ 338 3 1833+ 339 6 550 340 6 426 341 8 1834+ 342 6 1604+ 343 10 772+ 344 8 1146 345 6 371 346 8 883 347 6 1735+ 348 8 554 349 11 790 350 5 1340+ 351 11 490 352 3 1557+ 353 6 594 354 10 828+ 355 8 594 356 8 841+ 357 5 695+ 358 5 2556+ 359 6 1753 360 10 417 361 6 956 362 8 1846+ 363 8 1703+ 364 6 1720+ 365 6 1355+ 366 6 1603+ 367 8 476 368 8 1350+ 369 5 1341+ 370 3 2449+ 371 8 2286 372 6 456 373 6 536 374 5 612 375 6 2034 376 6 1990 377 10 2456 378 3 2205+ 379 6 544 380 10 336 381 6 2057+ 382 8 575 383 5 2011+ 384 8 537 385 3 2217+ 386 8 1814 387 6 890 388 5 1114+ 389 10 974+ 390 6 296+ 391 8 2320+ 392 8 795 393 8 867 394 5 1703+ 395 6 670 396 8 981 397 5 1094+ 398 5 755 399 10 1388 400 6 1387 401 10 535 402 6 1653+ 403 6 1904+ 404 8 1868+ 405 3 1767+ 406 6 855 407 6 1157 408 8 1869+ 409 8 1152+ 410 6 1401+ 411 6 918+ 412 10 745 413 8 1283+ 414 6 1481 415 8 1807+ 416 6 542 417 10 1441+ 418 8 1277+ 419 8 1486+ 420 5 273+ 421 10 177 422 6 545 423 6 1185+ 424 11 631+ 425 6 995+ 426 8 1088+ 427 6 877+ 428 8 798+ 429 8 2380+ 430 5 1679 431 10 498 432 8 2138+ 433 8 2175+ 434 5 2271+ 435 6 17+ 436 6 964 437 10 540 438 11 747 439 11 650 440 11 410 441 11 624 442 10 1560+ 443 11 455 444 5 1629+ 445 8 1730+ 446 6 1483+ 447 6 687 448 6 308 449 10 563 450 5 46+ 451 6 2144+ 452 10 344 453 6 945+ 454 6 1905+ 455 11 855 456 5 2370+ 457 6 853+ 458 8 692+ 459 8 475 460 5 2195+ 461 8 758+ 462 8 648 463 3 761+ 464 8 596+ 465 11 195 466 10 473 467 5 747+ 468 5 2659+ 469 11 1977 470 6 2401+ 471 5 1499+ 472 11 1856+ 473 11 595 474 5 2148+ 475 6 2126+ 476 8 1975 477 6 1641 478 8 1717+ 479 5 1858+ 480 5 2049+ 481 8 1502 482 3 1922+ 483 5 1818+ 484 11 1100+ 485 6 1499+ 486 6 359 487 8 1645+ 488 5 1356+ 489 6 1632+ 490 6 967+ 491 6 1091+ 492 6 918 493 6 557 494 5 1219 495 6 2170+ 496 6 729 497 10 1449 498 5 991 499 6 481 500 6 1655+ 501 6 857 502 6 369 503 5 1627+ 504 5 1578+ 505 8 732 506 8 460 507 6 1208+ 508 8 730 509 8 722+ 510 6 717+ 511 8 651+ 512 5 637+ 513 6 615+ 514 10 42+ 515 11 307 516 8 983 517 11 120 518 6 1525 519 8 1680+ 520 11 1730 521 8 805 522 8 2388+ 523 6 559 524 10 1977+ 525 6 476 526 5 1514+ 527 5 1617+ 528 6 1094 529 5 784 530 10 181 531 10 415 532 8 1120 533 10 316 534 8 637 535 6 247 536 8 888+ 537 10 622 538 6 806+ 539 6 1163+ 540 5 1721+ 541 5 741+ 542 6 372 543 6 1331+ 544 8 394 545 3 652+ 546 10 657+ 547 6 567+ 548 10 429+ 549 5 566+ 550 11 15+ 551 8 98 552 5 368+ 553 5 432+ 554 5 319+ 555 10 65+ 556 8 16+ 557 10 29+ 558 8 18+ 559 8 17+ 560 10 308 561 6 1965+ 562 11 548 563 10 293 564 8 2017+ 565 10 1093+ 566 3 792+ 567 6 586 568 6 1434+ 569 8 67+ 570 8 623+ 571 6 2128+ 572 6 1965+ 573 6 2161+ 574 10 1183 575 6 1108 576 5 2065+ 577 6 1598+ 578 6 491 579 10 1366 580 6 424+ 581 11 859 582 11 180 583 5 1625+ 584 3 1938+ 585 8 1343 586 6 646 587 6 2192+ 588 6 502 589 10 1675+ 590 11 1363 591 11 420 592 8 982 593 6 1459+ 594 6 1192+ 595 6 1264+ 596 8 1095+ 597 8 1078+ 598 3 737+ 599 8 461+ 600 11 465 601 11 842 602 6 918+ 603 8 374 604 6 1089+ 605 5 1527+ 606 8 285 607 6 1306 608 10 797 609 5 1441+ 610 6 343 611 8 936+ 612 5 195+ 613 6 503 614 11 827 615 5 1427+ 616 6 854+ 617 8 177 618 10 281 619 5 205 620 8 751+ 621 8 629 622 6 526+ 623 6 463+ 624 5 529+ 625 8 623+ 626 11 546+ 627 5 213+ 628 6 276+ 629 8 2010+ 630 8 2009+ 631 3 1984+ 632 10 1981+ 633 10 624 634 10 742 635 3 1818+ 636 8 1493 637 5 1432+ 638 5 801 639 6 1182+ 640 6 71+ 641 10 114+ 642 6 63+ 643 6 1722+ 644 5 1692+ 645 6 177+ 646 5 57+ 647 5 1152+ 648 6 733+ 649 6 1459 650 5 2237+ 651 6 933+ 652 5 2056+ 653 10 1729+ 654 10 2024+ 655 5 2039 656 6 2027+ 657 6 2007+ 658 6 1253 659 6 1789+ 660 8 1707+ 661 6 1714+ 662 5 1717+ 663 6 329 664 5 1624+ 665 6 1600+ 666 5 385 667 3 1475+ 668 5 1435+ 669 11 541+ 670 5 1329+ 671 8 1357+ 672 6 1343+ 673 5 748 674 5 1090 675 6 1219+ 676 5 553+ 677 8 662 678 5 969+ 679 8 974+ 680 8 866 681 10 504 682 6 721+ 683 11 186+ 684 8 769 685 6 727 686 8 1701 > predict(pfit, newdata = GBSG2[1:100,], type = "prob") $`1` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`2` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`3` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`4` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`5` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`6` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`7` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 33 2 NA NA NA $`8` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`9` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`10` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`11` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`12` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`13` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`14` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`15` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`16` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`17` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`18` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`19` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`20` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`21` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`22` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`23` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`24` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`25` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`26` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`27` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`28` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`29` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`30` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`31` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`32` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`33` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`34` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`35` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`36` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`37` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`38` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`39` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`40` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`41` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`42` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`43` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`44` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`45` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`46` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`47` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`48` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`49` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`50` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`51` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`52` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`53` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`54` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`55` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`56` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`57` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`58` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`59` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`60` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`61` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`62` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`63` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`64` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`65` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`66` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 33 2 NA NA NA $`67` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`68` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`69` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`70` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`71` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`72` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`73` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`74` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`75` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`76` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`77` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`78` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`79` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`80` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`81` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`82` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 33 2 NA NA NA $`83` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`84` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`85` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`86` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`87` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 33 2 NA NA NA $`88` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 87 55 742 577 1366 $`89` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`90` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`91` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`92` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`93` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`94` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 221 89 1989 1641 NA $`95` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`96` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`97` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 57 48 500 426 747 $`98` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA $`99` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 $`100` Call: survfit(formula = y ~ 1, weights = w, subset = w > 0) n events median 0.95LCL 0.95UCL [1,] 122 28 NA NA NA > predict(pfit, newdata = GBSG2[1:100,], type = "response") 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1989 1701 1701 1701 1989 500 Inf Inf 500 742 742 742 Inf 1989 Inf Inf 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 1701 Inf Inf 1701 1989 Inf 1989 1989 500 Inf 1989 1701 1989 1989 1989 1989 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Inf 1989 1701 1989 500 1701 1989 1701 1701 1701 1989 1989 1989 1989 1989 500 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 1701 1701 1989 1989 1989 742 1701 1989 1701 1701 742 1701 500 1701 1989 1701 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 1989 Inf 742 1701 500 1989 1701 1989 742 500 1701 500 1989 742 500 Inf 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 742 Inf 742 1701 1701 1989 Inf 742 500 1989 500 1989 Inf 1989 Inf Inf 97 98 99 100 500 Inf 1701 Inf > > ### multiple responses > f <- fitted(pfit) > f[["(response)"]] <- data.frame(srv = f[["(response)"]], hansi = runif(nrow(f))) > mp <- party(node_party(pfit), fitted = f, data = pfit$data) > class(mp) <- c("constparty", "party") > predict(mp, newdata = GBSG2[1:10,]) srv hansi 1 1989 0.5017739 2 1701 0.4933225 3 1701 0.4933225 4 1701 0.4933225 5 1989 0.5017739 6 500 0.4823559 7 Inf 0.4662471 8 Inf 0.4839262 9 500 0.4823559 10 742 0.5108953 > > ### pruning > ## create party > data("WeatherPlay", package = "partykit") > py <- party( + partynode(1L, + split = partysplit(1L, index = 1:3), + kids = list( + partynode(2L, + split = partysplit(3L, breaks = 75), + kids = list( + partynode(3L, info = "yes"), + partynode(4L, info = "no"))), + partynode(5L, + split = partysplit(3L, breaks = 20), + kids = list( + partynode(6L, info = "no"), + partynode(7L, info = "yes"))), + partynode(8L, + split = partysplit(4L, index = 1:2), + kids = list( + partynode(9L, info = "yes"), + partynode(10L, info = "no"))))), + WeatherPlay) > names(py) <- LETTERS[nodeids(py)] > > ## print > print(py) [A] root | [B] outlook in sunny | | [C] humidity <= 75: yes | | [D] humidity > 75: no | [E] outlook in overcast | | [F] humidity <= 20: no | | [G] humidity > 20: yes | [H] outlook in rainy | | [I] windy in false: yes | | [J] windy in true: no > (py5 <- nodeprune(py, 5)) [A] root | [B] outlook in sunny | | [C] humidity <= 75: yes | | [D] humidity > 75: no | [E] outlook in overcast: * | [H] outlook in rainy | | [I] windy in false: yes | | [J] windy in true: no > nodeids(py5) [1] 1 2 3 4 5 6 7 8 > (pyH <- nodeprune(py5, "H")) [A] root | [B] outlook in sunny | | [C] humidity <= 75: yes | | [D] humidity > 75: no | [E] outlook in overcast: * | [H] outlook in rainy: * > nodeids(pyH) [1] 1 2 3 4 5 6 > > ct <- ctree(Species ~ ., data = iris) > nt <- node_party(ctree(Species ~ ., data = iris)) > (ctp <- nodeprune(ct, 4)) ### party method Model formula: Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width Fitted party: [1] root | [2] Petal.Length <= 1.9: setosa (n = 50, err = 0.0%) | [3] Petal.Length > 1.9 | | [4] Petal.Width <= 1.7: versicolor (n = 54, err = 9.3%) | | [5] Petal.Width > 1.7: virginica (n = 46, err = 2.2%) Number of inner nodes: 2 Number of terminal nodes: 3 > (ntp <- nodeprune(nt, 4)) ### partynode method [1] root | [2] V4 <= 1.9 * | [3] V4 > 1.9 | | [4] V5 <= 1.7 * | | [5] V5 > 1.7 * > > ### check if both methods do the same > p1 <- predict(party(ntp, data = model.frame(ct)), type = "node") > p2 <- predict(ctp, type = "node") > stopifnot(max(abs(p1 - p2)) == 0) > > names(ct) <- LETTERS[nodeids(ct)] > (ctp <- nodeprune(ct, "D")) Model formula: Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width Fitted party: [A] root | [B] Petal.Length <= 1.9: setosa (n = 50, err = 0.0%) | [C] Petal.Length > 1.9 | | [D] Petal.Width <= 1.7: versicolor (n = 54, err = 9.3%) | | [G] Petal.Width > 1.7: virginica (n = 46, err = 2.2%) Number of inner nodes: 2 Number of terminal nodes: 3 > > table(predict(ct, type = "node"), + predict(ctp, type = "node")) 2 4 5 2 50 0 0 5 0 46 0 6 0 8 0 7 0 0 46 > > (ct <- nodeprune(ct, names(ct)[names(ct) != "A"])) Model formula: Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width Fitted party: [A] root | [B] Petal.Length <= 1.9: setosa (n = 50, err = 0.0%) | [C] Petal.Length > 1.9: versicolor (n = 100, err = 50.0%) Number of inner nodes: 1 Number of terminal nodes: 2 > table(predict(ct, type = "node")) 2 3 50 100 > > nodeprune(ct, "B") Model formula: Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width Fitted party: [A] root | [B] Petal.Length <= 1.9: setosa (n = 50, err = 0.0%) | [C] Petal.Length > 1.9: versicolor (n = 100, err = 50.0%) Number of inner nodes: 1 Number of terminal nodes: 2 > nodeprune(ct, "C") Model formula: Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width Fitted party: [A] root | [B] Petal.Length <= 1.9: setosa (n = 50, err = 0.0%) | [C] Petal.Length > 1.9: versicolor (n = 100, err = 50.0%) Number of inner nodes: 1 Number of terminal nodes: 2 > nodeprune(ct, "A") Model formula: Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width Fitted party: [A] root: setosa (n = 150, err = 66.7%) Number of inner nodes: 0 Number of terminal nodes: 1 > > options(digits = 3) > ### check different predict flavours for numeric responses > x <- runif(100) > dd <- data.frame(y = rnorm(length(x), mean = 2 * (x < .5)), x = x) > ct <- ctree(y ~ x, data = dd) > nd <- data.frame(x = (1:9) / 10) > predict(ct, newdata = nd, type = "node") 1 2 3 4 5 6 7 8 9 2 2 2 2 2 4 4 4 5 > predict(ct, newdata = nd, type = "response") 1 2 3 4 5 6 7 8 9 2.112 2.112 2.112 2.112 2.112 0.378 0.378 0.378 -0.511 > predict(ct, newdata = nd, type = "prob") $`1` Empirical CDF Call: ecdf(y) x[1:58] = -0.3, -0.1, 0.1, ..., 4, 4 $`2` Empirical CDF Call: ecdf(y) x[1:58] = -0.3, -0.1, 0.1, ..., 4, 4 $`3` Empirical CDF Call: ecdf(y) x[1:58] = -0.3, -0.1, 0.1, ..., 4, 4 $`4` Empirical CDF Call: ecdf(y) x[1:58] = -0.3, -0.1, 0.1, ..., 4, 4 $`5` Empirical CDF Call: ecdf(y) x[1:58] = -0.3, -0.1, 0.1, ..., 4, 4 $`6` Empirical CDF Call: ecdf(y) x[1:26] = -1, -0.7, -0.7, ..., 2, 2 $`7` Empirical CDF Call: ecdf(y) x[1:26] = -1, -0.7, -0.7, ..., 2, 2 $`8` Empirical CDF Call: ecdf(y) x[1:26] = -1, -0.7, -0.7, ..., 2, 2 $`9` Empirical CDF Call: ecdf(y) x[1:16] = -2, -2, -2, ..., 0.7, 1 > predict(ct, newdata = nd, type = "quantile") 10% 50% 90% 1 1.064 2.126 3.254 2 1.064 2.126 3.254 3 1.064 2.126 3.254 4 1.064 2.126 3.254 5 1.064 2.126 3.254 6 -0.534 0.396 1.361 7 -0.534 0.396 1.361 8 -0.534 0.396 1.361 9 -1.659 -0.383 0.485 > predict(ct, newdata = nd, type = "quantile", at = NULL) $`1` function (p, ...) quantile(y, probs = p, ...) $`2` function (p, ...) quantile(y, probs = p, ...) $`3` function (p, ...) quantile(y, probs = p, ...) $`4` function (p, ...) quantile(y, probs = p, ...) $`5` function (p, ...) quantile(y, probs = p, ...) $`6` function (p, ...) quantile(y, probs = p, ...) $`7` function (p, ...) quantile(y, probs = p, ...) $`8` function (p, ...) quantile(y, probs = p, ...) $`9` function (p, ...) quantile(y, probs = p, ...) > predict(ct, newdata = nd, type = "density") $`1` function (v) .approxfun(x, y, v, method, yleft, yright, f, na.rm) $`2` function (v) .approxfun(x, y, v, method, yleft, yright, f, na.rm) $`3` function (v) .approxfun(x, y, v, method, yleft, yright, f, na.rm) $`4` function (v) .approxfun(x, y, v, method, yleft, yright, f, na.rm) $`5` function (v) .approxfun(x, y, v, method, yleft, yright, f, na.rm) $`6` function (v) .approxfun(x, y, v, method, yleft, yright, f, na.rm) $`7` function (v) .approxfun(x, y, v, method, yleft, yright, f, na.rm) $`8` function (v) .approxfun(x, y, v, method, yleft, yright, f, na.rm) $`9` function (v) .approxfun(x, y, v, method, yleft, yright, f, na.rm) > predict(ct, newdata = nd, type = "density", at = (1:9) / 10) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] 1 0.0501 0.0493 0.0508 0.0565 0.0678 0.0854 0.109 0.138 0.169 2 0.0501 0.0493 0.0508 0.0565 0.0678 0.0854 0.109 0.138 0.169 3 0.0501 0.0493 0.0508 0.0565 0.0678 0.0854 0.109 0.138 0.169 4 0.0501 0.0493 0.0508 0.0565 0.0678 0.0854 0.109 0.138 0.169 5 0.0501 0.0493 0.0508 0.0565 0.0678 0.0854 0.109 0.138 0.169 6 0.5393 0.5764 0.5965 0.5940 0.5639 0.5057 0.429 0.350 0.290 7 0.5393 0.5764 0.5965 0.5940 0.5639 0.5057 0.429 0.350 0.290 8 0.5393 0.5764 0.5965 0.5940 0.5639 0.5057 0.429 0.350 0.290 9 0.3705 0.3422 0.3106 0.2778 0.2458 0.2160 0.189 0.166 0.145 > > proc.time() user system elapsed 1.514 0.104 1.051 partykit/tests/regtest-cforest.R0000644000176200001440000000756214172230001016526 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) library("partykit") stopifnot(require("party")) set.seed(29) ### regression airq <- airquality[complete.cases(airquality),] mtry <- ncol(airq) - 1L ntree <- 25 cf_partykit <- partykit::cforest(Ozone ~ ., data = airq, ntree = ntree, mtry = mtry) w <- do.call("cbind", cf_partykit$weights) cf_party <- party::cforest(Ozone ~ ., data = airq, control = party::cforest_unbiased(ntree = ntree, mtry = mtry), weights = w) p_partykit <- predict(cf_partykit) p_party <- predict(cf_party) stopifnot(max(abs(p_partykit - p_party)) < sqrt(.Machine$double.eps)) prettytree(cf_party@ensemble[[1]], inames = names(airq)[-1]) party(cf_partykit$nodes[[1]], data = model.frame(cf_partykit)) v_party <- do.call("rbind", lapply(1:5, function(i) party::varimp(cf_party))) v_partykit <- do.call("rbind", lapply(1:5, function(i) partykit::varimp(cf_partykit))) summary(v_party) summary(v_partykit) party::varimp(cf_party, conditional = TRUE) partykit::varimp(cf_partykit, conditional = TRUE) ### classification set.seed(29) mtry <- ncol(iris) - 1L ntree <- 25 cf_partykit <- partykit::cforest(Species ~ ., data = iris, ntree = ntree, mtry = mtry) w <- do.call("cbind", cf_partykit$weights) cf_party <- party::cforest(Species ~ ., data = iris, control = party::cforest_unbiased(ntree = ntree, mtry = mtry), weights = w) p_partykit <- predict(cf_partykit, type = "prob") p_party <- do.call("rbind", treeresponse(cf_party)) stopifnot(max(abs(unclass(p_partykit) - unclass(p_party))) < sqrt(.Machine$double.eps)) prettytree(cf_party@ensemble[[1]], inames = names(iris)[-5]) party(cf_partykit$nodes[[1]], data = model.frame(cf_partykit)) v_party <- do.call("rbind", lapply(1:5, function(i) party::varimp(cf_party))) v_partykit <- do.call("rbind", lapply(1:5, function(i) partykit::varimp(cf_partykit, risk = "mis"))) summary(v_party) summary(v_partykit) party::varimp(cf_party, conditional = TRUE) partykit::varimp(cf_partykit, risk = "misclass", conditional = TRUE) ### mean aggregation set.seed(29) ### fit forest cf <- partykit::cforest(dist ~ speed, data = cars, ntree = 100) ### prediction; scale = TRUE introduced in 1.2-1 pr <- predict(cf, newdata = cars[1,,drop = FALSE], type = "response", scale = TRUE) ### this is equivalent to w <- predict(cf, newdata = cars[1,,drop = FALSE], type = "weights") stopifnot(isTRUE(all.equal(pr, sum(w * cars$dist) / sum(w), check.attributes = FALSE))) ### check if this is the same as mean aggregation ### compute terminal node IDs for first obs nd1 <- predict(cf, newdata = cars[1,,drop = FALSE], type = "node") ### compute terminal nide IDs for all obs nd <- predict(cf, newdata = cars, type = "node") ### random forests weighs lw <- cf$weights ### compute mean predictions for each tree ### and extract mean for terminal node containing ### first observation np <- vector(mode = "list", length = length(lw)) m <- numeric(length(lw)) for (i in 1:length(lw)) { np[[i]] <- tapply(lw[[i]] * cars$dist, nd[[i]], sum) / tapply(lw[[i]], nd[[i]], sum) m[i] <- np[[i]][as.character(nd1[i])] } stopifnot(isTRUE(all.equal(mean(m), sum(w * cars$dist) / sum(w)))) ### check parallel variable importance (make this reproducible) if(.Platform$OS.type == "unix") { RNGkind("L'Ecuyer-CMRG") v1 <- partykit::varimp(cf_partykit, risk = "misclass", conditional = TRUE, cores = 2) v2 <- partykit::varimp(cf_partykit, risk = "misclass", conditional = TRUE, cores = 2) stopifnot(all.equal(v1, v2)) } ### check weights argument cf_partykit <- partykit::cforest(Species ~ ., data = iris, ntree = ntree, mtry = 4) w <- do.call("cbind", cf_partykit$weights) cf_2 <- partykit::cforest(Species ~ ., data = iris, ntree = ntree, mtry = 4, weights = w) stopifnot(max(abs(predict(cf_2, type = "prob") - predict(cf_partykit, type = "prob"))) < sqrt(.Machine$double.eps)) partykit/tests/constparty.Rout.save0000644000176200001440000004372314172230001017300 0ustar liggesusers R version 4.0.4 (2021-02-15) -- "Lost Library Book" Copyright (C) 2021 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > ### R code from vignette source 'constparty.Rnw' > > ### test here after removal of RWeka dependent code > > ################################################### > ### code chunk number 1: setup > ################################################### > options(width = 70) > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > set.seed(290875) > > > ################################################### > ### code chunk number 2: Titanic > ################################################### > data("Titanic", package = "datasets") > ttnc <- as.data.frame(Titanic) > ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] > names(ttnc)[2] <- "Gender" > > > ################################################### > ### code chunk number 3: rpart > ################################################### > library("rpart") > (rp <- rpart(Survived ~ ., data = ttnc, model = TRUE)) n= 2201 node), split, n, loss, yval, (yprob) * denotes terminal node 1) root 2201 711 No (0.6769650 0.3230350) 2) Gender=Male 1731 367 No (0.7879838 0.2120162) 4) Age=Adult 1667 338 No (0.7972406 0.2027594) * 5) Age=Child 64 29 No (0.5468750 0.4531250) 10) Class=3rd 48 13 No (0.7291667 0.2708333) * 11) Class=1st,2nd 16 0 Yes (0.0000000 1.0000000) * 3) Gender=Female 470 126 Yes (0.2680851 0.7319149) 6) Class=3rd 196 90 No (0.5408163 0.4591837) * 7) Class=1st,2nd,Crew 274 20 Yes (0.0729927 0.9270073) * > > > ################################################### > ### code chunk number 4: rpart-party > ################################################### > (party_rp <- as.party(rp)) Model formula: Survived ~ Class + Gender + Age Fitted party: [1] root | [2] Gender in Male | | [3] Age in Adult: No (n = 1667, err = 20.3%) | | [4] Age in Child | | | [5] Class in 3rd: No (n = 48, err = 27.1%) | | | [6] Class in 1st, 2nd: Yes (n = 16, err = 0.0%) | [7] Gender in Female | | [8] Class in 3rd: No (n = 196, err = 45.9%) | | [9] Class in 1st, 2nd, Crew: Yes (n = 274, err = 7.3%) Number of inner nodes: 4 Number of terminal nodes: 5 > > > ################################################### > ### code chunk number 5: rpart-plot-orig > ################################################### > plot(rp) > text(rp) > > > ################################################### > ### code chunk number 6: rpart-plot > ################################################### > plot(party_rp) > > > ################################################### > ### code chunk number 7: rpart-pred > ################################################### > all.equal(predict(rp), predict(party_rp, type = "prob"), + check.attributes = FALSE) [1] TRUE > > > ################################################### > ### code chunk number 8: rpart-fitted > ################################################### > str(fitted(party_rp)) 'data.frame': 2201 obs. of 2 variables: $ (fitted) : int 5 5 5 5 5 5 5 5 5 5 ... $ (response): Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ... > > > ################################################### > ### code chunk number 9: rpart-prob > ################################################### > prop.table(do.call("table", fitted(party_rp)), 1) (response) (fitted) No Yes 3 0.7972406 0.2027594 5 0.7291667 0.2708333 6 0.0000000 1.0000000 8 0.5408163 0.4591837 9 0.0729927 0.9270073 > > > ################################################### > ### code chunk number 10: J48 > ################################################### > #if (require("RWeka")) { > # j48 <- J48(Survived ~ ., data = ttnc) > #} else { > # j48 <- rpart(Survived ~ ., data = ttnc) > #} > #print(j48) > # > # > #################################################### > #### code chunk number 11: J48-party > #################################################### > #(party_j48 <- as.party(j48)) > # > # > #################################################### > #### code chunk number 12: J48-plot > #################################################### > #plot(party_j48) > # > # > #################################################### > #### code chunk number 13: J48-pred > #################################################### > #all.equal(predict(j48, type = "prob"), predict(party_j48, type = "prob"), > # check.attributes = FALSE) > > > ################################################### > ### code chunk number 14: PMML-Titantic > ################################################### > ttnc_pmml <- file.path(system.file("pmml", package = "partykit"), + "ttnc.pmml") > (ttnc_quest <- pmmlTreeModel(ttnc_pmml)) Loading required namespace: XML Model formula: Survived ~ Gender + Class + Age Fitted party: [1] root | [2] Gender in Female | | [3] Class in 3rd, Crew: Yes (n = 219, err = 49.8%) | | [4] Class in 1st, 2nd | | | [5] Class in 2nd: Yes (n = 106, err = 12.3%) | | | [6] Class in 1st: Yes (n = 145, err = 2.8%) | [7] Gender in Male | | [8] Class in 3rd, 2nd, Crew | | | [9] Age in Child: No (n = 59, err = 40.7%) | | | [10] Age in Adult | | | | [11] Class in 3rd, Crew | | | | | [12] Class in Crew: No (n = 862, err = 22.3%) | | | | | [13] Class in 3rd: No (n = 462, err = 16.2%) | | | | [14] Class in 2nd: No (n = 168, err = 8.3%) | | [15] Class in 1st: No (n = 180, err = 34.4%) Number of inner nodes: 7 Number of terminal nodes: 8 > > > ################################################### > ### code chunk number 15: PMML-Titanic-plot1 > ################################################### > plot(ttnc_quest) > > > ################################################### > ### code chunk number 16: ttnc2-reorder > ################################################### > ttnc2 <- ttnc[, names(ttnc_quest$data)] > for(n in names(ttnc2)) { + if(is.factor(ttnc2[[n]])) ttnc2[[n]] <- factor( + ttnc2[[n]], levels = levels(ttnc_quest$data[[n]])) + } > > > ################################################### > ### code chunk number 17: PMML-Titanic-augmentation > ################################################### > ttnc_quest2 <- party(ttnc_quest$node, + data = ttnc2, + fitted = data.frame( + "(fitted)" = predict(ttnc_quest, ttnc2, type = "node"), + "(response)" = ttnc2$Survived, + check.names = FALSE), + terms = terms(Survived ~ ., data = ttnc2) + ) > ttnc_quest2 <- as.constparty(ttnc_quest2) > > > ################################################### > ### code chunk number 18: PMML-Titanic-plot2 > ################################################### > plot(ttnc_quest2) > > > ################################################### > ### code chunk number 19: PMML-write > ################################################### > library("pmml") Loading required package: XML > tfile <- tempfile() > write(toString(pmml(rp)), file = tfile) > > > ################################################### > ### code chunk number 20: PMML-read > ################################################### > (party_pmml <- pmmlTreeModel(tfile)) Model formula: Survived ~ Class + Gender + Age Fitted party: [1] root | [2] Gender in Male | | [3] Age in Adult: No (n = 1667, err = 20.3%) | | [4] Age in Child | | | [5] Class in 3rd: No (n = 48, err = 27.1%) | | | [6] Class in 1st, 2nd: Yes (n = 16, err = 0.0%) | [7] Gender in Female | | [8] Class in 3rd: No (n = 196, err = 45.9%) | | [9] Class in 1st, 2nd, Crew: Yes (n = 274, err = 7.3%) Number of inner nodes: 4 Number of terminal nodes: 5 > all.equal(predict(party_rp, newdata = ttnc, type = "prob"), + predict(party_pmml, newdata = ttnc, type = "prob"), + check.attributes = FALSE) [1] TRUE > > > ################################################### > ### code chunk number 21: mytree-1 > ################################################### > findsplit <- function(response, data, weights, alpha = 0.01) { + + ## extract response values from data + y <- factor(rep(data[[response]], weights)) + + ## perform chi-squared test of y vs. x + mychisqtest <- function(x) { + x <- factor(x) + if(length(levels(x)) < 2) return(NA) + ct <- suppressWarnings(chisq.test(table(y, x), correct = FALSE)) + pchisq(ct$statistic, ct$parameter, log = TRUE, lower.tail = FALSE) + } + xselect <- which(names(data) != response) + logp <- sapply(xselect, function(i) mychisqtest(rep(data[[i]], weights))) + names(logp) <- names(data)[xselect] + + ## Bonferroni-adjusted p-value small enough? + if(all(is.na(logp))) return(NULL) + minp <- exp(min(logp, na.rm = TRUE)) + minp <- 1 - (1 - minp)^sum(!is.na(logp)) + if(minp > alpha) return(NULL) + + ## for selected variable, search for split minimizing p-value + xselect <- xselect[which.min(logp)] + x <- rep(data[[xselect]], weights) + + ## set up all possible splits in two kid nodes + lev <- levels(x[drop = TRUE]) + if(length(lev) == 2) { + splitpoint <- lev[1] + } else { + comb <- do.call("c", lapply(1:(length(lev) - 2), + function(x) combn(lev, x, simplify = FALSE))) + xlogp <- sapply(comb, function(q) mychisqtest(x %in% q)) + splitpoint <- comb[[which.min(xlogp)]] + } + + ## split into two groups (setting groups that do not occur to NA) + splitindex <- !(levels(data[[xselect]]) %in% splitpoint) + splitindex[!(levels(data[[xselect]]) %in% lev)] <- NA_integer_ + splitindex <- splitindex - min(splitindex, na.rm = TRUE) + 1L + + ## return split as partysplit object + return(partysplit(varid = as.integer(xselect), + index = splitindex, + info = list(p.value = 1 - (1 - exp(logp))^sum(!is.na(logp))))) + } > > > ################################################### > ### code chunk number 22: mytree-2 > ################################################### > growtree <- function(id = 1L, response, data, weights, minbucket = 30) { + + ## for less than 30 observations stop here + if (sum(weights) < minbucket) return(partynode(id = id)) + + ## find best split + sp <- findsplit(response, data, weights) + ## no split found, stop here + if (is.null(sp)) return(partynode(id = id)) + + ## actually split the data + kidids <- kidids_split(sp, data = data) + + ## set up all daugther nodes + kids <- vector(mode = "list", length = max(kidids, na.rm = TRUE)) + for (kidid in 1:length(kids)) { + ## select observations for current node + w <- weights + w[kidids != kidid] <- 0 + ## get next node id + if (kidid > 1) { + myid <- max(nodeids(kids[[kidid - 1]])) + } else { + myid <- id + } + ## start recursion on this daugther node + kids[[kidid]] <- growtree(id = as.integer(myid + 1), response, data, w) + } + + ## return nodes + return(partynode(id = as.integer(id), split = sp, kids = kids, + info = list(p.value = min(info_split(sp)$p.value, na.rm = TRUE)))) + } > > > ################################################### > ### code chunk number 23: mytree-3 > ################################################### > mytree <- function(formula, data, weights = NULL) { + + ## name of the response variable + response <- all.vars(formula)[1] + ## data without missing values, response comes last + data <- data[complete.cases(data), c(all.vars(formula)[-1], response)] + ## data is factors only + stopifnot(all(sapply(data, is.factor))) + + if (is.null(weights)) weights <- rep(1L, nrow(data)) + ## weights are case weights, i.e., integers + stopifnot(length(weights) == nrow(data) & + max(abs(weights - floor(weights))) < .Machine$double.eps) + + ## grow tree + nodes <- growtree(id = 1L, response, data, weights) + + ## compute terminal node number for each observation + fitted <- fitted_node(nodes, data = data) + ## return rich constparty object + ret <- party(nodes, data = data, + fitted = data.frame("(fitted)" = fitted, + "(response)" = data[[response]], + "(weights)" = weights, + check.names = FALSE), + terms = terms(formula)) + as.constparty(ret) + } > > > ################################################### > ### code chunk number 24: mytree-4 > ################################################### > (myttnc <- mytree(Survived ~ Class + Age + Gender, data = ttnc)) Model formula: Survived ~ Class + Age + Gender Fitted party: [1] root | [2] Gender in Male | | [3] Class in 1st | | | [4] Age in Child: Yes (n = 5, err = 0.0%) | | | [5] Age in Adult: No (n = 175, err = 32.6%) | | [6] Class in 2nd, 3rd, Crew | | | [7] Age in Child | | | | [8] Class in 2nd: Yes (n = 11, err = 0.0%) | | | | [9] Class in 3rd: No (n = 48, err = 27.1%) | | | [10] Age in Adult | | | | [11] Class in Crew: No (n = 862, err = 22.3%) | | | | [12] Class in 2nd, 3rd: No (n = 630, err = 14.1%) | [13] Gender in Female | | [14] Class in 3rd: No (n = 196, err = 45.9%) | | [15] Class in 1st, 2nd, Crew: Yes (n = 274, err = 7.3%) Number of inner nodes: 7 Number of terminal nodes: 8 > > > ################################################### > ### code chunk number 25: mytree-5 > ################################################### > plot(myttnc) > > > ################################################### > ### code chunk number 26: mytree-pval > ################################################### > nid <- nodeids(myttnc) > iid <- nid[!(nid %in% nodeids(myttnc, terminal = TRUE))] > (pval <- unlist(nodeapply(myttnc, ids = iid, + FUN = function(n) info_node(n)$p.value))) 1 2 3 6 7 0.000000e+00 2.965383e-06 1.756527e-03 6.933623e-05 8.975754e-06 10 13 2.992870e-05 0.000000e+00 > > > ################################################### > ### code chunk number 27: mytree-nodeprune > ################################################### > myttnc2 <- nodeprune(myttnc, ids = iid[pval > 1e-5]) > > > ################################################### > ### code chunk number 28: mytree-nodeprune-plot > ################################################### > plot(myttnc2) > > > ################################################### > ### code chunk number 29: mytree-glm > ################################################### > logLik(glm(Survived ~ Class + Age + Gender, data = ttnc, + family = binomial())) 'log Lik.' -1105.031 (df=6) > > > ################################################### > ### code chunk number 30: mytree-bs > ################################################### > bs <- rmultinom(25, nrow(ttnc), rep(1, nrow(ttnc)) / nrow(ttnc)) > > > ################################################### > ### code chunk number 31: mytree-ll > ################################################### > bloglik <- function(prob, weights) + sum(weights * dbinom(ttnc$Survived == "Yes", size = 1, + prob[,"Yes"], log = TRUE)) > > > ################################################### > ### code chunk number 32: mytree-bsll > ################################################### > f <- function(w) { + tr <- mytree(Survived ~ Class + Age + Gender, data = ttnc, weights = w) + bloglik(predict(tr, newdata = ttnc, type = "prob"), as.numeric(w == 0)) + } > apply(bs, 2, f) [1] -418.2675 -398.0958 -418.6230 -404.1996 -410.8889 -411.7570 [7] -374.9353 -412.6712 -421.7616 -393.9068 -400.0987 -373.6991 [13] -395.1191 -422.8247 -429.5351 -384.3696 -391.9081 -388.7349 [19] -399.7435 -409.1937 -391.9392 -409.1083 -399.7312 -391.7226 [25] -391.5488 > > > ################################################### > ### code chunk number 33: mytree-node > ################################################### > nttnc <- expand.grid(Class = levels(ttnc$Class), + Gender = levels(ttnc$Gender), Age = levels(ttnc$Age)) > nttnc Class Gender Age 1 1st Male Child 2 2nd Male Child 3 3rd Male Child 4 Crew Male Child 5 1st Female Child 6 2nd Female Child 7 3rd Female Child 8 Crew Female Child 9 1st Male Adult 10 2nd Male Adult 11 3rd Male Adult 12 Crew Male Adult 13 1st Female Adult 14 2nd Female Adult 15 3rd Female Adult 16 Crew Female Adult > > > ################################################### > ### code chunk number 34: mytree-prob > ################################################### > predict(myttnc, newdata = nttnc, type = "node") 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 4 8 9 8 15 15 14 15 5 12 12 11 15 15 14 15 > predict(myttnc, newdata = nttnc, type = "response") 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Yes Yes No No Yes Yes No Yes No No No No Yes Yes No Yes Levels: No Yes > predict(myttnc, newdata = nttnc, type = "prob") No Yes 1 0.0000000 1.0000000 2 0.0000000 1.0000000 3 0.7291667 0.2708333 4 0.0000000 1.0000000 5 0.0729927 0.9270073 6 0.0729927 0.9270073 7 0.5408163 0.4591837 8 0.0729927 0.9270073 9 0.6742857 0.3257143 10 0.8587302 0.1412698 11 0.8587302 0.1412698 12 0.7772622 0.2227378 13 0.0729927 0.9270073 14 0.0729927 0.9270073 15 0.5408163 0.4591837 16 0.0729927 0.9270073 > > > ################################################### > ### code chunk number 35: mytree-FUN > ################################################### > predict(myttnc, newdata = nttnc, FUN = function(y, w) + rank(table(rep(y, w)))) No Yes 1 1 2 2 1 2 3 2 1 4 2 1 5 1 2 6 1 2 7 2 1 8 1 2 9 2 1 10 2 1 11 2 1 12 2 1 13 1 2 14 1 2 15 2 1 16 1 2 > > > > proc.time() user system elapsed 3.175 0.098 3.258 partykit/tests/regtest-party.R0000644000176200001440000001033514646205274016234 0ustar liggesuserssuppressWarnings(RNGversion("3.5.2")) ## load package and fix seed library("partykit") set.seed(1) ## rpart: kyphosis data library("rpart") data("kyphosis", package = "rpart") fit <- rpart(Kyphosis ~ Age + Number + Start, data = kyphosis) pfit <- as.party(fit) all(predict(pfit, newdata = kyphosis, type = "node") == fit$where) ## J48: iris data if (require("RWeka")) { data("iris", package = "datasets") itree <- J48(Species ~ ., data = iris) pitree <- as.party(itree) stopifnot(all(predict(pitree) == predict(pitree, newdata = iris[, 3:4]))) print(all.equal(predict(itree, type = "prob", newdata = iris), predict(pitree, type = "prob", newdata = iris))) print(all.equal(predict(itree, newdata = iris), predict(pitree, newdata = iris))) ## rpart/J48: GlaucomaM data data("GlaucomaM", package = "TH.data") w <- runif(nrow(GlaucomaM)) fit <- rpart(Class ~ ., data = GlaucomaM, weights = w) pfit <- as.party(fit) print(all(predict(pfit, type = "node") == fit$where)) tmp <- GlaucomaM[sample(1:nrow(GlaucomaM), 100),] print(all.equal(predict(fit, type = "prob", newdata = tmp), predict(pfit, type = "prob", newdata = tmp))) print(all.equal(predict(fit, type = "class", newdata = tmp), predict(pfit, newdata = tmp))) itree <- J48(Class ~ ., data = GlaucomaM) pitree <- as.party(itree) print(all.equal(predict(itree, newdata = tmp, type = "prob"), predict(pitree, newdata = tmp, type = "prob"))) } ## rpart: airquality data data("airquality") aq <- subset(airquality, !is.na(Ozone)) w <- runif(nrow(aq), max = 3) aqr <- rpart(Ozone ~ ., data = aq, weights = w) aqp <- as.party(aqr) tmp <- subset(airquality, is.na(Ozone)) all.equal(predict(aqr, newdata = tmp), predict(aqp, newdata = tmp)) ## rpart: GBSG2 data data("GBSG2", package = "TH.data") library("survival") fit <- rpart(Surv(time, cens) ~ ., data = GBSG2) pfit <- as.party(fit) pfit$fitted predict(pfit, newdata = GBSG2[1:100,], type = "prob") predict(pfit, newdata = GBSG2[1:100,], type = "response") ### multiple responses f <- fitted(pfit) f[["(response)"]] <- data.frame(srv = f[["(response)"]], hansi = runif(nrow(f))) mp <- party(node_party(pfit), fitted = f, data = pfit$data) class(mp) <- c("constparty", "party") predict(mp, newdata = GBSG2[1:10,]) ### pruning ## create party data("WeatherPlay", package = "partykit") py <- party( partynode(1L, split = partysplit(1L, index = 1:3), kids = list( partynode(2L, split = partysplit(3L, breaks = 75), kids = list( partynode(3L, info = "yes"), partynode(4L, info = "no"))), partynode(5L, split = partysplit(3L, breaks = 20), kids = list( partynode(6L, info = "no"), partynode(7L, info = "yes"))), partynode(8L, split = partysplit(4L, index = 1:2), kids = list( partynode(9L, info = "yes"), partynode(10L, info = "no"))))), WeatherPlay) names(py) <- LETTERS[nodeids(py)] ## print print(py) (py5 <- nodeprune(py, 5)) nodeids(py5) (pyH <- nodeprune(py5, "H")) nodeids(pyH) ct <- ctree(Species ~ ., data = iris) nt <- node_party(ctree(Species ~ ., data = iris)) (ctp <- nodeprune(ct, 4)) ### party method (ntp <- nodeprune(nt, 4)) ### partynode method ### check if both methods do the same p1 <- predict(party(ntp, data = model.frame(ct)), type = "node") p2 <- predict(ctp, type = "node") stopifnot(max(abs(p1 - p2)) == 0) names(ct) <- LETTERS[nodeids(ct)] (ctp <- nodeprune(ct, "D")) table(predict(ct, type = "node"), predict(ctp, type = "node")) (ct <- nodeprune(ct, names(ct)[names(ct) != "A"])) table(predict(ct, type = "node")) nodeprune(ct, "B") nodeprune(ct, "C") nodeprune(ct, "A") options(digits = 3) ### check different predict flavours for numeric responses x <- runif(100) dd <- data.frame(y = rnorm(length(x), mean = 2 * (x < .5)), x = x) ct <- ctree(y ~ x, data = dd) nd <- data.frame(x = (1:9) / 10) predict(ct, newdata = nd, type = "node") predict(ct, newdata = nd, type = "response") predict(ct, newdata = nd, type = "prob") predict(ct, newdata = nd, type = "quantile") predict(ct, newdata = nd, type = "quantile", at = NULL) predict(ct, newdata = nd, type = "density") predict(ct, newdata = nd, type = "density", at = (1:9) / 10) partykit/MD50000644000176200001440000002033214723366102012435 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names(obj) extract_label <- function(node) { if(is.terminal(node)) return(rep.int("", 2L)) varlab <- character_split(split_node(node), meta)$name if(abbreviate > 0L) varlab <- abbreviate(varlab, as.integer(abbreviate)) ## FIXME: make more flexible rather than special-casing p-value if(pval) { nullna <- function(x) is.null(x) || is.na(x) pval <- suppressWarnings(try(!nullna(info_node(node)$p.value), silent = TRUE)) pval <- if(inherits(pval, "try-error")) FALSE else pval } if(pval) { pvalue <- node$info$p.value plab <- ifelse(pvalue < 10^(-3L), paste("p <", 10^(-3L)), paste("p =", round(pvalue, digits = 3L))) } else { plab <- "" } return(c(varlab, plab)) } maxstr <- function(node) { lab <- extract_label(node) klab <- if(is.terminal(node)) "" else unlist(lapply(kids_node(node), maxstr)) lab <- c(lab, klab) lab <- unlist(lapply(lab, function(x) strsplit(x, "\n"))) lab <- lab[which.max(nchar(lab))] if(length(lab) < 1L) lab <- "" return(lab) } nstr <- maxstr(node_party(obj)) if(nchar(nstr) < 6) nstr <- "aAAAAa" ### panel function for the inner nodes rval <- function(node) { pushViewport(viewport(gp = gp, name = paste("node_inner", id_node(node), "_gpar", sep = ""))) node_vp <- viewport( x = unit(0.5, "npc"), y = unit(0.5, "npc"), width = unit(1, "strwidth", nstr) * 1.3, height = unit(3, "lines"), name = paste("node_inner", id_node(node), sep = ""), gp = gp ) pushViewport(node_vp) xell <- c(seq(0, 0.2, by = 0.01), seq(0.2, 0.8, by = 0.05), seq(0.8, 1, by = 0.01)) yell <- sqrt(xell * (1-xell)) lab <- extract_label(node) fill <- rep(fill, length.out = 2L) grid.polygon(x = unit(c(xell, rev(xell)), "npc"), y = unit(c(yell, -yell)+0.5, "npc"), gp = gpar(fill = fill[1])) ## FIXME: something more general instead of pval ? grid.text(lab[1L], y = unit(1.5 + 0.5 * (lab[2L] != ""), "lines")) if(lab[2L] != "") grid.text(lab[2L], y = unit(1, "lines")) if(id) { nodeIDvp <- viewport(x = unit(0.5, "npc"), y = unit(1, "npc"), width = max(unit(1, "lines"), unit(1.3, "strwidth", nam[id_node(node)])), height = max(unit(1, "lines"), unit(1.3, "strheight", nam[id_node(node)]))) pushViewport(nodeIDvp) grid.rect(gp = gpar(fill = fill[2])) grid.text(nam[id_node(node)]) popViewport() } upViewport(2) } return(rval) } class(node_inner) <- "grapcon_generator" node_terminal <- function(obj, digits = 3, abbreviate = FALSE, fill = c("lightgray", "white"), id = TRUE, just = c("center", "top"), top = 0.85, align = c("center", "left", "right"), gp = NULL, FUN = NULL, height = NULL, width = NULL) { nam <- names(obj) extract_label <- function(node) formatinfo_node(node, FUN = FUN, default = c("terminal", "node")) maxstr <- function(node) { lab <- extract_label(node) klab <- if(is.terminal(node)) "" else unlist(lapply(kids_node(node), maxstr)) lab <- c(lab, klab) lab <- try(unlist(lapply(lab, function(x) strsplit(x, "\n"))), silent = TRUE) if(inherits(lab, "try-error")) { paste(rep("a", 9L), collapse = "") ## FIXME: completely ad-hoc: possibly throw warning? } else { return(lab[which.max(nchar(lab))]) } } nstr <- if(is.null(width)) maxstr(node_party(obj)) else paste(rep("a", width), collapse = "") just <- match.arg(just[1L], c("center", "centre", "top")) if(just == "centre") just <- "center" align <- match.arg(align[1L], c("center", "centre", "left", "right")) if(align == "centre") align <- "center" ### panel function for simple n, Y terminal node labeling rval <- function(node) { fill <- rep(fill, length.out = 2) lab <- extract_label(node) ## if gp is set, then an additional viewport may be ## required to appropriately evaluate strwidth unit if(!is.null(gp)) { outer_vp <- viewport(gp = gp) pushViewport(outer_vp) } if(is.null(height)) height <- length(lab) + 1L node_vp <- viewport(x = unit(0.5, "npc"), y = unit(if(just == "top") top else 0.5, "npc"), just = c("center", just), width = unit(1, "strwidth", nstr) * 1.1, height = unit(height, "lines"), name = paste("node_terminal", id_node(node), sep = ""), gp = if(is.null(gp)) gpar() else gp ) pushViewport(node_vp) grid.rect(gp = gpar(fill = fill[1])) for(i in seq_along(lab)) grid.text( x = switch(align, "center" = unit(0.5, "npc"), "left" = unit(1, "strwidth", "a"), "right" = unit(1, "npc") - unit(1, "strwidth", "a")), y = unit(length(lab) - i + 1, "lines"), lab[i], just = align) if(id) { nodeIDvp <- viewport(x = unit(0.5, "npc"), y = unit(1, "npc"), width = max(unit(1, "lines"), unit(1.3, "strwidth", nam[id_node(node)])), height = max(unit(1, "lines"), unit(1.3, "strheight", nam[id_node(node)]))) pushViewport(nodeIDvp) grid.rect(gp = gpar(fill = fill[2], lty = "solid")) grid.text(nam[id_node(node)]) popViewport() } if(is.null(gp)) upViewport() else upViewport(2) } return(rval) } class(node_terminal) <- "grapcon_generator" edge_simple <- function(obj, digits = 3, abbreviate = FALSE, justmin = Inf, just = c("alternate", "increasing", "decreasing", "equal"), fill = "white") { meta <- obj$data justfun <- function(i, split) { myjust <- if(mean(nchar(split)) > justmin) { match.arg(just, c("alternate", "increasing", "decreasing", "equal")) } else { "equal" } k <- length(split) rval <- switch(myjust, "equal" = rep.int(0, k), "alternate" = rep(c(0.5, -0.5), length.out = k), "increasing" = seq(from = -k/2, to = k/2, by = 1), "decreasing" = seq(from = k/2, to = -k/2, by = -1) ) unit(0.5, "npc") + unit(rval[i], "lines") } ### panel function for simple edge labelling function(node, i) { split <- character_split(split_node(node), meta, digits = digits)$levels y <- justfun(i, split) split <- split[i] # try() because the following won't work for split = "< 10 Euro", for example. if(any(grep(">", split) > 0) | any(grep("<", split) > 0)) { tr <- suppressWarnings(try(parse(text = paste("phantom(0)", split)), silent = TRUE)) if(!inherits(tr, "try-error")) split <- tr } grid.rect(y = y, gp = gpar(fill = fill, col = 0), width = unit(1, "strwidth", split)) grid.text(split, y = y, just = "center") } } class(edge_simple) <- "grapcon_generator" .plot_node <- function(node, xlim, ylim, nx, ny, terminal_panel, inner_panel, edge_panel, tnex = 2, drop_terminal = TRUE, debug = FALSE) { ### the workhorse for plotting trees ### set up viewport for terminal node if (is.terminal(node)) { x <- xlim[1] + diff(xlim)/2 y <- ylim[1] + 0.5 tn_vp <- viewport(x = unit(x, "native"), y = unit(y, "native") - unit(0.5, "lines"), width = unit(1, "native"), height = unit(tnex, "native") - unit(1, "lines"), just = c("center", "top"), name = paste("Node", id_node(node), sep = "")) pushViewport(tn_vp) if (debug) grid.rect(gp = gpar(lty = "dotted", col = 4)) terminal_panel(node) upViewport() return(NULL) } ## convenience function for computing relative position of splitting node pos_frac <- function(node) { if(is.terminal(node)) 0.5 else { width_kids <- sapply(kids_node(node), width) nk <- length(width_kids) rval <- if(nk %% 2 == 0) sum(width_kids[1:(nk/2)]) else mean(cumsum(width_kids)[nk/2 + c(-0.5, 0.5)]) rval/sum(width_kids) } } ## extract information split <- split_node(node) kids <- kids_node(node) width_kids <- sapply(kids, width) nk <- length(width_kids) ### position of inner node x0 <- xlim[1] + pos_frac(node) * diff(xlim) y0 <- max(ylim) ### relative positions of kids xfrac <- sapply(kids, pos_frac) x1lim <- xlim[1] + cumsum(c(0, width_kids))/sum(width_kids) * diff(xlim) x1 <- x1lim[1:nk] + xfrac * diff(x1lim) if (!drop_terminal) { y1 <- rep(y0 - 1, nk) } else { y1 <- ifelse(sapply(kids, is.terminal), tnex - 0.5, y0 - 1) } ### draw edges for(i in 1:nk) grid.lines(x = unit(c(x0, x1[i]), "native"), y = unit(c(y0, y1[i]), "native")) ### create viewport for inner node in_vp <- viewport(x = unit(x0, "native"), y = unit(y0, "native"), width = unit(1, "native"), height = unit(1, "native") - unit(1, "lines"), name = paste("Node", id_node(node), sep = "")) pushViewport(in_vp) if(debug) grid.rect(gp = gpar(lty = "dotted")) inner_panel(node) upViewport() ### position of labels y1max <- max(y1, na.rm = TRUE) ypos <- y0 - (y0 - y1max) * 0.5 xpos <- x0 - (x0 - x1) * 0.5 * (y0 - y1max)/(y0 - y1) ### setup labels for(i in 1:nk) { sp_vp <- viewport(x = unit(xpos[i], "native"), y = unit(ypos, "native"), width = unit(diff(x1lim)[i], "native"), height = unit(1, "lines"), name = paste("edge", id_node(node), "-", i, sep = "")) pushViewport(sp_vp) if(debug) grid.rect(gp = gpar(lty = "dotted", col = 2)) edge_panel(node, i) upViewport() } ## call workhorse for kids for(i in 1:nk) .plot_node(kids[[i]], c(x1lim[i], x1lim[i+1]), c(y1[i], 1), nx, ny, terminal_panel, inner_panel, edge_panel, tnex = tnex, drop_terminal = drop_terminal, debug = debug) } plot.party <- function(x, main = NULL, terminal_panel = node_terminal, tp_args = list(), inner_panel = node_inner, ip_args = list(), edge_panel = edge_simple, ep_args = list(), drop_terminal = FALSE, tnex = 1, newpage = TRUE, pop = TRUE, gp = gpar(), margins = NULL, ...) { ### extract tree node <- node_party(x) ### total number of terminal nodes nx <- width(node) ### maximal depth of the tree ny <- depth(node, root = TRUE) ## setup newpage if (newpage) grid.newpage() ## setup root viewport margins <- if(is.null(margins)) { c(1, 1, if(is.null(main)) 0 else 3, 1) } else { rep_len(margins, 4L) } root_vp <- viewport(layout = grid.layout(3, 3, heights = unit(c(margins[3L], 1, margins[1L]), c("lines", "null", "lines")), widths = unit(c(margins[2L], 1, margins[4L]), c("lines", "null", "lines"))), name = "root", gp = gp) pushViewport(root_vp) ## viewport for main title (if any) if (!is.null(main)) { main_vp <- viewport(layout.pos.col = 2, layout.pos.row = 1, name = "main") pushViewport(main_vp) grid.text(y = unit(1, "lines"), main, just = "center") upViewport() } ## setup viewport for tree tree_vp <- viewport(layout.pos.col = 2, layout.pos.row = 2, xscale = c(0, nx), yscale = c(0, ny + (tnex - 1)), name = "tree") pushViewport(tree_vp) ### setup panel functions (if necessary) if(inherits(terminal_panel, "grapcon_generator")) terminal_panel <- do.call("terminal_panel", c(list(x), as.list(tp_args))) if(inherits(inner_panel, "grapcon_generator")) inner_panel <- do.call("inner_panel", c(list(x), as.list(ip_args))) if(inherits(edge_panel, "grapcon_generator")) edge_panel <- do.call("edge_panel", c(list(x), as.list(ep_args))) if((nx <= 1 & ny <= 1)) { if(is.null(margins)) margins <- rep.int(1.5, 4) pushViewport(plotViewport(margins = margins, name = paste("Node", id_node(node), sep = ""))) terminal_panel(node) } else { ## call the workhorse .plot_node(node, xlim = c(0, nx), ylim = c(0, ny - 0.5 + (tnex - 1)), nx = nx, ny = ny, terminal_panel = terminal_panel, inner_panel = inner_panel, edge_panel = edge_panel, tnex = tnex, drop_terminal = drop_terminal, debug = FALSE) } upViewport() if (pop) popViewport() else upViewport() } plot.constparty <- function(x, main = NULL, terminal_panel = NULL, tp_args = list(), inner_panel = node_inner, ip_args = list(), edge_panel = edge_simple, ep_args = list(), type = c("extended", "simple"), drop_terminal = NULL, tnex = NULL, newpage = TRUE, pop = TRUE, gp = gpar(), ...) { ### compute default settings type <- match.arg(type) if (type == "simple") { x <- as.simpleparty(x) if (is.null(terminal_panel)) terminal_panel <- node_terminal if (is.null(tnex)) tnex <- 1 if (is.null(drop_terminal)) drop_terminal <- FALSE if (is.null(tp_args) || length(tp_args) < 1L) { tp_args <- list(FUN = .make_formatinfo_simpleparty(x, digits = getOption("digits") - 4L, sep = "\n")) } else { if(is.null(tp_args$FUN)) { tp_args$FUN <- .make_formatinfo_simpleparty(x, digits = getOption("digits") - 4L, sep = "\n") } } } else { if (is.null(terminal_panel)) { cl <- class(x$fitted[["(response)"]]) if("factor" %in% cl) { terminal_panel <- node_barplot } else if("Surv" %in% cl) { terminal_panel <- node_surv } else if ("data.frame" %in% cl) { terminal_panel <- node_mvar if (is.null(tnex)) tnex <- 2 * NCOL(x$fitted[["(response)"]]) } else { terminal_panel <- node_boxplot } } if (is.null(tnex)) tnex <- 2 if (is.null(drop_terminal)) drop_terminal <- TRUE } plot.party(x, main = main, terminal_panel = terminal_panel, tp_args = tp_args, inner_panel = inner_panel, ip_args = ip_args, edge_panel = edge_panel, ep_args = ep_args, drop_terminal = drop_terminal, tnex = tnex, newpage = newpage, pop = pop, gp = gp, ...) } node_barplot <- function(obj, col = "black", fill = NULL, bg = "white", beside = NULL, ymax = NULL, ylines = NULL, widths = 1, gap = NULL, reverse = NULL, rot = 0, just = c("center", "top"), id = TRUE, mainlab = NULL, text = c("none", "horizontal", "vertical"), gp = gpar()) { ## extract response y <- obj$fitted[["(response)"]] stopifnot(is.factor(y) || isTRUE(all.equal(round(y), y)) || is.data.frame(y)) ## FIXME: This could be avoided by ## predict_party(obj, nodeids(obj, terminal = TRUE), type = "prob") ## but only for terminal nodes ^^^^ probs_and_n <- function(x) { y1 <- x$fitted[["(response)"]] if(!is.factor(y1)) { if(is.data.frame(y1)) { y1 <- t(as.matrix(y1)) } else { y1 <- factor(y1, levels = min(y, na.rm = TRUE):max(y, na.rm = TRUE)) } } w <- x$fitted[["(weights)"]] if(is.null(w)) w <- rep.int(1L, length(y1)) sumw <- if(is.factor(y1)) tapply(w, y1, sum) else drop(y1 %*% w) sumw[is.na(sumw)] <- 0 prob <- c(sumw/sum(w), sum(w)) names(prob) <- c(if(is.factor(y1)) levels(y1) else rownames(y1), "nobs") prob } probs <- do.call("rbind", nodeapply(obj, nodeids(obj), probs_and_n, by_node = FALSE)) nobs <- probs[, "nobs"] probs <- probs[, -ncol(probs), drop = FALSE] if(is.factor(y)) { ylevels <- levels(y) if(is.null(beside)) beside <- if(length(ylevels) < 3L) FALSE else TRUE if(is.null(ymax)) ymax <- if(beside) 1.1 else 1 if(is.null(gap)) gap <- if(beside) 0.1 else 0 } else { if(is.null(beside)) beside <- TRUE if(is.null(ymax)) ymax <- if(beside) max(probs) * 1.1 else max(probs) ylevels <- colnames(probs) if(length(ylevels) < 2) ylevels <- "" if(is.null(gap)) gap <- if(beside) 0.1 else 0 } if(is.null(reverse)) reverse <- !beside if(is.null(fill)) fill <- gray.colors(length(ylevels)) if(is.null(ylines)) ylines <- if(beside) c(3, 2) else c(1.5, 2.5) ## text labels? if(isTRUE(text)) text <- "horizontal" if(!is.character(text)) text <- "none" text <- match.arg(text, c("none", "horizontal", "vertical")) ### panel function for barplots in nodes rval <- function(node) { ## id nid <- id_node(node) ## parameter setup pred <- probs[nid,] if(reverse) { pred <- rev(pred) ylevels <- rev(ylevels) } np <- length(pred) nc <- if(beside) np else 1 fill <- rep(fill, length.out = np) widths <- rep(widths, length.out = nc) col <- rep(col, length.out = nc) ylines <- rep(ylines, length.out = 2) gap <- gap * sum(widths) yscale <- c(0, ymax) xscale <- c(0, sum(widths) + (nc+1)*gap) top_vp <- viewport(layout = grid.layout(nrow = 2, ncol = 3, widths = unit(c(ylines[1], 1, ylines[2]), c("lines", "null", "lines")), heights = unit(c(1, 1), c("lines", "null"))), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste0("node_barplot", nid), gp = gp) pushViewport(top_vp) grid.rect(gp = gpar(fill = bg, col = 0)) ## main title top <- viewport(layout.pos.col=2, layout.pos.row=1) pushViewport(top) if (is.null(mainlab)) { mainlab <- if(id) { function(id, nobs) sprintf("Node %s (n = %s)", id, nobs) } else { function(id, nobs) sprintf("n = %s", nobs) } } if (is.function(mainlab)) { mainlab <- mainlab(names(obj)[nid], nobs[nid]) } grid.text(mainlab) popViewport() plot <- viewport(layout.pos.col=2, layout.pos.row=2, xscale=xscale, yscale=yscale, name = paste0("node_barplot", node$nodeID, "plot"), clip = FALSE) pushViewport(plot) if(beside) { xcenter <- cumsum(widths+gap) - widths/2 if(length(xcenter) > 1) grid.xaxis(at = xcenter, label = FALSE) grid.text(ylevels, x = xcenter, y = unit(-1, "lines"), just = just, rot = rot, default.units = "native", check.overlap = TRUE) grid.yaxis() grid.rect(gp = gpar(fill = "transparent")) grid.clip() for (i in 1:np) { grid.rect(x = xcenter[i], y = 0, height = pred[i], width = widths[i], just = c("center", "bottom"), default.units = "native", gp = gpar(col = col[i], fill = fill[i])) if(text != "none") { grid.text(x = xcenter[i], y = pred[i] + 0.025, label = paste(format(round(100 * pred[i], 1), nsmall = 1), "%", sep = ""), just = if(text == "horizontal") c("center", "bottom") else c("left", "center"), rot = if(text == "horizontal") 0 else 90, default.units = "native") } } } else { ycenter <- cumsum(pred) - pred if(np > 1) { grid.text(ylevels[1], x = unit(-1, "lines"), y = 0, just = c("left", "center"), rot = 90, default.units = "native", check.overlap = TRUE) grid.text(ylevels[np], x = unit(-1, "lines"), y = ymax, just = c("right", "center"), rot = 90, default.units = "native", check.overlap = TRUE) } if(np > 2) { grid.text(ylevels[-c(1,np)], x = unit(-1, "lines"), y = ycenter[-c(1,np)], just = "center", rot = 90, default.units = "native", check.overlap = TRUE) } grid.yaxis(main = FALSE) grid.clip() grid.rect(gp = gpar(fill = "transparent")) for (i in 1:np) { grid.rect(x = xscale[2]/2, y = ycenter[i], height = min(pred[i], ymax - ycenter[i]), width = widths[1], just = c("center", "bottom"), default.units = "native", gp = gpar(col = col[i], fill = fill[i])) } } grid.rect(gp = gpar(fill = "transparent")) upViewport(2) } return(rval) } class(node_barplot) <- "grapcon_generator" node_boxplot <- function(obj, col = "black", fill = "lightgray", bg = "white", width = 0.5, yscale = NULL, ylines = 3, cex = 0.5, id = TRUE, mainlab = NULL, gp = gpar()) { y <- obj$fitted[["(response)"]] stopifnot(is.numeric(y)) if (is.null(yscale)) yscale <- range(y) + c(-0.1, 0.1) * diff(range(y)) ### panel function for boxplots in nodes rval <- function(node) { ## extract data nid <- id_node(node) dat <- data_party(obj, nid) yn <- dat[["(response)"]] wn <- dat[["(weights)"]] if(is.null(wn)) wn <- rep(1, length(yn)) ## parameter setup x <- boxplot(rep.int(yn, wn), plot = FALSE) top_vp <- viewport(layout = grid.layout(nrow = 2, ncol = 3, widths = unit(c(ylines, 1, 1), c("lines", "null", "lines")), heights = unit(c(1, 1), c("lines", "null"))), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_boxplot", nid, sep = ""), gp = gp) pushViewport(top_vp) grid.rect(gp = gpar(fill = bg, col = 0)) ## main title top <- viewport(layout.pos.col=2, layout.pos.row=1) pushViewport(top) if (is.null(mainlab)) { mainlab <- if(id) { function(id, nobs) sprintf("Node %s (n = %s)", id, nobs) } else { function(id, nobs) sprintf("n = %s", nobs) } } if (is.function(mainlab)) { mainlab <- mainlab(names(obj)[nid], sum(wn)) } grid.text(mainlab) popViewport() plot <- viewport(layout.pos.col = 2, layout.pos.row = 2, xscale = c(0, 1), yscale = yscale, name = paste0("node_boxplot", nid, "plot"), clip = FALSE) pushViewport(plot) grid.yaxis() grid.rect(gp = gpar(fill = "transparent")) grid.clip() xl <- 0.5 - width/4 xr <- 0.5 + width/4 ## box & whiskers grid.lines(unit(c(xl, xr), "npc"), unit(x$stats[1], "native"), gp = gpar(col = col)) grid.lines(unit(0.5, "npc"), unit(x$stats[1:2], "native"), gp = gpar(col = col, lty = 2)) grid.rect(unit(0.5, "npc"), unit(x$stats[2], "native"), width = unit(width, "npc"), height = unit(diff(x$stats[c(2, 4)]), "native"), just = c("center", "bottom"), gp = gpar(col = col, fill = fill)) grid.lines(unit(c(0.5 - width/2, 0.5+width/2), "npc"), unit(x$stats[3], "native"), gp = gpar(col = col, lwd = 2)) grid.lines(unit(0.5, "npc"), unit(x$stats[4:5], "native"), gp = gpar(col = col, lty = 2)) grid.lines(unit(c(xl, xr), "npc"), unit(x$stats[5], "native"), gp = gpar(col = col)) ## outlier n <- length(x$out) if (n > 0) { index <- 1:n ## which(x$out > yscale[1] & x$out < yscale[2]) if (length(index) > 0) grid.points(unit(rep.int(0.5, length(index)), "npc"), unit(x$out[index], "native"), size = unit(cex, "char"), gp = gpar(col = col)) } upViewport(2) } return(rval) } class(node_boxplot) <- "grapcon_generator" node_surv <- function(obj, col = "black", bg = "white", yscale = c(0, 1), ylines = 2, id = TRUE, mainlab = NULL, gp = gpar(), ...) { ## extract response y <- obj$fitted[["(response)"]] stopifnot(inherits(y, "Surv")) ## helper functions mysurvfit <- function(y, weights, ...) survfit(y ~ 1, weights = weights) ### structure( ### survival:::survfitKM(x = gl(1, NROW(y)), y = y, casewt = weights, ...), ### class = "survfit") dostep <- function(x, y) { ### create a step function based on x, y coordinates ### modified from `survival:print.survfit' if (is.na(x[1] + y[1])) { x <- x[-1] y <- y[-1] } n <- length(x) if (n > 2) { # replace verbose horizonal sequences like # (1, .2), (1.4, .2), (1.8, .2), (2.3, .2), (2.9, .2), (3, .1) # with (1, .2), (3, .1). They are slow, and can smear the looks # of the line type. dupy <- c(TRUE, diff(y[-n]) !=0, TRUE) n2 <- sum(dupy) #create a step function xrep <- rep(x[dupy], c(1, rep(2, n2-1))) yrep <- rep(y[dupy], c(rep(2, n2-1), 1)) RET <- list(x = xrep, y = yrep) } else { if (n == 1) { RET <- list(x = x, y = y) } else { RET <- list(x = x[c(1,2,2)], y = y[c(1,1,2)]) } } return(RET) } ### panel function for Kaplan-Meier curves in nodes rval <- function(node) { ## extract data nid <- id_node(node) dat <- data_party(obj, nid) yn <- dat[["(response)"]] wn <- dat[["(weights)"]] if(is.null(wn)) wn <- rep(1, NROW(yn)) ## get Kaplan-Meier curver in node km <- mysurvfit(yn, weights = wn, ...) a <- dostep(km$time, km$surv) ## set up plot yscale <- yscale xscale <- c(0, max(y[,1], na.rm = TRUE)) top_vp <- viewport(layout = grid.layout(nrow = 2, ncol = 3, widths = unit(c(ylines, 1, 1), c("lines", "null", "lines")), heights = unit(c(1, 1), c("lines", "null"))), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_surv", nid, sep = ""), gp = gp) pushViewport(top_vp) grid.rect(gp = gpar(fill = bg, col = 0)) ## main title top <- viewport(layout.pos.col=2, layout.pos.row=1) pushViewport(top) if (is.null(mainlab)) { mainlab <- if(id) { function(id, nobs) sprintf("Node %s (n = %s)", id, nobs) } else { function(id, nobs) sprintf("n = %s", nobs) } } if (is.function(mainlab)) { mainlab <- mainlab(nid, sum(wn)) } grid.text(mainlab) popViewport() plot <- viewport(layout.pos.col=2, layout.pos.row=2, xscale=xscale, yscale = yscale, name = paste0("node_surv", nid, "plot"), clip = FALSE) pushViewport(plot) grid.xaxis() grid.yaxis() grid.rect(gp = gpar(fill = "transparent")) grid.clip() grid.lines(unit(a$x, "native"), unit(a$y, "native"), gp = gpar(col = col)) upViewport(2) } return(rval) } class(node_surv) <- "grapcon_generator" node_ecdf <- function(obj, col = "black", bg = "white", ylines = 2, id = TRUE, mainlab = NULL, gp = gpar(), ...) { ## extract response y <- obj$fitted[["(response)"]] stopifnot(inherits(y, "numeric") || inherits(y, "integer")) dostep <- function(f) { x <- knots(f) y <- f(x) ### create a step function based on x, y coordinates ### modified from `survival:print.survfit' if (is.na(x[1] + y[1])) { x <- x[-1] y <- y[-1] } n <- length(x) if (n > 2) { # replace verbose horizonal sequences like # (1, .2), (1.4, .2), (1.8, .2), (2.3, .2), (2.9, .2), (3, .1) # with (1, .2), (3, .1). They are slow, and can smear the looks # of the line type. dupy <- c(TRUE, diff(y[-n]) !=0, TRUE) n2 <- sum(dupy) #create a step function xrep <- rep(x[dupy], c(1, rep(2, n2-1))) yrep <- rep(y[dupy], c(rep(2, n2-1), 1)) RET <- list(x = xrep, y = yrep) } else { if (n == 1) { RET <- list(x = x, y = y) } else { RET <- list(x = x[c(1,2,2)], y = y[c(1,1,2)]) } } return(RET) } ### panel function for ecdf in nodes rval <- function(node) { ## extract data nid <- id_node(node) dat <- data_party(obj, nid) yn <- dat[["(response)"]] wn <- dat[["(weights)"]] if(is.null(wn)) wn <- rep(1, NROW(yn)) ## get ecdf in node f <- .pred_ecdf(yn, wn) a <- dostep(f) ## set up plot yscale <- c(0, 1) xscale <- range(y, na.rm = TRUE) a$x <- c(xscale[1], a$x[1], a$x, xscale[2]) a$x <- a$x - min(a$x) a$x <- a$x / max(a$x) a$y <- c(0, 0, a$y, 1) top_vp <- viewport(layout = grid.layout(nrow = 2, ncol = 3, widths = unit(c(ylines, 1, 1), c("lines", "null", "lines")), heights = unit(c(1, 1), c("lines", "null"))), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_ecdf", nid, sep = ""), gp = gp) pushViewport(top_vp) grid.rect(gp = gpar(fill = bg, col = 0)) ## main title top <- viewport(layout.pos.col=2, layout.pos.row=1) pushViewport(top) if (is.null(mainlab)) { mainlab <- if(id) { function(id, nobs) sprintf("Node %s (n = %s)", id, nobs) } else { function(id, nobs) sprintf("n = %s", nobs) } } if (is.function(mainlab)) { mainlab <- mainlab(nid, sum(wn)) } grid.text(mainlab) popViewport() plot <- viewport(layout.pos.col=2, layout.pos.row=2, xscale=xscale, yscale=yscale, name = paste0("node_surv", nid, "plot"), clip = FALSE) pushViewport(plot) grid.xaxis() grid.yaxis() grid.rect(gp = gpar(fill = "transparent")) grid.clip() grid.lines(a$x, a$y, gp = gpar(col = col)) upViewport(2) } return(rval) } class(node_ecdf) <- "grapcon_generator" node_mvar <- function(obj, which = NULL, id = TRUE, pop = TRUE, ylines = NULL, mainlab = NULL, varlab = TRUE, bg = "white", ...) { ## obtain dependent variables y <- obj$fitted[["(response)"]] ## fitted node ids fitted <- obj$fitted[["(fitted)"]] ## number of panels needed if(is.null(which)) which <- 1L:NCOL(y) k <- length(which) rval <- function(node) { tid <- id_node(node) nobs <- .nobs_party(obj, id = tid) ## set up top viewport top_vp <- viewport(layout = grid.layout(nrow = k, ncol = 2, widths = unit(c(ylines, 1), c("lines", "null")), heights = unit(k, "null")), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_mvar", tid, sep = "")) pushViewport(top_vp) grid.rect(gp = gpar(fill = bg, col = 0)) ## main title if (is.null(mainlab)) { mainlab <- if(id) { function(id, nobs) sprintf("Node %s (n = %s)", id, nobs) } else { function(id, nobs) sprintf("n = %s", nobs) } } if (is.function(mainlab)) { mainlab <- mainlab(tid, nobs) } for(i in 1L:k) { tmp <- obj tmp$fitted[["(response)"]] <- y[,which[i]] if(varlab) { nm <- names(y)[which[i]] if(i == 1L) nm <- paste(mainlab, nm, sep = ": ") } else { nm <- if(i == 1L) mainlab else "" } pfun <- switch(sapply(y, class)[which[i]], "Surv" = node_surv(tmp, id = id, mainlab = nm, ...), "factor" = node_barplot(tmp, id = id, mainlab = nm, ...), "ordered" = node_barplot(tmp, id = id, mainlab = nm, ...), node_boxplot(tmp, id = id, mainlab = nm, ...)) ## select panel plot_vpi <- viewport(layout.pos.col = 2L, layout.pos.row = i) pushViewport(plot_vpi) ## call panel function pfun(node) if(pop) popViewport() else upViewport() } if(pop) popViewport() else upViewport() } return(rval) } class(node_mvar) <- "grapcon_generator" partykit/R/pmmlTreeModel.R0000644000176200001440000002623114172230000015204 0ustar liggesuserspmmlTreeModel <- function(file, ...) { stopifnot(requireNamespace("XML")) as.party(XML::xmlRoot(XML::xmlTreeParse(file))) } as.party.XMLNode <- function(obj, ...) { stopifnot(requireNamespace("XML")) ## check whether XML specifies a TreeModel stopifnot(c("DataDictionary", "TreeModel") %in% names(obj)) if(any(warnx <- c("MiningBuildTask", "TransformationDictionary", "Extension") %in% names(obj))) warning(sprintf("%s not yet implemented", paste(names(obj)[warnx], collapse = ", "))) ## process header information if("Header" %in% names(obj)) { hdr <- obj[["Header"]] h_info <- c(Header = paste(as.character(XML::xmlAttrs(hdr)), collapse = ", ")) if(length(hdr) > 0L) { h_info <- c(h_info, XML::xmlSApply(hdr, function(x) paste(c(as.character(XML::xmlAttrs(x)), XML::xmlValue(x)), collapse = ", ") ) ) } } else { h_info <- NULL } ## parse data dictionary extract_empty_model_frame <- function(x) { ## extract DataDictionary dd <- x[["DataDictionary"]] ## currently we can only look at DataField if(!all(names(dd) == "DataField")) warning("data specifications other than DataField are not yet implemented") ## check columns nc <- as.numeric(XML::xmlAttrs(dd)["numberOfFields"]) if(!is.na(nc)) stopifnot(nc == length(dd)) ## set up data frame (only numeric variables) mf <- as.data.frame(rep(list(1), nc))[0,] names(mf) <- XML::xmlSApply(dd, function(x) XML::xmlAttrs(x)["name"]) ## modify class if necessary for(i in 1:nc) { optype <- XML::xmlAttrs(dd[[i]])["optype"] switch(optype, "categorical" = { mf[[i]] <- factor(integer(0), levels = XML::xmlSApply(dd[[i]], function(x) gsub("&", "&", XML::xmlAttrs(x)["value"], fixed = TRUE))) }, "ordinal" = { mf[[i]] <- factor(integer(0), ordered = TRUE, levels = XML::xmlSApply(dd[[i]], function(x) gsub("&", "&", XML::xmlAttrs(x)["value"], fixed = TRUE))) }, "continuous" = { dataType <- XML::xmlAttrs(dd[[i]])["dataType"] if(dataType == "integer") mf[[i]] <- integer(0) } ) } return(mf) } mf <- extract_empty_model_frame(obj) mf_names <- names(mf) mf_levels <- lapply(mf, levels) ## parse MiningSchema extract_terms <- function(x) { ## extract MiningSchema ms <- x[["TreeModel"]] stopifnot("MiningSchema" %in% names(ms)) ms <- ms[["MiningSchema"]] ## currently we can only look at MiningField if(!all(names(ms) == "MiningField")) warning("MiningField not yet implemented") ## extract variable info vars <- t(XML::xmlSApply(ms, XML::xmlAttrs)) if(sum(vars[,2] == "predicted") > 1) stop("multivariate responses not yet implemented") if(!all(vars[,2] %in% c("predicted", "active", "supplementary"))) warning("not yet implemented") ## set up formula ff <- as.formula(paste(vars[vars[,2] == "predicted",1], "~", paste(vars[vars[,2] != "predicted",1], collapse = " + "))) return(terms(ff)) } trms <- extract_terms(obj) ## parse TreeModel tm <- obj[["TreeModel"]] tm_info <- c(XML::xmlAttrs(tm), h_info) ## check response stopifnot(tm_info["functionName"] %in% c("classification", "regression")) mf_response <- mf[[deparse(attr(trms, "variables")[[2L]])]] if(tm_info["functionName"] == "classification") stopifnot(inherits(mf_response, "factor")) if(tm_info["functionName"] == "regression") stopifnot(is.numeric(mf_response)) ## convenience functions for parsing nodes is_terminal <- function(xnode) !("Node" %in% names(xnode)) is_root <- function(xnode) "True" %in% names(xnode) n_kids <- function(xnode) sum("Node" == names(xnode)) n_obs <- function(xnode) as.numeric(XML::xmlAttrs(xnode)["recordCount"]) has_surrogates <- function(x) { ns <- sum(c("SimplePredicate", "SimpleSetPredicate", "CompoundPredicate") %in% names(x)) if(ns != 1) stop("invalid PMML") if("CompoundPredicate" %in% names(x)) { if(identical(as.vector(XML::xmlAttrs(x[["CompoundPredicate"]])["booleanOperator"]), "surrogate")) return(TRUE) else return(FALSE) } else { return(FALSE) } } has_single_splits <- function(x) { wi <- which(names(x) %in% c("SimplePredicate", "SimpleSetPredicate", "CompoundPredicate")) sapply(wi, function(i) { if(names(x)[i] %in% c("SimplePredicate", "SimpleSetPredicate")) return(TRUE) if(identical(as.vector(XML::xmlAttrs(x[[i]])["booleanOperator"]), "or")) return(TRUE) stop("CompoundPredicate not yet implemented") }) } n_splits <- function(xnode) { wi <- which("Node" == names(xnode)) rval <- unique(sapply(wi, function(i) { xnodei <- if(has_surrogates(xnode[[i]])) xnode[[i]][["CompoundPredicate"]] else xnode[[i]] rval <- has_single_splits(xnodei) if(!all(rval)) stop("invalid PMML") sum(rval) })) if(length(rval) > 1) stop("invalid PMML") return(rval) } kid_ids <- function(xnode) { wi <- which("Node" == names(xnode)) rval <- sapply(wi, function(j) { as.vector(XML::xmlAttrs(xnode[[j]])["id"]) }) } get_pred <- function(xnode) { pred <- as.vector(XML::xmlAttrs(xnode)["score"]) if(is.na(pred)) return(NULL) if(is.numeric(mf_response)) as.numeric(pred) else factor(pred, levels = levels(mf_response)) } get_dist <- function(xnode) { wi <- which("ScoreDistribution" == names(xnode)) if(length(wi) < 1) return(NULL) rval <- sapply(wi, function(i) as.numeric(XML::xmlAttrs(xnode[[i]])["recordCount"])) names(rval) <- sapply(wi, function(i) XML::xmlAttrs(xnode[[i]])["value"]) if(inherits(mf_response, "factor")) rval <- rval[levels(mf_response)] return(rval) } get_error <- function(xnode) { if(tm_info["functionName"] != "classification") return(NULL) tab <- get_dist(xnode) if(is.null(tab)) return(NULL) c("%" = sum(100 * prop.table(tab)[names(tab) != get_pred(xnode)])) } get_extension <- function(xnode) { if(!("Extension" %in% names(xnode))) return(NULL) if(length(xnode[["Extension"]]) > 1) warning("currently only one Extension allowed") rval <- XML::xmlApply(xnode[["Extension"]][[1]], XML::xmlAttrs) names(rval) <- NULL rval <- unlist(rval) to_numeric <- function(x) { y <- suppressWarnings(as.numeric(x)) if(!is.null(y) && !is.na(y)) y else x } sapply(rval, to_numeric) } node_info <- function(xnode) list(prediction = get_pred(xnode), n = n_obs(xnode), error = get_error(xnode), distribution = get_dist(xnode), extension = get_extension(xnode)) get_split_prob <- function(xnode) { rval <- rep(0, n_kids(xnode)) wi <- XML::xmlAttrs(xnode)["defaultChild"] if(is.na(wi)) rval <- NULL else rval[which(kid_ids(xnode) == wi)] <- 1 return(rval) } get_split <- function(xnode, i, surrogates) { wi <- which("Node" == names(xnode)) rval <- sapply(wi, function(j) { nj <- if(surrogates) xnode[[j]][["CompoundPredicate"]] else xnode[[j]] if(any(c("SimplePredicate", "SimpleSetPredicate") %in% names(nj))) { wii <- which(names(nj) %in% c("SimplePredicate", "SimpleSetPredicate"))[i] c("predicateType" = as.vector(names(nj)[wii]), XML::xmlAttrs(nj[[wii]])) } else { wii <- which(names(nj) == "CompoundPredicate")[i] nj <- nj[[wii]] if(!identical(as.vector(XML::xmlAttrs(nj)["booleanOperator"]), "or")) stop("not yet implemented") if(any(names(nj) %in% c("SimpleSetPredicate", "CompoundPredicate"))) stop("not yet implemented") rvali <- sapply(which(names(nj) == "SimplePredicate"), function(j) c("predicateType" = as.vector(names(nj)[j]), XML::xmlAttrs(nj[[j]]))) if(is.null(dim(rvali))) rvali <- matrix(rvali, ncol = 1) stopifnot(length(unique(rvali["predicateType",])) == 1) stopifnot(length(unique(rvali["field",])) == 1) stopifnot(all(rvali["operator",] == "equal")) c("predicateType" = "simpleSetPredicate", "field" = rvali["field", 1], "booleanOperator" = "isIn") } }) stopifnot(length(unique(rval["predicateType",])) == 1) stopifnot(length(unique(rval["field",])) == 1) if(rval["predicateType", 1] == "SimplePredicate") { stopifnot(length(unique(rval["value",])) == 1) if(ncol(rval) != 2) stop("not yet implemented") if(!(identical(as.vector(sort(rval["operator",])), c("greaterThan", "lessOrEqual")) | identical(as.vector(sort(rval["operator",])), c("greaterOrEqual", "lessThan"))) ) stop("not yet implemented") partysplit( varid = which(rval["field", 1] == mf_names), breaks = as.numeric(rval["value", 1]), index = if(substr(rval["operator", 1], 1, 1) != "l") 2:1 else NULL, right = "lessOrEqual" %in% rval["operator",], prob = if(i == 1) get_split_prob(xnode) else NULL ) } else { varid <- which(rval["field", 1] == mf_names) lev <- mf_levels[[varid]] stopifnot(length(lev) > 1) idx <- rep(NA, length(lev)) lab <- lapply(wi, function(j) { nj <- if(surrogates) xnode[[j]][["CompoundPredicate"]] else xnode[[j]] if(any(names(nj) %in% c("SimplePredicate", "SimpleSetPredicate"))) { wii <- which(names(nj) %in% c("SimplePredicate", "SimpleSetPredicate"))[i] ar <- nj[[wii]][["Array"]] stopifnot(XML::xmlAttrs(ar)["type"] == "string") rv <- XML::xmlValue(ar) rv <- gsub(""", "\"", rv, fixed = TRUE) rv <- if(substr(rv, 1, 1) == "\"" & substr(rv, nchar(rv), nchar(rv)) == "\"") { strsplit(substr(rv, 2, nchar(rv) - 1), "\" \"")[[1]] } else { strsplit(rv, " ")[[1]] } stopifnot(length(rv) == as.numeric(XML::xmlAttrs(ar)["n"])) return(rv) } else { wii <- which(names(nj) == "CompoundPredicate")[i] as.vector(XML::xmlSApply(nj[[wii]], function(z) XML::xmlAttrs(z)["value"])) } }) for(j in 1:ncol(rval)) { if(rval["booleanOperator",j] == "isIn") idx[which(lev %in% lab[[j]])] <- j else idx[which(!(lev %in% lab[[j]]))] <- j } stopifnot(all(na.omit(idx) > 0)) if(min(idx, na.rm = TRUE) != 1) stop(sprintf("variable levels (%s) and split labels (%s)", paste(lev, collapse = ", "), paste(sapply(lab, paste, collapse = ", "), collapse = " | "))) partysplit( varid = varid, breaks = NULL, index = as.integer(idx), prob = if(i == 1) get_split_prob(xnode) else NULL ) } } ## function for setting up nodes ## (using global index ii) pmml_node <- function(xnode) { ii <<- ii + 1 if(is_terminal(xnode)) return(partynode(as.integer(ii), info = node_info(xnode) )) wi <- which("Node" == names(xnode)) ns <- n_splits(xnode) nd <- partynode(as.integer(ii), split = get_split(xnode, 1, has_surrogates(xnode[[wi[1]]])), kids = lapply(wi, function(j) pmml_node(xnode[[j]])), surrogates = if(ns < 2) NULL else lapply(2:ns, function(j) get_split(xnode, j, TRUE)), info = node_info(xnode) ) nd } ## set up node ii <- 0 if(is_root(tm[["Node"]])) nd <- pmml_node(tm[["Node"]]) else stop("root node not declared, invalid PMML?") ## set up party ## FIXME: extend info slot? pt <- party(node = nd, data = mf, fitted = NULL, terms = trms, names = NULL, info = tm_info) class(pt) <- c("simpleparty", class(pt)) return(pt) } partykit/R/modelparty.R0000644000176200001440000012160514172230000014617 0ustar liggesusersmob <- function(formula, data, subset, na.action, weights, offset, cluster, fit, control = mob_control(), ...) { ## check fitting function fitargs <- names(formals(fit)) if(!all(c("y", "x", "start", "weights", "offset") %in% fitargs)) { stop("no suitable fitting function specified") } ## augment fitting function (if necessary) if(!all(c("estfun", "object") %in% fitargs)) { afit <- function(y, x = NULL, start = NULL, weights = NULL, offset = NULL, cluster = NULL, ..., estfun = FALSE, object = FALSE) { obj <- if("cluster" %in% fitargs) { fit(y = y, x = x, start = start, weights = weights, offset = offset, cluster = cluster, ...) } else { fit(y = y, x = x, start = start, weights = weights, offset = offset, ...) } list( coefficients = coef(obj), objfun = -as.numeric(logLik(obj)), estfun = if(estfun) sandwich::estfun(obj) else NULL, object = if(object) obj else NULL ) } } else { if("cluster" %in% fitargs) { afit <- fit } else { afit <- function(y, x = NULL, start = NULL, weights = NULL, offset = NULL, cluster = NULL, ..., estfun = FALSE, object = FALSE) { fit(y = y, x = x, start = start, weights = weights, offset = offset, ..., estfun = estfun, object = object) } } } ## call cl <- match.call() if(missing(data)) data <- environment(formula) mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "data", "subset", "na.action", "weights", "offset", "cluster"), names(mf), 0L) mf <- mf[c(1L, m)] mf$drop.unused.levels <- TRUE ## formula FIXME: y ~ . or y ~ x | . oformula <- as.formula(formula) formula <- Formula::as.Formula(formula) if(length(formula)[2L] < 2L) { formula <- Formula::Formula(formula(Formula::as.Formula(formula(formula), ~ 0), rhs = 2L:1L)) xreg <- FALSE } else { if(length(formula)[2L] > 2L) { formula <- Formula::Formula(formula(formula, rhs = 1L:2L)) warning("Formula must not have more than two RHS parts") } xreg <- TRUE } mf$formula <- formula ## evaluate model.frame mf[[1L]] <- quote(stats::model.frame) mf <- eval(mf, parent.frame()) ## extract terms, response, regressor matrix (if any), partitioning variables mt <- terms(formula, data = data) mtY <- terms(formula, data = data, rhs = if(xreg) 1L else 0L) mtZ <- delete.response(terms(formula, data = data, rhs = 2L)) Y <- switch(control$ytype, "vector" = Formula::model.part(formula, mf, lhs = 1L)[[1L]], "matrix" = model.matrix(~ 0 + ., Formula::model.part(formula, mf, lhs = 1L)), "data.frame" = Formula::model.part(formula, mf, lhs = 1L) ) X <- if(!xreg) NULL else switch(control$xtype, "matrix" = model.matrix(mtY, mf), "data.frame" = Formula::model.part(formula, mf, rhs = 1L) ) if(!is.null(X) && ncol(X) < 1L) { X <- NULL xreg <- FALSE } if(xreg) { attr(X, "formula") <- formula(formula, rhs = 1L) attr(X, "terms") <- mtY attr(X, "offset") <- cl$offset attr(X, "xlevels") <- .getXlevels(mtY, mf) } Z <- Formula::model.part(formula, mf, rhs = 2L) n <- nrow(Z) nyx <- length(mf) - length(Z) - as.numeric("(weights)" %in% names(mf)) - as.numeric("(offset)" %in% names(mf)) - as.numeric("(cluster)" %in% names(mf)) varindex <- match(names(Z), names(mf)) ## weights and offset weights <- model.weights(mf) if(is.null(weights)) weights <- 1L if(length(weights) == 1L) weights <- rep.int(weights, n) weights <- as.vector(weights) offset <- if(xreg) model.offset(mf) else NULL cluster <- mf[["(cluster)"]] ## process pruning options (done here because of "n") if(!is.null(control$prune)) { if(is.character(control$prune)) { control$prune <- tolower(control$prune) control$prune <- match.arg(control$prune, c("aic", "bic", "none")) control$prune <- switch(control$prune, "aic" = { function(objfun, df, nobs) (2 * objfun[1L] + 2 * df[1L]) < (2 * objfun[2L] + 2 * df[2L]) }, "bic" = { function(objfun, df, nobs) (2 * objfun[1L] + log(n) * df[1L]) < (2 * objfun[2L] + log(n) * df[2L]) }, "none" = { NULL }) } if(!is.function(control$prune)) { warning("Unknown specification of 'prune'") control$prune <- NULL } } ## grow the actual tree nodes <- mob_partynode(Y = Y, X = X, Z = Z, weights = weights, offset = offset, cluster = cluster, fit = afit, control = control, varindex = varindex, ...) ## compute terminal node number for each observation fitted <- fitted_node(nodes, data = mf) fitted <- data.frame( "(fitted)" = fitted, ## "(response)" = Y, ## probably not really needed check.names = FALSE, row.names = rownames(mf)) if(!identical(weights, rep.int(1L, n))) fitted[["(weights)"]] <- weights if(!is.null(offset)) fitted[["(offset)"]] <- offset if(!is.null(cluster)) fitted[["(cluster)"]] <- cluster ## return party object rval <- party(nodes, data = if(control$model) mf else mf[0,], fitted = fitted, terms = mt, info = list( call = cl, formula = oformula, Formula = formula, terms = list(response = mtY, partitioning = mtZ), fit = afit, control = control, dots = list(...), nreg = max(0L, as.integer(xreg) * (nyx - NCOL(Y)))) ) class(rval) <- c("modelparty", class(rval)) return(rval) } ## set up partynode object mob_partynode <- function(Y, X, Z, weights = NULL, offset = NULL, cluster = NULL, fit, control = mob_control(), varindex = 1L:NCOL(Z), ...) { ## are there regressors? if(missing(X)) X <- NULL xreg <- !is.null(X) n <- nrow(Z) if(is.null(weights)) weights <- 1L if(length(weights) < n) weights <- rep(weights, length.out = n) ## control parameters (used repeatedly) minsize <- control$minsize if(!is.null(minsize) && !is.integer(minsize)) minsize <- as.integer(minsize) verbose <- control$verbose rnam <- c("estfun", "object") terminal <- lapply(rnam, function(x) x %in% control$terminal) inner <- lapply(rnam, function(x) x %in% control$inner) names(terminal) <- names(inner) <- rnam ## convenience functions w2n <- function(w) if(control$caseweights) sum(w) else sum(w > 0) suby <- function(y, index) { if(control$ytype == "vector") y[index] else y[index, , drop = FALSE] } subx <- if(xreg) { function(x, index) { sx <- x[index, , drop = FALSE] attr(sx, "contrasts") <- attr(x, "contrasts") attr(sx, "xlevels") <- attr(x, "xlevels") attr(sx, "formula") <- attr(x, "formula") attr(sx, "terms") <- attr(x, "terms") attr(sx, "offset") <- attr(x, "offset") sx } } else { function(x, index) NULL } subz <- function(z, index) z[index, , drop = FALSE] ## from strucchange root.matrix <- function(X) { if((ncol(X) == 1L)&&(nrow(X) == 1L)) return(sqrt(X)) else { X.eigen <- eigen(X, symmetric = TRUE) if(any(X.eigen$values < 0)) stop("Matrix is not positive semidefinite") sqomega <- sqrt(diag(X.eigen$values)) V <- X.eigen$vectors return(V %*% sqomega %*% t(V)) } } ## core mob_grow_* functions ## variable selection: given model scores, conduct ## all M-fluctuation tests for orderins in z mob_grow_fluctests <- function(estfun, z, weights, obj = NULL, cluster = NULL) { ## set up return values m <- NCOL(z) pval <- rep.int(NA_real_, m) stat <- rep.int(0, m) ifac <- rep.int(FALSE, m) ## variables to test mtest <- if(m <= control$mtry) 1L:m else sort(sample(1L:m, control$mtry)) ## estimating functions (dropping zero weight observations) process <- as.matrix(estfun) ww0 <- (weights > 0) process <- process[ww0, , drop = FALSE] z <- z[ww0, , drop = FALSE] k <- NCOL(process) n <- NROW(process) nobs <- if(control$caseweights && any(weights != 1L)) sum(weights) else n ## scale process process <- process/sqrt(nobs) vcov <- control$vcov if(is.null(obj)) vcov <- "opg" if(vcov != "opg") { bread <- vcov(obj) * nobs } if(vcov != "info") { ## correct scaling of estfun for variance estimate: ## - caseweights=FALSE: weights are integral part of the estfun -> squared in estimate ## - caseweights=TRUE: weights are just a factor in variance estimate -> require division by sqrt(weights) meat <- if(is.null(cluster)) { crossprod(if(control$caseweights) process/sqrt(weights) else process) } else { ## nclus <- length(unique(cluster)) ## nclus / (nclus - 1L) * crossprod(as.matrix(apply(if(control$caseweights) process/sqrt(weights) else process, 2L, tapply, as.numeric(cluster), sum))) } } J12 <- root.matrix(switch(vcov, "opg" = chol2inv(chol(meat)), "info" = bread, "sandwich" = bread %*% meat %*% bread )) process <- t(J12 %*% t(process)) ## NOTE: loses column names ## select parameters to test if(!is.null(control$parm)) { if(is.character(control$parm)) colnames(process) <- colnames(estfun) process <- process[, control$parm, drop = FALSE] } k <- NCOL(process) ## get critical values for supLM statistic from <- if(control$trim > 1) control$trim else ceiling(nobs * control$trim) from <- max(from, minsize) to <- nobs - from lambda <- ((nobs - from) * to)/(from * (nobs - to)) beta <- mob_beta_suplm logp.supLM <- function(x, k, lambda) { if(k > 40L) { ## use Estrella (2003) asymptotic approximation logp_estrella2003 <- function(x, k, lambda) -lgamma(k/2) + k/2 * log(x/2) - x/2 + log(abs(log(lambda) * (1 - k/x) + 2/x)) ## FIXME: Estrella only works well for large enough x ## hence require x > 1.5 * k for Estrella approximation and ## use an ad hoc interpolation for larger p-values p <- ifelse(x <= 1.5 * k, (x/(1.5 * k))^sqrt(k) * logp_estrella2003(1.5 * k, k, lambda), logp_estrella2003(x, k, lambda)) } else { ## use Hansen (1997) approximation nb <- ncol(beta) - 1L tau <- if(lambda < 1) lambda else 1/(1 + sqrt(lambda)) beta <- beta[(((k - 1) * 25 + 1):(k * 25)),] dummy <- beta[,(1L:nb)] %*% x^(0:(nb-1)) dummy <- dummy * (dummy > 0) pp <- pchisq(dummy, beta[,(nb+1)], lower.tail = FALSE, log.p = TRUE) if(tau == 0.5) { p <- pchisq(x, k, lower.tail = FALSE, log.p = TRUE) } else if(tau <= 0.01) { p <- pp[25L] } else if(tau >= 0.49) { p <- log((exp(log(0.5 - tau) + pp[1L]) + exp(log(tau - 0.49) + pchisq(x, k, lower.tail = FALSE, log.p = TRUE))) * 100) ## if p becomes so small that 'correct' weighted averaging does not work, resort to 'naive' averaging if(!is.finite(p)) p <- mean(c(pp[1L], pchisq(x, k, lower.tail = FALSE, log.p = TRUE))) } else { taua <- (0.51 - tau) * 50 tau1 <- floor(taua) p <- log(exp(log(tau1 + 1 - taua) + pp[tau1]) + exp(log(taua-tau1) + pp[tau1 + 1L])) ## if p becomes so small that 'correct' weighted averaging does not work, resort to 'naive' averaging if(!is.finite(p)) p <- mean(pp[tau1 + 0L:1L]) } } return(as.vector(p)) } ## compute statistic and p-value for each ordering for(i in mtest) { zi <- z[,i] if(length(unique(zi)) < 2L) next if(is.factor(zi)) { oi <- order(zi) proci <- process[oi, , drop = FALSE] ifac[i] <- TRUE iord <- is.ordered(zi) & (control$ordinal != "chisq") ## order partitioning variable zi <- zi[oi] # re-apply factor() added to drop unused levels zi <- factor(zi, levels = unique(zi)) # compute segment weights segweights <- if(control$caseweights) tapply(weights[oi], zi, sum) else table(zi) segweights <- as.vector(segweights)/nobs # compute statistic only if at least two levels are left if(length(segweights) < 2L) { stat[i] <- 0 pval[i] <- NA_real_ } else if(iord) { proci <- apply(proci, 2L, cumsum) tt0 <- head(cumsum(table(zi)), -1L) tt <- head(cumsum(segweights), -1L) if(control$ordinal == "max") { stat[i] <- max(abs(proci[tt0, ] / sqrt(tt * (1-tt)))) pval[i] <- log(as.numeric(1 - mvtnorm::pmvnorm( lower = -stat[i], upper = stat[i], mean = rep(0, length(tt)), sigma = outer(tt, tt, function(x, y) sqrt(pmin(x, y) * (1 - pmax(x, y)) / ((pmax(x, y) * (1 - pmin(x, y)))))) )^k)) } else { proci <- rowSums(proci^2) stat[i] <- max(proci[tt0] / (tt * (1-tt))) pval[i] <- log(strucchange::ordL2BB(segweights, nproc = k, nrep = control$nrep)$computePval(stat[i], nproc = k)) } } else { stat[i] <- sum(sapply(1L:k, function(j) (tapply(proci[,j], zi, sum)^2)/segweights)) pval[i] <- pchisq(stat[i], k*(length(levels(zi))-1), log.p = TRUE, lower.tail = FALSE) } } else { oi <- if(control$breakties) { mm <- sort(unique(zi)) mm <- ifelse(length(mm) > 1L, min(diff(mm))/10, 1) order(zi + runif(length(zi), min = -mm, max = +mm)) } else { order(zi) } proci <- process[oi, , drop = FALSE] proci <- apply(proci, 2L, cumsum) tt0 <- if(control$caseweights && any(weights != 1L)) cumsum(weights[oi]) else 1:n from_to <- tt0 >= from & tt0 <= to stat[i] <- if(sum(from_to) > 0L) { xx <- rowSums(proci^2) xx <- xx[from_to] tt <- tt0[from_to]/nobs max(xx/(tt * (1 - tt))) } else { 0 } pval[i] <- if(sum(from_to) > 0L) logp.supLM(stat[i], k, lambda) else NA } } ## select variable with minimal p-value best <- which.min(pval) if(length(best) < 1L) best <- NA rval <- list(pval = exp(pval), stat = stat, best = best) names(rval$pval) <- names(z) names(rval$stat) <- names(z) if(!all(is.na(rval$best))) names(rval$best) <- names(z)[rval$best] return(rval) } ### split in variable zselect, either ordered (numeric or ordinal) or nominal mob_grow_findsplit <- function(y, x, zselect, weights, offset, cluster, ...) { ## process minsize (to minimal number of observations) if(minsize > 0.5 & minsize < 1) minsize <- 1 - minsize if(minsize < 0.5) minsize <- ceiling(w2n(weights) * minsize) if(is.numeric(zselect)) { ## for numerical variables uz <- sort(unique(zselect)) if (length(uz) == 0L) stop("Cannot find admissible split point in partitioning variable") ## if starting values are not reused then the applyfun() is used for determining the split if(control$restart) { get_dev <- function(i) { zs <- zselect <= uz[i] if(w2n(weights[zs]) < minsize || w2n(weights[!zs]) < minsize) { return(Inf) } else { fit_left <- fit(y = suby(y, zs), x = subx(x, zs), start = NULL, weights = weights[zs], offset = offset[zs], cluster = cluster[zs], ...) fit_right <- fit(y = suby(y, !zs), x = subx(x, !zs), start = NULL, weights = weights[!zs], offset = offset[!zs], cluster = cluster[!zs], ...) return(fit_left$objfun + fit_right$objfun) } } dev <- unlist(control$applyfun(1L:length(uz), get_dev)) } else { ## alternatively use for() loop to go through all splits sequentially ## and reuse previous parameters as starting values dev <- vector(mode = "numeric", length = length(uz)) start_left <- NULL start_right <- NULL for(i in 1L:length(uz)) { zs <- zselect <= uz[i] if(control$restart || !identical(names(start_left), names(start_right)) || !identical(length(start_left), length(start_right))) { start_left <- NULL start_right <- NULL } if(w2n(weights[zs]) < minsize || w2n(weights[!zs]) < minsize) { dev[i] <- Inf } else { fit_left <- fit(y = suby(y, zs), x = subx(x, zs), start = start_left, weights = weights[zs], offset = offset[zs], cluster = cluster[zs], ...) fit_right <- fit(y = suby(y, !zs), x = subx(x, !zs), start = start_right, weights = weights[!zs], offset = offset[!zs], cluster = cluster[!zs], ...) start_left <- fit_left$coefficients start_right <- fit_right$coefficients dev[i] <- fit_left$objfun + fit_right$objfun } } } ## maybe none of the possible splits is admissible if(all(!is.finite(dev))) { split <- list( breaks = NULL, index = NULL ) } else { split <- list( breaks = if(control$numsplit == "center") { as.double(mean(uz[which.min(dev) + 0L:1L])) } else { as.double(uz[which.min(dev)]) }, index = NULL ) } } else { if(!is.ordered(zselect) & control$catsplit == "multiway") { return(list(breaks = NULL, index = seq_along(levels(zselect)))) } ## for categorical variables olevels <- levels(zselect) ## full set of original levels zselect <- factor(zselect) ## omit levels that do not occur in the data al <- mob_grow_getlevels(zselect) get_dev <- function(i) { w <- al[i,] zs <- zselect %in% levels(zselect)[w] if(w2n(weights[zs]) < minsize || w2n(weights[!zs]) < minsize) { return(Inf) } else { if(nrow(al) == 1L) 1 else { fit_left <- fit(y = suby(y, zs), x = subx(x, zs), start = NULL, weights = weights[zs], offset = offset[zs], cluster = cluster[zs], ...) fit_right <- fit(y = suby(y, !zs), x = subx(x, !zs), start = NULL, weights = weights[!zs], offset = offset[!zs], cluster = cluster[zs], ...) fit_left$objfun + fit_right$objfun } } } dev <- unlist(control$applyfun(1L:nrow(al), get_dev)) if(all(!is.finite(dev))) { split <- list( breaks = NULL, index = NULL ) } else { if(is.ordered(zselect)) { ## map back to set of full original levels split <- list( breaks = match(levels(zselect)[which.min(dev)], olevels), index = NULL ) } else { ## map back to set of full original levels ix <- structure(rep.int(NA_integer_, length(olevels)), .Names = olevels) ix[colnames(al)] <- !al[which.min(dev),] ix <- as.integer(ix) + 1L split <- list( breaks = NULL, index = ix ) } } } return(split) } ## grow tree by combining fluctuation tests for variable selection ## and split selection recursively mob_grow <- function(id = 1L, y, x, z, weights, offset, cluster, ...) { if(verbose) { if(id == 1L) cat("\n") cat(sprintf("-- Node %i %s\n", id, paste(rep("-", 32 - floor(log10(id)) + 1L), collapse = ""))) cat(sprintf("Number of observations: %s\n", w2n(weights))) ## cat(sprintf("Depth: %i\n", depth)) } ## fit model mod <- fit(y, x, weights = weights, offset = offset, cluster = cluster, ..., estfun = TRUE, object = terminal$object | control$vcov == "info") mod$test <- NULL mod$nobs <- w2n(weights) mod$p.value <- NULL ## set default for minsize if not specified if(is.null(minsize)) minsize <<- as.integer(ceiling(10L * length(mod$coefficients)/NCOL(y))) ## if too few observations or maximum depth: no split = return terminal node TERMINAL <- FALSE if(w2n(weights) < 2 * minsize) { if(verbose) cat(sprintf("Too few observations, stop splitting (minsize = %s)\n\n", minsize)) TERMINAL <- TRUE } if(depth >= control$maxdepth) { if(verbose) cat(sprintf("Maximum depth reached, stop splitting (maxdepth = %s)\n\n", control$maxdepth)) TERMINAL <- TRUE } if(TERMINAL) { return(partynode(id = id, info = mod)) } ## conduct all parameter instability tests test <- if(is.null(mod$estfun)) NULL else try(mob_grow_fluctests(mod$estfun, z, weights, mod$object, cluster)) if(!is.null(test) && !inherits(test, "try-error")) { if(control$bonferroni) { pval1 <- pmin(1, sum(!is.na(test$pval)) * test$pval) pval2 <- 1 - (1 - test$pval)^sum(!is.na(test$pval)) test$pval <- ifelse(!is.na(test$pval) & (test$pval > 0.001), pval2, pval1) } best <- test$best TERMINAL <- is.na(best) || test$pval[best] > control$alpha mod$p.value <- as.numeric(test$pval[best]) if (verbose) { cat("\nParameter instability tests:\n") print(rbind(statistic = test$stat, p.value = test$pval)) cat(sprintf("\nBest splitting variable: %s", names(test$stat)[best])) cat(sprintf("\nPerform split? %s", ifelse(TERMINAL, "no\n\n", "yes\n"))) } } else { if(verbose && inherits(test, "try-error")) cat("Parameter instability tests failed\n\n") TERMINAL <- TRUE test <- list(stat = NA, pval = NA) } ## update model information mod$test <- rbind("statistic" = test$stat, "p.value" = test$pval) if(TERMINAL) { return(partynode(id = id, info = mod)) } else { zselect <- z[[best]] sp <- mob_grow_findsplit(y, x, zselect, weights, offset, cluster, ...) ## split successful? if(is.null(sp$breaks) & is.null(sp$index)) { if(verbose) cat(sprintf("No admissable split found in %s\n\n", sQuote(names(test$stat)[best]))) return(partynode(id = id, info = mod)) } else { sp <- partysplit(as.integer(best), breaks = sp$breaks, index = sp$index) if(verbose) cat(sprintf("Selected split: %s\n\n", paste(character_split(sp, data = z)$levels, collapse = " | "))) } } ## actually split the data kidids <- kidids_split(sp, data = z) ## set-up all daugther nodes depth <<- depth + 1L kids <- vector(mode = "list", length = max(kidids)) for(kidid in 1L:max(kidids)) { ## select obs for current next node nxt <- kidids == kidid ## get next node id if(kidid > 1L) { myid <- max(nodeids(kids[[kidid - 1L]])) } else { myid <- id } ## start recursion on this daugther node kids[[kidid]] <- mob_grow(id = myid + 1L, suby(y, nxt), subx(x, nxt), subz(z, nxt), weights[nxt], offset[nxt], cluster[nxt], ...) } depth <<- depth - 1L ## shift split varid from z to mf sp$varid <- as.integer(varindex[sp$varid]) ## return nodes return(partynode(id = id, split = sp, kids = kids, info = mod)) } mob_prune <- function(node) { ## turn node to list nd <- as.list(node) ## if no pruning selected if(is.null(control$prune)) return(nd) ## node information (IDs, kids, ...) id <- seq_along(nd) kids <- lapply(nd, "[[", "kids") tmnl <- sapply(kids, is.null) ## check nodes that only have terminal kids check <- sapply(id, function(i) !tmnl[i] && all(tmnl[kids[[i]]])) while(any(check)) { ## pruning node information pnode <- which(check) objfun <- sapply(nd, function(x) x$info$objfun) pok <- sapply(pnode, function(i) control$prune( objfun = c(objfun[i], sum(objfun[kids[[i]]])), df = c(length(nd[[1]]$info$coefficients), length(kids[[i]]) * length(nd[[1]]$info$coefficients) + as.integer(control$dfsplit)), nobs = c(nd[[i]]$info$nobs, n) )) ## do any nodes need pruning? pnode <- pnode[pok] if(length(pnode) < 1L) break ## prune nodes and relabel IDs pkids <- sort(unlist(sapply(pnode, function(i) nd[[i]]$kids))) for(i in id) { nd[[i]]$kids <- if(nd[[i]]$id %in% pnode || is.null(kids[[i]])) { NULL } else { nd[[i]]$kids - sapply(kids[[i]], function(x) sum(pkids < x)) } } nd[pkids] <- NULL id <- seq_along(nd) for(i in id) nd[[i]]$id <- i ## node information kids <- lapply(nd, "[[", "kids") tmnl <- sapply(kids, is.null) check <- sapply(id, function(i) !tmnl[i] && all(tmnl[kids[[i]]])) } ## return pruned list return(nd) } ## grow tree depth <- 1L nodes <- mob_grow(id = 1L, Y, X, Z, weights, offset, cluster, ...) ## prune tree if(verbose && !is.null(control$prune)) cat("-- Post-pruning ---------------------------\n") nodes <- mob_prune(nodes) for(i in seq_along(nodes)) { if(is.null(nodes[[i]]$kids)) { nodes[[i]]$split <- NULL if(!terminal$estfun) nodes[[i]]$info$estfun <- NULL if(!terminal$object) nodes[[i]]$info$object <- NULL } else { if(!inner$estfun) nodes[[i]]$info$estfun <- NULL if(!inner$object) nodes[[i]]$info$object <- NULL } } ## return as partynode as.partynode(nodes) } ## determine all possible splits for a factor, both nominal and ordinal mob_grow_getlevels <- function(z) { nl <- nlevels(z) if(inherits(z, "ordered")) { indx <- diag(nl) indx[lower.tri(indx)] <- 1 indx <- indx[-nl, , drop = FALSE] rownames(indx) <- levels(z)[-nl] } else { mi <- 2^(nl - 1L) - 1L indx <- matrix(0, nrow = mi, ncol = nl) for (i in 1L:mi) { ii <- i for (l in 1L:nl) { indx[i, l] <- ii %% 2L ii <- ii %/% 2L } } rownames(indx) <- apply(indx, 1L, function(x) paste(levels(z)[x > 0], collapse = "+")) } colnames(indx) <- as.character(levels(z)) storage.mode(indx) <- "logical" indx } ## control splitting parameters mob_control <- function(alpha = 0.05, bonferroni = TRUE, minsize = NULL, maxdepth = Inf, mtry = Inf, trim = 0.1, breakties = FALSE, parm = NULL, dfsplit = TRUE, prune = NULL, restart = TRUE, verbose = FALSE, caseweights = TRUE, ytype = "vector", xtype = "matrix", terminal = "object", inner = terminal, model = TRUE, numsplit = "left", catsplit = "binary", vcov = "opg", ordinal = "chisq", nrep = 10000, minsplit = minsize, minbucket = minsize, applyfun = NULL, cores = NULL) { ## transform defaults if(missing(minsize) & !missing(minsplit)) minsize <- minsplit if(missing(minsize) & !missing(minbucket)) minsize <- minbucket ## no mtry if infinite or non-positive if(is.finite(mtry)) { mtry <- if(mtry < 1L) Inf else as.integer(mtry) } ## data types for formula processing ytype <- match.arg(ytype, c("vector", "data.frame", "matrix")) xtype <- match.arg(xtype, c("data.frame", "matrix")) ## what to store in inner/terminal nodes if(!is.null(terminal)) terminal <- as.vector(sapply(terminal, match.arg, c("estfun", "object"))) if(!is.null(inner)) inner <- as.vector(sapply(inner, match.arg, c("estfun", "object"))) ## how to split and how to select splitting variables numsplit <- match.arg(tolower(numsplit), c("left", "center", "centre")) if(numsplit == "centre") numsplit <- "center" catsplit <- match.arg(tolower(catsplit), c("binary", "multiway")) vcov <- match.arg(tolower(vcov), c("opg", "info", "sandwich")) ordinal <- match.arg(tolower(ordinal), c("l2", "max", "chisq")) ## apply infrastructure for determining split points if(is.null(applyfun)) { applyfun <- if(is.null(cores)) { lapply } else { function(X, FUN, ...) parallel::mclapply(X, FUN, ..., mc.cores = cores) } } ## return list with all options rval <- list(alpha = alpha, bonferroni = bonferroni, minsize = minsize, maxdepth = maxdepth, mtry = mtry, trim = ifelse(is.null(trim), minsize, trim), breakties = breakties, parm = parm, dfsplit = dfsplit, prune = prune, restart = restart, verbose = verbose, caseweights = caseweights, ytype = ytype, xtype = xtype, terminal = terminal, inner = inner, model = model, numsplit = numsplit, catsplit = catsplit, vcov = vcov, ordinal = ordinal, nrep = nrep, applyfun = applyfun) return(rval) } ## methods concerning call/formula/terms/etc. ## (default methods work for terms and update) formula.modelparty <- function(x, extended = FALSE, ...) if(extended) x$info$Formula else x$info$formula getCall.modelparty <- function(x, ...) x$info$call model.frame.modelparty <- function(formula, ...) { mf <- formula$data if(nrow(mf) > 0L) return(mf) dots <- list(...) nargs <- dots[match(c("data", "na.action", "subset"), names(dots), 0L)] mf <- formula$info$call mf <- mf[c(1L, match(c("formula", "data", "subset", "na.action"), names(mf), 0L))] mf$drop.unused.levels <- TRUE mf[[1L]] <- quote(stats::model.frame) mf[names(nargs)] <- nargs if(is.null(env <- environment(formula$info$terms))) env <- parent.frame() mf$formula <- Formula::Formula(as.formula(mf$formula)) eval(mf, env) } weights.modelparty <- function(object, ...) { fit <- object$fitted ww <- if(!is.null(w <- fit[["(weights)"]])) w else rep.int(1L, NROW(fit)) structure(ww, .Names = rownames(fit)) } ## methods concerning model/parameters/loglik/etc. coef.modelparty <- function(object, node = NULL, drop = TRUE, ...) { if(is.null(node)) node <- nodeids(object, terminal = TRUE) cf <- do.call("rbind", nodeapply(object, ids = node, FUN = function(n) info_node(n)$coefficients)) if(drop) drop(cf) else cf } refit.modelparty <- function(object, node = NULL, drop = TRUE, ...) { ## by default use all ids if(is.null(node)) node <- nodeids(object) ## estimated coefficients cf <- nodeapply(object, ids = node, FUN = function(n) info_node(n)$coefficients) ## model.frame mf <- model.frame(object) weights <- weights(object) offset <- model.offset(mf) cluster <- mf[["(cluster)"]] ## fitted ids fitted <- object$fitted[["(fitted)"]] ## response variables Y <- switch(object$info$control$ytype, "vector" = Formula::model.part(object$info$Formula, mf, lhs = 1L)[[1L]], "matrix" = model.matrix(~ 0 + ., Formula::model.part(object$info$Formula, mf, lhs = 1L)), "data.frame" = Formula::model.part(object$info$Formula, mf, lhs = 1L) ) hasx <- object$info$nreg >= 1L | attr(object$info$terms$response, "intercept") > 0L X <- if(!hasx) NULL else switch(object$info$control$xtype, "matrix" = model.matrix(object$info$terms$response, mf), "data.frame" = Formula::model.part(object$info$Formula, mf, rhs = 1L) ) if(!is.null(X)) { attr(X, "formula") <- formula(object$info$Formula, rhs = 1L) attr(X, "terms") <- object$info$terms$response attr(X, "offset") <- object$info$call$offset } suby <- function(y, index) { if(object$info$control$ytype == "vector") y[index] else y[index, , drop = FALSE] } subx <- if(hasx) { function(x, index) { sx <- x[index, , drop = FALSE] attr(sx, "contrasts") <- attr(x, "contrasts") attr(sx, "xlevels") <- attr(x, "xlevels") attr(sx, "formula") <- attr(x, "formula") attr(sx, "terms") <- attr(x, "terms") attr(sx, "offset") <- attr(x, "offset") sx } } else { function(x, index) NULL } ## fitting function afit <- object$info$fit ## refit rval <- lapply(seq_along(node), function(i) { ix <- fitted %in% nodeids(object, from = node[i], terminal = TRUE) args <- list(y = suby(Y, ix), x = subx(X, ix), start = cf[[i]], weights = weights[ix], offset = offset[ix], cluster = cluster[ix], object = TRUE) args <- c(args, object$info$dots) do.call("afit", args)$object }) names(rval) <- node ## drop? if(drop & length(rval) == 1L) rval <- rval[[1L]] ## return return(rval) } apply_to_models <- function(object, node = NULL, FUN = NULL, drop = FALSE, ...) { if(is.null(node)) node <- nodeids(object, terminal = FALSE) if(is.null(FUN)) FUN <- function(object, ...) object rval <- if("object" %in% object$info$control$terminal) { nodeapply(object, node, function(n) FUN(info_node(n)$object)) } else { lapply(refit.modelparty(object, node, drop = FALSE), FUN) } names(rval) <- node if(drop & length(node) == 1L) rval <- rval[[1L]] return(rval) } logLik.modelparty <- function(object, dfsplit = NULL, ...) { if(is.null(dfsplit)) dfsplit <- object$info$control$dfsplit dfsplit <- as.integer(dfsplit) ids <- nodeids(object, terminal = TRUE) ll <- apply_to_models(object, node = ids, FUN = logLik) dfsplit <- dfsplit * (length(object) - length(ll)) structure( sum(as.numeric(ll)), df = sum(sapply(ll, function(x) attr(x, "df"))) + dfsplit, nobs = nobs(object), class = "logLik" ) } nobs.modelparty <- function(object, ...) { sum(unlist(nodeapply(object, nodeids(object, terminal = TRUE), function(n) info_node(n)$nobs ))) } deviance.modelparty <- function(object, ...) { ids <- nodeids(object, terminal = TRUE) dev <- apply_to_models(object, node = ids, FUN = deviance) sum(unlist(dev)) } summary.modelparty <- function(object, node = NULL, ...) { ids <- if(is.null(node)) nodeids(object, terminal = TRUE) else node rval <- apply_to_models(object, node = ids, FUN = summary) if(length(ids) == 1L) rval[[1L]] else rval } sctest.modelparty <- function(object, node = NULL, ...) { ids <- if(is.null(node)) nodeids(object, terminal = FALSE) else node rval <- nodeapply(object, ids, function(n) info_node(n)$test) names(rval) <- ids if(length(ids) == 1L) rval[[1L]] else rval } print.modelparty <- function(x, node = NULL, FUN = NULL, digits = getOption("digits") - 4L, header = TRUE, footer = TRUE, title = NULL, objfun = "", ...) { digits <- max(c(0, digits)) if(objfun != "") objfun <- paste(" (", objfun, ")", sep = "") if(is.null(title)) title <- sprintf("Model-based recursive partitioning (%s)", deparse(x$info$call$fit)) if(is.null(node)) { header_panel <- if(header) function(party) { c(title, "", "Model formula:", deparse(party$info$formula), "", "Fitted party:", "") } else function(party) "" footer_panel <- if(footer) function(party) { n <- width(party) n <- format(c(length(party) - n, n)) info <- nodeapply(x, ids = nodeids(x, terminal = TRUE), FUN = function(n) c(length(info_node(n)$coefficients), info_node(n)$objfun)) k <- mean(sapply(info, "[", 1L)) of <- format(sum(sapply(info, "[", 2L)), digits = getOption("digits")) c("", paste("Number of inner nodes: ", n[1L]), paste("Number of terminal nodes:", n[2L]), paste("Number of parameters per node:", format(k, digits = getOption("digits"))), paste("Objective function", objfun, ": ", of, sep = ""), "") } else function (party) "" if(is.null(FUN)) { FUN <- function(x) c(sprintf(": n = %s", x$nobs), capture.output(print(x$coefficients))) } terminal_panel <- function(node) formatinfo_node(node, default = "*", prefix = NULL, FUN = FUN) print.party(x, terminal_panel = terminal_panel, header_panel = header_panel, footer_panel = footer_panel, ...) } else { node <- as.integer(node) info <- nodeapply(x, ids = node, FUN = function(n) info_node(n)[c("coefficients", "objfun", "test")]) for(i in seq_along(node)) { if(i == 1L) { cat(paste(title, "\n", collapse = "")) } else { cat("\n") } cat(sprintf("-- Node %i --\n", node[i])) cat("\nEstimated parameters:\n") print(info[[i]]$coefficients) cat(sprintf("\nObjective function:\n%s\n", format(info[[i]]$objfun))) cat("\nParameter instability tests:\n") print(info[[i]]$test) } } invisible(x) } predict.modelparty <- function(object, newdata = NULL, type = "node", ...) { ## predicted node ids node <- predict.party(object, newdata = newdata) if(identical(type, "node")) return(node) ## obtain fitted model objects ids <- sort(unique(as.integer(node))) mod <- apply_to_models(object, node = ids) ## obtain predictions pred <- if(is.character(type)) { function(object, newdata = NULL, ...) predict(object, newdata = newdata, type = type, ...) } else { type } if("newdata" %in% names(formals(pred))) { ix <- lapply(seq_along(ids), function(i) which(node == ids[i])) preds <- lapply(seq_along(ids), function(i) pred(mod[[i]], newdata = newdata[ix[[i]], , drop = FALSE], ...)) nc <- NCOL(preds[[1L]]) rval <- if(nc > 1L) { matrix(0, nrow = length(node), ncol = nc, dimnames = list(names(node), colnames(preds[[1L]]))) } else { rep(preds[[1L]], length.out = length(node)) } for(i in seq_along(ids)) { if(nc > 1L) { rval[ix[[i]], ] <- preds[[i]] rownames(rval) <- names(node) } else { rval[ix[[i]]] <- preds[[i]] names(rval) <- names(node) } } } else { rval <- lapply(mod, pred, ...) if(NCOL(rval[[1L]]) > 1L) { rval <- do.call("rbind", rval) rownames(rval) <- ids rval <- rval[as.character(node), , drop = FALSE] rownames(rval) <- names(node) rval <- drop(rval) } else { ## provide a c() method for factors locally c.factor <- function(...) { args <- list(...) lev <- levels(args[[1L]]) args[[1L]] <- unclass(args[[1L]]) rval <- do.call("c", args) factor(rval, levels = 1L:length(lev), labels = lev) } rval <- do.call("c", rval) names(rval) <- ids rval <- rval[as.character(node)] names(rval) <- names(node) } } return(rval) } fitted.modelparty <- function(object, ...) { ## fitted nodes node <- predict.party(object, type = "node") ## obtain fitted model objects ids <- nodeids(object, terminal = TRUE) fit <- apply_to_models(object, node = ids, FUN = fitted) nc <- NCOL(fit[[1L]]) rval <- if(nc > 1L) { matrix(0, nrow = length(ids), ncol = nc, dimnames = list(names(node), colnames(fit[[1L]]))) } else { rep(fit[[1L]], length.out = length(node)) } for(i in seq_along(ids)) { if(nc > 1L) { rval[node == ids[i], ] <- fit[[i]] rownames(rval) <- names(node) } else { rval[node == ids[i]] <- fit[[i]] names(rval) <- names(node) } } return(rval) } residuals.modelparty <- function(object, ...) { ## fitted nodes node <- predict.party(object, type = "node") ## obtain fitted model objects ids <- nodeids(object, terminal = TRUE) res <- apply_to_models(object, node = ids, FUN = residuals) nc <- NCOL(res[[1L]]) rval <- if(nc > 1L) { matrix(0, nrow = length(ids), ncol = nc, dimnames = list(names(node), colnames(res[[1L]]))) } else { rep(res[[1L]], length.out = length(node)) } for(i in seq_along(ids)) { if(nc > 1L) { rval[node == ids[i], ] <- res[[i]] rownames(rval) <- names(node) } else { rval[node == ids[i]] <- res[[i]] names(rval) <- names(node) } } return(rval) } plot.modelparty <- function(x, terminal_panel = NULL, FUN = NULL, tp_args = NULL, ...) { if(is.null(terminal_panel)) { if(is.null(FUN)) { FUN <- function(x) { cf <- x$coefficients cf <- matrix(cf, ncol = 1, dimnames = list(names(cf), "")) c(sprintf("n = %s", x$nobs), "Estimated parameters:", strwrap(capture.output(print(cf, digits = 4L))[-1L])) } } terminal_panel <- do.call("node_terminal", c(list(obj = x, FUN = FUN), tp_args)) tp_args <- NULL } plot.party(x, terminal_panel = terminal_panel, tp_args = tp_args, ...) } ### AIC-based pruning prune.lmtree <- function(tree, type = "AIC", ...) { ## special handling for AIC and BIC ptype <- pmatch(tolower(type), c("aic", "bic"), nomatch = 0L) if(ptype == 1L) { type <- function(objfun, df, nobs) (nobs[1L] * log(objfun[1L]) + 2 * df[1L]) < (nobs[1L] * log(objfun[2L]) + 2 * df[2L]) } else if(ptype == 2L) { type <- function(objfun, df, nobs) (nobs[1L] * log(objfun[1L]) + log(nobs[2L]) * df[1L]) < (nobs[1L] * log(objfun[2L]) + log(nobs[2L]) * df[2L]) } NextMethod() } prune.modelparty <- function(tree, type = "AIC", ...) { ## prepare pruning function if(is.character(type)) { type <- tolower(type) type <- match.arg(type, c("aic", "bic", "none")) type <- switch(type, "aic" = { function(objfun, df, nobs) (2 * objfun[1L] + 2 * df[1L]) < (2 * objfun[2L] + 2 * df[2L]) }, "bic" = { function(objfun, df, nobs) (2 * objfun[1L] + log(n) * df[1L]) < (2 * objfun[2L] + log(n) * df[2L]) }, "none" = { NULL } ) } if(!is.function(type)) { warning("Unknown specification of 'type'") return(tree) } ## degrees of freedom dfsplit <- tree$info$control$dfsplit ## turn node to list node <- tree$node nd <- as.list(node) ## node information (IDs, kids, ...) id <- seq_along(nd) kids <- lapply(nd, "[[", "kids") tmnl <- sapply(kids, is.null) ## check nodes that only have terminal kids check <- sapply(id, function(i) !tmnl[i] && all(tmnl[kids[[i]]])) while(any(check)) { ## pruning node information pnode <- which(check) objfun <- sapply(nd, function(x) x$info$objfun) n <- nrow(tree$fitted) pok <- sapply(pnode, function(i) type( objfun = c(objfun[i], sum(objfun[kids[[i]]])), df = c(length(nd[[1]]$info$coefficients), length(kids[[i]]) * length(nd[[1]]$info$coefficients) + as.integer(dfsplit)), nobs = c(nd[[i]]$info$nobs, n) )) ## do any nodes need pruning? pnode <- pnode[pok] if(length(pnode) < 1L) break ## prune tree <- nodeprune.party(tree, ids = pnode) node <- tree$node nd <- as.list(node) ## node information kids <- lapply(nd, "[[", "kids") tmnl <- sapply(kids, is.null) id <- seq_along(nd) check <- sapply(id, function(i) !tmnl[i] && all(tmnl[kids[[i]]])) } ## return pruned tree return(tree) } .mfluc_test <- function(...) stop("not yet implemented") partykit/R/print.R0000644000176200001440000001245014172230000013570 0ustar liggesusersprint.partynode <- function(x, data = NULL, names = NULL, inner_panel = function(node) "", terminal_panel = function(node) " *", prefix = "", first = TRUE, digits = getOption("digits") - 2, ...) { ids <- nodeids(x) if(first) { if(is.null(names)) names <- as.character(ids) cat(paste(prefix, "[", names[which(ids == id_node(x))], "] root", sep = "")) if(is.terminal(x)) { char <- terminal_panel(x) if(length(char) > 1L) { cat(paste(char[1L], "\n", paste(prefix, " ", char[-1L], sep = "", collapse = "\n"), sep = ""), "\n") } else { cat(char, "\n") } } else { cat("\n") } } if (length(x) > 0) { ## add indentation nextprefix <- paste(prefix, "| ", sep = "") ## split labels slabs <- character_split(split_node(x), data = data, digits = digits, ...) slabs <- ifelse(substr(slabs$levels, 1, 1) %in% c("<", ">"), paste(slabs$name, slabs$levels), paste(slabs$name, "in", slabs$levels)) ## kid labels knodes <- kids_node(x) knam <- sapply(knodes, function(z) names[which(ids == id_node(z))]) klabs <- sapply(knodes, function(z) if(is.terminal(z)) { char <- terminal_panel(z) if(length(char) > 1L) { paste(char[1L], "\n", paste(nextprefix, " ", char[-1L], sep = "", collapse = "\n"), sep = "") } else { char } } else { paste(inner_panel(z), collapse = "\n") }) ## merge, cat, and call recursively labs <- paste("| ", prefix, "[", knam, "] ", slabs, klabs, "\n", sep = "") for (i in 1:length(x)) { cat(labs[i]) print.partynode(x[i], data = data, names = names[match(nodeids(x[i]), ids)], inner_panel = inner_panel, terminal_panel = terminal_panel, prefix = nextprefix, first = FALSE, digits = digits, ...) } } } print.party <- function(x, terminal_panel = function(node) formatinfo_node(node, default = "*", prefix = ": "), tp_args = list(), inner_panel = function(node) "", ip_args = list(), header_panel = function(party) "", footer_panel = function(party) "", digits = getOption("digits") - 2, ...) { ## header cat(paste(header_panel(x), collapse = "\n")) ## nodes if(inherits(terminal_panel, "grapcon_generator")) terminal_panel <- do.call("terminal_panel", c(list(x), as.list(tp_args))) if(inherits(inner_panel, "grapcon_generator")) inner_panel <- do.call("inner_panel", c(list(x), as.list(ip_args))) print(node_party(x), x$data, names = names(x), terminal_panel = terminal_panel, inner_panel = inner_panel, digits = digits, ...) ## footer cat(paste(footer_panel(x), collapse = "\n")) } print.constparty <- function(x, FUN = NULL, digits = getOption("digits") - 4, header = NULL, footer = TRUE, ...) { if(is.null(FUN)) return(print(as.simpleparty(x), digits = digits, header = header, footer = footer, ...)) digits <- max(c(0, digits)) ## FIXME: terms/call/? for "ctree" objects if(is.null(header)) header <- !is.null(terms(x)) header_panel <- if(header) function(party) { c("", "Model formula:", deparse(formula(terms(party))), "", "Fitted party:", "") } else function(party) "" footer_panel <- if(footer) function(party) { n <- width(party) n <- format(c(length(party) - n, n)) c("", paste("Number of inner nodes: ", n[1]), paste("Number of terminal nodes:", n[2]), "") } else function (party) "" y <- x$fitted[["(response)"]] w <- x$fitted[["(weights)"]] if(is.null(w)) { wdigits <- 0 wsym <- "n" } else { if(isTRUE(all.equal(w, round(w)))) { wdigits <- 0 wsym <- "n" } else { wdigits <- max(c(0, digits - 2)) wsym <- "w" } } yclass <- .response_class(y) if(yclass == "ordered") yclass <- "factor" if(!(yclass %in% c("Surv", "factor"))) yclass <- "numeric" if(is.null(FUN)) FUN <- switch(yclass, "numeric" = function(y, w, digits) { yhat <- .pred_numeric_response(y, w) yerr <- sum(w * (y - yhat)^2) digits2 <- max(c(0, digits - 2)) paste(format(round(yhat, digits = digits), nsmall = digits), " (", wsym, " = ", format(round(sum(w), digits = wdigits), nsmall = wdigits), ", err = ", format(round(yerr, digits = digits2), nsmall = digits2), ")", sep = "") }, "Surv" = function(y, w, digits) { paste(format(round(.pred_Surv_response(y, w), digits = digits), nsmall = digits), " (", wsym, " = ", format(round(sum(w), digits = wdigits), nsmall = wdigits), ")", sep = "") }, "factor" = function(y, w, digits) { tab <- round(.pred_factor(y, w) * sum(w)) mc <- round(100 * (1 - max(tab)/sum(w)), digits = max(c(0, digits - 2))) paste(names(tab)[which.max(tab)], " (", wsym, " = ", format(round(sum(w), digits = wdigits), nsmall = wdigits), ", err = ", mc, "%)", sep = "") } ) node_labs <- nodeapply(x, nodeids(x), function(node) { y1 <- node$fitted[["(response)"]] w <- node$fitted[["(weights)"]] if(is.null(w)) w <- rep.int(1L, NROW(y1)) FUN(y1, w, digits) }, by_node = FALSE) node_labs <- paste(":", format(do.call("c", node_labs))) terminal_panel <- function(node) node_labs[id_node(node)] print.party(x, terminal_panel = terminal_panel, header_panel = header_panel, footer_panel = footer_panel, ...) } partykit/R/node.R0000644000176200001440000002147314172230000013366 0ustar liggesusers partynode <- function(id, split = NULL, kids = NULL, surrogates = NULL, info = NULL) { if (!is.integer(id) || length(id) != 1) { id <- as.integer(id0 <- id) if (any(is.na(id)) || !isTRUE(all.equal(id0, id)) || length(id) != 1) stop(sQuote("id"), " ", "must be a single integer") } if (is.null(split) != is.null(kids)) { stop(sQuote("split"), " ", "and", " ", sQuote("kids"), " ", "must either both be specified or unspecified") } if (!is.null(kids)) { if (!(is.list(kids) && all(sapply(kids, inherits, "partynode"))) || length(kids) < 2) stop(sQuote("kids"), " ", "must be an integer vector or a list of", " ", sQuote("partynode"), " ", "objects") } if (!is.null(surrogates)) { if (!is.list(surrogates) || any(!sapply(surrogates, inherits, "partysplit"))) stop(sQuote("split"), " ", "is not a list of", " ", sQuote("partysplit"), " ", "objects") } node <- list(id = id, split = split, kids = kids, surrogates = surrogates, info = info) class(node) <- "partynode" return(node) } is.partynode <- function(x) { if (!inherits(x, "partynode")) return(FALSE) rval <- diff(nodeids(x, terminal = FALSE)) isTRUE(all.equal(unique(rval), 1)) } as.partynode <- function(x, ...) UseMethod("as.partynode") as.partynode.partynode <- function(x, from = NULL, recursive = TRUE, ...) { if(is.null(from)) from <- id_node(x) from <- as.integer(from) if (!recursive) { if(is.partynode(x) & id_node(x) == from) return(x) } id <- from - 1L new_node <- function(x) { id <<- id + 1L if(is.terminal(x)) return(partynode(id, info = info_node(x))) partynode(id, split = split_node(x), kids = lapply(kids_node(x), new_node), surrogates = surrogates_node(x), info = info_node(x)) } return(new_node(x)) } as.partynode.list <- function(x, ...) { if (!all(sapply(x, inherits, what = "list"))) stop("'x' has to be a list of lists") if (!all(sapply(x, function(x) "id" %in% names(x)))) stop("each list in 'x' has to define a node 'id'") ok <- sapply(x, function(x) all(names(x) %in% c("id", "split", "kids", "surrogates", "info"))) if (any(!ok)) sapply(which(!ok), function(i) warning(paste("list element", i, "defines additional elements:", paste(names(x[[i]])[!(names(x[[i]]) %in% c("id", "split", "kids", "surrogates", "info"))], collapse = ", ")))) ids <- as.integer(sapply(x, function(node) node$id)) if(any(duplicated(ids))) stop("nodeids must be unique integers") x <- x[order(ids)] ids <- ids[order(ids)] new_recnode <- function(i) { x_i <- x[[which(ids == i)]] if (is.null(x_i$kids)) partynode(id = x_i$id, info = x_i$info) else partynode(id = x_i$id, split = x_i$split, kids = lapply(x_i$kids, new_recnode), surrogates = x_i$surrogates, info = x_i$info) } ret <- new_recnode(ids[1L]) ### duplicates recursion but makes sure ### that the ids are in pre-order notation with ### from defined in as.partynode.partynode ### as.partynode(ret, ...) } as.list.partynode <- function(x, ...) { ids <- nodeids(x) obj <- vector(mode = "list", length = length(ids)) thisnode <- NULL nodelist <- function(node) { if (is.terminal(node)) obj[[which(ids == id_node(node))]] <<- list(id = id_node(node), info = info_node(node)) else { thisnode <<- list(id = id_node(node), split = split_node(node), kids = sapply(kids_node(node), function(k) id_node(k))) if (!is.null(surrogates_node(node))) thisnode$surrogates <- surrogates_node(node) if (!is.null(info_node(node))) thisnode$info <- info_node(node) obj[[which(ids == id_node(node))]] <<- thisnode lapply(kids_node(node), nodelist) } } nodelist(x) return(obj) } id_node <- function(node) { if (!(inherits(node, "partynode"))) stop(sQuote("node"), " ", "is not an object of class", " ", sQuote("node")) node$id } kids_node <- function(node) { if (!(inherits(node, "partynode"))) stop(sQuote("node"), " ", "is not an object of class", " ", sQuote("node")) node$kids } info_node <- function(node) { if (!(inherits(node, "partynode"))) stop(sQuote("node"), " ", "is not an object of class", " ", sQuote("node")) node$info } formatinfo_node <- function(node, FUN = NULL, default = "", prefix = NULL, ...) { info <- info_node(node) ## FIXME: better dispatch to workhorse FUN probably needed in the future, e.g.: ## (1) formatinfo() generic with formatinfo.default() as below, ## (2) supply default FUN from party$info$formatinfo() or similar. if(is.null(FUN)) FUN <- function(x, ...) { if(is.null(x)) x <- "" if(!is.object(x) & is.atomic(x)) x <- as.character(x) if(!is.character(x)) x <- capture.output(print(x), ...) x } info <- if(is.null(info)) default else FUN(info, ...) if(!is.null(prefix)) { info <- if(length(info) > 1L) c(prefix, info) else paste(prefix, info, sep = "") } info } ### FIXME: permutation and surrogate splits: is only the primary ### variable permuted? kidids_node <- function(node, data, vmatch = 1:ncol(data), obs = NULL, perm = NULL) { primary <- split_node(node) surrogates <- surrogates_node(node) ### perform primary split x <- kidids_split(primary, data, vmatch, obs) ### surrogate / random splits if needed if (any(is.na(x))) { ### surrogate splits if (length(surrogates) >= 1) { for (surr in surrogates) { nax <- is.na(x) if (!any(nax)) break; x[nax] <- kidids_split(surr, data, vmatch, obs = obs)[nax] } } nax <- is.na(x) ### random splits if (any(nax)) { prob <- prob_split(primary) x[nax] <- sample(1:length(prob), sum(nax), prob = prob, replace = TRUE) } } ### permute variable `perm' _after_ dealing with surrogates etc. if (!is.null(perm)) { if (is.integer(perm)) { if (varid_split(primary) %in% perm) x <- .resample(x) } else { if (is.null(obs)) obs <- 1:nrow(data) strata <- perm[[varid_split(primary)]] if (!is.null(strata)) { strata <- strata[obs, drop = TRUE] for (s in levels(strata)) x[strata == s] <- .resample(x[strata == s]) } } } return(x) } fitted_node <- function(node, data, vmatch = 1:ncol(data), obs = 1:nrow(data), perm = NULL) { ### should be equivalent to: # return(.Call("R_fitted_node", node, data, vmatch, as.integer(obs), # as.integer(perm))) if (is.logical(obs)) obs <- which(obs) if (is.terminal(node)) return(rep(id_node(node), length(obs))) retid <- nextid <- kidids_node(node, data, vmatch, obs, perm) for (i in unique(nextid)) { indx <- nextid == i retid[indx] <- fitted_node(kids_node(node)[[i]], data, vmatch, obs[indx], perm) } return(retid) } length.partynode <- function(x) length(kids_node(x)) "[.partynode" <- "[[.partynode" <- function(x, i, ...) { if (!(length(i) == 1 && is.numeric(i))) stop(sQuote("x"), " ", "is incorrect node") kids_node(x)[[i]] } split_node <- function(node) { if (!(inherits(node, "partynode"))) stop(sQuote("node"), " ", "is not an object of class", " ", sQuote("node")) node$split } surrogates_node <- function(node) { if (!(inherits(node, "partynode"))) stop(sQuote("node"), " ", "is not an object of class", " ", sQuote("node")) node$surrogates } is.terminal <- function(x, ...) UseMethod("is.terminal") is.terminal.partynode <- function(x, ...) { kids <- is.null(kids_node(x)) split <- is.null(split_node(x)) if (kids != split) stop("x", " ", "is incorrect node") kids } ## ## depth generic now taken from package 'grid' ## depth <- function(x, ...) ## UseMethod("depth") depth.partynode <- function(x, root = FALSE, ...) { if (is.terminal(x)) return(as.integer(root)) max(sapply(kids_node(x), depth, root = root)) + 1L } width <- function(x, ...) UseMethod("width") width.partynode <- function(x, ...) { if (is.terminal(x)) return(1) sum(sapply(kids_node(x), width.partynode)) } partykit/R/ctree.R0000644000176200001440000005061014230544657013563 0ustar liggesusers .ctree_select <- function(...) function(model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } .ctree_split <- function(...) function(model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } .ctree_test <- function(model, trafo, data, subset, weights, j, SPLITONLY = FALSE, ctrl) { ix <- data$zindex[[j]] ### data[[j, type = "index"]] iy <- data$yxindex ### data[["yx", type = "index"]] Y <- model$estfun if (!is.null(iy)) { stopifnot(NROW(levels(iy)) == (NROW(Y) - 1)) return(.ctree_test_2d(data = data, j = j, Y = Y, iy = iy, subset = subset, weights = weights, SPLITONLY = SPLITONLY, ctrl = ctrl)) } stopifnot(NROW(Y) == length(ix)) NAyx <- data$yxmissings ### data[["yx", type = "missings"]] NAz <- data$missings[[j]] ### data[[j, type = "missings"]] if (ctrl$MIA && (ctrl$splittest || SPLITONLY)) { subsetNArm <- subset[!(subset %in% NAyx)] } else { subsetNArm <- subset[!(subset %in% c(NAyx, NAz))] } ### report by Kevin Ummel: _all_ obs being missing lead to ### subset being ignored completely if (length(subsetNArm) == 0) return(list(statistic = NA, p.value = NA)) return(.ctree_test_1d(data = data, j = j, Y = Y, subset = subsetNArm, weights = weights, SPLITONLY = SPLITONLY, ctrl = ctrl)) } .partysplit <- function(varid, breaks = NULL, index = NULL, right = TRUE, prob = NULL, info = NULL) { ret <- list(varid = varid, breaks = breaks, index = index, right = right, prob = prob, info = info) class(ret) <- "partysplit" ret } .ctree_test_1d <- function(data, j, Y, subset, weights, SPLITONLY = FALSE, ctrl) { x <- data[[j]] MIA <- FALSE if (ctrl$MIA) { NAs <- data$missings[[j]] ### data[[j, type = "missings"]] MIA <- (length(NAs) > 0) } ### X for (ordered) factors is always dummy matrix if (is.factor(x) || is.ordered(x)) X <- data$zindex[[j]] ### data[[j, type = "index"]] scores <- data[[j, type = "scores"]] ORDERED <- is.ordered(x) || is.numeric(x) ux <- Xleft <- Xright <- NULL if (ctrl$splittest || SPLITONLY) { MAXSELECT <- TRUE if (is.numeric(x)) { X <- data$zindex[[j]] ###data[[j, type = "index"]] ux <- levels(X) } if (MIA) { Xlev <- attr(X, "levels") Xleft <- X + 1L Xleft[NAs] <- 1L Xright <- X Xright[NAs] <- as.integer(length(Xlev) + 1L) attr(Xleft, "levels") <- c(NA, Xlev) attr(Xright, "levels") <- c(Xlev, NA) } } else { MAXSELECT <- FALSE if (is.numeric(x)) { if (storage.mode(x) == "double") { X <- x } else { X <- as.double(x) ### copy when necessary } } MIA <- FALSE } cluster <- data[["(cluster)"]] .ctree_test_internal(x = x, X = X, ix = NULL, Xleft = Xleft, Xright = Xright, ixleft = NULL, ixright = NULL, ux = ux, scores = scores, j = j, Y = Y, iy = NULL, subset = subset, weights = weights, cluster = cluster, MIA = MIA, SPLITONLY = SPLITONLY, MAXSELECT = MAXSELECT, ORDERED = ORDERED, ctrl = ctrl) } .ctree_test_2d <- function(data, Y, iy, j, subset, weights, SPLITONLY = FALSE, ctrl) { x <- data[[j]] ix <- data$zindex[[j]] ### data[[j, type = "index"]] ux <- attr(ix, "levels") MIA <- FALSE if (ctrl$MIA) MIA <- any(ix[subset] == 0) ### X for (ordered) factors is always dummy matrix if (is.factor(x) || is.ordered(x)) X <- integer(0) scores <- data[[j, type = "scores"]] ORDERED <- is.ordered(x) || is.numeric(x) if (ctrl$splittest || SPLITONLY) { MAXSELECT <- TRUE X <- integer(0) if (MIA) { Xlev <- attr(ix, "levels") ixleft <- ix + 1L ixright <- ix ixright[ixright == 0L] <- as.integer(length(Xlev) + 1L) attr(ixleft, "levels") <- c(NA, Xlev) attr(ixright, "levels") <- c(Xlev, NA) Xleft <- Xright <- X } } else { MAXSELECT <- FALSE MIA <- FALSE if (is.numeric(x)) X <- matrix(c(0, as.double(attr(ix, "levels"))), ncol = 1) } cluster <- data[["(cluster)"]] .ctree_test_internal(x = x, X = X, ix = ix, Xleft = Xleft, Xright = Xright, ixleft = ixleft, ixright = ixright, ux = ux, scores = scores, j = j, Y = Y, iy = iy, subset = subset, weights = weights, cluster = cluster, MIA = MIA, SPLITONLY = SPLITONLY, MAXSELECT = MAXSELECT, ORDERED = ORDERED, ctrl = ctrl) } .ctree_test_internal <- function(x, X, ix, Xleft, Xright, ixleft, ixright, ux, scores, j, Y , iy, subset, weights, cluster, MIA, SPLITONLY, MAXSELECT, ORDERED, ctrl) { if (SPLITONLY) { nresample <- 0L varonly <- TRUE pvalue <- FALSE teststat <- ctrl$splitstat } else { nresample <- ifelse("MonteCarlo" %in% ctrl$testtype, ctrl$nresample, 0L) pvalue <- !("Teststatistic" %in% ctrl$testtype) if (ctrl$splittest) { if (ctrl$teststat != ctrl$splitstat) warning("Using different test statistics for testing and splitting") teststat <- ctrl$splitstat if (nresample == 0 && pvalue) stop("MonteCarlo approximation mandatory for splittest = TRUE") } else { teststat <- ctrl$teststat } varonly <- "MonteCarlo" %in% ctrl$testtype && teststat == "maxtype" } ### see libcoin if (MAXSELECT) { if (!is.null(cluster)) varonly <- FALSE } else { if (is.ordered(x) && !ctrl$splittest) varonly <- FALSE } ### if (MIA) use tst as fallback ### compute linear statistic + expecation and covariance lev <- LinStatExpCov(X = X, Y = Y, ix = ix, iy = iy, subset = subset, weights = weights, block = cluster, nresample = nresample, varonly = varonly, checkNAs = FALSE) ### in some cases, estfun() might return NAs which we don't check if (any(is.na(lev$LinearStatistic))) { if (!is.null(iy)) { Ytmp <- Y[iy[subset] + 1L,] } else { Ytmp <- Y[subset,] } cc <- complete.cases(Ytmp) if (!all(cc)) { ### only NAs left if (SPLITONLY) return(NULL) return(list(statistic = NA, p.value = NA)) } lev <- LinStatExpCov(X = X, Y = Y, ix = ix, iy = iy, subset = subset, weights = weights, block = cluster, nresample = nresample, varonly = varonly, checkNAs = TRUE) } if (!MAXSELECT) { if (is.ordered(x) && !ctrl$splittest) lev <- libcoin::lmult(matrix(scores, nrow = 1), lev) } ### check if either X or Y were unique vr <- lev$Variance vr[is.na(vr)] <- 0 if (all(vr < ctrl$tol)) { if (SPLITONLY) return(NULL) return(list(statistic = NA, p.value = NA)) } ### compute test statistic and log(1 - p-value) tst <- doTest(lev, teststat = teststat, pvalue = pvalue, lower = TRUE, log = TRUE, ordered = ORDERED, maxselect = MAXSELECT, minbucket = ctrl$minbucket, pargs = ctrl$pargs) if (MIA) { ### compute linear statistic + expecation and covariance lev <- LinStatExpCov(X = Xleft, Y = Y, ix = ixleft, iy = iy, subset = subset, weights = weights, block = cluster, nresample = nresample, varonly = varonly, checkNAs = FALSE) ### compute test statistic and log(1 - p-value) tstleft <- doTest(lev, teststat = teststat, pvalue = pvalue, lower = TRUE, log = TRUE, ordered = ORDERED, minbucket = ctrl$minbucket, pargs = ctrl$pargs) ### compute linear statistic + expecation and covariance lev <- LinStatExpCov(X = Xright, Y = Y, ix = ixright, iy = iy, subset = subset, weights = weights, block = cluster, nresample = nresample, varonly = varonly, checkNAs = FALSE) ### compute test statistic and log(1 - p-value) tstright <- doTest(lev, teststat = teststat, pvalue = pvalue, lower = TRUE, log = TRUE, ordered = ORDERED, minbucket = ctrl$minbucket, pargs = ctrl$pargs) } if (!SPLITONLY) { if (MIA) { tst <- tstleft if (tst$TestStatistic < tstright$TestStatistic) tst <- tstright } return(list(statistic = log(pmax(tst$TestStatistic, .Machine$double.eps)), p.value = tst$p.value)) } ret <- NULL if (MIA && !any(is.na(tst$index))) { if (ORDERED) { if (tstleft$TestStatistic >= tstright$TestStatistic) { if (all(tst$index == 1)) { ### case C ret <- .partysplit(as.integer(j), breaks = Inf, index = 1L:2L, prob = as.double(0:1)) } else { sp <- tstleft$index - 1L ### case A if (!is.ordered(x)) { ### interpolate split-points, see https://arxiv.org/abs/1611.04561 if (ctrl$intersplit & sp < length(ux)) { sp <- (ux[sp] + ux[sp + 1]) / 2 ### use weighted mean here? } else { sp <- ux[sp] ### X <= sp vs. X > sp } } ret <- .partysplit(as.integer(j), breaks = sp, index = 1L:2L, prob = as.double(rev(0:1))) } } else { ### case C was handled above (tstleft = tstright in this case) sp <- tstright$index ### case B if (!is.ordered(x)) { ### interpolate split-points, see https://arxiv.org/abs/1611.04561 if (ctrl$intersplit & sp < length(ux)) { sp <- (ux[sp] + ux[sp + 1]) / 2 } else { sp <- ux[sp] ### X <= sp vs. X > sp } } ret <- .partysplit(as.integer(j), breaks = sp, index = 1L:2L, prob = as.double(0:1)) } } else { sp <- tstleft$index[-1L] ### tstleft = tstright for unordered factors if (length(unique(sp)) == 1L) { ### case C ret <- .partysplit(as.integer(j), index = as.integer(tst$index) + 1L) } else { ### always case A ret <- .partysplit(as.integer(j), index = as.integer(sp) + 1L, prob = as.double(rev(0:1))) } } } else { sp <- tst$index if (all(is.na(sp))) return(NULL) if (ORDERED) { if (!is.ordered(x)) ### interpolate split-points, see https://arxiv.org/abs/1611.04561 if (ctrl$intersplit & sp < length(ux)) { sp <- (ux[sp] + ux[sp + 1]) / 2 } else { sp <- ux[sp] ### X <= sp vs. X > sp } ret <- .partysplit(as.integer(j), breaks = sp, index = 1L:2L) } else { ret <- .partysplit(as.integer(j), index = as.integer(sp) + 1L) } } return(ret) } ctree_control <- function ( teststat = c("quadratic", "maximum"), splitstat = c("quadratic", "maximum"), ### much better for q > 1, max was default splittest = FALSE, testtype = c("Bonferroni", "MonteCarlo", "Univariate", "Teststatistic"), pargs = GenzBretz(), nmax = c("yx" = Inf, "z" = Inf), alpha = 0.05, mincriterion = 1 - alpha, logmincriterion = log(mincriterion), minsplit = 20L, minbucket = 7L, minprob = 0.01, stump = FALSE, maxvar = Inf, lookahead = FALSE, ### try trafo() for daugther nodes before implementing the split MIA = FALSE, ### DOI: 10.1016/j.patrec.2008.01.010 nresample = 9999L, tol = sqrt(.Machine$double.eps), maxsurrogate = 0L, numsurrogate = FALSE, mtry = Inf, maxdepth = Inf, multiway = FALSE, splittry = 2L, intersplit = FALSE, majority = FALSE, caseweights = TRUE, applyfun = NULL, cores = NULL, saveinfo = TRUE, update = NULL, splitflavour = c("ctree", "exhaustive") ) { testtype <- match.arg(testtype, several.ok = TRUE) if (length(testtype) == 4) testtype <- testtype[1] ttesttype <- testtype if (length(testtype) > 1) { stopifnot(all(testtype %in% c("Bonferroni", "MonteCarlo"))) ttesttype <- "MonteCarlo" } if (MIA && maxsurrogate > 0) warning("Mixing MIA splits with surrogate splits does not make sense") if (MIA && majority) warning("Mixing MIA splits with majority does not make sense") splitstat <- match.arg(splitstat) teststat <- match.arg(teststat) if (!caseweights) stop("only caseweights currently implemented in ctree") splitflavour <- match.arg(splitflavour) c(extree_control(criterion = ifelse("Teststatistic" %in% testtype, "statistic", "p.value"), logmincriterion = logmincriterion, minsplit = minsplit, minbucket = minbucket, minprob = minprob, nmax = nmax, maxvar = maxvar, stump = stump, lookahead = lookahead, mtry = mtry, maxdepth = maxdepth, multiway = multiway, splittry = splittry, maxsurrogate = maxsurrogate, numsurrogate = numsurrogate, majority = majority, caseweights = caseweights, applyfun = applyfun, saveinfo = saveinfo, ### always selectfun = .ctree_select(), splitfun = if (splitflavour == "ctree") .ctree_split() else .objfun_test(), svselectfun = .ctree_select(), svsplitfun =.ctree_split(minbucket = 0), bonferroni = "Bonferroni" %in% testtype, update = update), list(teststat = teststat, splitstat = splitstat, splittest = splittest, pargs = pargs, testtype = ttesttype, nresample = nresample, tol = tol, intersplit = intersplit, MIA = MIA)) } ctree <- function(formula, data, subset, weights, na.action = na.pass, offset, cluster, control = ctree_control(...), ytrafo = NULL, converged = NULL, scores = NULL, doFit = TRUE, ...) { ## set up model.frame() call mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "data", "subset", "na.action", "weights", "offset", "cluster", "scores"), names(mf), 0L) mf <- mf[c(1L, m)] mf$yx <- "none" if (is.function(ytrafo)) { if (all(c("y", "x") %in% names(formals(ytrafo)))) mf$yx <- "matrix" } mf$nmax <- control$nmax ## evaluate model.frame mf[[1L]] <- quote(partykit::extree_data) d <- eval(mf, parent.frame()) subset <- .start_subset(d) weights <- model.weights(model.frame(d)) if (is.function(ytrafo)) { if (is.null(control$update)) control$update <- TRUE nf <- names(formals(ytrafo)) if (all(c("data", "weights", "control") %in% nf)) ytrafo <- ytrafo(data = d, weights = weights, control = control) nf <- names(formals(ytrafo)) stopifnot(all(c("subset", "weights", "info", "estfun", "object") %in% nf) || all(c("y", "x", "weights", "offset", "start") %in% nf)) } else { if (is.null(control$update)) control$update <- FALSE stopifnot(length(d$variables$x) == 0) mfyx <- model.frame(d, yxonly = TRUE) mfyx[["(weights)"]] <- mfyx[["(offset)"]] <- NULL yvars <- names(mfyx) for (yvar in yvars) { sc <- d[[yvar, "scores"]] if (!is.null(sc)) attr(mfyx[[yvar]], "scores") <- sc } Y <- .y2infl(mfyx, response = d$variables$y, ytrafo = ytrafo) if (!is.null(iy <- d[["yx", type = "index"]])) { Y <- rbind(0, Y) } ytrafo <- function(subset, weights, info, estfun, object, ...) list(estfun = Y, unweighted = TRUE) ### unweighted = TRUE prevents estfun / w in extree_fit } if (is.function(converged)) { stopifnot(all(c("data", "weights", "control") %in% names(formals(converged)))) converged <- converged(d, weights, control = control) } else { converged <- TRUE } update <- function(subset, weights, control, doFit = TRUE) extree_fit(data = d, trafo = ytrafo, converged = converged, partyvars = d$variables$z, subset = subset, weights = weights, ctrl = control, doFit = doFit) if (!doFit) return(list(d = d, update = update)) tree <- update(subset = subset, weights = weights, control = control) trafo <- tree$trafo tree <- tree$nodes mf <- model.frame(d) if (is.null(weights)) weights <- rep(1, nrow(mf)) fitted <- data.frame("(fitted)" = fitted_node(tree, mf), "(weights)" = weights, check.names = FALSE) fitted[[3]] <- mf[, d$variables$y, drop = TRUE] names(fitted)[3] <- "(response)" ret <- party(tree, data = mf, fitted = fitted, info = list(call = match.call(), control = control)) ret$update <- update ret$trafo <- trafo class(ret) <- c("constparty", class(ret)) ### doesn't work for Surv objects # ret$terms <- terms(formula, data = mf) ret$terms <- d$terms$all ### need to adjust print and plot methods ### for multivariate responses ### if (length(response) > 1) class(ret) <- "party" return(ret) } .logrank_trafo <- function(...) return(coin::logrank_trafo(...)) ### convert response y to influence function h(y) .y2infl <- function(data, response, ytrafo = NULL) { if (length(response) == 1) { if (!is.null(ytrafo[[response]])) { yfun <- ytrafo[[response]] rtype <- "user-defined" } else { rtype <- .response_class(data[[response]]) } response <- data[[response]] infl <- switch(rtype, "user-defined" = yfun(response), "factor" = { X <- model.matrix(~ response - 1) if (nlevels(response) > 2) return(X) return(X[,-1, drop = FALSE]) }, "ordered" = { sc <- attr(response, "scores") if (is.null(sc)) sc <- 1L:nlevels(response) sc <- as.numeric(sc) return(matrix(sc[as.integer(response)], ncol = 1)) }, "numeric" = response, "Surv" = .logrank_trafo(response), stop("unknown response class") ) } else { ### multivariate response infl <- lapply(response, .y2infl, data = data) tmp <- do.call("cbind", infl) attr(tmp, "assign") <- rep(1L:length(infl), sapply(infl, NCOL)) infl <- tmp } if (!is.matrix(infl)) infl <- matrix(infl, ncol = 1) storage.mode(infl) <- "double" return(infl) } sctest.constparty <- function(object, node = NULL, ...) { if(is.null(node)) { ids <- nodeids(object, terminal = FALSE) ### all nodes } else { ids <- node } rval <- nodeapply(object, ids, function(n) { crit <- info_node(n)$criterion if (is.null(crit)) return(NULL) ret <- crit[c("statistic", "p.value"),,drop = FALSE] ret }) names(rval) <- ids if(length(ids) == 1L) return(rval[[1L]]) return(rval) } partykit/R/lmtree.R0000644000176200001440000001012014172230000013714 0ustar liggesusers## simple wrapper function to specify fitter and return class lmtree <- function(formula, data, subset, na.action, weights, offset, cluster, ...) { ## TODO: variance as model parameter ## use dots for setting up mob_control control <- mob_control(...) if(control$vcov != "opg") { warning('only vcov = "opg" supported in lmtree') control$vcov <- "opg" } if(!is.null(control$prune)) { if(is.character(control$prune)) { control$prune <- tolower(control$prune) control$prune <- match.arg(control$prune, c("aic", "bic", "none")) control$prune <- switch(control$prune, "aic" = { function(objfun, df, nobs) (nobs[1L] * log(objfun[1L]) + 2 * df[1L]) < (nobs[1L] * log(objfun[2L]) + 2 * df[2L]) }, "bic" = { function(objfun, df, nobs) (nobs[1L] * log(objfun[1L]) + log(nobs[2L]) * df[1L]) < (nobs[1L] * log(objfun[2L]) + log(nobs[2L]) * df[2L]) }, "none" = { NULL }) } if(!is.function(control$prune)) { warning("unknown specification of 'prune'") control$prune <- NULL } } ## keep call cl <- match.call(expand.dots = TRUE) ## extend formula if necessary f <- Formula::Formula(formula) if(length(f)[2L] == 1L) { attr(f, "rhs") <- c(list(1), attr(f, "rhs")) formula[[3L]] <- formula(f)[[3L]] } else { f <- NULL } ## call mob m <- match.call(expand.dots = FALSE) if(!is.null(f)) m$formula <- formula m$fit <- lmfit m$control <- control if("..." %in% names(m)) m[["..."]] <- NULL m[[1L]] <- as.call(quote(partykit::mob)) rval <- eval(m, parent.frame()) ## extend class and keep original call rval$info$call <- cl class(rval) <- c("lmtree", class(rval)) return(rval) } ## actual fitting function for mob() lmfit <- function(y, x, start = NULL, weights = NULL, offset = NULL, cluster = NULL, ..., estfun = FALSE, object = FALSE) { ## add intercept-only regressor matrix (if missing) ## NOTE: does not have terms/formula if(is.null(x)) x <- matrix(1, nrow = NROW(y), ncol = 1L, dimnames = list(NULL, "(Intercept)")) ## call lm fitting function if(is.null(weights) || identical(as.numeric(weights), rep.int(1, length(weights)))) { z <- lm.fit(x, y, offset = offset, ...) weights <- 1 } else { z <- lm.wfit(x, y, w = weights, offset = offset, ...) } ## list structure rval <- list( coefficients = z$coefficients, objfun = sum(weights * z$residuals^2), estfun = NULL, object = NULL ) ## add estimating functions (if desired) if(estfun) { rval$estfun <- as.vector(z$residuals) * weights * x[, !is.na(z$coefficients), drop = FALSE] } ## add model (if desired) if(object) { class(z) <- c(if(is.matrix(z$fitted)) "mlm", "lm") z$offset <- if(is.null(offset)) 0 else offset z$contrasts <- attr(x, "contrasts") z$xlevels <- attr(x, "xlevels") cl <- as.call(expression(lm)) cl$formula <- attr(x, "formula") if(!is.null(offset)) cl$offset <- attr(x, "offset") z$call <- cl z$terms <- attr(x, "terms") rval$object <- z } return(rval) } ## methods print.lmtree <- function(x, title = "Linear model tree", objfun = "residual sum of squares", ...) { print.modelparty(x, title = title, objfun = objfun, ...) } predict.lmtree <- function(object, newdata = NULL, type = "response", ...) { ## FIXME: possible to get default? if(is.null(newdata) & !identical(type, "node")) stop("newdata has to be provided") predict.modelparty(object, newdata = newdata, type = type, ...) } plot.lmtree <- function(x, terminal_panel = node_bivplot, tp_args = list(), tnex = NULL, drop_terminal = NULL, ...) { nreg <- if(is.null(tp_args$which)) x$info$nreg else length(tp_args$which) if(nreg < 1L & missing(terminal_panel)) { plot.constparty(as.constparty(x), tp_args = tp_args, tnex = tnex, drop_terminal = drop_terminal, ...) } else { if(is.null(tnex)) tnex <- if(is.null(terminal_panel)) 1L else 2L * nreg if(is.null(drop_terminal)) drop_terminal <- !is.null(terminal_panel) plot.modelparty(x, terminal_panel = terminal_panel, tp_args = tp_args, tnex = tnex, drop_terminal = drop_terminal, ...) } } partykit/R/cforest.R0000644000176200001440000002650014172230000014102 0ustar liggesusers ### constructor for forest objects constparties <- function(nodes, data, weights, fitted = NULL, terms = NULL, info = NULL) { stopifnot(all(sapply(nodes, function(x) inherits(x, "partynode")))) stopifnot(inherits(data, "data.frame")) stopifnot(inherits(weights, "list")) if(!is.null(fitted)) { stopifnot(inherits(fitted, "data.frame")) stopifnot(nrow(data) == 0L | nrow(data) == nrow(fitted)) if (nrow(data) == 0L) stopifnot("(response)" %in% names(fitted)) } else { stopifnot(nrow(data) > 0L) stopifnot(!is.null(terms)) fitted <- data.frame("(response)" = model.response(model.frame(terms, data = data, na.action = na.pass)), check.names = FALSE) } ret <- list(nodes = nodes, data = data, weights = weights, fitted = fitted) class(ret) <- c("constparties", "parties") if(!is.null(terms)) { stopifnot(inherits(terms, "terms")) ret$terms <- terms } if (!is.null(info)) ret$info <- info ret } .perturb <- function(replace = FALSE, fraction = .632) { ret <- function(prob) { if (replace) { rw <- rmultinom(1, size = length(prob), prob = prob) } else { rw <- integer(length(prob)) i <- sample(1:length(prob), ceiling(fraction * length(prob)), prob = prob) rw[i] <- 1L } as.integer(rw) } ret } cforest <- function ( formula, data, weights, subset, offset, cluster, strata, na.action = na.pass, control = ctree_control( teststat = "quad", testtype = "Univ", mincriterion = 0, saveinfo = FALSE, ...), ytrafo = NULL, scores = NULL, ntree = 500L, perturb = list(replace = FALSE, fraction = 0.632), mtry = ceiling(sqrt(nvar)), applyfun = NULL, cores = NULL, trace = FALSE, ... ) { ### get the call and the calling environment for .urp_tree call <- match.call(expand.dots = TRUE) oweights <- NULL if (!missing(weights)) oweights <- weights m <- match(c("formula", "data", "subset", "na.action", "offset", "cluster", "scores", "ytrafo", "control", "converged"), names(call), 0L) ctreecall <- call[c(1L, m)] ctreecall$doFit <- FALSE if (!is.null(oweights)) ctreecall$weights <- 1:NROW(oweights) ctreecall$control <- control ### put ... into ctree_control() ctreecall[[1L]] <- quote(partykit::ctree) tree <- eval(ctreecall, parent.frame()) if (is.null(control$update)) control$update <- is.function(ytrafo) d <- tree$d updatefun <- tree$update nvar <- sum(d$variables$z > 0) control$mtry <- mtry control$applyfun <- lapply strata <- d[["(strata)"]] if (!is.null(strata)) { if (!is.factor(strata)) stop("strata is not a single factor") } probw <- NULL iweights <- model.weights(model.frame(d)) if (!is.null(oweights)) { if (is.matrix(oweights)) { weights <- oweights[iweights,,drop = FALSE] } else { weights <- oweights[iweights] } } else { weights <- NULL } rm(oweights) rm(iweights) N <- nrow(model.frame(d)) rw <- NULL if (!is.null(weights)) { if (is.matrix(weights)) { if (ncol(weights) == ntree && nrow(weights) == N) { rw <- unclass(as.data.frame(weights)) rw <- lapply(rw, function(w) rep(1:length(w), w)) weights <- integer(0) } else { stop(sQuote("weights"), "argument incorrect") } } else { probw <- weights / sum(weights) } } else { weights <- integer(0) } idx <- .start_subset(d) frctn <- pmin(1, sum(perturb$fraction)) if (is.null(rw)) { ### for honesty testing purposes only if (frctn == 1) { rw <- lapply(1:ntree, function(b) idx) } else { if (is.null(strata)) { size <- N if (!perturb$replace) size <- floor(size * frctn) rw <- replicate(ntree, sample(idx, size = size, replace = perturb$replace, prob = probw[idx]), simplify = FALSE) } else { frac <- if (!perturb$replace) frctn else 1 rw <- replicate(ntree, function() do.call("c", tapply(idx, strata[idx], function(i) sample(i, size = length(i) * frac, replace = perturb$replace, prob = probw[i])))) } } } ### honesty: fraction = c(p1, p2) with p1 + p2 <= 1 ### p1 is the fraction of samples used for tree induction ### p2 is the fraction used for honest predictions (nearest neighbor ### weights) ### works for subsampling only if (!perturb$replace && length(perturb$fraction) == 2L) { frctn <- perturb$fraction[2L] if (is.null(strata)) { size <- N if (!perturb$replace) size <- floor(size * frctn) hn <- lapply(1:ntree, function(b) sample(rw[[b]], size = size, replace = perturb$replace, prob = probw[rw[[b]]])) } else { frac <- if (!perturb$replace) frctn else 1 hn <- lapply(1:ntree, function(b) do.call("c", tapply(rw[[b]], strata[rw[[b]]], function(i) sample(i, size = length(i) * frac, replace = perturb$replace, prob = probw[i])))) } rw <- lapply(1:ntree, function(b) rw[[b]][!(rw[[b]] %in% hn[[b]])]) tmp <- hn hn <- rw rw <- tmp } else { hn <- NULL } ## apply infrastructure for determining split points ## use RNGkind("L'Ecuyer-CMRG") to make this reproducible if (is.null(applyfun)) { applyfun <- if(is.null(cores)) { lapply } else { function(X, FUN, ...) parallel::mclapply(X, FUN, ..., mc.set.seed = TRUE, mc.cores = cores) } } trafo <- updatefun(sort(rw[[1]]), integer(0), control, doFit = FALSE) if (trace) pb <- txtProgressBar(style = 3) forest <- applyfun(1:ntree, function(b) { if (trace) setTxtProgressBar(pb, b/ntree) ret <- updatefun(sort(rw[[b]]), integer(0), control) ### honesty: prune-off empty nodes if (!is.null(hn)) { nid <- nodeids(ret$nodes, terminal = TRUE) nd <- unique(fitted_node(ret$nodes, data = d$data, obs = hn[[b]])) prn <- nid[!nid %in% nd] if (length(prn) > 0) ret <- list(nodes = nodeprune(ret$nodes, ids = prn), trafo = ret$trafo) } # trafo <<- ret$trafo ret$nodes }) if (trace) close(pb) fitted <- data.frame(idx = 1:N) mf <- model.frame(d) fitted[[2]] <- mf[, d$variables$y, drop = TRUE] names(fitted)[2] <- "(response)" if (length(weights) > 0) fitted[["(weights)"]] <- weights ### turn subsets in weights (maybe we can avoid this?) rw <- lapply(rw, function(x) as.integer(tabulate(x, nbins = length(idx)))) control$applyfun <- applyfun ret <- constparties(nodes = forest, data = mf, weights = rw, fitted = fitted, terms = d$terms$all, info = list(call = match.call(), control = control)) if (!is.null(hn)) ret$honest_weights <- lapply(hn, function(x) as.integer(tabulate(x, nbins = length(idx)))) ret$trafo <- trafo ret$predictf <- d$terms$z class(ret) <- c("cforest", class(ret)) return(ret) } predict.cforest <- function(object, newdata = NULL, type = c("response", "prob", "weights", "node"), OOB = FALSE, FUN = NULL, simplify = TRUE, scale = TRUE, ...) { responses <- object$fitted[["(response)"]] forest <- object$nodes nd <- object$data vmatch <- 1:ncol(nd) NOnewdata <- TRUE if (!is.null(newdata)) { factors <- which(sapply(nd, is.factor)) xlev <- lapply(factors, function(x) levels(nd[[x]])) names(xlev) <- names(nd)[factors] xlev <- xlev[attr(object$predictf, "term.labels")] nd <- model.frame(object$predictf, ### all variables W/O response data = newdata, na.action = na.pass, xlev = xlev) OOB <- FALSE vmatch <- match(names(object$data), names(nd)) NOnewdata <- FALSE } nam <- rownames(nd) type <- match.arg(type) ### return terminal node ids for data or newdata if (type == "node") return(lapply(forest, fitted_node, data = nd, vmatch = vmatch, ...)) ### extract weights: use honest weights when available if (is.null(object$honest_weights)) { rw <- object$weights } else { rw <- object$honest_weights OOB <- FALSE } w <- 0L applyfun <- lapply if (!is.null(object$info)) applyfun <- object$info$control$applyfun fdata <- lapply(forest, fitted_node, data = object$data, ...) if (NOnewdata && OOB) { fnewdata <- list() } else { fnewdata <- lapply(forest, fitted_node, data = nd, vmatch = vmatch, ...) } w <- .rfweights(fdata, fnewdata, rw, scale) # for (b in 1:length(forest)) { # ids <- nodeids(forest[[b]], terminal = TRUE) # fnewdata <- fitted_node(forest[[b]], nd, vmatch = vmatch, ...) # fdata <- fitted_node(forest[[b]], object$data, ...) # tw <- rw[[b]] # pw <- sapply(ids, function(i) tw * (fdata == i)) # ret <- pw[, match(fnewdata, ids), drop = FALSE] # ### obs which are in-bag for this tree don't contribute # if (OOB) ret[,tw > 0] <- 0 # w <- w + ret # } # # #w <- Reduce("+", bw) # if (!is.matrix(w)) w <- matrix(w, ncol = 1) if (type == "weights") { ret <- w colnames(ret) <- nam rownames(ret) <- rownames(responses) return(ret) } pfun <- function(response) { if (is.null(FUN)) { rtype <- class(response)[1] if (rtype == "ordered") rtype <- "factor" if (rtype == "integer") rtype <- "numeric" FUN <- switch(rtype, "Surv" = if (type == "response") .pred_Surv_response else .pred_Surv, "factor" = if (type == "response") .pred_factor_response else .pred_factor, "numeric" = if (type == "response") .pred_numeric_response else .pred_ecdf) } ret <- vector(mode = "list", length = ncol(w)) for (j in 1:ncol(w)) ret[[j]] <- FUN(response, w[,j]) ret <- as.array(ret) dim(ret) <- NULL names(ret) <- nam if (simplify) ret <- .simplify_pred(ret, names(ret), names(ret)) ret } if (!is.data.frame(responses)) { ret <- pfun(responses) } else { ret <- lapply(responses, pfun) if (all(sapply(ret, is.atomic))) ret <- as.data.frame(ret) names(ret) <- colnames(responses) } ret } model.frame.cforest <- function(formula, ...) { class(formula) <- "party" model.frame(formula, ...) } partykit/R/zzz.R0000644000176200001440000000161614172230000013273 0ustar liggesusersregister_s3_method <- function(pkg, generic, class, fun = NULL) { stopifnot(is.character(pkg), length(pkg) == 1L) stopifnot(is.character(generic), length(generic) == 1L) stopifnot(is.character(class), length(class) == 1L) if (is.null(fun)) { fun <- get(paste0(generic, ".", class), envir = parent.frame()) } else { stopifnot(is.function(fun)) } if (pkg %in% loadedNamespaces()) { registerS3method(generic, class, fun, envir = asNamespace(pkg)) } # Always register hook in case package is later unloaded & reloaded setHook( packageEvent(pkg, "onLoad"), function(...) { registerS3method(generic, class, fun, envir = asNamespace(pkg)) } ) } .onLoad <- function(libname, pkgname) { if(getRversion() < "3.6.0") { register_s3_method("strucchange", "sctest", "constparty") register_s3_method("strucchange", "sctest", "modelparty") } invisible() } partykit/R/extree.R0000644000176200001440000011077314673217736013772 0ustar liggesusers .select <- function(model, trafo, data, subset, weights, whichvar, ctrl, FUN) { ret <- list(criteria = matrix(NA, nrow = 2L, ncol = ncol(model.frame(data)))) rownames(ret$criteria) <- c("statistic", "p.value") colnames(ret$criteria) <- names(model.frame(data)) if (length(whichvar) == 0) return(ret) ### allow joint MC in the absense of missings; fix seeds ### write ctree_test / ... with whichvar and loop over variables there ### for (j in whichvar) { tst <- FUN(model = model, trafo = trafo, data = data, subset = subset, weights = weights, j = j, SPLITONLY = FALSE, ctrl = ctrl) ret$criteria["statistic",j] <- tst$statistic ret$criteria["p.value",j] <- tst$p.value } ret } .split <- function(model, trafo, data, subset, weights, whichvar, ctrl, FUN) { if (length(whichvar) == 0) return(NULL) for (j in whichvar) { x <- model.frame(data)[[j]] if (ctrl$multiway && is.factor(x) && !is.ordered(x) && (ctrl$maxsurrogate == 0) && nlevels(x[subset, drop = TRUE]) > 1) { index <- 1L:nlevels(x) xt <- libcoin::ctabs(ix = unclass(x), weights = weights, subset = subset)[-1] index[xt == 0] <- NA ### maybe multiway is not so smart here as ### nodes with nobs < minbucket could result index[xt > 0 & xt < ctrl$minbucket] <- nlevels(x) + 1L if (length(unique(index)) == 1) { ret <- NULL } else { index <- unclass(factor(index)) ret <- partysplit(as.integer(j), index = as.integer(index)) } } else { ret <- FUN(model = model, trafo = trafo, data = data, subset = subset, weights = weights, j = j, SPLITONLY = TRUE, ctrl = ctrl) } ### check if trafo can be successfully applied to all daugther nodes ### (converged = TRUE) if (ctrl$lookahead & !is.null(ret)) { sp <- kidids_split(ret, model.frame(data), obs = subset) conv <- sapply(unique(na.omit(sp)), function(i) isTRUE(trafo(subset[sp == i & !is.na(sp)], weights = weights)$converged)) if (!all(conv)) ret <- NULL } if (!is.null(ret)) break() } return(ret) } .objfun_select <- function(...) function(model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .objfun_test) } .objfun_split <- function(...) function(model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .objfun_test) } ### which.max(x) gives first max in case of ties ### order(x) puts length(x) last. This lead to confusion ### regarding the selected p-value and split variable .which.max <- function(x) { x[!is.finite(x)] <- -Inf order(x)[length(x)] } ### unbiased recursive partitioning: set up new node .extree_node <- function ( id = 1L, ### id of this node data, ### full data, readonly trafo, selectfun, ### variable selection splitfun, ### split selection svselectfun, ### same for surrogate splits svsplitfun, ### same for surrogate splits partyvars, ### partytioning variables ### a subset of 1:ncol(model.frame(data)) weights = integer(0L), ### optional case weights subset, ### subset of 1:nrow(data) ### for identifying obs for this node ctrl, ### extree_control() info = NULL, cenv = NULL ### environment for depth and maxid ) { ### depth keeps track of the depth of the tree ### which has to be < than maxdepth ### maxit is the largest id in the left subtree if (is.null(cenv)) { cenv <- new.env() assign("depth", 0L, envir = cenv) assign("splitvars", rep(0L, length(partyvars)), envir = cenv) } depth <- get("depth", envir = cenv) assign("maxid", id, envir = cenv) if (depth >= ctrl$maxdepth) return(partynode(as.integer(id))) ### check for stumps if (id > 1L && ctrl$stump) return(partynode(as.integer(id))) ### sw is basically the number of observations ### which has to be > minsplit in order to consider ### the node for splitting if (length(weights) > 0L) { if (ctrl$caseweights) { sw <- sum(weights[subset]) } else { sw <- sum(weights[subset] > 0L) } } else { sw <- length(subset) } if (sw < ctrl$minsplit) return(partynode(as.integer(id))) ### split variables used so far splitvars <- get("splitvars", envir = cenv) if (sum(splitvars) < ctrl$maxvar) { ### all variables subject to splitting svars <- which(partyvars > 0) } else { ### only those already used for splitting in other nodes are ### eligible svars <- which(partyvars > 0 & splitvars > 0) } if (ctrl$mtry < Inf) { mtry <- min(length(svars), ctrl$mtry) svars <- .resample(svars, size = mtry, prob = partyvars[svars]) } thismodel <- trafo(subset = subset, weights = weights, info = info, estfun = TRUE, object = TRUE) if (is.null(thismodel)) return(partynode(as.integer(id))) ### update sample size constraints on possible splits ### need to do this here because selectfun might consider splits mb <- ctrl$minbucket mp <- ctrl$minprob swp <- ceiling(sw * mp) if (mb < swp) mb <- as.integer(swp) thisctrl <- ctrl thisctrl$minbucket <- mb ### compute test statistics and p-values ### for _unbiased_ variable selection sf <- selectfun(model = thismodel, trafo = trafo, data = data, subset = subset, weights = weights, whichvar = svars, ctrl = thisctrl) if (inherits(sf, "partysplit")) { thissplit <- sf info <- nodeinfo <- thismodel[!(names(thismodel) %in% c("estfun"))] info$nobs <- sw if (!ctrl$saveinfo) info <- NULL } else { if (ctrl$bonferroni) ### make sure to correct for _non-constant_ variables only sf$criteria["p.value",] <- sf$criteria["p.value",] * sum(!is.na(sf$criteria["p.value",])) ### selectfun might return other things later to be used for info p <- sf$criteria crit <- p[ctrl$criterion,,drop = TRUE] if (all(is.na(crit))) return(partynode(as.integer(id))) crit[is.na(crit)] <- -Inf ### crit is maximised, but there might be ties ties <- which(abs(crit - max(crit, na.rm = TRUE)) < sqrt(.Machine$double.xmin)) if (length(ties) > 1) { ### add a small value (< 1/1000) to crit derived from rank of ### teststat crit[ties] <- crit[ties] + rank(p["statistic", ties]) / (sum(ties) * 1000) } ### switch from log(1 - pval) to pval for info slots ### switch from log(statistic) to statistic ### criterion stays on log scale to replicate variable selection p <- rbind(p, criterion = crit) p["statistic",] <- exp(p["statistic",]) p["p.value",] <- -expm1(p["p.value",]) pmin <- p["p.value", .which.max(crit)] names(pmin) <- colnames(model.frame(data))[.which.max(crit)] ### report on tests actually performed only p <- p[,!is.na(p["statistic",]) & is.finite(p["statistic",]), drop = FALSE] info <- nodeinfo <- c(list(criterion = p, p.value = pmin), sf[!(names(sf) %in% c("criteria", "converged"))], thismodel[!(names(thismodel) %in% c("estfun"))]) info$nobs <- sw if (!ctrl$saveinfo) info <- NULL ### nothing "significant" if (all(crit <= ctrl$logmincriterion)) return(partynode(as.integer(id), info = info)) ### at most ctrl$splittry variables with meaningful criterion st <- pmin(sum(is.finite(crit)), ctrl$splittry) jsel <- rev(order(crit))[1:st] jsel <- jsel[crit[jsel] > ctrl$logmincriterion] if (!is.null(sf$splits)) { ### selectfun may return of a list of partysplit objects; use these for ### splitting; selectfun is responsible for making sure lookahead is implemented thissplit <- sf$splits[[jsel[1]]] } else { ### try to find an admissible split in data[, jsel] thissplit <- splitfun(model = thismodel, trafo = trafo, data = data, subset = subset, weights = weights, whichvar = jsel, ctrl = thisctrl) } } ### failed split search: if (is.null(thissplit)) return(partynode(as.integer(id), info = info)) ### successful split search: set-up node ret <- partynode(as.integer(id)) ret$split <- thissplit ret$info <- info splitvars[thissplit$varid] <- 1L assign("splitvars", splitvars, cenv) ### determine observations for splitting (only non-missings) snotNA <- subset[!subset %in% data[[varid_split(thissplit), type = "missings"]]] if (length(snotNA) == 0) return(partynode(as.integer(id), info = info)) ### and split observations kidids <- kidids_node(ret, model.frame(data), obs = snotNA) ### compute probability of going left / right prob <- tabulate(kidids) / length(kidids) # names(dimnames(prob)) <- NULL if (ctrl$majority) ### go with majority prob <- as.double((1L:length(prob)) %in% .which.max(prob)) if (is.null(ret$split$prob)) ret$split$prob <- prob ### compute surrogate splits if (ctrl$maxsurrogate > 0L) { pv <- partyvars pv[varid_split(thissplit)] <- 0 pv <- which(pv > 0) if (ctrl$numsurrogate) pv <- pv[sapply(model.frame(data)[, pv], function(x) is.numeric(x) || is.ordered(x))] ret$surrogates <- .extree_surrogates(kidids, data = data, weights = weights, subset = snotNA, whichvar = pv, selectfun = svselectfun, splitfun = svsplitfun, ctrl = ctrl) } kidids <- kidids_node(ret, model.frame(data), obs = subset) ### proceed recursively kids <- vector(mode = "list", length = max(kidids)) nextid <- id + 1L for (k in 1L:max(kidids)) { nextsubset <- subset[kidids == k] assign("depth", depth + 1L, envir = cenv) kids[[k]] <- .extree_node(id = nextid, data = data, trafo = trafo, selectfun = selectfun, splitfun = splitfun, svselectfun = svselectfun, svsplitfun = svsplitfun, partyvars = partyvars, weights = weights, subset = nextsubset, ctrl = ctrl, info = nodeinfo, cenv = cenv) ### was: nextid <- max(nodeids(kids[[k]])) + 1L nextid <- get("maxid", envir = cenv) + 1L } ret$kids <- kids return(ret) } ### unbiased recursive partitioning: surrogate splits .extree_surrogates <- function ( split, ### integer vector with primary kidids data, ### full data, readonly weights, subset, ### subset of 1:nrow(data) with ### non-missings in primary split whichvar, ### partytioning variables selectfun, ### variable selection and split ### function splitfun, ctrl ### ctree_control() ) { if (length(whichvar) == 0) return(NULL) ms <- max(split) if (ms != 2) return(NULL) ### ie no multiway splits! dm <- matrix(0, nrow = nrow(model.frame(data)), ncol = ms) dm[cbind(subset, split)] <- 1 thismodel <- list(estfun = dm) sf <- selectfun(model = thismodel, trafo = NULL, data = data, subset = subset, weights = weights, whichvar = whichvar, ctrl = ctrl) p <- sf$criteria ### partykit always used p-values, so expect some differences crit <- p[ctrl$criterion,,drop = TRUE] ### crit is maximised, but there might be ties ties <- which(abs(crit - max(crit, na.rm = TRUE)) < .Machine$double.eps) if (length(ties) > 1) { ### add a small value (< 1/1000) to crit derived from order of ### teststat crit[ties] <- crit[ties] + order(p["statistic", ties]) / (sum(ties) * 1000) } ret <- vector(mode = "list", length = min(c(length(whichvar), ctrl$maxsurrogate))) for (i in 1L:length(ret)) { jsel <- .which.max(crit) thisctrl <- ctrl thisctrl$minbucket <- 0L sp <- splitfun(model = thismodel, trafo = NULL, data = data, subset = subset, weights = weights, whichvar = jsel, ctrl = ctrl) if (is.null(sp)) next ret[[i]] <- sp tmp <- kidids_split(ret[[i]], model.frame(data), obs = subset) ### this needs fixing for multiway "split" tab <- table(tmp, split) if (tab[1, 1] < tab[1, 2]) { indx <- ret[[i]]$index ret[[i]]$index[indx == 1] <- 2L ret[[i]]$index[indx == 2] <- 1L } ### crit[.which.max(crit)] <- -Inf } ret <- ret[!sapply(ret, is.null)] if (length(ret) == 0L) ret <- NULL return(ret) } extree_fit <- function(data, trafo, converged, selectfun = ctrl$selectfun, splitfun = ctrl$splitfun, svselectfun = ctrl$svselectfun, svsplitfun = ctrl$svsplitfun, partyvars, subset, weights, ctrl, doFit = TRUE) { ret <- list() ### use data$vars$z as default for partyvars ### try to avoid doFit nf <- names(formals(trafo)) if (all(c("subset", "weights", "info", "estfun", "object") %in% nf)) { mytrafo <- trafo } else { stopifnot(all(c("y", "x", "offset", "weights", "start") %in% nf)) stopifnot(!is.null(yx <- data$yx)) mytrafo <- function(subset, weights, info, estfun = FALSE, object = FALSE, ...) { iy <- data[["yx", type = "index"]] if (is.null(iy)) { NAyx <- data[["yx", type = "missing"]] y <- yx$y x <- yx$x offset <- attr(yx$x, "offset") ### other ways of handling NAs necessary? subset <- subset[!(subset %in% NAyx)] if (NCOL(y) > 1) { y <- y[subset,,drop = FALSE] } else { y <- y[subset] } if (!is.null(x)) { ax <- attributes(x) ax$dim <- NULL ax$dimnames <- NULL x <- x[subset,,drop = FALSE] for (a in names(ax)) attr(x, a) <- ax[[a]] ### terms, formula, ... for predict } w <- weights[subset] offset <- offset[subset] cluster <- data[["(cluster)"]][subset] if (all(c("estfun", "object") %in% nf)) { m <- trafo(y = y, x = x, offset = offset, weights = w, start = info$coef, cluster = cluster, estfun = estfun, object = object, ...) } else { obj <- trafo(y = y, x = x, offset = offset, weights = w, start = info$coef, cluster = cluster, ...) m <- list(coefficients = coef(obj), objfun = -as.numeric(logLik(obj)), estfun = NULL, object = NULL) if (estfun) m$estfun <- sandwich::estfun(obj) if (object) m$object <- obj } if (!is.null(ef <- m$estfun)) { ### ctree expects unweighted scores if (!isTRUE(m$unweighted) && is.null(selectfun) && ctrl$testflavour == "ctree") m$estfun <- m$estfun / w Y <- matrix(0, nrow = nrow(model.frame(data)), ncol = ncol(ef)) Y[subset,] <- m$estfun m$estfun <- Y } } else { w <- libcoin::ctabs(ix = iy, subset = subset, weights = weights)[-1] offset <- attr(yx$x, "offset") cluster <- model.frame(data, yxonly = TRUE)[["(cluster)"]] if (all(c("estfun", "object") %in% nf)) { m <- trafo(y = yx$y, x = yx$x, offset = offset, weights = w, start = info$coef, cluster = cluster, estfun = estfun, object = object, ...) } else { obj <- trafo(y = yx$y, x = yx$x, offset = offset, weights = w, start = info$coef, cluster = cluster, ...) m <- list(coefficients = coef(obj), objfun = -as.numeric(logLik(obj)), estfun = NULL, object = NULL) if (estfun) m$estfun <- sandwich::estfun(obj) if (object) m$object <- obj if (!is.null(obj$unweighted)) m$unweighted <- obj$unweighted m$converged <- obj$converged ### may or may not exist } ### unweight scores in ctree or weight scores in ### mfluc (means: for each variable again) ### ctree expects unweighted scores if (!is.null(m$estfun)) { if (!isTRUE(m$unweighted) && is.null(selectfun) && ctrl$testflavour == "ctree") m$estfun <- m$estfun / w } if (!is.null(ef <- m$estfun)) m$estfun <- rbind(0, ef) } return(m) } } if (!ctrl$update) { rootestfun <- mytrafo(subset = subset, weights = weights) updatetrafo <- function(subset, weights, info, ...) return(rootestfun) } else { updatetrafo <- function(subset, weights, info, ...) { ret <- mytrafo(subset = subset, weights = weights, info = info, ...) if (is.null(ret$converged)) ret$converged <- TRUE conv <- TRUE if (is.function(converged)) conv <- converged(subset, weights) ret$converged <- ret$converged && conv if (!ret$converged) return(NULL) ret } } nm <- c("model", "trafo", "data", "subset", "weights", "whichvar", "ctrl") stopifnot(all(nm == names(formals(selectfun)))) stopifnot(all(nm == names(formals(splitfun)))) stopifnot(all(nm == names(formals(svselectfun)))) stopifnot(all(nm == names(formals(svsplitfun)))) if (!doFit) return(mytrafo) list(nodes = .extree_node(id = 1, data = data, trafo = updatetrafo, selectfun = selectfun, splitfun = splitfun, svselectfun = svselectfun, svsplitfun = svsplitfun, partyvars = partyvars, weights = weights, subset = subset, ctrl = ctrl), trafo = mytrafo) } ## extensible tree (model) function extree_data <- function(formula, data, subset, na.action = na.pass, weights, offset, cluster, strata, scores = NULL, yx = c("none", "matrix"), ytype = c("vector", "data.frame", "matrix"), nmax = c("yx" = Inf, "z" = Inf), ...) { ## call cl <- match.call() yx <- match.arg(yx, choices = c("none", "matrix")) ytype <- match.arg(ytype, choices = c("vector", "data.frame", "matrix")) ## 'formula' may either be a (multi-part) formula or a list noformula <- !inherits(formula, "formula") if(noformula) { ## formula needs to be a 'list' (if it is not a 'formula') if(!inherits(formula, "list")) stop("unsupported specification of 'formula'") ## specified formula elements and overall call elements fonam <- names(formula) clnam <- names(cl)[-1L] vanam <- c("y", "x", "z", "weights", "offset", "cluster", "strata") ## y and z (and optionally x) need to be in formula if(!all(c("y", "z") %in% fonam)) stop("'formula' needs to specify at least a response 'y' and partitioning variables 'z'") if(!("x" %in% fonam)) formula$x <- NULL ## furthermore weights/offset/cluster/strata may be in formula or call vars <- formula[vanam] names(vars) <- vanam if("weights" %in% clnam) { clvar <- try(weights, silent = TRUE) vars[["weights"]] <- c(vars[["weights"]], if(!inherits(clvar, "try-error")) clvar else deparse(cl$weights)) } if("offset" %in% clnam) { clvar <- try(offset, silent = TRUE) vars[["offset"]] <- c(vars[["offset"]], if(!inherits(clvar, "try-error")) clvar else deparse(cl$offset)) } if("cluster" %in% clnam) { clvar <- try(cluster, silent = TRUE) vars[["cluster"]] <- c(vars[["cluster"]], if(!inherits(clvar, "try-error")) clvar else deparse(cl$cluster)) } if("strata" %in% clnam) { clvar <- try(strata, silent = TRUE) vars[["strata"]] <- c(vars[["strata"]], if(!inherits(clvar, "try-error")) clvar else deparse(cl$strata)) } ## sanity checking for(v in vanam) { if(!is.null(vars[[v]]) && !(is.numeric(vars[[v]]) | is.character(vars[[v]]) | is.logical(vars[[v]]))) { warning(sprintf("unknown specification of '%s', must be character, numeric, or logical", v)) vars[v] <- list(NULL) } } if(!missing(subset)) warning("'subset' argument ignored in list specification of 'formula'") if(!missing(na.action)) warning("'na.action' argument ignored in list specification of 'formula'") ## no terms (by default) mt <- NULL } else { ## set up model.frame() call mf <- match.call(expand.dots = FALSE) mf$na.action <- na.action ### evaluate na.action if(missing(data)) data <- environment(formula) m <- match(c("formula", "data", "subset", "na.action", "weights", "offset", "cluster", "strata"), names(mf), 0L) mf <- mf[c(1L, m)] mf$drop.unused.levels <- TRUE mf$dot <- "sequential" ## formula processing oformula <- as.formula(formula) formula <- Formula::as.Formula(formula) mf$formula <- formula npart <- length(formula) if(any(npart < 1L)) stop("'formula' must specify at least one left-hand and one right-hand side") npart <- npart[2L] ## evaluate model.frame mf[[1L]] <- quote(stats::model.frame) mf <- eval(mf, parent.frame()) ## extract terms in various combinations mt <- list( "all" = terms(formula, data = data, dot = "sequential"), "y" = terms(formula, data = data, rhs = 0L, dot = "sequential"), "z" = terms(formula, data = data, lhs = 0L, rhs = npart, dot = "sequential") ) if(npart > 1L) { mt$yx <-terms(formula, data = data, rhs = 1L, dot = "sequential") for(i in 1L:(npart-1L)) { mt[[paste("x", if(i == 1L) "" else i, sep = "")]] <- terms( formula, data = data, lhs = 0L, rhs = i, dot = "sequential") } } ## extract variable lists vars <- list( y = .get_term_labels(mt$y), x = unique(unlist(lapply(grep("^x", names(mt)), function(i) .get_term_labels(mt[[i]])))), z = .get_term_labels(mt$z), weights = if("(weights)" %in% names(mf)) "(weights)" else NULL, offset = if("(offset)" %in% names(mf)) "(offset)" else NULL, cluster = if("(cluster)" %in% names(mf)) "(cluster)" else NULL, strata = if("(strata)" %in% names(mf)) "(strata)" else NULL ) ymult <- length(vars$y) >= 1L if(!ymult) vars$y <- names(mf)[1L] ## FIXME: store information which variable(s) went into (weights), (offset), (cluster) ## (strata) ## idea: check (x and) z vs. deparse(cl$weights), deparse(cl$offset), deparse(cl$cluster) ## check wether offset was inside the formula if(!is.null(off <- attr(mt$x, "offset"))) { if(is.null(vars$offset)) mf[["(offset)"]] <- rep.int(0, nrow(mf)) for(i in off) mf[["(offset)"]] <- mf[["(offset)"]] + mf[[i]] vars$offset <- "(offset)" } } ## canonicalize y/x/z term labels vanam <- if(noformula) names(data) else names(mf) ## z to numeric if(is.null(vars$z)) stop("at least one 'z' variable must be specified") if(is.integer(vars$z)) vars$z <- vanam[vars$z] if(is.character(vars$z)) vars$z <- vanam %in% vars$z if(is.logical(vars$z)) vars$z <- as.numeric(vars$z) if(is.null(names(vars$z))) names(vars$z) <- vanam vars$z <- vars$z[vanam] if(any(is.na(vars$z))) vars$z[is.na(vars$z)] <- 0 vars$z <- as.numeric(vars$z) ## all others to integer for(v in c("y", "x", "weights", "offset", "cluster", "strata")) { if(!is.null(vars[[v]])) { if(is.character(vars[[v]])) vars[[v]] <- match(vars[[v]], vanam) if(is.logical(vars[[v]])) vars[[v]] <- which(vars[[v]]) if(any(is.na(vars[[v]]))) { vars[[v]] <- vars[[v]][!is.na(vars[[v]])] warning(sprintf("only found the '%s' variables: %s", v, paste(vanam[vars[[v]]], collapse = ", "))) } } vars[[v]] <- unique(as.integer(vars[[v]])) } if(is.null(vars$y)) stop("at least one 'y' variable must be specified") ## FIXME: subsequently fitting, testing, splitting ## - fit: either pre-processed _and_ subsetted data --or-- full data object plus subset vector ## - test: additionally needs fit output --and-- fit function ## - split: additionally needs test output ## - tbd: control of all details ret <- list( data = if(noformula) data else mf, variables = vars, terms = mt ) mf <- ret$data yxvars <- c(vars$y, vars$x, vars$offset, vars$cluster) zerozvars <- which(vars$z == 0) ret$scores <- vector(mode = "list", length = length(ret$variables$z)) names(ret$scores) <- names(mf) if (!is.null(scores)) ret$scores[names(scores)] <- scores if (length(nmax) == 1) nmax <- c("yx" = nmax, "z" = nmax) ### make meanlevels an argument and make sure intersplit is TRUE ret$zindex <- inum::inum(mf, ignore = names(mf)[zerozvars], total = FALSE, nmax = nmax["z"], meanlevels = FALSE) if (is.finite(nmax["yx"])) { ret$yxindex <- inum::inum(mf[, yxvars, drop = FALSE], total = TRUE, as.interval = names(mf)[vars$y], complete.cases.only = TRUE, nmax = nmax["yx"], meanlevels = FALSE) yxmf <- attr(ret$yxindex, "levels") yxmf[["(weights)"]] <- NULL attr(ret$yxindex, "levels") <- yxmf } else { ret$yxindex <- NULL yxmf <- mf } ret$missings <- lapply(ret$data, function(x) which(is.na(x))) ret$yxmissings <- sort(unique(do.call("c", ret$missings[yxvars]))) ## FIXME: separate object with options for: discretization, condensation, some NA handling ## below is just "proof-of-concept" implementation using plain model.matrix() which could ## be included as one option... if (yx == "matrix") { ## fake formula/terms if necessary formula <- Formula::as.Formula(sprintf("%s ~ %s | %s", paste(vanam[vars$y], collapse = " + "), if(length(vars$x) > 0L) paste(vanam[vars$x], collapse = " + ") else "0", paste(vanam[vars$z > 0], collapse = " + ") )) mt <- list( "all" = terms(formula), "y" = terms(formula, data = data, rhs = 0L), "z" = terms(formula, data = data, lhs = 0L, rhs = 2L), "yx" = terms(formula, data = data, rhs = 1L), "x" = terms(formula, data = data, lhs = 0L, rhs = 1L) ) ymult <- length(vars$y) > 1L npart <- 2L if (ytype == "vector" && !ymult) { yx <- list("y" = yxmf[, vanam[vars$y], drop = TRUE]) } else if (ytype == "data.frame") { yx <- list("y" = yxmf[vanam[vars$y]]) } else { ### ytype = "matrix" Ytmp <- model.matrix(~ 0 + ., Formula::model.part(formula, yxmf, lhs = TRUE)) ### are there cases where Ytmp already has missings? if (is.finite(nmax["yx"])) { Ymat <- Ytmp } else { if (length(ret$yxmissings) == 0) { Ymat <- Ytmp } else { Ymat <- matrix(0, nrow = NROW(yxmf), ncol = NCOL(Ytmp)) Ymat[-ret$yxmissings,] <- Ytmp } } yx <- list("y" = Ymat) } for(i in (1L:npart)[-npart]) { ni <- paste("x", if(i == 1L) "" else i, sep = "") ti <- if(!ymult & npart == 2L) mt$yx else mt[[ni]] Xtmp <- model.matrix(ti, yxmf) if (is.finite(nmax["yx"])) { Xmat <- Xtmp } else { if (length(ret$yxmissings) == 0) { Xmat <- Xtmp } else { Xmat <- matrix(0, nrow = NROW(yxmf), ncol = NCOL(Xtmp)) Xmat[-ret$yxmissings,] <- Xtmp } } yx[[ni]] <- Xmat if(ncol(yx[[ni]]) < 1L) { yx[[ni]] <- NULL } else { attr(yx[[ni]], "formula") <- formula(formula, rhs = i) attr(yx[[ni]], "terms") <- ti attr(yx[[ni]], "offset") <- yxmf[["(offset)"]] } } ret$yx <- yx } class(ret) <- "extree_data" ret } model.frame.extree_data <- function(formula, yxonly = FALSE, ...) { if (!yxonly) return(formula$data) if (!is.null(formula$yxindex)) return(attr(formula$yxindex, "levels")) vars <- formula$variables return(formula$data[, c(vars$y, vars$x, vars$offset, vars$cluster),drop = FALSE]) } ## for handling of non-standard variable names within extree_data() by mimicking ## handling of such variables in model.frame() etc. in "stats" prompted by ## https://stackoverflow.com/questions/64660889/ctree-ignores-variables-with-non-syntactic-names .deparse_variables <- function(x) paste(deparse(x, width.cutoff = 500L, backtick = !is.symbol(x) && is.language(x)), collapse = " ") .get_term_labels <- function(terms, delete_response = FALSE) { ## ## with just standard variable names one could use: ## attr(terms, "term.labels") ## delete response from terms (if needed) if(delete_response) terms <- delete.response(terms) ## with non-standard variable names -> deparse to handle `...` correctly vapply(attr(terms, "variables"), .deparse_variables, " ")[-1L] } ### document how to extract slots fast "[[.extree_data" <- function(x, i, type = c("original", "index", "scores", "missings")) { type <- match.arg(type, choices = c("original", "index", "scores", "missings")) switch(type, "original" = { if (i == "yx") return(model.frame(x, yxonly = TRUE)) mf <- model.frame(x) ### [[.data.frame needs lots of memory class(mf) <- "list" return(mf[[i]]) }, "index" = { if (i == "yx" || i %in% c(x$variables$y, x$variables$x)) return(x$yxindex) ### may be NULL return(x$zindex[[i]]) }, "scores" = { f <- x[[i]] if (is.ordered(f)) { sc <- x$scores[[i]] if (is.null(sc)) sc <- 1:nlevels(f) return(sc) } return(NULL) }, "missings" = { if (i == "yx" || i %in% c(x$variables$y, x$variables$x)) return(x$yxmissings) x$missings[[i]] } ) } ### control arguments needed in this file extree_control <- function ( criterion, logmincriterion, minsplit = 20L, minbucket = 7L, minprob = 0.01, nmax = Inf, maxvar = Inf, stump = FALSE, lookahead = FALSE, ### try trafo() for daugther nodes before implementing the split maxsurrogate = 0L, numsurrogate = FALSE, mtry = Inf, maxdepth = Inf, multiway = FALSE, splittry = 2L, majority = FALSE, caseweights = TRUE, applyfun = NULL, cores = NULL, saveinfo = TRUE, bonferroni = FALSE, update = NULL, selectfun, splitfun, svselectfun, svsplitfun ) { ## apply infrastructure for determining split points if (is.null(applyfun)) { applyfun <- if(is.null(cores)) { lapply } else { function(X, FUN, ...) parallel::mclapply(X, FUN, ..., mc.cores = cores) } } ### well, it is implemented but not correctly so if (multiway & maxsurrogate > 0L) stop("surrogate splits currently not implemented for multiway splits") list(criterion = criterion, logmincriterion = logmincriterion, minsplit = minsplit, minbucket = minbucket, minprob = minprob, maxvar = max(c(1, maxvar)), stump = stump, nmax = nmax, lookahead = lookahead, mtry = mtry, maxdepth = maxdepth, multiway = multiway, splittry = splittry, maxsurrogate = maxsurrogate, numsurrogate = numsurrogate, majority = majority, caseweights = caseweights, applyfun = applyfun, saveinfo = saveinfo, bonferroni = bonferroni, update = update, selectfun = selectfun, splitfun = splitfun, svselectfun = svselectfun, svsplitfun = svsplitfun) } .objfun_test <- function(model, trafo, data, subset, weights, j, SPLITONLY, ctrl) { x <- data[[j]] NAs <- data[[j, type = "missing"]] if (all(subset %in% NAs)) { if (SPLITONLY) return(NULL) return(list(statistic = NA, p.value = NA)) } ix <- data[[j, type = "index"]] ux <- attr(ix, "levels") ixtab <- libcoin::ctabs(ix = ix, weights = weights, subset = subset)[-1] ORDERED <- is.ordered(x) || is.numeric(x) linfo <- rinfo <- model minlogLik <- nosplitll <- trafo(subset = subset, weights = weights, info = model, estfun = FALSE)$objfun sp <- NULL if (ORDERED) { ll <- ctrl$applyfun(which(ixtab > 0), function(u) { sleft <- subset[LEFT <- (ix[subset] <= u)] sright <- subset[!LEFT] if (length(weights) > 0 && ctrl$caseweights) { if (sum(weights[sleft]) < ctrl$minbucket || sum(weights[sright]) < ctrl$minbucket) return(Inf); } else { if (length(sleft) < ctrl$minbucket || length(sright) < ctrl$minbucket) return(Inf); } if (ctrl$restart) { linfo <- NULL rinfo <- NULL } linfo <- trafo(subset = sleft, weights = weights, info = linfo, estfun = FALSE) rinfo <- trafo(subset = sright, weights = weights, info = rinfo, estfun = FALSE) ll <- linfo$objfun + rinfo$objfun return(ll) }) minlogLik <- min(unlist(ll)) if(minlogLik < nosplitll) sp <- which(ixtab > 0)[which.min(unlist(ll))] } else { xsubs <- factor(x[subset]) ## stop if only one level left if(nlevels(xsubs) < 2) { if (SPLITONLY) { return(NULL) } else { return(list(statistic = NA, p.value = NA)) } } splits <- .mob_grow_getlevels(xsubs) ll <- ctrl$applyfun(1:nrow(splits), function(u) { sleft <- subset[LEFT <- xsubs %in% levels(xsubs)[splits[u,]]] sright <- subset[!LEFT] if (length(weights) > 0 && ctrl$caseweights) { if (sum(weights[sleft]) < ctrl$minbucket || sum(weights[sright]) < ctrl$minbucket) return(Inf); } else { if (length(sleft) < ctrl$minbucket || length(sright) < ctrl$minbucket) return(Inf); } if (ctrl$restart) { linfo <- NULL rinfo <- NULL } linfo <- trafo(subset = sleft, weights = weights, info = linfo, estfun = FALSE) rinfo <- trafo(subset = sright, weights = weights, info = rinfo, estfun = FALSE) ll <- linfo$objfun + rinfo$objfun return(ll) }) minlogLik <- min(unlist(ll)) if(minlogLik < nosplitll) { sp <- splits[which.min(unlist(ll)),] + 1L levs <- levels(x) if(length(sp) != length(levs)) { sp <- sp[levs] names(sp) <- levs } } } if (!SPLITONLY){ ## split only if logLik improves due to splitting minlogLik <- ifelse(minlogLik == nosplitll, NA, minlogLik) return(list(statistic = -minlogLik, p.value = NA)) ### .extree_node maximises } if (is.null(sp) || all(is.na(sp))) return(NULL) if (ORDERED) { ### interpolate split-points, see https://arxiv.org/abs/1611.04561 if (!is.factor(x) & ctrl$intersplit & sp < length(ux)) { sp <- (ux[sp] + ux[sp + 1]) / 2 } else { sp <- ux[sp] ### x <= sp vs. x > sp } if (is.factor(sp)) sp <- as.integer(sp) ret <- partysplit(as.integer(j), breaks = sp, index = 1L:2L) } else { ret <- partysplit(as.integer(j), index = as.integer(sp)) } return(ret) } .start_subset <- function(data) { ret <- 1:NROW(model.frame(data)) if (length(data$yxmissings) > 0) ret <- ret[!(ret %in% data$yxmissings)] ret } partykit/R/party.R0000644000176200001440000005415514723336543013630 0ustar liggesusers## FIXME: data in party ## - currently assumed to be a data.frame ## - potentially empty ## - the following are all assumed to work: ## dim(data), names(data) ## sapply(data, class), lapply(data, levels) ## - potentially these need to be modified if data/terms ## should be able to deal with data bases party <- function(node, data, fitted = NULL, terms = NULL, names = NULL, info = NULL) { stopifnot(inherits(node, "partynode")) stopifnot(inherits(data, "data.frame")) ### make sure all split variables are there ids <- nodeids(node)[!nodeids(node) %in% nodeids(node, terminal = TRUE)] varids <- unique(unlist(nodeapply(node, ids = ids, FUN = function(x) varid_split(split_node(x))))) stopifnot(varids %in% 1:ncol(data)) if(!is.null(fitted)) { stopifnot(inherits(fitted, "data.frame")) stopifnot(nrow(data) == 0L | nrow(data) == nrow(fitted)) # try to provide default variable "(fitted)" if(nrow(data) > 0L) { if(!("(fitted)" %in% names(fitted))) fitted[["(fitted)"]] <- fitted_node(node, data = data) } else { stopifnot("(fitted)" == names(fitted)[1L]) } nt <- nodeids(node, terminal = TRUE) stopifnot(all(fitted[["(fitted)"]] %in% nt)) node <- as.partynode(node, from = 1L) nt2 <- nodeids(node, terminal = TRUE) fitted[["(fitted)"]] <- nt2[match(fitted[["(fitted)"]], nt)] } else { node <- as.partynode(node, from = 1L) # default "(fitted)" if(nrow(data) > 0L & missing(fitted)) fitted <- data.frame("(fitted)" = fitted_node(node, data = data), check.names = FALSE) } party <- list(node = node, data = data, fitted = fitted, terms = NULL, names = NULL, info = info) class(party) <- "party" if(!is.null(terms)) { stopifnot(inherits(terms, "terms")) party$terms <- terms } if (!is.null(names)) { n <- length(nodeids(party, terminal = FALSE)) if (length(names) != n) stop("invalid", " ", sQuote("names"), " ", "argument") party$names <- names } party } length.party <- function(x) length(nodeids(x)) names.party <- function(x) .names_party(x) "names<-.party" <- function(x, value) { n <- length(nodeids(x, terminal = FALSE)) if (!is.null(value) && length(value) != n) stop("invalid", " ", sQuote("names"), " ", "argument") x$names <- value x } .names_party <- function(party) { names <- party$names if (is.null(names)) names <- as.character(nodeids(party, terminal = FALSE)) names } node_party <- function(party) { stopifnot(inherits(party, "party")) party$node } is.constparty <- function(party) { stopifnot(inherits(party, "party")) if (!is.null(party$fitted)) return(all(c("(fitted)", "(response)") %in% names(party$fitted))) return(FALSE) } as.constparty <- function(obj, ...) { if(!inherits(obj, "party")) obj <- as.party(obj) if (!is.constparty(obj)) { if(is.null(obj$fitted)) obj$fitted <- data.frame("(fitted)" = predict(obj, type = "node"), check.names = FALSE) if(!("(fitted)" %in% names(obj$fitted))) obj$fitted["(fitted)"] <- predict(obj, type = "node") if(!("(response)" %in% names(obj$fitted))) obj$fitted["(response)"] <- model.response(model.frame(obj)) if(!("(weights)" %in% names(obj$fitted))) { w <- model.weights(model.frame(obj)) if(is.null(w) && any(w != 1L)) obj$fitted["(weights)"] <- w } } if (is.constparty(obj)) { ret <- obj class(ret) <- c("constparty", class(obj)) return(ret) } stop("cannot coerce object of class", " ", sQuote(class(obj)), " ", "to", " ", sQuote("constparty")) } "[.party" <- "[[.party" <- function(x, i, ...) { if (is.character(i) && !is.null(names(x))) i <- which(names(x) %in% i) stopifnot(length(i) == 1 & is.numeric(i)) stopifnot(i <= length(x) & i >= 1) i <- as.integer(i) dat <- data_party(x, i) if (!is.null(x$fitted)) { findx <- which("(fitted)" == names(dat))[1] fit <- dat[,findx:ncol(dat), drop = FALSE] dat <- dat[,-(findx:ncol(dat)), drop = FALSE] if (ncol(dat) == 0) dat <- x$data } else { fit <- NULL dat <- x$data } nam <- names(x)[nodeids(x, from = i, terminal = FALSE)] recFun <- function(node) { if (id_node(node) == i) return(node) kid <- sapply(kids_node(node), id_node) return(recFun(node[[max(which(kid <= i))]])) } node <- recFun(node_party(x)) ret <- party(node = node, data = dat, fitted = fit, terms = x$terms, names = nam, info = x$info) class(ret) <- class(x) ret } nodeids <- function(obj, ...) UseMethod("nodeids") nodeids.partynode <- function(obj, from = NULL, terminal = FALSE, ...) { if(is.null(from)) from <- id_node(obj) id <- function(node, record = TRUE, terminal = FALSE) { if(!record) return(NULL) if(!terminal) return(id_node(node)) else if(is.terminal(node)) return(id_node(node)) else return(NULL) } rid <- function(node, record = TRUE, terminal = FALSE) { myid <- id(node, record = record, terminal = terminal) if(is.terminal(node)) return(myid) kids <- kids_node(node) kids_record <- if(record) rep(TRUE, length(kids)) else sapply(kids, id_node) == from return(c(myid, unlist(lapply(1:length(kids), function(i) rid(kids[[i]], record = kids_record[i], terminal = terminal))) )) } return(rid(obj, from == id_node(obj), terminal)) } nodeids.party <- function(obj, from = NULL, terminal = FALSE, ...) nodeids(node_party(obj), from = from, terminal = terminal, ...) nodeapply <- function(obj, ids = 1, FUN = NULL, ...) UseMethod("nodeapply") nodeapply.party <- function(obj, ids = 1, FUN = NULL, by_node = TRUE, ...) { stopifnot(isTRUE(all.equal(ids, round(ids)))) ids <- as.integer(ids) if(is.null(FUN)) FUN <- function(x, ...) x if (length(ids) == 0) return(NULL) if (by_node) { rval <- nodeapply(node_party(obj), ids = ids, FUN = FUN, ...) } else { rval <- lapply(ids, function(i) FUN(obj[[i]], ...)) } names(rval) <- names(obj)[ids] return(rval) } nodeapply.partynode <- function(obj, ids = 1, FUN = NULL, ...) { stopifnot(isTRUE(all.equal(ids, round(ids)))) ids <- as.integer(ids) if(is.null(FUN)) FUN <- function(x, ...) x if (length(ids) == 0) return(NULL) rval <- vector(mode = "list", length = length(ids)) rval_id <- rep(0, length(ids)) i <- 1 recFUN <- function(node, ...) { if(id_node(node) %in% ids) { rval_id[i] <<- id_node(node) rval[[i]] <<- FUN(node, ...) i <<- i + 1 } kids <- kids_node(node) if(length(kids) > 0) { for(j in 1:length(kids)) recFUN(kids[[j]]) } invisible(TRUE) } foo <- recFUN(obj) rval <- rval[match(ids, rval_id)] return(rval) } predict.party <- function(object, newdata = NULL, perm = NULL, ...) { ### compute fitted node ids first fitted <- if(is.null(newdata) && is.null(perm)) { object$fitted[["(fitted)"]] } else { if (is.null(newdata)) newdata <- model.frame(object) terminal <- nodeids(object, terminal = TRUE) if(max(terminal) == 1L) { rep.int(1L, NROW(newdata)) } else { inner <- 1L:max(terminal) inner <- inner[-terminal] primary_vars <- nodeapply(object, ids = inner, by_node = TRUE, FUN = function(node) { varid_split(split_node(node)) }) surrogate_vars <- nodeapply(object, ids = inner, by_node = TRUE, FUN = function(node) { surr <- surrogates_node(node) if(is.null(surr)) return(NULL) else return(sapply(surr, varid_split)) }) vnames <- names(object$data) ### the splits of nodes with a primary split in perm ### will be permuted if (!is.null(perm)) { if (is.character(perm)) { stopifnot(all(perm %in% vnames)) perm <- match(perm, vnames) } else { ### perm is a named list of factors coding strata ### (for varimp(..., conditional = TRUE) stopifnot(all(names(perm) %in% vnames)) stopifnot(all(sapply(perm, is.factor))) tmp <- vector(mode = "list", length = length(vnames)) tmp[match(names(perm), vnames)] <- perm perm <- tmp } } ## ## FIXME: the is.na() call takes loooong on large data sets ## unames <- if(any(sapply(newdata, is.na))) ## vnames[unique(unlist(c(primary_vars, surrogate_vars)))] ## else ## vnames[unique(unlist(primary_vars))] unames <- vnames[unique(unlist(c(primary_vars, surrogate_vars)))] vclass <- structure(lapply(object$data, class), .Names = vnames) ndnames <- names(newdata) ndclass <- structure(lapply(newdata, class), .Names = ndnames) checkclass <- all(sapply(unames, function(x) isTRUE(all.equal(vclass[[x]], ndclass[[x]])))) factors <- sapply(unames, function(x) inherits(object$data[[x]], "factor")) checkfactors <- all(sapply(unames[factors], function(x) isTRUE(all.equal(levels(object$data[[x]]), levels(newdata[[x]]))))) ## FIXME: inform about wrong classes / factor levels? if(all(unames %in% ndnames) && checkclass && checkfactors) { vmatch <- match(vnames, ndnames) fitted_node(node_party(object), data = newdata, vmatch = vmatch, perm = perm) } else { if (!is.null(object$terms)) { ### this won't work for multivariate responses ### xlev <- lapply(unames[factors], function(x) levels(object$data[[x]])) names(xlev) <- unames[factors] mf <- model.frame(delete.response(object$terms), newdata, xlev = xlev) fitted_node(node_party(object), data = mf, vmatch = match(vnames, names(mf)), perm = perm) } else stop("") ## FIXME: write error message } } } ### compute predictions predict_party(object, fitted, newdata, ...) } predict_party <- function(party, id, newdata = NULL, ...) UseMethod("predict_party") ### do nothing expect returning the fitted ids predict_party.default <- function(party, id, newdata = NULL, FUN = NULL, ...) { if (length(list(...)) > 1) warning("argument(s)", " ", sQuote(names(list(...))), " ", "have been ignored") ## get observation names: either node names or ## observation names from newdata nam <- if(is.null(newdata)) { if(is.null(rnam <- rownames(data_party(party)))) names(party)[id] else rnam } else { rownames(newdata) } if(length(nam) != length(id)) nam <- NULL if (!is.null(FUN)) return(.simplify_pred(nodeapply(party, nodeids(party, terminal = TRUE), FUN, by_node = TRUE), id, nam)) ## special case: fitted ids return(structure(id, .Names = nam)) } predict_party.constparty <- function(party, id, newdata = NULL, type = c("response", "prob", "quantile", "density", "node"), at = if (type == "quantile") c(0.1, 0.5, 0.9), FUN = NULL, simplify = TRUE, ...) { ## extract fitted information response <- party$fitted[["(response)"]] weights <- party$fitted[["(weights)"]] fitted <- party$fitted[["(fitted)"]] if (is.null(weights)) weights <- rep(1, NROW(response)) ## get observation names: either node names or ## observation names from newdata nam <- if(is.null(newdata)) names(party)[id] else rownames(newdata) if(length(nam) != length(id)) nam <- NULL ## match type type <- match.arg(type) ## special case: fitted ids if(type == "node") return(structure(id, .Names = nam)) ### multivariate response if (is.data.frame(response)) { ret <- lapply(response, function(r) { ret <- .predict_party_constparty(node_party(party), fitted = fitted, response = r, weights, id = id, type = type, at = at, FUN = FUN, ...) if (simplify) .simplify_pred(ret, id, nam) else ret }) if (all(sapply(ret, is.atomic))) ret <- as.data.frame(ret) names(ret) <- colnames(response) return(ret) } ### univariate response ret <- .predict_party_constparty(node_party(party), fitted = fitted, response = response, weights = weights, id = id, type = type, at = at, FUN = FUN, ...) if (simplify) .simplify_pred(ret, id, nam) else ret[as.character(id)] } ### functions for node prediction based on fitted / response .pred_Surv <- function(y, w) { if (length(y) == 0) return(NA) survfit(y ~ 1, weights = w, subset = w > 0) } .pred_Surv_response <- function(y, w) { if (length(y) == 0) return(NA) .median_survival_time(.pred_Surv(y, w)) } .pred_factor <- function(y, w) { lev <- levels(y) sumw <- tapply(w, y, sum) sumw[is.na(sumw)] <- 0 prob <- sumw / sum(w) names(prob) <- lev return(prob) } .pred_factor_response <- function(y, w) { prob <- .pred_factor(y, w) return(factor(which.max(prob), levels = 1:nlevels(y), labels = levels(y), ordered = is.ordered(y))) return(prob) } .pred_numeric_response <- function(y, w) weighted.mean(y, w, na.rm = TRUE) .pred_ecdf <- function(y, w) { if (length(y) == 0) return(NA) iw <- as.integer(round(w)) if (max(abs(w - iw)) < sqrt(.Machine$double.eps)) { y <- rep(y, w) return(ecdf(y)) } else { stop("cannot compute empirical distribution function with non-integer weights") } } .pred_quantile <- function(y, w) { y <- rep(y, w) function(p, ...) quantile(y, probs = p, ...) } .pred_density <- function(y, w) { ### we only have integer-valued weights and density complains ### about weights since R 4.3.0 (because bandwidth selection doesn't ### work with weights) yw <- rep(y, w) d <- density(yw) approxfun(d[1:2], rule = 2) } ### workhorse: compute predictions based on fitted / response data .predict_party_constparty <- function(node, fitted, response, weights, id = id, type = c("response", "prob", "quantile", "density"), at = if (type == "quantile") c(0.1, 0.5, 0.9), FUN = NULL, ...) { type <- match.arg(type) if (is.null(FUN)) { rtype <- class(response)[1] if (rtype == "ordered") rtype <- "factor" if (rtype == "integer") rtype <- "numeric" if (rtype == "AsIs") rtype <- "numeric" if (type %in% c("quantile", "density") && rtype != "numeric") stop("quantile and density estimation currently only implemented for numeric responses") FUN <- switch(rtype, "Surv" = if (type == "response") .pred_Surv_response else .pred_Surv, "factor" = if (type == "response") .pred_factor_response else .pred_factor, "numeric" = switch(type, "response" = .pred_numeric_response, "prob" = .pred_ecdf, "quantile" = .pred_quantile, "density" = .pred_density) ) } ## empirical distribution in each leaf if (all(id %in% fitted)) { tab <- tapply(1:NROW(response), fitted, function(i) FUN(response[i], weights[i]), simplify = FALSE) } else { ### id may also refer to inner nodes tab <- as.array(lapply(sort(unique(id)), function(i) { index <- fitted %in% nodeids(node, i, terminal = TRUE) ret <- FUN(response[index], weights[index]) ### no information about i in fitted if (all(!index)) ret[1] <- NA return(ret) })) names(tab) <- as.character(sort(unique(id))) } if (inherits(tab[[1]], "function") && !is.null(at)) tab <- lapply(tab, function(f) f(at)) tn <- names(tab) dim(tab) <- NULL names(tab) <- tn tab } ### simplify structure of predictions .simplify_pred <- function(tab, id, nam) { if (all(sapply(tab, length) == 1) & all(sapply(tab, is.atomic))) { ret <- do.call("c", tab) names(ret) <- names(tab) ### R 4.1.x allows to call c() on factors, this is needed for ### backward-compatibility ret <- if (is.factor(tab[[1]]) & !is.factor(ret)) factor(ret[as.character(id)], levels = 1:length(levels(tab[[1]])), labels = levels(tab[[1]]), ordered = is.ordered(tab[[1]])) else ret[as.character(id)] names(ret) <- nam } else if (length(unique(sapply(tab, length))) == 1 & all(sapply(tab, is.numeric))) { ret <- matrix(unlist(tab), nrow = length(tab), byrow = TRUE) colnames(ret) <- names(tab[[1]]) rownames(ret) <- names(tab) ret <- ret[as.character(id),, drop = FALSE] rownames(ret) <- nam } else { ret <- tab[as.character(id)] names(ret) <- nam } ret } data_party <- function(party, id = 1L) UseMethod("data_party") data_party.default <- function(party, id = 1L) { extract <- function(id) { if(is.null(party$fitted)) if(nrow(party$data) == 0) return(NULL) else stop("cannot subset data without fitted ids") ### which terminal nodes follow node number id? nt <- nodeids(party, id, terminal = TRUE) wi <- party$fitted[["(fitted)"]] %in% nt ret <- if (nrow(party$data) == 0) subset(party$fitted, wi) else subset(cbind(party$data[, !(names(party$data) %in% names(party$fitted)), drop = FALSE], party$fitted), wi) ret } if (length(id) > 1) return(lapply(id, extract)) else return(extract(id)) } width.party <- function(x, ...) { width(node_party(x), ...) } depth.party <- function(x, root = FALSE, ...) { depth(node_party(x), root = root, ...) } getCall.party <- function(x, ...) { x$info$call } getCall.constparties <- function(x, ...) { x$info$call } formula.party <- function(x, ...) { x <- terms(x) NextMethod() } model.frame.party <- function(formula, ...) { mf <- formula$data if(nrow(mf) > 0L) return(mf) dots <- list(...) nargs <- dots[match(c("data", "na.action", "subset"), names(dots), 0L)] mf <- getCall(formula) mf <- mf[c(1L, match(c("formula", "data", "subset", "na.action"), names(mf), 0L))] mf$drop.unused.levels <- TRUE mf[[1L]] <- quote(stats::model.frame) mf[names(nargs)] <- nargs if(is.null(env <- environment(terms(formula)))) env <- parent.frame() eval(mf, env) } nodeprune <- function(x, ids, ...) UseMethod("nodeprune") nodeprune.partynode <- function(x, ids, ...) { stopifnot(ids %in% nodeids(x)) ### compute indices path to each node ### to be pruned off idxs <- lapply(ids, .get_path, obj = x) ### [[.partynode is NOT [[.list cls <- class(x) x <- unclass(x) for (i in 1:length(idxs)) { ## path to be pruned idx <- idxs[[i]] if(!is.null(idx)) { ### check if we already pruned-off this node tmp <- try(x[[idx]], silent = TRUE) if(inherits(tmp, "try-error")) next() ### prune node by introducing a "new" terminal node x[[idx]] <- partynode(id = id_node(tmp), info = info_node(tmp)) } else { ## if idx path is NULL prune everything x[2L:4L] <- NULL } } class(x) <- cls return(as.partynode(x, from = 1L)) } nodeprune.default <- function(x, ids, ...) stop("No", sQuote("nodeprune"), "method for class", class(x), "implemented") .list.rules.party <- function(x, i = NULL, ...) { if (is.null(i)) i <- nodeids(x, terminal = TRUE) if (length(i) > 1) { ret <- sapply(i, .list.rules.party, x = x) names(ret) <- if (is.character(i)) i else names(x)[i] return(ret) } if (is.character(i) && !is.null(names(x))) i <- which(names(x) %in% i) stopifnot(length(i) == 1 & is.numeric(i)) stopifnot(i <= length(x) & i >= 1) i <- as.integer(i) dat <- data_party(x, i) if (!is.null(x$fitted)) { findx <- which("(fitted)" == names(dat))[1] fit <- dat[,findx:ncol(dat), drop = FALSE] dat <- dat[,-(findx:ncol(dat)), drop = FALSE] if (ncol(dat) == 0) dat <- x$data } else { fit <- NULL dat <- x$data } rule <- c() recFun <- function(node) { if (id_node(node) == i) return(NULL) kid <- sapply(kids_node(node), id_node) whichkid <- max(which(kid <= i)) split <- split_node(node) ivar <- varid_split(split) svar <- names(dat)[ivar] index <- index_split(split) if (is.factor(dat[, svar])) { if (is.null(index)) index <- ((1:nlevels(dat[, svar])) > breaks_split(split)) + 1 slevels <- levels(dat[, svar])[index == whichkid] srule <- paste(svar, " %in% c(\"", paste(slevels, collapse = "\", \"", sep = ""), "\")", sep = "") } else { if (is.null(index)) index <- 1:length(kid) breaks <- cbind(c(-Inf, breaks_split(split)), c(breaks_split(split), Inf)) sbreak <- breaks[index == whichkid,] right <- right_split(split) srule <- c() if (is.finite(sbreak[1])) srule <- c(srule, paste(svar, ifelse(right, ">", ">="), sbreak[1])) if (is.finite(sbreak[2])) srule <- c(srule, paste(svar, ifelse(right, "<=", "<"), sbreak[2])) srule <- paste(srule, collapse = " & ") } rule <<- c(rule, srule) return(recFun(node[[whichkid]])) } node <- recFun(node_party(x)) paste(rule, collapse = " & ") } partykit/R/as.party.R0000644000176200001440000001702714172230000014202 0ustar liggesusersas.party <- function(obj, ...) UseMethod("as.party") as.party.rpart <- function(obj, data = TRUE, ...) { ff <- obj$frame n <- nrow(ff) ### it is no longer allowed to overwrite rpart::model.frame.rpart ### make sure to use our own implementation ### which works without `model = TRUE' in the rpart call mf <- model_frame_rpart(obj) ## check if any of the variables in the model frame is a "character" ## and convert to "factor" if necessary for(i in which(sapply(mf, function(x) class(x)[1L]) == "character")) mf[[i]] <- factor(mf[[i]]) rpart_fitted <- function() { ret <- as.data.frame(matrix(nrow = NROW(mf), ncol = 0)) ret[["(fitted)"]] <- obj$where ret[["(response)"]] <- model.response(mf) ret[["(weights)"]] <- model.weights(mf) ret } fitted <- rpart_fitted() # special case of no splits if (n == 1) { node <- partynode(1L) } else { is.leaf <- (ff$var == "") vnames <- ff$var[!is.leaf] #the variable names for the primary splits index <- cumsum(c(1, ff$ncompete + ff$nsurrogate + 1*(!is.leaf))) splitindex <- list() splitindex$primary <- numeric(n) splitindex$primary[!is.leaf] <- index[c(!is.leaf, FALSE)] splitindex$surrogate <- lapply(1L:n, function(i) { prim <- splitindex$primary[i] if (prim < 1 || ff[i, "nsurrogate"] == 0) return(NULL) else return(prim + ff[i, "ncompete"] + 1L:ff[i, "nsurrogate"]) }) rpart_kids <- function(i) { if (is.leaf[i]) return(NULL) else return(c(i + 1L, which((cumsum(!is.leaf[-(1L:i)]) + 1L) == cumsum(is.leaf[-(1L:i)]))[1L] + 1L + i)) } rpart_onesplit <- function(j) { if (j < 1) return(NULL) idj <- which(rownames(obj$split)[j] == names(mf)) ### numeric if (abs(obj$split[j, "ncat"]) == 1) { ret <- partysplit(varid = idj, breaks = as.double(obj$split[j, "index"]), right = FALSE, index = if(obj$split[j, "ncat"] > 0) 2L:1L) } else { index <- obj$csplit[obj$split[j, "index"],] mfj <- mf[, rownames(obj$split)[j]] ### csplit has columns 1L:max(nlevels) for all factors ### index <- index[1L:obj$split[j, "ncat"]] ??? safer ??? index <- index[1L:nlevels(mfj)] index[index == 2L] <- NA ### level not present in split index[index == 3L] <- 2L ### 1..left, 3..right if(inherits(mfj, "ordered")) { ret <- partysplit(varid = idj, breaks = which(diff(index) != 0L) + 1L, right = FALSE, index = unique(index)) } else { ret <- partysplit(varid = idj, index = as.integer(index)) } } ret } rpart_split <- function(i) rpart_onesplit(splitindex$primary[i]) rpart_surrogates <- function(i) lapply(splitindex$surrogate[[i]], rpart_onesplit) rpart_node <- function(i) { if (is.null(rpart_kids(i))) return(partynode(as.integer(i))) nd <- partynode(as.integer(i), split = rpart_split(i), kids = lapply(rpart_kids(i), rpart_node), surrogates = rpart_surrogates(i)) ### determine majority for (non-random) splitting left <- nodeids(kids_node(nd)[[1L]], terminal = TRUE) right <- nodeids(kids_node(nd)[[2L]], terminal = TRUE) nd$split$prob <- c(0, 0) nl <- sum(fitted[["(fitted)"]] %in% left) nr <- sum(fitted[["(fitted)"]] %in% right) nd$split$prob <- if (nl > nr) c(1, 0) else c(0, 1) nd$split$prob <- as.double(nd$split$prob) return(nd) } node <- rpart_node(1) } rval <- party(node = node, data = if(data) mf else mf[0L,], fitted = fitted, terms = obj$terms, info = list(method = "rpart")) class(rval) <- c("constparty", class(rval)) return(rval) } model_frame_rpart <- function(formula, ...) { ## if model.frame is stored, simply extract if(!is.null(formula$model)) return(formula$model) ## otherwise reevaluate model.frame using original call mf <- formula$call mf <- mf[c(1L, match(c("formula", "data", "subset", "na.action", "weights"), names(mf), 0L))] if (is.null(mf$na.action)) mf$na.action <- rpart::na.rpart # mf$drop.unused.levels <- TRUE mf[[1L]] <- quote(stats::model.frame) ## use terms instead of formula in call mf$formula <- formula$terms ## evaluate in the right environment and return env <- if(!is.null(environment(formula$terms))) environment(formula$terms) else parent.frame() mf <- eval(mf, env) return(mf) } as.party.Weka_tree <- function(obj, data = TRUE, ...) { ## needs RWeka and rJava stopifnot(requireNamespace("RWeka")) ## J48 tree? (can be transformed to "constparty") j48 <- inherits(obj, "J48") ## construct metadata mf <- model.frame(obj) mf_class <- sapply(mf, function(x) class(x)[1L]) mf_levels <- lapply(mf, levels) x <- rJava::.jcall(obj$classifier, "S", "graph") if(j48) { info <- NULL } else { info <- RWeka::parse_Weka_digraph(x, plainleaf = FALSE)$nodes[, 2L] info <- strsplit(info, " (", fixed = TRUE) info <- lapply(info, function(x) if(length(x) == 1L) x else c(x[1L], paste("(", x[-1L], sep = ""))) } x <- RWeka::parse_Weka_digraph(x, plainleaf = TRUE) nodes <- x$nodes edges <- x$edges is.leaf <- x$nodes[, "splitvar"] == "" weka_tree_kids <- function(i) { if (is.leaf[i]) return(NULL) else return(which(nodes[,"name"] %in% edges[nodes[i,"name"] == edges[,"from"], "to"])) } weka_tree_split <- function(i) { if(is.leaf[i]) return(NULL) var_id <- which(nodes[i, "splitvar"] == names(mf)) edges <- edges[nodes[i,"name"] == edges[,"from"], "label"] split <- Map(c, sub("^([[:punct:]]+).*$", "\\1", edges), sub("^([[:punct:]]+) *", "", edges)) ## ## for J48 the following suffices ## split <- strsplit(edges[nodes[i,"name"] == edges[,"from"], "label"], " ") if(mf_class[var_id] %in% c("ordered", "factor")) { stopifnot(all(sapply(split, head, 1) == "=")) stopifnot(all(sapply(split, tail, 1) %in% mf_levels[[var_id]])) split <- partysplit(varid = as.integer(var_id), index = match(mf_levels[[var_id]], sapply(split, tail, 1))) } else { breaks <- unique(as.numeric(sapply(split, tail, 1))) breaks <- if(mf_class[var_id] == "integer") as.integer(breaks) else as.double(breaks) ## FIXME: check stopifnot(length(breaks) == 1 && !is.na(breaks)) stopifnot(all(sapply(split, head, 1) %in% c("<=", ">"))) split <- partysplit(varid = as.integer(var_id), breaks = breaks, right = TRUE, index = if(split[[1L]][1L] == ">") 2L:1L) } return(split) } weka_tree_node <- function(i) { if(is.null(weka_tree_kids(i))) return(partynode(as.integer(i), info = info[[i]])) partynode(as.integer(i), split = weka_tree_split(i), kids = lapply(weka_tree_kids(i), weka_tree_node)) } node <- weka_tree_node(1) if(j48) { pty <- party( node = node, data = if(data) mf else mf[0L,], fitted = data.frame("(fitted)" = fitted_node(node, mf), "(response)" = model.response(mf), check.names = FALSE), terms = obj$terms, info = list(method = "J4.8")) class(pty) <- c("constparty", class(pty)) } else { pty <- party( node = node, data = mf[0L,], fitted = data.frame("(fitted)" = fitted_node(node, mf), check.names = FALSE), terms = obj$terms, info = list(method = class(obj)[1L])) } return(pty) } partykit/R/prune.R0000644000176200001440000000245014172230000013564 0ustar liggesusers nodeprune.party <- function(x, ids, ...) { ### map names to nodeids if (!is.numeric(ids)) ids <- match(ids, names(x)) stopifnot(ids %in% nodeids(x)) ### compute indices path to each node ### to be pruned off idxs <- lapply(ids, .get_path, obj = node_party(x)) ### [[.party is NOT [[.list cls <- class(x) x <- unclass(x) ni <- which(names(x) == "node") for (i in 1:length(idxs)) { idx <- c(ni, idxs[[i]]) ### check if we already pruned-off this node tmp <- try(x[[idx]], silent = TRUE) if (inherits(tmp, "try-error")) next() ### node ids of off-pruned daugther nodes idrm <- nodeids(x[[idx]])[-1] ### prune node by introducing a "new" terminal node x[[idx]] <- partynode(id = id_node(x[[idx]]), info = info_node(x[[idx]])) ### constparty only: make sure the node ids in ### fitted are corrected if (length(idrm) > 0) { if(!is.null(x$fitted) && "(fitted)" %in% names(x$fitted)) { j <- x$fitted[["(fitted)"]] %in% idrm x$fitted[["(fitted)"]][j] <- ids[i] } } } ### reindex to 1:max(nodeid) class(x) <- cls oldids <- nodeids(x) newids <- 1:length(nodeids(x)) nodeids(x) <- newids ### this takes also care of $fitted! return(x) } partykit/R/utils.R0000644000176200001440000000674314172230000013604 0ustar liggesusers ### length(x) == 1 will lead to sample.int instead of sample; ### see example(sample) .resample <- function(x, ...) x[sample.int(length(x), ...)] .median_survival_time <- function(x) { minmin <- function(y, xx) { if (any(!is.na(y) & y==.5)) { if (any(!is.na(y) & y <.5)) .5*(min(xx[!is.na(y) & y==.5]) + min(xx[!is.na(y) & y<.5])) else .5*(min(xx[!is.na(y) & y==.5]) + max(xx[!is.na(y) & y==.5])) } else min(xx[!is.na(y) & y<=.5]) } med <- suppressWarnings(minmin(x$surv, x$time)) return(med) } get_paths <- function(obj, i) { id0 <- nodeids(obj) if (inherits(obj, "party")) obj <- node_party(obj) if (!inherits(obj, "partynode")) stop(sQuote("obj"), " is not an object of class partynode") i <- as.integer(i) if (!all(i %in% id0)) stop(sQuote("i"), " does not match node identifiers of ", sQuote("obj")) lapply(i, function(id) { if (id == 1L) return(1L) .get_path(obj, id) }) } ### get the recursive index ### obj is of class "partynode" .get_path <- function(obj, i) { idx <- c() recFun <- function(node, i) { if (id_node(node) == i) return(NULL) idx <<- c(idx, which(names(unclass(node)) == "kids")) kid <- sapply(kids_node(node), id_node) nextid <- max(which(kid <= i)) idx <<- c(idx, nextid) return(recFun(node[[nextid]], i)) } out <- recFun(obj, i) return(idx) } ### shall we export this functionality? "nodeids<-" <- function(obj, value) UseMethod("nodeids<-") "nodeids<-.party" <- function(obj, value) { id0 <- nodeids(obj) id1 <- as.integer(value) stopifnot(identical(id1, 1:length(id0))) idxs <- lapply(id0, .get_path, obj = node_party(obj)) x <- unclass(obj) ni <- which(names(x) == "node") nm <- x$names for (i in 1:length(idxs)) x[[c(ni, idxs[[i]])]]$id <- id1[i] class(x) <- class(obj) if (!is.null(nm)) names(x) <- nm[id0] return(x) } "nodeids<-.constparty" <- "nodeids<-.modelparty" <- function(obj, value) { id0 <- nodeids(obj) cls <- class(obj) class(obj) <- "party" nodeids(obj) <- value id1 <- nodeids(obj) obj$fitted[["(fitted)"]] <- id1[match(fitted(obj)[["(fitted)"]], id0)] class(obj) <- cls obj } ### ## determine all possible splits for a factor, both nominal and ordinal .mob_grow_getlevels <- function(z) { nl <- nlevels(z) if(inherits(z, "ordered")) { indx <- diag(nl) indx[lower.tri(indx)] <- 1 indx <- indx[-nl, , drop = FALSE] rownames(indx) <- levels(z)[-nl] } else { mi <- 2^(nl - 1L) - 1L indx <- matrix(0, nrow = mi, ncol = nl) for (i in 1L:mi) { ii <- i for (l in 1L:nl) { indx[i, l] <- ii %% 2L ii <- ii %/% 2L } } rownames(indx) <- apply(indx, 1L, function(x) paste(levels(z)[x > 0], collapse = "+")) } colnames(indx) <- as.character(levels(z)) storage.mode(indx) <- "logical" indx } .rfweights <- function(fdata, fnewdata, rw, scale) w <- .Call(R_rfweights, fdata, fnewdata, rw, scale) ### determine class of response .response_class <- function(x) { if (is.factor(x)) { if (is.ordered(x)) return("ordered") return("factor") } if (inherits(x, "Surv")) return("Surv") if (inherits(x, "survfit")) return("survfit") if (inherits(x, "AsIs")) return("numeric") if (is.integer(x)) return("numeric") if (is.numeric(x)) return("numeric") return("unknown") } partykit/R/varimp.R0000644000176200001440000002130714172230000013733 0ustar liggesusers logLik.constparty <- function(object, newdata, weights, perm = NULL, ...) { y <- object$fitted[["(response)"]] if (missing(newdata)) { fitted <- if (is.null(perm)) { object$fitted[["(fitted)"]] } else { ### no need to watch vmatch because newdata is always mf if (!is.null(perm)) { vnames <- names(object$data) if (is.character(perm)) { stopifnot(all(perm %in% vnames)) perm <- match(perm, vnames) } else { ### perm is a named list of factors coding strata ### (for varimp(..., conditional = TRUE) stopifnot(all(names(perm) %in% vnames)) stopifnot(all(sapply(perm, is.factor))) tmp <- vector(mode = "list", length = length(vnames)) tmp[match(names(perm), vnames)] <- perm perm <- tmp } } fitted_node(node_party(object), data = object$data, perm = perm) } pr <- predict_party(object, id = fitted, newdata = object$data, type = ifelse(inherits(y, "factor"), "prob", "response"), ...) } else { pr <- predict(object, newdata = newdata, type = ifelse(inherits(y, "factor"), "prob", "response"), ...) } ll <- switch(.response_class(y), "integer" = { -(y - pr)^2 }, "numeric" = { -(y - pr)^2 }, "factor" = { log(pmax(pr[cbind(1:length(y), unclass(y))], sqrt(.Machine$double.eps))) }, "ordered" = { log(pmax(pr[cbind(1:length(y), unclass(y))], sqrt(.Machine$double.eps))) }, "Surv" = stop("not yet implemented"), stop("not yet implemented") ) if (missing(weights)) weights <- data_party(object)[["(weights)"]] if (is.null(weights)) return(sum(ll) / length(y)) return(sum(weights * ll) / sum(weights)) } miscls <- function(object, newdata, weights, perm = NULL, ...) { y <- object$fitted[["(response)"]] stopifnot(is.factor(y)) if (missing(newdata)) { fitted <- if (is.null(perm)) { object$fitted[["(fitted)"]] } else { ### no need to watch vmatch because newdata is always mf if (!is.null(perm)) { vnames <- names(object$data) if (is.character(perm)) { stopifnot(all(perm %in% vnames)) perm <- match(perm, vnames) } else { ### perm is a named list of factors coding strata ### (for varimp(..., conditional = TRUE) stopifnot(all(names(perm) %in% vnames)) stopifnot(all(sapply(perm, is.factor))) tmp <- vector(mode = "list", length = length(vnames)) tmp[match(names(perm), vnames)] <- perm perm <- tmp } } fitted_node(node_party(object), data = object$data, perm = perm) } pr <- predict_party(object, id = fitted, newdata = object$data, type = "response", ...) } else { pr <- predict(object, newdata = newdata, type = "response", ...) } ll <- unclass(y) != unclass(pr) if (missing(weights)) weights <- data_party(object)[["(weights)"]] if (is.null(weights)) return(sum(ll) / length(y)) return(sum(weights * ll) / sum(weights)) } varimp <- function(object, nperm = 1L, ...) UseMethod("varimp") varimp.constparty <- function(object, nperm = 1L, risk = c("loglik", "misclassification"), conditions = NULL, mincriterion = 0, ...) { if (!is.function(risk)) { risk <- match.arg(risk) ### risk is _NEGATIVE_ log-likelihood risk <- switch(risk, "loglik" = function(...) -logLik(...), "misclassification" = miscls) } if (mincriterion > 0) stop("mincriterion not yet implemented") ### use nodeprune psplitids <- unique(do.call("c", nodeapply(node_party(object), ids = nodeids(node_party(object)), FUN = function(x) split_node(x)$varid))) vnames <- names(object$data) psplitvars <- vnames[psplitids] ret <- numeric(length(psplitvars)) names(ret) <- psplitvars for (vn in psplitvars) { cvn <- conditions[[vn]] if (is.null(cvn)) { perm <- vn } else { blocks <- .get_psplits(object, cvn) if (length(blocks) == 0) blocks <- factor(rep(1, nrow(object$data))) perm <- vector(mode = "list", length = 1) names(perm) <- vn perm[[vn]] <- blocks } for (p in 1:nperm) ret[vn] <- ret[vn] + risk(object, perm = perm, ...) } ret <- ret / nperm - risk(object, ...) ret } gettree <- function(object, tree = 1L, ...) UseMethod("gettree") gettree.cforest <- function(object, tree = 1L, ...) { ft <- object$fitted ft[["(weights)"]] <- object$weights[[tree]] ret <- party(object$nodes[[tree]], data = object$data, fitted = ft) ret$terms <- object$terms class(ret) <- c("constparty", class(ret)) ret } .create_cond_list <- function(object, threshold) { d <- object$data response <- names(d)[attr(object$terms, "response")] xnames <- all.vars(object$terms) xnames <- xnames[xnames != response] ret <- lapply(xnames, function(x) { tmp <- ctree(as.formula(paste(x, "~", paste(xnames[xnames != x], collapse = "+"))), data = d, control = ctree_control(teststat = "quad", testtype = "Univariate", stump = TRUE)) pval <- info_node(node_party(tmp))$criterion["p.value",] pval[is.na(pval)] <- 1 ### make the meaning of threshold equal to partykit ret <- names(pval)[(1 - pval) > threshold] if (length(ret) == 0) return(NULL) return(ret) }) names(ret) <- xnames return(ret) } .get_psplits <- function(object, xnames) { d <- object$data ret <- lapply(xnames, function(xn) { id <- which(colnames(d) == xn) psplits <- nodeapply(node_party(object), ids = nodeids(node_party(object)), FUN = function(x) { if (is.null(x)) return(NULL) if (is.terminal(x)) return(NULL) if (split_node(x)$varid == id) return(split_node(x)) return(NULL) }) psplits <- psplits[!sapply(psplits, is.null)] if (length(psplits) > 0) return(do.call("interaction", lapply(lapply(psplits, kidids_split, data = d), factor, exclude = NULL))[, drop = TRUE]) return(NULL) }) ret <- ret[!sapply(ret, is.null)] if (length(ret) > 0) { if (length(ret) == 1) return(factor(ret[[1]], exclude = NULL)) ### get rid of empty levels quickly; do.call("interaction", ret) ### explodes for (i in 2:length(ret)) ret[[1]] <- factor(interaction(ret[[1]], ret[[i]])[, drop = TRUE], exclude = NULL) return(ret[[1]]) } return(NULL) } varimp.cforest <- function(object, nperm = 1L, OOB = TRUE, risk = c("loglik", "misclassification"), conditional = FALSE, threshold = .2, applyfun = NULL, cores = NULL, ...) { ret <- matrix(NA, nrow = length(object$nodes), ncol = ncol(object$data)) colnames(ret) <- names(object$data) if (conditional) { conditions <- .create_cond_list(object, threshold) } else { conditions <- NULL } ## apply infrastructure if (is.null(applyfun)) { applyfun <- if(is.null(cores)) { lapply } else { function(X, FUN, ...) parallel::mclapply(X, FUN, ..., mc.set.seed = TRUE, mc.cores = cores) } } vi <- applyfun(1:length(object$nodes), function(b) { tree <- gettree(object, b) if (OOB) { oobw <- as.integer(object$weights[[b]] == 0) vi <- varimp(tree, nperm = nperm, risk = risk, conditions = conditions, weights = oobw, ...) } else { vi <- varimp(tree, nperm = nperm, risk = risk, conditions = conditions, ...) } return(vi) }) for (b in 1:length(object$nodes)) ret[b, match(names(vi[[b]]), colnames(ret))] <- vi[[b]] ret <- colMeans(ret, na.rm = TRUE) ret[!sapply(ret, is.na)] } partykit/R/simpleparty.R0000644000176200001440000001524114172230000015006 0ustar liggesusers.make_formatinfo_simpleparty <- function(x, digits = getOption("digits") - 4, sep = "") { ## digit processing digits <- max(c(0, digits)) digits2 <- max(c(0, digits - 2)) ## type of predictions y <- node_party(x)$info$prediction yclass <- .response_class(y) if(yclass == "ordered") yclass <- "factor" if(!(yclass %in% c("survfit", "factor"))) yclass <- "numeric" ## type of weights n <- node_party(x)$info$n if(is.null(names(n))) { wdigits <- 0 wsym <- "n" } else { if(names(n) == "w") { wdigits <- max(c(0, digits - 2)) wsym <- "w" } else { wdigits <- 0 wsym <- "n" } } ## compute terminal node labels FUN <- function(info) { yhat <- info$prediction if (yclass == "survfit") { yhat <- .median_survival_time(yhat) yclass <- "numeric" } if(yclass == "numeric") yhat <- format(round(yhat, digits = digits), nsmall = digits) w <- info$n yerr <- if(is.null(info$error)) "" else paste(", err = ", format(round(info$error, digits = digits2), nsmall = digits2), names(info$error), sep = "") rval <- paste(yhat, sep, " (", wsym, " = ", format(round(w, digits = wdigits), nsmall = wdigits), yerr, ")", sep = "") unlist(strsplit(rval, "\n")) } return(FUN) } plot.simpleparty <- function(x, digits = getOption("digits") - 4, tp_args = NULL, ...) { if(is.null(tp_args)) tp_args <- list(FUN = .make_formatinfo_simpleparty(x, digits = digits, sep = "\n")) plot.party(x, tp_args = tp_args, ...) } print.simpleparty <- function(x, digits = getOption("digits") - 4, header = NULL, footer = TRUE, ...) { ## header panel if(is.null(header)) header <- !is.null(terms(x)) header_panel <- if(header) function(party) { c("", "Model formula:", deparse(formula(terms(party))), "", "Fitted party:", "") } else function(party) "" ## footer panel footer_panel <- if(footer) function(party) { n <- width(party) n <- format(c(length(party) - n, n)) c("", paste("Number of inner nodes: ", n[1]), paste("Number of terminal nodes:", n[2]), "") } else function (party) "" ## terminal panel terminal_panel <- function(node) formatinfo_node(node, FUN = .make_formatinfo_simpleparty(x, digits = digits), default = "*", prefix = ": ") print.party(x, terminal_panel = terminal_panel, header_panel = header_panel, footer_panel = footer_panel, ...) } predict_party.simpleparty <- function(party, id, newdata = NULL, type = c("response", "prob", "node"), ...) { ## get observation names: either node names or ## observation names from newdata nam <- if(is.null(newdata)) names(party)[id] else rownames(newdata) if(length(nam) != length(id)) nam <- NULL ## match type type <- match.arg(type) ## special case: fitted ids if(type == "node") return(structure(id, .Names = nam)) ## predictions if(type == "response") { FUN <- function(x) x$info$prediction } else { if(is.null(node_party(party)$info$distribution)) stop("probabilities not available") scale <- any(node_party(party)$info$distribution > 1) FUN <- function(x) if(scale) prop.table(x$info$distribution) else x$info$distribution } predict_party.default(party, id, nam, FUN = FUN, ...) } as.simpleparty <- function(obj, ...) UseMethod("as.simpleparty") as.simpleparty.simpleparty <- function(obj, ...) obj as.simpleparty.party <- function(obj, ...) { if (is.simpleparty(obj)) { class(obj) <- unique(c("simpleparty", class(obj))) return(obj) } if (is.constparty(obj)) return(as.simpleparty(as.constparty(obj))) stop("cannot coerce objects of class ", sQuote(class(obj)), " to class ", sQuote("simpleparty")) } as.simpleparty.XMLNode <- function(obj, ...) as.party(obj) as.simpleparty.constparty <- function(obj, ...) { ## extract and delete fitted fit <- obj$fitted obj$fitted <- NULL ## response info rtype <- .response_class(fit[["(response)"]]) if (rtype == "ordered") rtype <- "factor" if (rtype == "integer") rtype <- "numeric" ## extract fitted info FUN <- function(node, fitted) { fitted <- subset(fitted, fitted[["(fitted)"]] %in% nodeids(node, terminal = TRUE)) if (nrow(fitted) == 0) return(list(prediction = NA, n = 0, error = NA, distribution = NULL)) y <- fitted[["(response)"]] w <- fitted[["(weights)"]] if(is.null(w)) { w <- rep(1, nrow(fitted)) wnam <- "n" } else { wnam <- if(isTRUE(all.equal(w, round(w)))) "n" else "w" } ## extract p.value (if any) pval <- function(node) { p <- info_node(node) if(is.list(p)) p$p.value else NULL } switch(rtype, "numeric" = { yhat <- .pred_numeric_response(y, w) list(prediction = yhat, n = structure(sum(w), .Names = wnam), error = sum(w * (y - yhat)^2), distribution = NULL, p.value = pval(node)) }, "factor" = { yhat <- .pred_factor_response(y, w) ytab <- round(.pred_factor(y, w) * sum(w)) list(prediction = yhat, n = structure(sum(w), .Names = wnam), error = structure(sum(100 * prop.table(ytab)[names(ytab) != yhat]), .Names = "%"), distribution = ytab, p.value = pval(node)) }, "Surv" = { list(prediction = .pred_Surv(y, w), n = structure(sum(w), .Names = wnam), error = NULL, distribution = NULL, p.value = pval(node)) ## FIXME: change distribution format? }) } ## convenience function for computing kid ids fit2id <- function(fit, idlist) { fit <- factor(fit) nlevels <- levels(fit) for(i in 1:length(idlist)) nlevels[match(idlist[[i]], levels(fit))] <- i levels(fit) <- nlevels ret <- factor(as.numeric(as.character(fit)), labels = 1:length(idlist), levels = 1:length(idlist)) ret } ## cycle through node new_node <- function(onode, fitted) { if(is.terminal(onode)) return(partynode(id = onode$id, split = NULL, kids = NULL, surrogates = NULL, info = FUN(onode, fitted))) kids <- kids_node(onode) kids_tid <- lapply(kids, nodeids, terminal = TRUE) kids_fitted <- base::split.data.frame(fitted, fit2id(fitted[["(fitted)"]], kids_tid), drop = FALSE) partynode(id = onode$id, split = onode$split, kids = lapply(1:length(kids), function(i) new_node(kids[[i]], kids_fitted[[i]])), surrogates = onode$surrogates, info = FUN(onode, fitted)) } obj$node <- new_node(node_party(obj), fit) class(obj) <- c("simpleparty", "party") return(obj) } is.simpleparty <- function(party) { chkinfo <- function(node) all(c("prediction", "n", "error", "distribution") %in% names(info_node(node))) all(nodeapply(party, ids = nodeids(party), FUN = chkinfo, by_node = TRUE)) } partykit/R/mob-pvalue.R0000644000176200001440000013030414172230000014502 0ustar liggesusersmob_beta_suplm <- structure( c(-0.0648467, -0.15305667, -0.23071675, -0.29247661, -0.35706588, -0.40514715, -0.45248386, -0.50458517, -0.55009159, -0.60241623, -0.64308746, -0.68833676, -0.73136161, -0.78078198, -0.82894221, -0.88430133, -0.9499265, -0.98828874, -1.04892713, -1.11527783, -1.14992644, -1.24010871, -1.38522113, -1.48296473, -1.78738608, -0.03933112, -0.14650989, -0.28765583, -0.35528752, -0.49538961, -0.58780544, -0.66900489, -0.77825803, -0.87260977, -0.96782445, -1.07358977, -1.12531079, -1.16041007, -1.2975797, -1.36743697, -1.43012785, -1.53311747, -1.65273586, -1.79350728, -1.9117747, -2.02659329, -2.18499383, -2.3765858, -2.51267262, -3.05559851, -0.1250856, -0.27323021, -0.43148524, -0.48172245, -0.6898932, -0.7928579, -0.85066146, -1.06133796, -1.11977435, -1.20203015, 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"978", "979", "980", "981", "982", "983", "984", "985", "986", "987", "988", "989", "990", "991", "992", "993", "994", "995", "996", "997", "998", "999", "1000"), c("V1", "V2", "V3"))) partykit/R/glmtree.R0000644000176200001440000001252514172230000014076 0ustar liggesusers## simple wrapper function to specify fitter and return class glmtree <- function(formula, data, subset, na.action, weights, offset, cluster, family = gaussian, epsilon = 1e-8, maxit = 25, method = "glm.fit", ...) { ## use dots for setting up mob_control control <- mob_control(...) ## keep call cl <- match.call(expand.dots = TRUE) ## extend formula if necessary f <- Formula::Formula(formula) if(length(f)[2L] == 1L) { attr(f, "rhs") <- c(list(1), attr(f, "rhs")) formula[[3L]] <- formula(f)[[3L]] } else { f <- NULL } ## process family if(inherits(family, "family")) { fam <- TRUE } else { fam <- FALSE if(is.character(family)) family <- get(family) if(is.function(family)) family <- family() } ## distinguish whether glm should be fixed for case weights or not glmfit0 <- function(y, x, start = NULL, weights = NULL, offset = NULL, cluster = NULL, ..., estfun = FALSE, object = FALSE, caseweights = TRUE) { glmfit(y = y, x = x, start = start, weights = weights, offset = offset, cluster = cluster, ..., estfun = estfun, object = object, caseweights = control$caseweights) } ## call mob m <- match.call(expand.dots = FALSE) if(!is.null(f)) m$formula <- formula m$fit <- glmfit0 m$control <- control m$epsilon <- epsilon m$maxit <- maxit m$method <- method if("..." %in% names(m)) m[["..."]] <- NULL if(!fam) m$family <- family m[[1L]] <- as.call(quote(partykit::mob)) rval <- eval(m, parent.frame()) ## extend class and keep original call rval$info$call <- cl rval$info$family <- family$family class(rval) <- c("glmtree", class(rval)) return(rval) } ## actual fitting function for mob() glmfit <- function(y, x, start = NULL, weights = NULL, offset = NULL, cluster = NULL, ..., estfun = FALSE, object = FALSE, caseweights = TRUE) { ## catch control arguments args <- list(...) ctrl <- list() for(n in c("epsilon", "maxit")) { if(n %in% names(args)) { ctrl[[n]] <- args[[n]] args[[n]] <- NULL } } args$control <- do.call("glm.control", ctrl) ## add intercept-only regressor matrix (if missing) ## NOTE: does not have terms/formula if(is.null(x)) x <- matrix(1, nrow = NROW(y), ncol = 1L, dimnames = list(NULL, "(Intercept)")) ## call glm fitting function (defaulting to glm.fit) glm.method <- if("method" %in% names(args)) args[["method"]] else "glm.fit" args[["method"]] <- NULL args <- c(list(x = x, y = y, start = start, weights = weights, offset = offset), args) z <- do.call(glm.method, args) ## degrees of freedom df <- z$rank if(z$family$family %in% c("gaussian", "Gamma", "inverse.gaussian")) df <- df + 1 if(substr(z$family$family, 1L, 5L) != "quasi") objfun <- z$aic/2 - df else objfun <- z$deviance ## list structure rval <- list( coefficients = z$coefficients, objfun = objfun, estfun = NULL, object = NULL ) ## add estimating functions (if desired) if(estfun) { wres <- as.vector(z$residuals) * z$weights dispersion <- if(substr(z$family$family, 1L, 17L) %in% c("poisson", "binomial", "Negative Binomial")) { 1 } else { ## for case weights: fix dispersion estimate if(!is.null(weights) && caseweights) { sum(wres^2/weights, na.rm = TRUE)/sum(z$weights, na.rm = TRUE) } else { sum(wres^2, na.rm = TRUE)/sum(z$weights, na.rm = TRUE) } } rval$estfun <- wres * x[, !is.na(z$coefficients), drop = FALSE]/dispersion } ## add model (if desired) if(object) { class(z) <- c("glm", "lm") z$offset <- if(is.null(offset)) 0 else offset z$contrasts <- attr(x, "contrasts") z$xlevels <- attr(x, "xlevels") cl <- as.call(expression(glm)) cl$formula <- attr(x, "formula") if(!is.null(offset)) cl$offset <- attr(x, "offset") z$call <- cl z$terms <- attr(x, "terms") ## for case weights: change degrees of freedom if(!is.null(weights) && caseweights) { z$df.null <- z$df.null - sum(weights > 0) + sum(weights) z$df.residual <- z$df.residual - sum(weights > 0) + sum(weights) } rval$object <- z } return(rval) } ## methods print.glmtree <- function(x, title = NULL, objfun = NULL, ...) { if(is.null(title)) title <- sprintf("Generalized linear model tree (family: %s)", x$info$family) if(is.null(objfun)) objfun <- if(substr(x$info$family, 1L, 5L) != "quasi") "negative log-likelihood" else "deviance" print.modelparty(x, title = title, objfun = objfun, ...) } predict.glmtree <- function(object, newdata = NULL, type = "response", ...) { ## FIXME: possible to get default? if(is.null(newdata) & !identical(type, "node")) stop("newdata has to be provided") predict.modelparty(object, newdata = newdata, type = type, ...) } plot.glmtree <- function(x, terminal_panel = node_bivplot, tp_args = list(), tnex = NULL, drop_terminal = NULL, ...) { nreg <- if(is.null(tp_args$which)) x$info$nreg else length(tp_args$which) if(nreg < 1L & missing(terminal_panel)) { plot.constparty(as.constparty(x), tp_args = tp_args, tnex = tnex, drop_terminal = drop_terminal, ...) } else { if(is.null(tnex)) tnex <- if(is.null(terminal_panel)) 1L else 2L * nreg if(is.null(drop_terminal)) drop_terminal <- !is.null(terminal_panel) plot.modelparty(x, terminal_panel = terminal_panel, tp_args = tp_args, tnex = tnex, drop_terminal = drop_terminal, ...) } } partykit/R/mob-plot.R0000644000176200001440000002155114172230000014167 0ustar liggesusersnode_bivplot <- function(mobobj, which = NULL, id = TRUE, pop = TRUE, pointcol = "black", pointcex = 0.5, boxcol = "black", boxwidth = 0.5, boxfill = "lightgray", bg = "white", fitmean = TRUE, linecol = "red", cdplot = FALSE, fivenum = TRUE, breaks = NULL, ylines = NULL, xlab = FALSE, ylab = FALSE, margins = rep(1.5, 4), mainlab = NULL, ...) { ## obtain dependent variable mf <- model.frame(mobobj) y <- Formula::model.part(mobobj$info$Formula, mf, lhs = 1L, rhs = 0L) if(isTRUE(ylab)) ylab <- names(y) if(identical(ylab, FALSE)) ylab <- "" if(is.null(ylines)) ylines <- ifelse(identical(ylab, ""), 0, 2) y <- y[[1L]] ## obtain explanatory variables X <- Formula::model.part(mobobj$info$Formula, mf, lhs = 0L, rhs = 1L) ## fitted node ids fitted <- mobobj$fitted[["(fitted)"]] ## if no explanatory variables: behave like plot.constparty if(inherits(X, "try-error")) { rval <- switch(.response_class(y), "Surv" = node_surv(mobobj, id = id, mainlab = mainlab, ...), "factor" = node_barplot(mobobj, id = id, mainlab = mainlab, ...), "ordered" = node_barplot(mobobj, id = id, mainlab = mainlab, ...), node_boxplot(mobobj, ...)) return(rval) } ## reverse levels for spine/CD plot if(is.factor(y)) y <- factor(y, levels = rev(levels(y))) ## number of panels needed if(is.null(which)) which <- 1L:NCOL(X) X <- X[,which,drop=FALSE] k <- NCOL(X) xlab <- if(!identical(xlab, FALSE)) { if(isTRUE(xlab)) colnames(X) else rep(xlab, length.out = k) } else rep("", k) ## set up appropriate panel functions if(is.factor(y)) { ## CD plots and spine plots ## re-use implementation from vcd package if(!requireNamespace("vcd")) stop(sprintf("Package %s is required for spine/CD plots", sQuote("vcd"))) if(cdplot) { num_fun <- function(x, y, yfit, i, name, ...) { vcd::cd_plot(x, y, xlab = xlab[i], ylab = ylab, name = name, newpage = FALSE, margins = margins, pop = FALSE, ...) if(fitmean) { #FIXME# downViewport(name = name) grid.lines(x, yfit, default.units = "native", gp = gpar(col = linecol)) if(pop) popViewport() else upViewport() } else { #FIXME# if(pop) popViewport() else upViewport() } } } else { xscale <- if(is.null(breaks)) { if(fivenum) lapply(X, function(z) {if(is.factor(z)) 1 else fivenum(z) }) else lapply(X, function(z) {if(is.factor(z)) 1 else hist(z, plot = FALSE)$breaks }) } else { if(is.list(breaks)) breaks else list(breaks) } num_fun <- function(x, y, yfit, i, name, ...) { vcd::spine(x, y, xlab = xlab[i], ylab = ylab, name = name, newpage = FALSE, margins = margins, pop = FALSE, breaks = xscale[[i]], ...) if(fitmean) { #FIXME# downViewport(name = name) xaux <- cut(x, breaks = xscale[[i]], include.lowest = TRUE) yfit <- unlist(tapply(yfit, xaux, mean)) xaux <- prop.table(table(xaux)) xaux <- cumsum(xaux) - xaux/2 grid.lines(xaux, yfit, default.units = "native", gp = gpar(col = linecol)) grid.points(xaux, yfit, default.units = "native", gp = gpar(col = linecol, cex = pointcex), pch = 19) if(pop) popViewport() else upViewport() } else { #FIXME# if(pop) popViewport() else upViewport() } } } cat_fun <- function(x, y, yfit, i, name, ...) { vcd::spine(x, y, xlab = xlab[i], ylab = ylab, name = name, newpage = FALSE, margins = margins, pop = FALSE, ...) if(fitmean) { #FIXME# downViewport(name = name) yfit <- unlist(tapply(yfit, x, mean)) xaux <- prop.table(table(x)) xaux <- cumsum(xaux + 0.02) - xaux/2 - 0.02 grid.lines(xaux, yfit, default.units = "native", gp = gpar(col = linecol)) grid.points(xaux, yfit, default.units = "native", gp = gpar(col = linecol, cex = pointcex), pch = 19) if(pop) popViewport() else upViewport() } else { #FIXME# if(pop) popViewport() else upViewport() } } } else { xscale <- sapply(X, function(z) {if(is.factor(z)) c(1, length(levels(z))) else range(z) }) yscale <- range(y) + c(-0.1, 0.1) * diff(range(y)) ## scatter plots and box plots num_fun <- function(x, y, yfit, i, name, ...) { xscale[,i] <- xscale[,i] + c(-0.1, 0.1) * diff(xscale[,i]) pushViewport(plotViewport(margins = margins, name = name, yscale = yscale, xscale = xscale[,i])) grid.points(x, y, gp = gpar(col = pointcol, cex = pointcex)) if(fitmean) { grid.lines(x, yfit, default.units = "native", gp = gpar(col = linecol)) } grid.xaxis(at = c(ceiling(xscale[1L,i]*10), floor(xscale[2L,i]*10))/10) grid.yaxis(at = c(ceiling(yscale[1L]), floor(yscale[2L]))) grid.rect(gp = gpar(fill = "transparent")) if(ylab != "") grid.text(ylab, y = unit(0.5, "npc"), x = unit(-2.5, "lines"), rot = 90) if(xlab[i] != "") grid.text(xlab[i], x = unit(0.5, "npc"), y = unit(-2, "lines")) if(pop) popViewport() else upViewport() } cat_fun <- function(x, y, yfit, i, name, ...) { xlev <- levels(x) pushViewport(plotViewport(margins = margins, name = name, yscale = yscale, xscale = c(0.3, xscale[2L,i]+0.7))) for(j in seq_along(xlev)) { by <- boxplot(y[x == xlev[j]], plot = FALSE) xl <- j - boxwidth/4 xr <- j + boxwidth/4 ## box & whiskers grid.lines(unit(c(xl, xr), "native"), unit(by$stats[1L], "native"), gp = gpar(col = boxcol)) grid.lines(unit(j, "native"), unit(by$stats[1L:2L], "native"), gp = gpar(col = boxcol, lty = 2)) grid.rect(unit(j, "native"), unit(by$stats[2L], "native"), width = unit(boxwidth, "native"), height = unit(diff(by$stats[2:3]), "native"), just = c("center", "bottom"), gp = gpar(col = boxcol, fill = boxfill)) grid.rect(unit(j, "native"), unit(by$stats[3L], "native"), width = unit(boxwidth, "native"), height = unit(diff(by$stats[3L:4L]), "native"), just = c("center", "bottom"), gp = gpar(col = boxcol, fill = boxfill)) grid.lines(unit(j, "native"), unit(by$stats[4L:5L], "native"), gp = gpar(col = boxcol, lty = 2)) grid.lines(unit(c(xl, xr), "native"), unit(by$stats[5L], "native"), gp = gpar(col = boxcol)) ## outlier n <- length(by$out) if (n > 0L) { grid.points(unit(rep.int(j, n), "native"), unit(by$out, "native"), size = unit(0.5, "char"), gp = gpar(col = boxcol)) } } if(fitmean) { yfit <- unlist(tapply(yfit, x, mean)) grid.lines(seq_along(xlev), yfit, default.units = "native", gp = gpar(col = linecol)) grid.points(seq_along(xlev), yfit, default.units = "native", gp = gpar(col = linecol, cex = pointcex), pch = 19) } grid.rect(gp = gpar(fill = "transparent")) grid.xaxis(at = 1L:length(xlev), label = xlev) grid.yaxis(at = c(ceiling(yscale[1L]), floor(yscale[2L]))) if(ylab != "") grid.text(ylab, y = unit(0.5, "npc"), x = unit(-3, "lines"), rot = 90) if(xlab[i] != "") grid.text(xlab[i], x = unit(0.5, "npc"), y = unit(-2, "lines")) if(pop) popViewport() else upViewport() } } rval <- function(node) { ## node index nid <- id_node(node) ix <- fitted %in% nodeids(mobobj, from = nid, terminal = TRUE) ## dependent variable y <- y[ix] ## set up top viewport top_vp <- viewport(layout = grid.layout(nrow = k, ncol = 2, widths = unit(c(ylines, 1), c("lines", "null")), heights = unit(k, "null")), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_mob", nid, sep = "")) pushViewport(top_vp) grid.rect(gp = gpar(fill = bg, col = 0)) ## main title top <- viewport(layout.pos.col = 2, layout.pos.row = 1) pushViewport(top) if (is.null(mainlab)) { mainlab <- if(id) { function(id, nobs) sprintf("Node %s (n = %s)", id, nobs) } else { function(id, nobs) sprintf("n = %s", nobs) } } if (is.function(mainlab)) { mainlab <- mainlab(nid, info_node(node)$nobs) } grid.text(mainlab, y = unit(1, "npc") - unit(0.75, "lines")) popViewport() for(i in 1L:k) { ## get x and y xi <- X[ix, i] o <- order(xi) yi <- y[o] xi <- xi[o] yfit <- if(is.null(node$info$object)) { fitted(refit.modelparty(mobobj, node = nid))[o] } else { fitted(node$info$object)[o] } ## select panel plot_vpi <- viewport(layout.pos.col = 2L, layout.pos.row = i) pushViewport(plot_vpi) ## call panel function if(is.factor(xi)) cat_fun(xi, yi, yfit, i, paste("node_mob", nid, "-", i, sep = ""), ...) else num_fun(xi, yi, yfit, i, paste("node_mob", nid, "-", i, sep = ""), ...) if(pop) popViewport() else upViewport() } if(pop) popViewport() else upViewport() } return(rval) } class(node_bivplot) <- "grapcon_generator" partykit/R/split.R0000644000176200001440000001712014172230000013566 0ustar liggesusers partysplit <- function(varid, breaks = NULL, index = NULL, right = TRUE, prob = NULL, info = NULL) { ### informal class for splits split <- vector(mode = "list", length = 6) names(split) <- c("varid", "breaks", "index", "right", "prob", "info") ### split is an id referring to a variable if (!is.integer(varid)) stop(sQuote("varid"), " ", "is not integer") split$varid <- varid if (is.null(breaks) && is.null(index)) stop("either", " ", sQuote("breaks"), " ", "or", " ", sQuote("index"), " ", "must be given") ### vec if (!is.null(breaks)) { if (is.numeric(breaks) && (length(breaks) >= 1)) { ### FIXME: I think we need to make sure breaks are double in C split$breaks <- as.double(breaks) } else { stop(sQuote("break"), " ", "should be a numeric vector containing at least one element") } } if (!is.null(index)) { if (is.integer(index)) { if (!(length(index) >= 2)) stop(sQuote("index"), " ", "has less than two elements") if (!(min(index, na.rm = TRUE) == 1)) stop("minimum of", " ", sQuote("index"), " ", "is not equal to 1") if (!all.equal(diff(sort(unique(index))), rep(1, max(index, na.rm = TRUE) - 1))) stop(sQuote("index"), " ", "is not a contiguous sequence") split$index <- index } else { stop(sQuote("index"), " ", "is not a class", " ", sQuote("integer")) } if (!is.null(breaks)) { if (length(breaks) != (length(index) - 1)) stop("length of", " ", sQuote("breaks"), " ", "does not match length of", " ", sQuote("index")) } } if (is.logical(right) & !is.na(right)) split$right <- right else stop(sQuote("right"), " ", "is not a logical") if (!is.null(prob)) { if (!is.double(prob) || (any(prob < 0) | any(prob > 1) | !isTRUE(all.equal(sum(prob), 1)))) stop(sQuote("prob"), " ", "is not a vector of probabilities") if (!is.null(index)) { if (!(max(index, na.rm = TRUE) == length(prob))) stop("incorrect", " ", sQuote("index")) } if (!is.null(breaks) && is.null(index)) { if (!(length(breaks) == (length(prob) - 1))) stop("incorrect", " ", sQuote("breaks")) } split$prob <- prob } if (!is.null(info)) split$info <- info class(split) <- "partysplit" return(split) } varid_split <- function(split) { if (!(inherits(split, "partysplit"))) stop(sQuote("split"), " ", "is not an object of class", " ", sQuote("partysplit")) split$varid } breaks_split <- function(split) { if (!(inherits(split, "partysplit"))) stop(sQuote("split"), " ", "is not an object of class", " ", sQuote("partysplit")) split$breaks } index_split <- function(split) { if (!(inherits(split, "partysplit"))) stop(sQuote("split"), " ", "is not an object of class", " ", sQuote("partysplit")) split$index } right_split <- function(split) { if (!(inherits(split, "partysplit"))) stop(sQuote("split"), " ", "is not an object of class", " ", sQuote("partysplit")) split$right } prob_split <- function(split) { if (!(inherits(split, "partysplit"))) stop(sQuote("split"), " ", "is not an object of class", " ", sQuote("partysplit")) prob <- split$prob if (!is.null(prob)) return(prob) ### either breaks or index must be there if (is.null(index <- index_split(split))) { if (is.null(breaks <- breaks_split(split))) stop("neither", " ", sQuote("prob"), " ", "nor", " ", sQuote("index"), " ", "or", sQuote("breaks"), " ", "given for", " ", sQuote("split")) nkids <- length(breaks) + 1 } else { nkids <- max(index, na.rm = TRUE) } prob <- rep(1, nkids) / nkids return(prob) } info_split <- function(split) { if (!(inherits(split, "partysplit"))) stop(sQuote("split"), " ", "is not an object of class", " ", sQuote("partysplit")) split$info } kidids_split <- function(split, data, vmatch = 1:length(data), obs = NULL) { id <- varid_split(split) class(data) <- "list" ### speed up x <- data[[vmatch[id]]] if (!is.null(obs)) x <- x[obs] if (is.null(breaks_split(split))) { if (storage.mode(x) != "integer") stop("variable", " ", vmatch[id], " ", "is not integer") } else { ### labels = FALSE returns integers and is faster ### use findInterval instead of cut? # x <- cut.default(as.numeric(x), labels = FALSE, # breaks = unique(c(-Inf, breaks_split(split), Inf)), ### breaks_split(split) = Inf possible (MIA) # right = right_split(split)) x <- .bincode(as.numeric(x), # labels = FALSE, breaks = unique(c(-Inf, breaks_split(split), Inf)), ### breaks_split(split) = Inf possible (MIA) right = right_split(split)) ### } index <- index_split(split) ### empty factor levels correspond to NA and return NA here ### and thus the corresponding observations will be treated ### as missing values (surrogate or random splits): if (!is.null(index)) x <- index[x] return(x) } character_split <- function(split, data = NULL, digits = getOption("digits") - 2) { varid <- varid_split(split) if (!is.null(data)) { ## names and labels lev <- lapply(data, levels)[[varid]] mlab <- names(data)[varid] ## determine split type type <- sapply(data, function(x) class(x)[1])[varid_split(split)] type[!(type %in% c("factor", "ordered"))] <- "numeric" } else { ## (bad) default names and labels lev <- NULL mlab <- paste("V", varid, sep = "") type <- "numeric" } ## process defaults for breaks and index breaks <- breaks_split(split) index <- index_split(split) right <- right_split(split) if (is.null(breaks)) breaks <- 1:(length(index) - 1) if (is.null(index)) index <- 1:(length(breaks) + 1) ## check whether ordered are really ordered if (type == "ordered") { if (length(breaks) > 1) type <- "factor" } ### format ordered multiway splits? switch(type, "factor" = { nindex <- index[cut(seq_along(lev), c(-Inf, breaks, Inf), right = right)] dlab <- as.vector(tapply(lev, nindex, paste, collapse = ", ")) }, "ordered" = { if (length(breaks) == 1) { if (right) dlab <- paste(c("<=", ">"), lev[breaks], sep = " ") else dlab <- paste(c("<", ">="), lev[breaks], sep = " ") } else { stop("") ### see above } dlab <- dlab[index] }, "numeric" = { breaks <- round(breaks, digits) if (length(breaks) == 1) { if (right) dlab <- paste(c("<=", ">"), breaks, sep = " ") else dlab <- paste(c("<", ">="), breaks, sep = " ") } else { dlab <- levels(cut(0, breaks = c(-Inf, breaks, Inf), right = right)) } dlab <- as.vector(tapply(dlab, index, paste, collapse = " | ")) } ) return(list(name = mlab, levels = dlab)) } partykit/cleanup0000755000176200001440000000150114723350654013504 0ustar liggesusers#!/bin/sh for f in ./src/*.*o; do rm -f $f done for f in ./src/*~; do rm -f $f done for f in ./R/*~; do rm -f $f done for f in ./man/*~; do rm -f $f done for f in *~; do rm -f $f done for f in .*~; do rm -f $f done for f in ./tests/*~; do rm -f $f done for f in ./tests/*.ps; do rm -f $f done for f in ./vignettes/*~; do rm -f $f done for f in ./vignettes/*.log; do rm -f $f done for f in ./vignettes/*.out; do rm -f $f done for f in ./vignettes/*.bbl; do rm -f $f done for f in ./vignettes/*.blg; do rm -f $f done for f in ./vignettes/*.brf; do rm -f $f done for f in ./vignettes/*.aux; do rm -f $f done for f in ./vignettes/*.tpt; do rm -f $f done for f in ./vignettes/Rplots*; do rm -f $f done find . -name "DEADJOE" -exec rm -f {} \; exit 0 partykit/demo/0000755000176200001440000000000014172227777013065 5ustar liggesuserspartykit/demo/00Index0000644000176200001440000000011714172227777014216 0ustar liggesusersmemory-speed Some memory and speed comparisons for rpart, J48, and constparty partykit/demo/memory-speed.R0000644000176200001440000000261414172227777015621 0ustar liggesusers### packages and data library("rpart") library("RWeka") library("partykit") data("Shuttle", package = "mlbench") ### fit rpart and J48 trees rp <- rpart(Class ~ ., data = Shuttle) j48 <- J48(Class ~ ., data = Shuttle) ### convert to party system.time(party_rp <- as.party(rp)) system.time(party_j48 <- as.party(j48)) ### check depth/width depth(party_rp) width(party_rp) depth(party_j48) width(party_j48) ### compare object sizes osize <- function(x) print(object.size(x), units = "Kb") osize(rp) ## rpart representation osize(party_rp) ## full party (with terms, fitted values) osize(node_party(party_rp)) ## only the raw partynode osize(j48) ## J48 tree in external Java pointer osize(party_j48) ## full party (with terms, fitted values) osize(node_party(party_j48)) ## only the raw partynode osize(Shuttle) ## learning data (not stored in any tree) ### set-up large prediction sample set.seed(1) nd <- Shuttle[sample(1:nrow(Shuttle), 1e6, replace = TRUE), ] ### compare predictions (speed and accuracy) system.time(p_rp <- predict(rp, newdata = nd, type = "prob")) system.time(p_party_rp <- predict(party_rp, newdata = nd, type = "prob")) all.equal(p_rp, p_party_rp) system.time(p_j48 <- predict(j48, newdata = nd)) system.time(p_party_j48 <- predict(party_j48, newdata = nd)) all.equal(p_j48, p_party_j48, check.attributes = FALSE) partykit/vignettes/0000755000176200001440000000000014723350653014141 5ustar liggesuserspartykit/vignettes/ctree.Rnw0000644000176200001440000015516214172230001015723 0ustar liggesusers\documentclass[nojss]{jss} %\VignetteIndexEntry{ctree: Conditional Inference Trees} %\VignetteDepends{coin, TH.data, survival, strucchange, Formula, sandwich, datasets} %\VignetteKeywords{conditional inference, non-parametric models, recursive partitioning} %\VignettePackage{partykit} %% packages \usepackage{amstext} \usepackage{amsfonts} \usepackage{amsmath} \usepackage{thumbpdf} \usepackage{rotating} %% need no \usepackage{Sweave} \usepackage[utf8]{inputenc} %% commands \newcommand{\fixme}[1]{\emph{\marginpar{FIXME} (#1)}} \renewcommand{\Prob}{\mathbb{P} } \renewcommand{\E}{\mathbb{E}} \newcommand{\V}{\mathbb{V}} \newcommand{\Var}{\mathbb{V}} \newcommand{\R}{\mathbb{R} } \newcommand{\N}{\mathbb{N} } %%\newcommand{\C}{\mathbb{C} } \newcommand{\argmin}{\operatorname{argmin}\displaylimits} \newcommand{\argmax}{\operatorname{argmax}\displaylimits} \newcommand{\LS}{\mathcal{L}_n} \newcommand{\TS}{\mathcal{T}_n} \newcommand{\LSc}{\mathcal{L}_{\text{comb},n}} \newcommand{\LSbc}{\mathcal{L}^*_{\text{comb},n}} \newcommand{\F}{\mathcal{F}} \newcommand{\A}{\mathcal{A}} \newcommand{\yn}{y_{\text{new}}} \newcommand{\z}{\mathbf{z}} \newcommand{\X}{\mathbf{X}} \newcommand{\Y}{\mathbf{Y}} \newcommand{\sX}{\mathcal{X}} \newcommand{\sY}{\mathcal{Y}} \newcommand{\T}{\mathbf{T}} \newcommand{\x}{\mathbf{x}} \renewcommand{\a}{\mathbf{a}} \newcommand{\xn}{\mathbf{x}_{\text{new}}} \newcommand{\y}{\mathbf{y}} \newcommand{\w}{\mathbf{w}} \newcommand{\ws}{\mathbf{w}_\cdot} \renewcommand{\t}{\mathbf{t}} \newcommand{\M}{\mathbf{M}} \renewcommand{\vec}{\text{vec}} \newcommand{\B}{\mathbf{B}} \newcommand{\K}{\mathbf{K}} \newcommand{\W}{\mathbf{W}} \newcommand{\D}{\mathbf{D}} \newcommand{\I}{\mathbf{I}} \newcommand{\bS}{\mathbf{S}} \newcommand{\cellx}{\pi_n[\x]} \newcommand{\partn}{\pi_n(\mathcal{L}_n)} \newcommand{\err}{\text{Err}} \newcommand{\ea}{\widehat{\text{Err}}^{(a)}} \newcommand{\ecv}{\widehat{\text{Err}}^{(cv1)}} \newcommand{\ecvten}{\widehat{\text{Err}}^{(cv10)}} \newcommand{\eone}{\widehat{\text{Err}}^{(1)}} \newcommand{\eplus}{\widehat{\text{Err}}^{(.632+)}} \newcommand{\eoob}{\widehat{\text{Err}}^{(oob)}} \newcommand{\bft}{\mathbf{t}} \hyphenation{Qua-dra-tic} \title{\texttt{ctree}: Conditional Inference Trees} \Plaintitle{ctree: Conditional Inference Trees} \author{Torsten Hothorn\\Universit\"at Z\"urich \And Kurt Hornik\\Wirtschaftsuniversit\"at Wien \And Achim Zeileis\\Universit\"at Innsbruck} \Plainauthor{Torsten Hothorn, Kurt Hornik, Achim Zeileis} \Abstract{ This vignette describes the new reimplementation of conditional inference trees (CTree) in the \proglang{R} package \pkg{partykit}. CTree is a non-parametric class of regression trees embedding tree-structured regression models into a well defined theory of conditional inference procedures. It is applicable to all kinds of regression problems, including nominal, ordinal, numeric, censored as well as multivariate response variables and arbitrary measurement scales of the covariates. The vignette comprises a practical guide to exploiting the flexible and extensible computational tools in \pkg{partykit} for fitting and visualizing conditional inference trees. } \Keywords{conditional inference, non-parametric models, recursive partitioning} \Address{ Torsten Hothorn\\ Institut f\"ur Epidemiologie, Biostatistik und Pr\"avention \\ Universit\"at Z\"urich \\ Hirschengraben 84\\ CH-8001 Z\"urich, Switzerland \\ E-mail: \email{Torsten.Hothorn@R-project.org}\\ URL: \url{http://user.math.uzh.ch/hothorn/}\\ Kurt Hornik \\ Institute for Statistics and Mathematics\\ WU Wirtschaftsuniversit\"at Wien\\ Welthandelsplatz 1 \\ 1020 Wien, Austria\\ E-mail: \email{Kurt.Hornik@R-project.org} \\ URL: \url{http://statmath.wu.ac.at/~hornik/}\\ Achim Zeileis \\ Department of Statistics \\ Faculty of Economics and Statistics \\ Universit\"at Innsbruck \\ Universit\"atsstr.~15 \\ 6020 Innsbruck, Austria \\ E-mail: \email{Achim.Zeileis@R-project.org} \\ URL: \url{http://eeecon.uibk.ac.at/~zeileis/} } \begin{document} <>= suppressWarnings(RNGversion("3.5.2")) options(width = 70, SweaveHooks = list(leftpar = function() par(mai = par("mai") * c(1, 1.1, 1, 1)))) require("partykit") require("coin") require("strucchange") require("coin") require("Formula") require("survival") require("sandwich") set.seed(290875) @ \setkeys{Gin}{width=\textwidth} \section{Overview} This vignette describes conditional inference trees \citep{Hothorn+Hornik+Zeileis:2006} along with its new and improved reimplementation in package \pkg{partykit}. Originally, the method was implemented in the package \pkg{party} almost entirely in \proglang{C} while the new implementation is now almost entirely in \proglang{R}. In particular, this has the advantage that all the generic infrastructure from \pkg{partykit} can be reused, making many computations more modular and easily extensible. Hence, \code{partykit::ctree} is the new reference implementation that will be improved and developed further in the future. In almost all cases, the two implementations will produce identical trees. In exceptional cases, additional parameters have to be specified in order to ensure backward compatibility. These and novel features in \code{ctree:partykit} are introduced in Section~\ref{sec:novel}. \section{Introduction} The majority of recursive partitioning algorithms are special cases of a simple two-stage algorithm: First partition the observations by univariate splits in a recursive way and second fit a constant model in each cell of the resulting partition. The most popular implementations of such algorithms are `CART' \citep{Breiman+Friedman+Olshen:1984} and `C4.5' \citep{Quinlan:1993}. Not unlike AID, both perform an exhaustive search over all possible splits maximizing an information measure of node impurity selecting the covariate showing the best split. This approach has two fundamental problems: overfitting and a selection bias towards covariates with many possible splits. With respect to the overfitting problem \cite{Mingers:1987} notes that the algorithm \begin{quote} [\ldots] has no concept of statistical significance, and so cannot distinguish between a significant and an insignificant improvement in the information measure. \end{quote} With conditional inference trees \citep[see][for a full description of its methodological foundations]{Hothorn+Hornik+Zeileis:2006} we enter at the point where \cite{White+Liu:1994} demand for \begin{quote} [\ldots] a \textit{statistical} approach [to recursive partitioning] which takes into account the \textit{distributional} properties of the measures. \end{quote} We present a unified framework embedding recursive binary partitioning into the well defined theory of permutation tests developed by \cite{Strasser+Weber:1999}. The conditional distribution of statistics measuring the association between responses and covariates is the basis for an unbiased selection among covariates measured at different scales. Moreover, multiple test procedures are applied to determine whether no significant association between any of the covariates and the response can be stated and the recursion needs to stop. \section{Recursive binary partitioning} \label{algo} We focus on regression models describing the conditional distribution of a response variable $\Y$ given the status of $m$ covariates by means of tree-structured recursive partitioning. The response $\Y$ from some sample space $\sY$ may be multivariate as well. The $m$-dimensional covariate vector $\X = (X_1, \dots, X_m)$ is taken from a sample space $\sX = \sX_1 \times \cdots \times \sX_m$. Both response variable and covariates may be measured at arbitrary scales. We assume that the conditional distribution $D(\Y | \X)$ of the response $\Y$ given the covariates $\X$ depends on a function $f$ of the covariates \begin{eqnarray*} D(\Y | \X) = D(\Y | X_1, \dots, X_m) = D(\Y | f( X_1, \dots, X_m)), \end{eqnarray*} where we restrict ourselves to partition based regression relationships, i.e., $r$ disjoint cells $B_1, \dots, B_r$ partitioning the covariate space $\sX = \bigcup_{k = 1}^r B_k$. A model of the regression relationship is to be fitted based on a learning sample $\LS$, i.e., a random sample of $n$ independent and identically distributed observations, possibly with some covariates $X_{ji}$ missing, \begin{eqnarray*} \LS & = & \{ (\Y_i, X_{1i}, \dots, X_{mi}); i = 1, \dots, n \}. \end{eqnarray*} A generic algorithm for recursive binary partitioning for a given learning sample $\LS$ can be formulated using non-negative integer valued case weights $\w = (w_1, \dots, w_n)$. Each node of a tree is represented by a vector of case weights having non-zero elements when the corresponding observations are elements of the node and are zero otherwise. The following algorithm implements recursive binary partitioning: \begin{enumerate} \item For case weights $\w$ test the global null hypothesis of independence between any of the $m$ covariates and the response. Stop if this hypothesis cannot be rejected. Otherwise select the covariate $X_{j^*}$ with strongest association to $\Y$. \item Choose a set $A^* \subset \sX_{j^*}$ in order to split $\sX_{j^*}$ into two disjoint sets $A^*$ and $\sX_{j^*} \setminus A^*$. The case weights $\w_\text{left}$ and $\w_\text{right}$ determine the two subgroups with $w_{\text{left},i} = w_i I(X_{j^*i} \in A^*)$ and $w_{\text{right},i} = w_i I(X_{j^*i} \not\in A^*)$ for all $i = 1, \dots, n$ ($I(\cdot)$ denotes the indicator function). \item Recursively repeat steps 1 and 2 with modified case weights $\w_\text{left}$ and $\w_\text{right}$, respectively. \end{enumerate} The separation of variable selection and splitting procedure into steps 1 and 2 of the algorithm is the key for the construction of interpretable tree structures not suffering a systematic tendency towards covariates with many possible splits or many missing values. In addition, a statistically motivated and intuitive stopping criterion can be implemented: We stop when the global null hypothesis of independence between the response and any of the $m$ covariates cannot be rejected at a pre-specified nominal level~$\alpha$. The algorithm induces a partition $\{B_1, \dots, B_r\}$ of the covariate space $\sX$, where each cell $B \in \{B_1, \dots, B_r\}$ is associated with a vector of case weights. \section{Recursive partitioning by conditional inference} \label{framework} In the main part of this section we focus on step 1 of the generic algorithm. Unified tests for independence are constructed by means of the conditional distribution of linear statistics in the permutation test framework developed by \cite{Strasser+Weber:1999}. The determination of the best binary split in one selected covariate and the handling of missing values is performed based on standardized linear statistics within the same framework as well. \subsection{Variable selection and stopping criteria} At step 1 of the generic algorithm given in Section~\ref{algo} we face an independence problem. We need to decide whether there is any information about the response variable covered by any of the $m$ covariates. In each node identified by case weights $\w$, the global hypothesis of independence is formulated in terms of the $m$ partial hypotheses $H_0^j: D(\Y | X_j) = D(\Y)$ with global null hypothesis $H_0 = \bigcap_{j = 1}^m H_0^j$. When we are not able to reject $H_0$ at a pre-specified level $\alpha$, we stop the recursion. If the global hypothesis can be rejected, we measure the association between $\Y$ and each of the covariates $X_j, j = 1, \dots, m$, by test statistics or $P$-values indicating the deviation from the partial hypotheses $H_0^j$. For notational convenience and without loss of generality we assume that the case weights $w_i$ are either zero or one. The symmetric group of all permutations of the elements of $(1, \dots, n)$ with corresponding case weights $w_i = 1$ is denoted by $S(\LS, \w)$. A more general notation is given in the Appendix. We measure the association between $\Y$ and $X_j, j = 1, \dots, m$, by linear statistics of the form \begin{eqnarray} \label{linstat} \T_j(\LS, \w) = \vec \left( \sum_{i=1}^n w_i g_j(X_{ji}) h(\Y_i, (\Y_1, \dots, \Y_n))^\top \right) \in \R^{p_jq} \end{eqnarray} where $g_j: \sX_j \rightarrow \R^{p_j}$ is a non-random transformation of the covariate $X_j$. The transformation may be specified using the \code{xtrafo} argument (Note: this argument is currently not implemented in \code{partykit::ctree} but is available from \code{party::ctree}). %%If, for example, a ranking \textit{both} %%\code{x1} and \code{x2} is required, %%<>= %%party:::ctree(y ~ x1 + x2, data = ls, xtrafo = function(data) trafo(data, %%numeric_trafo = rank)) %%@ %%can be used. The \emph{influence function} $h: \sY \times \sY^n \rightarrow \R^q$ depends on the responses $(\Y_1, \dots, \Y_n)$ in a permutation symmetric way. %%, i.e., $h(\Y_i, (\Y_1, \dots, \Y_n)) = h(\Y_i, (\Y_{\sigma(1)}, \dots, %%\Y_{\sigma(n)}))$ for all permutations $\sigma \in S(\LS, \w)$. Section~\ref{examples} explains how to choose $g_j$ and $h$ in different practical settings. A $p_j \times q$ matrix is converted into a $p_jq$ column vector by column-wise combination using the `vec' operator. The influence function can be specified using the \code{ytrafo} argument. The distribution of $\T_j(\LS, \w)$ under $H_0^j$ depends on the joint distribution of $\Y$ and $X_j$, which is unknown under almost all practical circumstances. At least under the null hypothesis one can dispose of this dependency by fixing the covariates and conditioning on all possible permutations of the responses. This principle leads to test procedures known as \textit{permutation tests}. The conditional expectation $\mu_j \in \R^{p_jq}$ and covariance $\Sigma_j \in \R^{p_jq \times p_jq}$ of $\T_j(\LS, \w)$ under $H_0$ given all permutations $\sigma \in S(\LS, \w)$ of the responses are derived by \cite{Strasser+Weber:1999}: \begin{eqnarray} \mu_j & = & \E(\T_j(\LS, \w) | S(\LS, \w)) = \vec \left( \left( \sum_{i = 1}^n w_i g_j(X_{ji}) \right) \E(h | S(\LS, \w))^\top \right), \nonumber \\ \Sigma_j & = & \V(\T_j(\LS, \w) | S(\LS, \w)) \nonumber \\ & = & \frac{\ws}{\ws - 1} \V(h | S(\LS, \w)) \otimes \left(\sum_i w_i g_j(X_{ji}) \otimes w_i g_j(X_{ji})^\top \right) \label{expectcovar} \\ & - & \frac{1}{\ws - 1} \V(h | S(\LS, \w)) \otimes \left( \sum_i w_i g_j(X_{ji}) \right) \otimes \left( \sum_i w_i g_j(X_{ji})\right)^\top \nonumber \end{eqnarray} where $\ws = \sum_{i = 1}^n w_i$ denotes the sum of the case weights, $\otimes$ is the Kronecker product and the conditional expectation of the influence function is \begin{eqnarray*} \E(h | S(\LS, \w)) = \ws^{-1} \sum_i w_i h(\Y_i, (\Y_1, \dots, \Y_n)) \in \R^q \end{eqnarray*} with corresponding $q \times q$ covariance matrix \begin{eqnarray*} \V(h | S(\LS, \w)) = \ws^{-1} \sum_i w_i \left(h(\Y_i, (\Y_1, \dots, \Y_n)) - \E(h | S(\LS, \w)) \right) \\ \left(h(\Y_i, (\Y_1, \dots, \Y_n)) - \E(h | S(\LS, \w))\right)^\top. \end{eqnarray*} Having the conditional expectation and covariance at hand we are able to standardize a linear statistic $\T \in \R^{pq}$ of the form (\ref{linstat}) for some $p \in \{p_1, \dots, p_m\}$. Univariate test statistics~$c$ mapping an observed multivariate linear statistic $\bft \in \R^{pq}$ into the real line can be of arbitrary form. An obvious choice is the maximum of the absolute values of the standardized linear statistic \begin{eqnarray*} c_\text{max}(\bft, \mu, \Sigma) = \max_{k = 1, \dots, pq} \left| \frac{(\bft - \mu)_k}{\sqrt{(\Sigma)_{kk}}} \right| \end{eqnarray*} utilizing the conditional expectation $\mu$ and covariance matrix $\Sigma$. The application of a quadratic form $c_\text{quad}(\bft, \mu, \Sigma) = (\bft - \mu) \Sigma^+ (\bft - \mu)^\top$ is one alternative, although computationally more expensive because the Moore-Penrose inverse $\Sigma^+$ of $\Sigma$ is involved. The type of test statistic to be used can be specified by means of the \code{ctree\_control} function, for example <>= ctree_control(teststat = "max") @ uses $c_\text{max}$ and <>= ctree_control(teststat = "quad") @ takes $c_\text{quad}$ (the default). It is important to note that the test statistics $c(\bft_j, \mu_j, \Sigma_j), j = 1, \dots, m$, cannot be directly compared in an unbiased way unless all of the covariates are measured at the same scale, i.e., $p_1 = p_j, j = 2, \dots, m$. In order to allow for an unbiased variable selection we need to switch to the $P$-value scale because $P$-values for the conditional distribution of test statistics $c(\T_j(\LS, \w), \mu_j, \Sigma_j)$ can be directly compared among covariates measured at different scales. In step 1 of the generic algorithm we select the covariate with minimum $P$-value, i.e., the covariate $X_{j^*}$ with $j^* = \argmin_{j = 1, \dots, m} P_j$, where \begin{displaymath} P_j = \Prob_{H_0^j}(c(\T_j(\LS, \w), \mu_j, \Sigma_j) \ge c(\bft_j, \mu_j, \Sigma_j) | S(\LS, \w)) \end{displaymath} denotes the $P$-value of the conditional test for $H_0^j$. So far, we have only addressed testing each partial hypothesis $H_0^j$, which is sufficient for an unbiased variable selection. A global test for $H_0$ required in step 1 can be constructed via an aggregation of the transformations $g_j, j = 1, \dots, m$, i.e., using a linear statistic of the form \begin{eqnarray*} \T(\LS, \w) = \vec \left( \sum_{i=1}^n w_i \left(g_1(X_{1i})^\top, \dots, g_m(X_{mi})^\top\right)^\top h(\Y_i, (\Y_1, \dots, \Y_n))^\top \right). %%\in \R^{\sum_j p_jq} \end{eqnarray*} However, this approach is less attractive for learning samples with missing values. Universally applicable approaches are multiple test procedures based on $P_1, \dots, P_m$. Simple Bonferroni-adjusted $P$-values (the adjustment $1 - (1 - P_j)^m$ is used), available via <>= ctree_control(testtype = "Bonferroni") @ or a min-$P$-value resampling approach (Note: resampling is currently not implemented in \code{partykit::ctree}) %<>= %party:::ctree_control(testtype = "MonteCarlo") %@ are just examples and we refer to the multiple testing literature \citep[e.g.,][]{Westfall+Young:1993} for more advanced methods. We reject $H_0$ when the minimum of the adjusted $P$-values is less than a pre-specified nominal level $\alpha$ and otherwise stop the algorithm. In this sense, $\alpha$ may be seen as a unique parameter determining the size of the resulting trees. \subsection{Splitting criteria} Once we have selected a covariate in step 1 of the algorithm, the split itself can be established by any split criterion, including those established by \cite{Breiman+Friedman+Olshen:1984} or \cite{Shih:1999}. Instead of simple binary splits, multiway splits can be implemented as well, for example utilizing the work of \cite{OBrien:2004}. However, most splitting criteria are not applicable to response variables measured at arbitrary scales and we therefore utilize the permutation test framework described above to find the optimal binary split in one selected covariate $X_{j^*}$ in step~2 of the generic algorithm. The goodness of a split is evaluated by two-sample linear statistics which are special cases of the linear statistic (\ref{linstat}). For all possible subsets $A$ of the sample space $\sX_{j^*}$ the linear statistic \begin{eqnarray*} \T^A_{j^*}(\LS, \w) = \vec \left( \sum_{i=1}^n w_i I(X_{j^*i} \in A) h(\Y_i, (\Y_1, \dots, \Y_n))^\top \right) \in \R^{q} \end{eqnarray*} induces a two-sample statistic measuring the discrepancy between the samples $\{ \Y_i | w_i > 0 \text{ and } X_{ji} \in A; i = 1, \dots, n\}$ and $\{ \Y_i | w_i > 0 \text{ and } X_{ji} \not\in A; i = 1, \dots, n\}$. The conditional expectation $\mu_{j^*}^A$ and covariance $\Sigma_{j^*}^A$ can be computed by (\ref{expectcovar}). The split $A^*$ with a test statistic maximized over all possible subsets $A$ is established: \begin{eqnarray} \label{split} A^* = \argmax_A c(\bft_{j^*}^A, \mu_{j^*}^A, \Sigma_{j^*}^A). \end{eqnarray} The statistics $c(\bft_{j^*}^A, \mu_{j^*}^A, \Sigma_{j^*}^A)$ are available for each node with %<>= %party:::ctree_control(savesplitstats = TRUE) %@ and can be used to depict a scatter plot of the covariate $\sX_{j^*}$ against the statistics (Note: this feature is currently not implemented in \pkg{partykit}). Note that we do not need to compute the distribution of $c(\bft_{j^*}^A, \mu_{j^*}^A, \Sigma_{j^*}^A)$ in step~2. In order to anticipate pathological splits one can restrict the number of possible subsets that are evaluated, for example by introducing restrictions on the sample size or the sum of the case weights in each of the two groups of observations induced by a possible split. For example, <>= ctree_control(minsplit = 20) @ requires the sum of the weights in both the left and right daughter node to exceed the value of $20$. \subsection{Missing values and surrogate splits} If an observation $X_{ji}$ in covariate $X_j$ is missing, we set the corresponding case weight $w_i$ to zero for the computation of $\T_j(\LS, \w)$ and, if we would like to split in $X_j$, in $\T_{j}^A(\LS, \w)$ as well. Once a split $A^*$ in $X_j$ has been implemented, surrogate splits can be established by searching for a split leading to roughly the same division of the observations as the original split. One simply replaces the original response variable by a binary variable $I(X_{ji} \in A^*)$ coding the split and proceeds as described in the previous part. The number of surrogate splits can be controlled using <>= ctree_control(maxsurrogate = 3) @ \subsection{Fitting and inspecting a tree} For the sake of simplicity, we use a learning sample <>= ls <- data.frame(y = gl(3, 50, labels = c("A", "B", "C")), x1 = rnorm(150) + rep(c(1, 0, 0), c(50, 50, 50)), x2 = runif(150)) @ in the following illustrations. In \code{partykit::ctree}, the dependency structure and the variables may be specified in a traditional formula based way <>= library("partykit") ctree(y ~ x1 + x2, data = ls) @ Case counts $\w$ may be specified using the \code{weights} argument. Once we have fitted a conditional tree via <>= ct <- ctree(y ~ x1 + x2, data = ls) @ we can inspect the results via a \code{print} method <>= ct @ or by looking at a graphical representation as in Figure~\ref{party-plot1}. \begin{figure}[t!] \centering <>= plot(ct) @ \caption{A graphical representation of a classification tree. \label{party-plot1}} \end{figure} Each node can be extracted by its node number, i.e., the root node is <>= ct[1] @ This object is an object of class <>= class(ct[1]) @ and we refer to the manual pages for a description of those elements. The \code{predict} function computes predictions in the space of the response variable, in our case a factor <>= predict(ct, newdata = ls) @ When we are interested in properties of the conditional distribution of the response given the covariates, we use <>= predict(ct, newdata = ls[c(1, 51, 101),], type = "prob") @ which, in our case, is a data frame with conditional class probabilities. We can determine the node numbers of nodes some new observations are falling into by <>= predict(ct, newdata = ls[c(1,51,101),], type = "node") @ Finally, the \code{sctest} method can be used to extract the test statistics and $p$-values computed in each node. The function \code{sctest} is used because for the \code{mob} algorithm such a method (for \underline{s}tructural \underline{c}hange \underline{test}s) is also provided. To make the generic available, the \pkg{strucchange} package needs to be loaded (otherwise \code{sctest.constparty} would have to be called directly). <>= library("strucchange") sctest(ct) @ Here, we see that \code{x1} leads to a significant test result in the root node and is hence used for splitting. In the kid nodes, no more significant results are found and hence splitting stops. For other data sets, other stopping criteria might also be relevant (e.g., the sample size restrictions \code{minsplit}, \code{minbucket}, etc.). In case, splitting stops due to these, the test results may also be \code{NULL}. \section{Examples} \label{examples} \subsection{Univariate continuous or discrete regression} For a univariate numeric response $\Y \in \R$, the most natural influence function is the identity $h(\Y_i, (\Y_1, \dots, \Y_n)) = \Y_i$. In case some observations with extremely large or small values have been observed, a ranking of the observations may be appropriate: $h(\Y_i, (\Y_1, \dots, \Y_n)) = \sum_{k=1}^n w_k I(\Y_k \le \Y_i)$ for $i = 1, \dots, n$. Numeric covariates can be handled by the identity transformation $g_{ji}(x) = x$ (ranks are possible, too). Nominal covariates at levels $1, \dots, K$ are represented by $g_{ji}(k) = e_K(k)$, the unit vector of length $K$ with $k$th element being equal to one. Due to this flexibility, special test procedures like the Spearman test, the Wilcoxon-Mann-Whitney test or the Kruskal-Wallis test and permutation tests based on ANOVA statistics or correlation coefficients are covered by this framework. Splits obtained from (\ref{split}) maximize the absolute value of the standardized difference between two means of the values of the influence functions. For prediction, one is usually interested in an estimate of the expectation of the response $\E(\Y | \X = \x)$ in each cell, an estimate can be obtained by \begin{eqnarray*} \hat{\E}(\Y | \X = \x) = \left(\sum_{i=1}^n w_i(\x)\right)^{-1} \sum_{i=1}^n w_i(\x) \Y_i. \end{eqnarray*} \subsection{Censored regression} The influence function $h$ may be chosen as Logrank or Savage scores taking censoring into account and one can proceed as for univariate continuous regression. This is essentially the approach first published by \cite{Segal:1988}. An alternative is the weighting scheme suggested by \cite{Molinaro+Dudiot+VanDerLaan:2003}. A weighted Kaplan-Meier curve for the case weights $\w(\x)$ can serve as prediction. \subsection{$J$-class classification} The nominal response variable at levels $1, \dots, J$ is handled by influence functions\linebreak $h(\Y_i, (\Y_1, \dots, \Y_n)) = e_J(\Y_i)$. Note that for a nominal covariate $X_j$ at levels $1, \dots, K$ with $g_{ji}(k) = e_K(k)$ the corresponding linear statistic $\T_j$ is a vectorized contingency table. The conditional class probabilities can be estimated via \begin{eqnarray*} \hat{\Prob}(\Y = y | \X = \x) = \left(\sum_{i=1}^n w_i(\x)\right)^{-1} \sum_{i=1}^n w_i(\x) I(\Y_i = y), \quad y = 1, \dots, J. \end{eqnarray*} \subsection{Ordinal regression} Ordinal response variables measured at $J$ levels, and ordinal covariates measured at $K$ levels, are associated with score vectors $\xi \in \R^J$ and $\gamma \in \R^K$, respectively. Those scores reflect the `distances' between the levels: If the variable is derived from an underlying continuous variable, the scores can be chosen as the midpoints of the intervals defining the levels. The linear statistic is now a linear combination of the linear statistic $\T_j$ of the form \begin{eqnarray*} \M \T_j(\LS, \w) & = & \vec \left( \sum_{i=1}^n w_i \gamma^\top g_j(X_{ji}) \left(\xi^\top h(\Y_i, (\Y_1, \dots, \Y_n)\right)^\top \right) \end{eqnarray*} with $g_j(x) = e_K(x)$ and $h(\Y_i, (\Y_1, \dots, \Y_n)) = e_J(\Y_i)$. If both response and covariate are ordinal, the matrix of coefficients is given by the Kronecker product of both score vectors $\M = \xi \otimes \gamma \in \R^{1, KJ}$. In case the response is ordinal only, the matrix of coefficients $\M$ is a block matrix \begin{eqnarray*} \M = \left( \begin{array}{ccc} \xi_1 & & 0 \\ & \ddots & \\ 0 & & \xi_1 \end{array} \right| %%\left. %% \begin{array}{ccc} %% \xi_2 & & 0 \\ %% & \ddots & \\ %% 0 & & \xi_2 %% \end{array} \right| %%\left. \begin{array}{c} \\ \hdots \\ \\ \end{array} %%\right. \left| \begin{array}{ccc} \xi_q & & 0 \\ & \ddots & \\ 0 & & \xi_q \end{array} \right) %%\in \R^{K, KJ} %%\end{eqnarray*} \text{ or } %%and if one covariate is ordered %%\begin{eqnarray*} %%\M = \left( %% \begin{array}{cccc} %% \gamma & 0 & & 0 \\ %% 0 & \gamma & & \vdots \\ %% 0 & 0 & \hdots & 0 \\ %% \vdots & \vdots & & 0 \\ %% 0 & 0 & & \gamma %% \end{array} %% \right) \M = \text{diag}(\gamma) %%\in \R^{J, KJ} \end{eqnarray*} when one covariate is ordered but the response is not. For both $\Y$ and $X_j$ being ordinal, the corresponding test is known as linear-by-linear association test \citep{Agresti:2002}. Scores can be supplied to \code{ctree} using the \code{scores} argument, see Section~\ref{illustrations} for an example. \subsection{Multivariate regression} For multivariate responses, the influence function is a combination of influence functions appropriate for any of the univariate response variables discussed in the previous paragraphs, e.g., indicators for multiple binary responses \citep{Zhang:1998,Noh+Song+Park:2004}, Logrank or Savage scores for multiple failure times %%\citep[for example tooth loss times, ][]{SuFan2004} and the original observations or a rank transformation for multivariate regression \citep{Death:2002}. \section{Illustrations and applications} \label{illustrations} In this section, we present regression problems which illustrate the potential fields of application of the methodology. Conditional inference trees based on $c_\text{quad}$-type test statistics using the identity influence function for numeric responses and asymptotic $\chi^2$ distribution are applied. For the stopping criterion a simple Bonferroni correction is used and we follow the usual convention by choosing the nominal level of the conditional independence tests as $\alpha = 0.05$. \subsection{Tree pipit abundance} <>= data("treepipit", package = "coin") tptree <- ctree(counts ~ ., data = treepipit) @ \begin{figure}[t!] \centering <>= plot(tptree, terminal_panel = node_barplot) @ \caption{Conditional regression tree for the tree pipit data.} \end{figure} <>= p <- info_node(node_party(tptree))$p.value n <- table(predict(tptree, type = "node")) @ The impact of certain environmental factors on the population density of the tree pipit \textit{Anthus trivialis} %%in Frankonian oak forests is investigated by \cite{Mueller+Hothorn:2004}. The occurrence of tree pipits was recorded several times at $n = 86$ stands which were established on a long environmental gradient. Among nine environmental factors, the covariate showing the largest association to the number of tree pipits is the canopy overstorey $(P = \Sexpr{round(p, 3)})$. Two groups of stands can be distinguished: Sunny stands with less than $40\%$ canopy overstorey $(n = \Sexpr{n[1]})$ show a significantly higher density of tree pipits compared to darker stands with more than $40\%$ canopy overstorey $(n = \Sexpr{n[2]})$. This result is important for management decisions in forestry enterprises: Cutting the overstorey with release of old oaks creates a perfect habitat for this indicator species of near natural forest environments. \subsection{Glaucoma and laser scanning images} <>= data("GlaucomaM", package = "TH.data") gtree <- ctree(Class ~ ., data = GlaucomaM) @ <>= sp <- split_node(node_party(gtree))$varID @ Laser scanning images taken from the eye background are expected to serve as the basis of an automated system for glaucoma diagnosis. Although prediction is more important in this application \citep{Mardin+Hothorn+Peters:2003}, a simple visualization of the regression relationship is useful for comparing the structures inherent in the learning sample with subject matter knowledge. For $98$ patients and $98$ controls, matched by age and gender, $62$ covariates describing the eye morphology are available. The data is part of the \pkg{TH.data} package, \url{http://CRAN.R-project.org}). The first split in Figure~\ref{glaucoma} separates eyes with a volume above reference less than $\Sexpr{sp} \text{ mm}^3$ in the inferior part of the optic nerve head (\code{vari}). Observations with larger volume are mostly controls, a finding which corresponds to subject matter knowledge: The volume above reference measures the thickness of the nerve layer, expected to decrease with a glaucomatous damage of the optic nerve. Further separation is achieved by the volume above surface global (\code{vasg}) and the volume above reference in the temporal part of the optic nerve head (\code{vart}). \setkeys{Gin}{width=.9\textwidth} \begin{figure}[p!] \centering <>= plot(gtree) @ \caption{Conditional inference tree for the glaucoma data. For each inner node, the Bonferroni-adjusted $P$-values are given, the fraction of glaucomatous eyes is displayed for each terminal node. \label{glaucoma}} <>= plot(gtree, inner_panel = node_barplot, edge_panel = function(...) invisible(), tnex = 1) @ \caption{Conditional inference tree for the glaucoma data with the fraction of glaucomatous eyes displayed for both inner and terminal nodes. \label{glaucoma-inner}} \end{figure} The plot in Figure~\ref{glaucoma} is generated by <>= plot(gtree) @ \setkeys{Gin}{width=\textwidth} and shows the distribution of the classes in the terminal nodes. This distribution can be shown for the inner nodes as well, namely by specifying the appropriate panel generating function (\code{node\_barplot} in our case), see Figure~\ref{glaucoma-inner}. <>= plot(gtree, inner_panel = node_barplot, edge_panel = function(...) invisible(), tnex = 1) @ %% TH: split statistics are not saved in partykit %As mentioned in Section~\ref{framework}, it might be interesting to have a %look at the split statistics the split point estimate was derived from. %Those statistics can be extracted from the \code{splitstatistic} element %of a split and one can easily produce scatterplots against the selected %covariate. For all three inner nodes of \code{gtree}, we produce such a %plot in Figure~\ref{glaucoma-split}. For the root node, the estimated split point %seems very natural, since the process of split statistics seems to have a %clear maximum indicating that the simple split point model is something %reasonable to assume here. This is less obvious for nodes $2$ and, %especially, $3$. % %\begin{figure}[t!] %\centering %<>= %cex <- 1.6 %inner <- nodes(gtree, c(1, 2, 5)) %layout(matrix(1:length(inner), ncol = length(inner))) %out <- sapply(inner, function(i) { % splitstat <- i$psplit$splitstatistic % x <- GlaucomaM[[i$psplit$variableName]][splitstat > 0] % plot(x, splitstat[splitstat > 0], main = paste("Node", i$nodeID), % xlab = i$psplit$variableName, ylab = "Statistic", ylim = c(0, 10), % cex.axis = cex, cex.lab = cex, cex.main = cex) % abline(v = i$psplit$splitpoint, lty = 3) %}) %@ %\caption{Split point estimation in each inner node. The process of % the standardized two-sample test statistics for each possible % split point in the selected input variable is show. % The estimated split point is given as vertical dotted line. % \label{glaucoma-split}} %\end{figure} The class predictions of the tree for the learning sample (and for new observations as well) can be computed using the \code{predict} function. A comparison with the true class memberships is done by <>= table(predict(gtree), GlaucomaM$Class) @ When we are interested in conditional class probabilities, the \code{predict(, type = "prob")} method must be used. A graphical representation is shown in Figure~\ref{glaucoma-probplot}. \setkeys{Gin}{width=.5\textwidth} \begin{figure}[t!] \centering <>= prob <- predict(gtree, type = "prob")[,1] + runif(nrow(GlaucomaM), min = -0.01, max = 0.01) splitvar <- character_split(split_node(node_party(gtree)), data = data_party(gtree))$name plot(GlaucomaM[[splitvar]], prob, pch = as.numeric(GlaucomaM$Class), ylab = "Conditional Class Prob.", xlab = splitvar) abline(v = split_node(node_party(gtree))$breaks, lty = 2) legend(0.15, 0.7, pch = 1:2, legend = levels(GlaucomaM$Class), bty = "n") @ \caption{Estimated conditional class probabilities (slightly jittered) for the Glaucoma data depending on the first split variable. The vertical line denotes the first split point. \label{glaucoma-probplot}} \end{figure} \subsection{Node positive breast cancer} Recursive partitioning for censored responses has attracted a lot of interest \citep[e.g.,][]{Segal:1988,LeBlanc+Crowley:1992}. Survival trees using $P$-value adjusted Logrank statistics are used by \cite{Schumacher+Hollaender+Schwarzer:2001a} for the evaluation of prognostic factors for the German Breast Cancer Study Group (GBSG2) data, a prospective controlled clinical trial on the treatment of node positive breast cancer patients. Here, we use Logrank scores as well. Complete data of seven prognostic factors of $686$ women are used for prognostic modeling, the dataset is available within the \pkg{TH.data} package. The number of positive lymph nodes (\code{pnodes}) and the progesterone receptor (\code{progrec}) have been identified as prognostic factors in the survival tree analysis by \cite{Schumacher+Hollaender+Schwarzer:2001a}. Here, the binary variable coding whether a hormonal therapy was applied or not (\code{horTh}) additionally is part of the model depicted in Figure~\ref{gbsg2}, which was fitted using the following code: <>= data("GBSG2", package = "TH.data") library("survival") (stree <- ctree(Surv(time, cens) ~ ., data = GBSG2)) @ \setkeys{Gin}{width=\textwidth} \begin{figure}[t!] \centering <>= plot(stree) @ \caption{Tree-structured survival model for the GBSG2 data and the distribution of survival times in the terminal nodes. The median survival time is displayed in each terminal node of the tree. \label{gbsg2}} \end{figure} The estimated median survival time for new patients is less informative compared to the whole Kaplan-Meier curve estimated from the patients in the learning sample for each terminal node. We can compute those `predictions' by means of the \code{treeresponse} method <>= pn <- predict(stree, newdata = GBSG2[1:2,], type = "node") n <- predict(stree, type = "node") survfit(Surv(time, cens) ~ 1, data = GBSG2, subset = (n == pn[1])) survfit(Surv(time, cens) ~ 1, data = GBSG2, subset = (n == pn[2])) @ \subsection{Mammography experience} <>= data("mammoexp", package = "TH.data") mtree <- ctree(ME ~ ., data = mammoexp) @ \setkeys{Gin}{width=.9\textwidth, keepaspectratio=TRUE} \begin{figure}[t!] \centering <>= plot(mtree) @ \caption{Ordinal regression for the mammography experience data with the fractions of (never, within a year, over one year) given in the nodes. No admissible split was found for node 5 because only $5$ of $91$ women reported a family history of breast cancer and the sample size restrictions would require more than $5$ observations in each daughter node. \label{mammoexp}} \end{figure} Ordinal response variables are common in investigations where the response is a subjective human interpretation. We use an example given by \cite{Hosmer+Lemeshow:2000}, p.~264, studying the relationship between the mammography experience (never, within a year, over one year) and opinions about mammography expressed in questionnaires answered by $n = 412$ women. The resulting partition based on scores $\xi = (1,2,3)$ is given in Figure~\ref{mammoexp}. Women who (strongly) agree with the question `You do not need a mammogram unless you develop symptoms' seldomly have experienced a mammography. The variable \code{benefit} is a score with low values indicating a strong agreement with the benefits of the examination. For those women in (strong) disagreement with the first question above, low values of \code{benefit} identify persons being more likely to have experienced such an examination at all. \subsection{Hunting spiders} Finally, we take a closer look at a challenging dataset on animal abundance first reported by \cite{VanDerAart+SmeenkEnserink:1975} and re-analyzed by \cite{Death:2002} using regression trees dealing with multivariate responses. The abundance of $12$ hunting spider species is regressed on six environmental variables (\code{water}, \code{sand}, \code{moss}, \code{reft}, \code{twigs} and \code{herbs}) for $n = 28$ observations. Because of the small sample size we allow for a split if at least $5$ observations are element of a node The prognostic factor \code{water} found by \cite{Death:2002} is confirmed by the model shown in Figures~\ref{spider1} and~\ref{spider2} which additionally identifies \code{reft}. The data are available in package \pkg{mvpart} \citep{mvpart}. <>= data("HuntingSpiders", package = "partykit") sptree <- ctree(arct.lute + pard.lugu + zora.spin + pard.nigr + pard.pull + aulo.albi + troc.terr + alop.cune + pard.mont + alop.acce + alop.fabr + arct.peri ~ herbs + reft + moss + sand + twigs + water, data = HuntingSpiders, teststat = "max", minsplit = 5, pargs = GenzBretz(abseps = .1, releps = .1)) @ \setkeys{Gin}{width=\textwidth, keepaspectratio=TRUE} \begin{figure}[t!] \centering <>= plot(sptree, terminal_panel = node_barplot) @ \caption{Regression tree for hunting spider abundance with bars for the mean of each response. \label{spider1}} \end{figure} \setkeys{Gin}{height=.93\textheight, keepaspectratio=TRUE} \begin{figure}[p!] \centering <>= plot(sptree) @ \caption{Regression tree for hunting spider abundance with boxplots for each response. \label{spider2}} \end{figure} \section{Backward compatibility and novel functionality} \label{sec:novel} \code{partykit::ctree} is a complete reimplementation of \code{party::ctree}. The latter reference implementation is based on a monolithic \proglang{C} core and an \proglang{S4}-based \proglang{R} interface. The novel implementation of conditional inference trees in \pkg{partykit} is much more modular and was almost entirely written in \proglang{R} (package \pkg{partykit} does not contain any foreign language code as of version 1.2-0). Permutation tests are computed in the dedicated \proglang{R} add-on package \pkg{libcoin}. Nevertheless, both implementations will almost every time produce the same tree. There are, naturally, exceptions where ensuring backward-compatibility requires specific choices of hyper parameters in \code{partykit::ctree_control}. We will demonstrate how one can compute the same trees in \pkg{partykit} and \pkg{party} in this section. In addition, some novel features introduced in \pkg{partykit} 1.2-0 are described. \subsection{Regression} <>= library("party") set.seed(290875) @ We use the \code{airquality} data from package \pkg{party} and fit a regression tree after removal of missing response values. There are missing values in one of the explanatory variables, so we ask for three surrogate splits to be set-up: <>= data("airquality", package = "datasets") airq <- subset(airquality, !is.na(Ozone)) (airct_party <- party::ctree(Ozone ~ ., data = airq, controls = party::ctree_control(maxsurrogate = 3))) mean((airq$Ozone - predict(airct_party))^2) @ For this specific example, the same call produces the same tree under both \pkg{party} and \pkg{partykit}. To ensure this also for other patterns of missingness, the \code{numsurrogate} flag needs to be set in order to restrict the evaluation of surrogate splits to numeric variables only (this is a restriction hard-coded in \pkg{party}): <>= (airct_partykit <- partykit::ctree(Ozone ~ ., data = airq, control = partykit::ctree_control(maxsurrogate = 3, numsurrogate = TRUE))) mean((airq$Ozone - predict(airct_partykit))^2) table(predict(airct_party, type = "node"), predict(airct_partykit, type = "node")) max(abs(predict(airct_party) - predict(airct_partykit))) @ The results are identical as are the underlying test statistics: <>= airct_party@tree$criterion info_node(node_party(airct_partykit)) @ \code{partykit} has a nicer way or presenting the variable selection test statistics on the scale of the statistics and the $p$-values. In addition, the criterion to be maximised (here: $\log(1 - p-\text{value})$) is given. \subsection{Classification} For classification tasks with more than two classes, the default in \pkg{party} is a maximum-type test statistic on the multidimensional test statistic when computing splits. \pkg{partykit} employs a quadratic test statistic by default, because it was found to produce better splits empirically. One can switch-back to the old behaviour using the \code{splitstat} argument: <>= (irisct_party <- party::ctree(Species ~ .,data = iris)) (irisct_partykit <- partykit::ctree(Species ~ .,data = iris, control = partykit::ctree_control(splitstat = "maximum"))) table(predict(irisct_party, type = "node"), predict(irisct_partykit, type = "node")) @ The interface for computing conditional class probabilities changed from <>= tr_party <- treeresponse(irisct_party, newdata = iris) @ to <>= tr_partykit <- predict(irisct_partykit, type = "prob", newdata = iris) max(abs(do.call("rbind", tr_party) - tr_partykit)) @ leading to identical results. For ordinal regression, the conditional class probabilities can be computed in the very same way: <>= ### ordinal regression data("mammoexp", package = "TH.data") (mammoct_party <- party::ctree(ME ~ ., data = mammoexp)) ### estimated class probabilities tr_party <- treeresponse(mammoct_party, newdata = mammoexp) (mammoct_partykit <- partykit::ctree(ME ~ ., data = mammoexp)) ### estimated class probabilities tr_partykit <- predict(mammoct_partykit, newdata = mammoexp, type = "prob") max(abs(do.call("rbind", tr_party) - tr_partykit)) @ \subsection{Survival Analysis} Like in classification analysis, the \code{treeresponse} function from package \code{party} was replaced by the \code{predict} function with argument \code{type = "prob"} in \pkg{partykit}. The default survival trees are identical: <>= data("GBSG2", package = "TH.data") (GBSG2ct_party <- party::ctree(Surv(time, cens) ~ .,data = GBSG2)) (GBSG2ct_partykit <- partykit::ctree(Surv(time, cens) ~ .,data = GBSG2)) @ as are the conditional Kaplan-Meier estimators <>= tr_party <- treeresponse(GBSG2ct_party, newdata = GBSG2) tr_partykit <- predict(GBSG2ct_partykit, newdata = GBSG2, type = "prob") all.equal(lapply(tr_party, function(x) unclass(x)[!(names(x) %in% "call")]), lapply(tr_partykit, function(x) unclass(x)[!(names(x) %in% "call")]), check.names = FALSE) @ \subsection{New Features} \pkg{partykit} comes with additional arguments in \code{ctree_control} allowing a more detailed control over the tree growing. \begin{description} \item[\code{alpha}]: The user can optionally change the default nominal level of $\alpha = 0.05$; \code{mincriterion} is updated to $1 - \alpha$ and \code{logmincriterion} is then $\log(1 - \alpha)$. The latter allows variable selection on the scale of $\log(1 - p\text{-value})$: <>= (airct_partykit_1 <- partykit::ctree(Ozone ~ ., data = airq, control = partykit::ctree_control(maxsurrogate = 3, alpha = 0.001, numsurrogate = FALSE))) depth(airct_partykit_1) mean((airq$Ozone - predict(airct_partykit_1))^2) @ Lower values of $\alpha$ lead to smaller trees. \item[\code{splittest}]: This enables the computation of $p$-values for maximally selected statistics for variable selection. The default test statistic is not particularly powerful against cutpoint-alternatives but much faster to compute. Currently, $p$-value approximations are not available, so one has to rely on resampling for $p$-value estimation <>= (airct_partykit <- partykit::ctree(Ozone ~ ., data = airq, control = partykit::ctree_control(maxsurrogate = 3, splittest = TRUE, testtype = "MonteCarlo"))) @ \item[\code{saveinfo}]: Reduces the memory footprint by not storing test results as part of the tree. The core information about trees is then roughly half the size needed by \code{party}. \item[\code{nmax}]: Restricts the number of possible cutpoints to \code{nmax}, basically by treating all explanatory variables as ordered factors defined at quantiles of underlying numeric variables. This is mainly implemented in package \pkg{libcoin}. For the standard \code{ctree}, it is only appropriate to use in classification problems, where is can lead to substantial speed-ups: <>= (irisct_partykit_1 <- partykit::ctree(Species ~ .,data = iris, control = partykit::ctree_control(splitstat = "maximum", nmax = 25))) table(predict(irisct_partykit), predict(irisct_partykit_1)) @ \item[\code{multiway}]: Implements multiway splits in unordered factors, each level defines a corresponding daughter node: <>= GBSG2$tgrade <- factor(GBSG2$tgrade, ordered = FALSE) (GBSG2ct_partykit <- partykit::ctree(Surv(time, cens) ~ tgrade, data = GBSG2, control = partykit::ctree_control(multiway = TRUE, alpha = .5))) @ \item[\code{majority = FALSE}]: enables random assignment of non-splitable observations to daughter nodes preserving the node distribution. With \code{majority = TRUE}, these observations go with the majority (the only available behaviour of in \code{party::ctree}). \end{description} Two arguments of \code{ctree} are also interesting. The novel \code{cluster} argument allows conditional inference trees to be fitted to (simple forms of) correlated observations. For each cluster, the variance of the test statistics used for variable selection and also splitting is computed separately, leading to stratified permutation tests (in the sense that only observations within clusters are permuted). For example, we can cluster the data in the \code{airquality} dataset by month to be used as cluster variable: <>= airq$month <- factor(airq$Month) (airct_partykit_3 <- partykit::ctree(Ozone ~ Solar.R + Wind + Temp, data = airq, cluster = month, control = partykit::ctree_control(maxsurrogate = 3))) info_node(node_party(airct_partykit_3)) mean((airq$Ozone - predict(airct_partykit_3))^2) @ This reduces the number of partitioning variables and makes multiplicity adjustment less costly. The \code{ytrafo} argument has be made more general. \pkg{party} is not able to update influence functions $h$ within nodes. With the novel formula-based interface, users can create influence functions which are newly evaluated in each node. The following example illustrates how one can compute a survival tree with updated logrank scores: <>= ### with weight-dependent log-rank scores ### log-rank trafo for observations in this node only (= weights > 0) h <- function(y, x, start = NULL, weights, offset, estfun = TRUE, object = FALSE, ...) { if (is.null(weights)) weights <- rep(1, NROW(y)) s <- logrank_trafo(y[weights > 0,,drop = FALSE]) r <- rep(0, length(weights)) r[weights > 0] <- s list(estfun = matrix(as.double(r), ncol = 1), converged = TRUE, unweighted = TRUE) } partykit::ctree(Surv(time, cens) ~ ., data = GBSG2, ytrafo = h) @ The results are usually not very sensitive to (simple) updated influence functions. However, when one uses score functions of more complex models as influence functions (similar to the \code{mob} family of trees), it is necessary to refit models in each node. For example, we are interested in a normal linear model for ozone concentration given temperature; both the intercept and the regression coefficient for temperature shall vary across nodes of a tree. Such a ``permutation-based'' MOB, here taking clusters into account, can be set-up using <>= ### normal varying intercept / varying coefficient model (aka "mob") h <- function(y, x, start = NULL, weights = NULL, offset = NULL, cluster = NULL, ...) glm(y ~ 0 + x, family = gaussian(), start = start, weights = weights, ...) (airct_partykit_4 <- partykit::ctree(Ozone ~ Temp | Solar.R + Wind, data = airq, cluster = month, ytrafo = h, control = partykit::ctree_control(maxsurrogate = 3))) airq$node <- factor(predict(airct_partykit_4, type = "node")) summary(m <- glm(Ozone ~ node + node:Temp - 1, data = airq)) mean((predict(m) - airq$Ozone)^2) @ Both intercept and effect of temperature change considerably between nodes. The corresponding MOB can be fitted using <>= airq_lmtree <- partykit::lmtree(Ozone ~ Temp | Solar.R + Wind, data = airq, cluster = month) info_node(node_party(airq_lmtree)) mean((predict(airq_lmtree, newdata = airq) - airq$Ozone)^2) @ The $p$-values in the root node are similar but the two procedures find different splits. \code{mob} (and therefore \code{lmtree}) directly search for splits by optimising the objective function for all possible splits whereas \code{ctree} only works with the score functions. Argument \code{xtrafo} allowing the user to change the transformations $g_j$ of the covariates was removed from the user interface. <>= detach(package:party) @ \bibliography{party} \end{document} partykit/vignettes/ctree.Rout.save0000644000176200001440000007355514415224553017067 0ustar liggesusers > suppressWarnings(RNGversion("3.5.2")) > options(width = 70, SweaveHooks = list(leftpar = function() par(mai = par("mai") * + c(1, 1.1, 1, 1)))) > require("partykit") Loading required package: partykit Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > require("coin") Loading required package: coin Loading required package: survival > require("strucchange") Loading required package: strucchange Loading required package: zoo Attaching package: ‘zoo’ The following objects are masked from ‘package:base’: as.Date, as.Date.numeric Loading required package: sandwich > require("coin") > require("Formula") Loading required package: Formula > require("survival") > require("sandwich") > set.seed(290875) > ctree_control(teststat = "max") $criterion [1] "p.value" $logmincriterion [1] -0.05129329 $minsplit [1] 20 $minbucket [1] 7 $minprob [1] 0.01 $maxvar [1] Inf $stump [1] FALSE $nmax yx z Inf Inf $lookahead [1] FALSE $mtry [1] Inf $maxdepth [1] Inf $multiway [1] FALSE $splittry [1] 2 $maxsurrogate [1] 0 $numsurrogate [1] FALSE $majority [1] FALSE $caseweights [1] TRUE $applyfun function (X, FUN, ...) { FUN <- match.fun(FUN) if (!is.vector(X) || is.object(X)) X <- as.list(X) .Internal(lapply(X, FUN)) } $saveinfo [1] TRUE $bonferroni [1] TRUE $update NULL $selectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $splitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svselectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svsplitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $teststat [1] "maximum" $splitstat [1] "quadratic" $splittest [1] FALSE $pargs $maxpts [1] 25000 $abseps [1] 0.001 $releps [1] 0 attr(,"class") [1] "GenzBretz" $testtype [1] "Bonferroni" $nresample [1] 9999 $tol [1] 1.490116e-08 $intersplit [1] FALSE $MIA [1] FALSE > ctree_control(teststat = "quad") $criterion [1] "p.value" $logmincriterion [1] -0.05129329 $minsplit [1] 20 $minbucket [1] 7 $minprob [1] 0.01 $maxvar [1] Inf $stump [1] FALSE $nmax yx z Inf Inf $lookahead [1] FALSE $mtry [1] Inf $maxdepth [1] Inf $multiway [1] FALSE $splittry [1] 2 $maxsurrogate [1] 0 $numsurrogate [1] FALSE $majority [1] FALSE $caseweights [1] TRUE $applyfun function (X, FUN, ...) { FUN <- match.fun(FUN) if (!is.vector(X) || is.object(X)) X <- as.list(X) .Internal(lapply(X, FUN)) } $saveinfo [1] TRUE $bonferroni [1] TRUE $update NULL $selectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $splitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svselectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svsplitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $teststat [1] "quadratic" $splitstat [1] "quadratic" $splittest [1] FALSE $pargs $maxpts [1] 25000 $abseps [1] 0.001 $releps [1] 0 attr(,"class") [1] "GenzBretz" $testtype [1] "Bonferroni" $nresample [1] 9999 $tol [1] 1.490116e-08 $intersplit [1] FALSE $MIA [1] FALSE > ctree_control(testtype = "Bonferroni") $criterion [1] "p.value" $logmincriterion [1] -0.05129329 $minsplit [1] 20 $minbucket [1] 7 $minprob [1] 0.01 $maxvar [1] Inf $stump [1] FALSE $nmax yx z Inf Inf $lookahead [1] FALSE $mtry [1] Inf $maxdepth [1] Inf $multiway [1] FALSE $splittry [1] 2 $maxsurrogate [1] 0 $numsurrogate [1] FALSE $majority [1] FALSE $caseweights [1] TRUE $applyfun function (X, FUN, ...) { FUN <- match.fun(FUN) if (!is.vector(X) || is.object(X)) X <- as.list(X) .Internal(lapply(X, FUN)) } $saveinfo [1] TRUE $bonferroni [1] TRUE $update NULL $selectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $splitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svselectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svsplitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $teststat [1] "quadratic" $splitstat [1] "quadratic" $splittest [1] FALSE $pargs $maxpts [1] 25000 $abseps [1] 0.001 $releps [1] 0 attr(,"class") [1] "GenzBretz" $testtype [1] "Bonferroni" $nresample [1] 9999 $tol [1] 1.490116e-08 $intersplit [1] FALSE $MIA [1] FALSE > ctree_control(minsplit = 20) $criterion [1] "p.value" $logmincriterion [1] -0.05129329 $minsplit [1] 20 $minbucket [1] 7 $minprob [1] 0.01 $maxvar [1] Inf $stump [1] FALSE $nmax yx z Inf Inf $lookahead [1] FALSE $mtry [1] Inf $maxdepth [1] Inf $multiway [1] FALSE $splittry [1] 2 $maxsurrogate [1] 0 $numsurrogate [1] FALSE $majority [1] FALSE $caseweights [1] TRUE $applyfun function (X, FUN, ...) { FUN <- match.fun(FUN) if (!is.vector(X) || is.object(X)) X <- as.list(X) .Internal(lapply(X, FUN)) } $saveinfo [1] TRUE $bonferroni [1] TRUE $update NULL $selectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $splitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svselectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svsplitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $teststat [1] "quadratic" $splitstat [1] "quadratic" $splittest [1] FALSE $pargs $maxpts [1] 25000 $abseps [1] 0.001 $releps [1] 0 attr(,"class") [1] "GenzBretz" $testtype [1] "Bonferroni" $nresample [1] 9999 $tol [1] 1.490116e-08 $intersplit [1] FALSE $MIA [1] FALSE > ctree_control(maxsurrogate = 3) $criterion [1] "p.value" $logmincriterion [1] -0.05129329 $minsplit [1] 20 $minbucket [1] 7 $minprob [1] 0.01 $maxvar [1] Inf $stump [1] FALSE $nmax yx z Inf Inf $lookahead [1] FALSE $mtry [1] Inf $maxdepth [1] Inf $multiway [1] FALSE $splittry [1] 2 $maxsurrogate [1] 3 $numsurrogate [1] FALSE $majority [1] FALSE $caseweights [1] TRUE $applyfun function (X, FUN, ...) { FUN <- match.fun(FUN) if (!is.vector(X) || is.object(X)) X <- as.list(X) .Internal(lapply(X, FUN)) } $saveinfo [1] TRUE $bonferroni [1] TRUE $update NULL $selectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $splitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svselectfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .select(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $svsplitfun function (model, trafo, data, subset, weights, whichvar, ctrl) { args <- list(...) ctrl[names(args)] <- args .split(model, trafo, data, subset, weights, whichvar, ctrl, FUN = .ctree_test) } $teststat [1] "quadratic" $splitstat [1] "quadratic" $splittest [1] FALSE $pargs $maxpts [1] 25000 $abseps [1] 0.001 $releps [1] 0 attr(,"class") [1] "GenzBretz" $testtype [1] "Bonferroni" $nresample [1] 9999 $tol [1] 1.490116e-08 $intersplit [1] FALSE $MIA [1] FALSE > ls <- data.frame(y = gl(3, 50, labels = c("A", "B", + "C")), x1 = rnorm(150) + rep(c(1, 0, 0), c(50, 50, 50)), + x2 = runif(150)) > library("partykit") > ctree(y ~ x1 + x2, data = ls) Model formula: y ~ x1 + x2 Fitted party: [1] root | [2] x1 <= 0.82552: C (n = 96, err = 57.3%) | [3] x1 > 0.82552: A (n = 54, err = 42.6%) Number of inner nodes: 1 Number of terminal nodes: 2 > ct <- ctree(y ~ x1 + x2, data = ls) > ct Model formula: y ~ x1 + x2 Fitted party: [1] root | [2] x1 <= 0.82552: C (n = 96, err = 57.3%) | [3] x1 > 0.82552: A (n = 54, err = 42.6%) Number of inner nodes: 1 Number of terminal nodes: 2 > plot(ct) > ct[1] Model formula: y ~ x1 + x2 Fitted party: [1] root | [2] x1 <= 0.82552: C (n = 96, err = 57.3%) | [3] x1 > 0.82552: A (n = 54, err = 42.6%) Number of inner nodes: 1 Number of terminal nodes: 2 > class(ct[1]) [1] "constparty" "party" > predict(ct, newdata = ls) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 A A A A C A C A C C A A C A A A A 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 C A C A A A C A A A C C A A C A A 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 C A A C C C A A C C C C A A A A A 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 A C C C C A C C A C C C C C C A A 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 A A A C C A C A C C C C C C C C C 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 C C C A C A C A C C C C C C C C A 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 C C C A C C A C C C C C C C A C C 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 C C C C C C C C C C C C C C C C C 137 138 139 140 141 142 143 144 145 146 147 148 149 150 C A C C C C A C C A C A C A Levels: A B C > predict(ct, newdata = ls[c(1, 51, 101), ], type = "prob") A B C 1 0.5740741 0.2592593 0.1666667 51 0.5740741 0.2592593 0.1666667 101 0.1979167 0.3750000 0.4270833 > predict(ct, newdata = ls[c(1, 51, 101), ], type = "node") 1 51 101 3 3 2 > library("strucchange") > sctest(ct) $`1` x1 x2 statistic 2.299131e+01 4.0971294 p.value 2.034833e-05 0.2412193 $`2` x1 x2 statistic 2.6647107 4.3628130 p.value 0.4580906 0.2130228 $`3` x1 x2 statistic 2.1170497 2.8275567 p.value 0.5735483 0.4272879 > data("treepipit", package = "coin") > tptree <- ctree(counts ~ ., data = treepipit) > plot(tptree, terminal_panel = node_barplot) > p <- info_node(node_party(tptree))$p.value > n <- table(predict(tptree, type = "node")) > data("GlaucomaM", package = "TH.data") > gtree <- ctree(Class ~ ., data = GlaucomaM) > sp <- split_node(node_party(gtree))$varID > plot(gtree) > plot(gtree, inner_panel = node_barplot, edge_panel = function(...) invisible(), + tnex = 1) > table(predict(gtree), GlaucomaM$Class) glaucoma normal glaucoma 74 5 normal 24 93 > prob <- predict(gtree, type = "prob")[, 1] + runif(nrow(GlaucomaM), + min = -0.01, max = 0.01) > splitvar <- character_split(split_node(node_party(gtree)), + data = data_party(gtree))$name > plot(GlaucomaM[[splitvar]], prob, pch = as.numeric(GlaucomaM$Class), + ylab = "Conditional Class Prob.", xlab = splitvar) > abline(v = split_node(node_party(gtree))$breaks, lty = 2) > legend(0.15, 0.7, pch = 1:2, legend = levels(GlaucomaM$Class), + bty = "n") > data("GBSG2", package = "TH.data") > library("survival") > (stree <- ctree(Surv(time, cens) ~ ., data = GBSG2)) Model formula: Surv(time, cens) ~ horTh + age + menostat + tsize + tgrade + pnodes + progrec + estrec Fitted party: [1] root | [2] pnodes <= 3 | | [3] horTh in no: 2093.000 (n = 248) | | [4] horTh in yes: Inf (n = 128) | [5] pnodes > 3 | | [6] progrec <= 20: 624.000 (n = 144) | | [7] progrec > 20: 1701.000 (n = 166) Number of inner nodes: 3 Number of terminal nodes: 4 > plot(stree) > pn <- predict(stree, newdata = GBSG2[1:2, ], type = "node") > n <- predict(stree, type = "node") > survfit(Surv(time, cens) ~ 1, data = GBSG2, subset = (n == + pn[1])) Call: survfit(formula = Surv(time, cens) ~ 1, data = GBSG2, subset = (n == pn[1])) n events median 0.95LCL 0.95UCL [1,] 248 88 2093 1814 NA > survfit(Surv(time, cens) ~ 1, data = GBSG2, subset = (n == + pn[2])) Call: survfit(formula = Surv(time, cens) ~ 1, data = GBSG2, subset = (n == pn[2])) n events median 0.95LCL 0.95UCL [1,] 166 77 1701 1174 2018 > data("mammoexp", package = "TH.data") > mtree <- ctree(ME ~ ., data = mammoexp) > plot(mtree) > data("HuntingSpiders", package = "partykit") > sptree <- ctree(arct.lute + pard.lugu + zora.spin + + pard.nigr + pard.pull + aulo.albi + troc.terr + alop.cune + + pard.mont + alop.acce .... [TRUNCATED] > plot(sptree, terminal_panel = node_barplot) > plot(sptree) > library("party") Loading required package: modeltools Loading required package: stats4 Attaching package: ‘party’ The following objects are masked from ‘package:partykit’: cforest, ctree, ctree_control, edge_simple, mob, mob_control, node_barplot, node_bivplot, node_boxplot, node_inner, node_surv, node_terminal, varimp > set.seed(290875) > data("airquality", package = "datasets") > airq <- subset(airquality, !is.na(Ozone)) > (airct_party <- party::ctree(Ozone ~ ., data = airq, + controls = party::ctree_control(maxsurrogate = 3))) Conditional inference tree with 5 terminal nodes Response: Ozone Inputs: Solar.R, Wind, Temp, Month, Day Number of observations: 116 1) Temp <= 82; criterion = 1, statistic = 56.086 2) Wind <= 6.9; criterion = 0.998, statistic = 12.969 3)* weights = 10 2) Wind > 6.9 4) Temp <= 77; criterion = 0.997, statistic = 11.599 5)* weights = 48 4) Temp > 77 6)* weights = 21 1) Temp > 82 7) Wind <= 10.3; criterion = 0.997, statistic = 11.712 8)* weights = 30 7) Wind > 10.3 9)* weights = 7 > mean((airq$Ozone - predict(airct_party))^2) [1] 403.6668 > (airct_partykit <- partykit::ctree(Ozone ~ ., data = airq, + control = partykit::ctree_control(maxsurrogate = 3, numsurrogate = TRUE))) Model formula: Ozone ~ Solar.R + Wind + Temp + Month + Day Fitted party: [1] root | [2] Temp <= 82 | | [3] Wind <= 6.9: 55.600 (n = 10, err = 21946.4) | | [4] Wind > 6.9 | | | [5] Temp <= 77: 18.479 (n = 48, err = 3956.0) | | | [6] Temp > 77: 31.143 (n = 21, err = 4620.6) | [7] Temp > 82 | | [8] Wind <= 10.3: 81.633 (n = 30, err = 15119.0) | | [9] Wind > 10.3: 48.714 (n = 7, err = 1183.4) Number of inner nodes: 4 Number of terminal nodes: 5 > mean((airq$Ozone - predict(airct_partykit))^2) [1] 403.6668 > table(predict(airct_party, type = "node"), predict(airct_partykit, + type = "node")) 3 5 6 8 9 3 10 0 0 0 0 5 0 48 0 0 0 6 0 0 21 0 0 8 0 0 0 30 0 9 0 0 0 0 7 > max(abs(predict(airct_party) - predict(airct_partykit))) [1] 0 > airct_party@tree$criterion $statistic Solar.R Wind Temp Month Day 13.34761286 41.61369618 56.08632426 3.11265955 0.02011554 $criterion Solar.R Wind Temp Month Day 9.987069e-01 1.000000e+00 1.000000e+00 6.674119e-01 1.824984e-05 $maxcriterion [1] 1 > info_node(node_party(airct_partykit)) $criterion Solar.R Wind Temp Month statistic 13.347612859 4.161370e+01 5.608632e+01 3.1126596 p.value 0.001293090 5.560572e-10 3.467894e-13 0.3325881 criterion -0.001293926 -5.560572e-10 -3.467894e-13 -0.4043478 Day statistic 0.02011554 p.value 0.99998175 criterion -10.91135399 $p.value Temp 3.467894e-13 $unweighted [1] TRUE $nobs [1] 116 > (irisct_party <- party::ctree(Species ~ ., data = iris)) Conditional inference tree with 4 terminal nodes Response: Species Inputs: Sepal.Length, Sepal.Width, Petal.Length, Petal.Width Number of observations: 150 1) Petal.Length <= 1.9; criterion = 1, statistic = 140.264 2)* weights = 50 1) Petal.Length > 1.9 3) Petal.Width <= 1.7; criterion = 1, statistic = 67.894 4) Petal.Length <= 4.8; criterion = 0.999, statistic = 13.865 5)* weights = 46 4) Petal.Length > 4.8 6)* weights = 8 3) Petal.Width > 1.7 7)* weights = 46 > (irisct_partykit <- partykit::ctree(Species ~ ., data = iris, + control = partykit::ctree_control(splitstat = "maximum"))) Model formula: Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width Fitted party: [1] root | [2] Petal.Length <= 1.9: setosa (n = 50, err = 0.0%) | [3] Petal.Length > 1.9 | | [4] Petal.Width <= 1.7 | | | [5] Petal.Length <= 4.8: versicolor (n = 46, err = 2.2%) | | | [6] Petal.Length > 4.8: versicolor (n = 8, err = 50.0%) | | [7] Petal.Width > 1.7: virginica (n = 46, err = 2.2%) Number of inner nodes: 3 Number of terminal nodes: 4 > table(predict(irisct_party, type = "node"), predict(irisct_partykit, + type = "node")) 2 5 6 7 2 50 0 0 0 5 0 46 0 0 6 0 0 8 0 7 0 0 0 46 > tr_party <- treeresponse(irisct_party, newdata = iris) > tr_partykit <- predict(irisct_partykit, type = "prob", + newdata = iris) > max(abs(do.call("rbind", tr_party) - tr_partykit)) [1] 0 > data("mammoexp", package = "TH.data") > (mammoct_party <- party::ctree(ME ~ ., data = mammoexp)) Conditional inference tree with 3 terminal nodes Response: ME Inputs: SYMPT, PB, HIST, BSE, DECT Number of observations: 412 1) SYMPT <= Agree; criterion = 1, statistic = 29.933 2)* weights = 113 1) SYMPT > Agree 3) PB <= 8; criterion = 0.988, statistic = 9.17 4)* weights = 208 3) PB > 8 5)* weights = 91 > tr_party <- treeresponse(mammoct_party, newdata = mammoexp) > (mammoct_partykit <- partykit::ctree(ME ~ ., data = mammoexp)) Model formula: ME ~ SYMPT + PB + HIST + BSE + DECT Fitted party: [1] root | [2] SYMPT <= Agree: Never (n = 113, err = 15.9%) | [3] SYMPT > Agree | | [4] PB <= 8: Never (n = 208, err = 60.1%) | | [5] PB > 8: Never (n = 91, err = 38.5%) Number of inner nodes: 2 Number of terminal nodes: 3 > tr_partykit <- predict(mammoct_partykit, newdata = mammoexp, + type = "prob") > max(abs(do.call("rbind", tr_party) - tr_partykit)) [1] 0 > data("GBSG2", package = "TH.data") > (GBSG2ct_party <- party::ctree(Surv(time, cens) ~ + ., data = GBSG2)) Conditional inference tree with 4 terminal nodes Response: Surv(time, cens) Inputs: horTh, age, menostat, tsize, tgrade, pnodes, progrec, estrec Number of observations: 686 1) pnodes <= 3; criterion = 1, statistic = 56.156 2) horTh == {yes}; criterion = 0.965, statistic = 8.113 3)* weights = 128 2) horTh == {no} 4)* weights = 248 1) pnodes > 3 5) progrec <= 20; criterion = 0.999, statistic = 14.941 6)* weights = 144 5) progrec > 20 7)* weights = 166 > (GBSG2ct_partykit <- partykit::ctree(Surv(time, cens) ~ + ., data = GBSG2)) Model formula: Surv(time, cens) ~ horTh + age + menostat + tsize + tgrade + pnodes + progrec + estrec Fitted party: [1] root | [2] pnodes <= 3 | | [3] horTh in no: 2093.000 (n = 248) | | [4] horTh in yes: Inf (n = 128) | [5] pnodes > 3 | | [6] progrec <= 20: 624.000 (n = 144) | | [7] progrec > 20: 1701.000 (n = 166) Number of inner nodes: 3 Number of terminal nodes: 4 > tr_party <- treeresponse(GBSG2ct_party, newdata = GBSG2) > tr_partykit <- predict(GBSG2ct_partykit, newdata = GBSG2, + type = "prob") > all.equal(lapply(tr_party, function(x) unclass(x)[!(names(x) %in% + "call")]), lapply(tr_partykit, function(x) unclass(x)[!(names(x) %in% + .... [TRUNCATED] [1] TRUE > (airct_partykit_1 <- partykit::ctree(Ozone ~ ., data = airq, + control = partykit::ctree_control(maxsurrogate = 3, alpha = 0.001, + nu .... [TRUNCATED] Model formula: Ozone ~ Solar.R + Wind + Temp + Month + Day Fitted party: [1] root | [2] Temp <= 82: 26.544 (n = 79, err = 42531.6) | [3] Temp > 82: 75.405 (n = 37, err = 22452.9) Number of inner nodes: 1 Number of terminal nodes: 2 > depth(airct_partykit_1) [1] 1 > mean((airq$Ozone - predict(airct_partykit_1))^2) [1] 560.2113 > (airct_partykit <- partykit::ctree(Ozone ~ ., data = airq, + control = partykit::ctree_control(maxsurrogate = 3, splittest = TRUE, + t .... [TRUNCATED] Model formula: Ozone ~ Solar.R + Wind + Temp + Month + Day Fitted party: [1] root | [2] Temp <= 82 | | [3] Wind <= 6.9: 55.600 (n = 10, err = 21946.4) | | [4] Wind > 6.9 | | | [5] Temp <= 77 | | | | [6] Solar.R <= 78: 12.533 (n = 15, err = 723.7) | | | | [7] Solar.R > 78: 21.182 (n = 33, err = 2460.9) | | | [8] Temp > 77 | | | | [9] Solar.R <= 148: 20.000 (n = 7, err = 652.0) | | | | [10] Solar.R > 148: 36.714 (n = 14, err = 2664.9) | [11] Temp > 82 | | [12] Temp <= 87 | | | [13] Wind <= 8.6: 72.308 (n = 13, err = 8176.8) | | | [14] Wind > 8.6: 45.571 (n = 7, err = 617.7) | | [15] Temp > 87: 90.059 (n = 17, err = 3652.9) Number of inner nodes: 7 Number of terminal nodes: 8 > (irisct_partykit_1 <- partykit::ctree(Species ~ ., + data = iris, control = partykit::ctree_control(splitstat = "maximum", + nmax = 25 .... [TRUNCATED] Model formula: Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width Fitted party: [1] root | [2] Petal.Width <= 0.6: setosa (n = 50, err = 0.0%) | [3] Petal.Width > 0.6 | | [4] Petal.Width <= 1.7 | | | [5] Petal.Length <= 4.8: versicolor (n = 46, err = 2.2%) | | | [6] Petal.Length > 4.8: versicolor (n = 8, err = 50.0%) | | [7] Petal.Width > 1.7: virginica (n = 46, err = 2.2%) Number of inner nodes: 3 Number of terminal nodes: 4 > table(predict(irisct_partykit), predict(irisct_partykit_1)) setosa versicolor virginica setosa 50 0 0 versicolor 0 54 0 virginica 0 0 46 > GBSG2$tgrade <- factor(GBSG2$tgrade, ordered = FALSE) > (GBSG2ct_partykit <- partykit::ctree(Surv(time, cens) ~ + tgrade, data = GBSG2, control = partykit::ctree_control(multiway = TRUE, + alpha .... [TRUNCATED] Model formula: Surv(time, cens) ~ tgrade Fitted party: [1] root | [2] tgrade in I: Inf (n = 81) | [3] tgrade in II: 1730.000 (n = 444) | [4] tgrade in III: 1337.000 (n = 161) Number of inner nodes: 1 Number of terminal nodes: 3 > airq$month <- factor(airq$Month) > (airct_partykit_3 <- partykit::ctree(Ozone ~ Solar.R + + Wind + Temp, data = airq, cluster = month, control = partykit::ctree_control(maxsurrog .... [TRUNCATED] Model formula: Ozone ~ Solar.R + Wind + Temp Fitted party: [1] root | [2] Temp <= 82 | | [3] Temp <= 76: 18.250 (n = 48, err = 4199.0) | | [4] Temp > 76 | | | [5] Wind <= 6.9: 71.857 (n = 7, err = 15510.9) | | | [6] Wind > 6.9 | | | | [7] Temp <= 81: 32.412 (n = 17, err = 4204.1) | | | | [8] Temp > 81: 23.857 (n = 7, err = 306.9) | [9] Temp > 82 | | [10] Wind <= 10.3: 81.633 (n = 30, err = 15119.0) | | [11] Wind > 10.3: 48.714 (n = 7, err = 1183.4) Number of inner nodes: 5 Number of terminal nodes: 6 > info_node(node_party(airct_partykit_3)) $criterion Solar.R Wind Temp statistic 14.4805065501 3.299881e+01 4.783766e+01 p.value 0.0004247923 2.766464e-08 1.389038e-11 criterion -0.0004248826 -2.766464e-08 -1.389038e-11 $p.value Temp 1.389038e-11 $unweighted [1] TRUE $nobs [1] 116 > mean((airq$Ozone - predict(airct_partykit_3))^2) [1] 349.3382 > h <- function(y, x, start = NULL, weights, offset, + estfun = TRUE, object = FALSE, ...) { + if (is.null(weights)) + weights <- re .... [TRUNCATED] > partykit::ctree(Surv(time, cens) ~ ., data = GBSG2, + ytrafo = h) Model formula: Surv(time, cens) ~ horTh + age + menostat + tsize + tgrade + pnodes + progrec + estrec Fitted party: [1] root | [2] pnodes <= 3 | | [3] horTh in no: 2093.000 (n = 248) | | [4] horTh in yes: Inf (n = 128) | [5] pnodes > 3 | | [6] progrec <= 20: 624.000 (n = 144) | | [7] progrec > 20: 1701.000 (n = 166) Number of inner nodes: 3 Number of terminal nodes: 4 > h <- function(y, x, start = NULL, weights = NULL, + offset = NULL, cluster = NULL, ...) glm(y ~ 0 + x, family = gaussian(), + start = star .... [TRUNCATED] > (airct_partykit_4 <- partykit::ctree(Ozone ~ Temp | + Solar.R + Wind, data = airq, cluster = month, ytrafo = h, + control = partykit::ctre .... [TRUNCATED] Model formula: Ozone ~ Temp + (Solar.R + Wind) Fitted party: [1] root | [2] Wind <= 5.7: 98.692 (n = 13, err = 11584.8) | [3] Wind > 5.7 | | [4] Wind <= 8 | | | [5] Wind <= 6.9: 55.286 (n = 14, err = 11330.9) | | | [6] Wind > 6.9: 50.824 (n = 17, err = 15400.5) | | [7] Wind > 8: 27.306 (n = 72, err = 25705.3) Number of inner nodes: 3 Number of terminal nodes: 4 > airq$node <- factor(predict(airct_partykit_4, type = "node")) > summary(m <- glm(Ozone ~ node + node:Temp - 1, data = airq)) Call: glm(formula = Ozone ~ node + node:Temp - 1, data = airq) Coefficients: Estimate Std. Error t value Pr(>|t|) node2 300.0527 93.4828 3.210 0.001750 ** node5 -217.3416 51.3970 -4.229 4.94e-05 *** node6 -178.9333 58.1093 -3.079 0.002632 ** node7 -82.2722 17.9951 -4.572 1.29e-05 *** node2:Temp -2.2922 1.0626 -2.157 0.033214 * node5:Temp 3.2989 0.6191 5.328 5.47e-07 *** node6:Temp 2.8059 0.7076 3.965 0.000132 *** node7:Temp 1.4769 0.2408 6.133 1.45e-08 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for gaussian family taken to be 329.3685) Null deviance: 331029 on 116 degrees of freedom Residual deviance: 35572 on 108 degrees of freedom AIC: 1011.4 Number of Fisher Scoring iterations: 2 > mean((predict(m) - airq$Ozone)^2) [1] 306.6534 > airq_lmtree <- partykit::lmtree(Ozone ~ Temp | Solar.R + + Wind, data = airq, cluster = month) > info_node(node_party(airq_lmtree)) $coefficients (Intercept) Temp -147.64607 2.43911 $objfun [1] 62367.44 $object Call: lm(formula = Ozone ~ Temp) Coefficients: (Intercept) Temp -147.646 2.439 $nobs [1] 111 $p.value [1] 0.003498545 $test Solar.R Wind statistic 8.5761635 18.881769795 p.value 0.2771841 0.003498545 > mean((predict(airq_lmtree, newdata = airq) - airq$Ozone)^2) [1] 371.5366 > detach(package:party) *** Run successfully completed *** > proc.time() user system elapsed 5.352 7.306 4.194 partykit/vignettes/partykit.Rout.save0000644000176200001440000001641714172230001017607 0ustar liggesusers > suppressWarnings(RNGversion("3.5.2")) > options(width = 70) > library("partykit") Loading required package: grid Loading required package: libcoin Loading required package: mvtnorm > set.seed(290875) > data("WeatherPlay", package = "partykit") > WeatherPlay outlook temperature humidity windy play 1 sunny 85 85 false no 2 sunny 80 90 true no 3 overcast 83 86 false yes 4 rainy 70 96 false yes 5 rainy 68 80 false yes 6 rainy 65 70 true no 7 overcast 64 65 true yes 8 sunny 72 95 false no 9 sunny 69 70 false yes 10 rainy 75 80 false yes 11 sunny 75 70 true yes 12 overcast 72 90 true yes 13 overcast 81 75 false yes 14 rainy 71 91 true no > py <- party(partynode(1, split = partysplit(1, index = 1:3), + kids = list(partynode(2, split = partysplit(3, breaks = 75), + kids = l .... [TRUNCATED] > plot(py) > sp_o <- partysplit(1, index = 1:3) > sp_h <- partysplit(3, breaks = 75) > sp_w <- partysplit(4, index = 1:2) > pn <- partynode(1, split = sp_o, kids = list(partynode(2, + split = sp_h, kids = list(partynode(3, info = "yes"), partynode(4, + info .... [TRUNCATED] > pn [1] root | [2] V1 in (-Inf,1] | | [3] V3 <= 75 * | | [4] V3 > 75 * | [5] V1 in (1,2] * | [6] V1 in (2, Inf] | | [7] V4 <= 1 * | | [8] V4 > 1 * > py <- party(pn, WeatherPlay) > print(py) [1] root | [2] outlook in sunny | | [3] humidity <= 75: yes | | [4] humidity > 75: no | [5] outlook in overcast: yes | [6] outlook in rainy | | [7] windy in false: yes | | [8] windy in true: no > predict(py, head(WeatherPlay)) 1 2 3 4 5 6 4 4 5 7 7 8 > length(py) [1] 8 > width(py) [1] 5 > depth(py) [1] 2 > py[6] [6] root | [7] windy in false: yes | [8] windy in true: no > py2 <- py > names(py2) [1] "1" "2" "3" "4" "5" "6" "7" "8" > names(py2) <- LETTERS[1:8] > py2 [A] root | [B] outlook in sunny | | [C] humidity <= 75: yes | | [D] humidity > 75: no | [E] outlook in overcast: yes | [F] outlook in rainy | | [G] windy in false: yes | | [H] windy in true: no > nodeids(py) [1] 1 2 3 4 5 6 7 8 > nodeids(py, terminal = TRUE) [1] 3 4 5 7 8 > nodeapply(py, ids = c(1, 7), FUN = function(n) n$info) $`1` NULL $`7` [1] "yes" > nodeapply(py, ids = nodeids(py, terminal = TRUE), + FUN = function(n) paste("Play decision:", n$info)) $`3` [1] "Play decision: yes" $`4` [1] "Play decision: no" $`5` [1] "Play decision: yes" $`7` [1] "Play decision: yes" $`8` [1] "Play decision: no" > predict(py, FUN = function(n) paste("Play decision:", + n$info)) 1 2 3 "Play decision: no" "Play decision: no" "Play decision: yes" 4 5 6 "Play decision: yes" "Play decision: yes" "Play decision: no" 7 8 9 "Play decision: yes" "Play decision: no" "Play decision: yes" 10 11 12 "Play decision: yes" "Play decision: yes" "Play decision: yes" 13 14 "Play decision: yes" "Play decision: no" > print(py, terminal_panel = function(n) c(", then the play decision is:", + toupper(n$info))) [1] root | [2] outlook in sunny | | [3] humidity <= 75, then the play decision is: | | YES | | [4] humidity > 75, then the play decision is: | | NO | [5] outlook in overcast, then the play decision is: | YES | [6] outlook in rainy | | [7] windy in false, then the play decision is: | | YES | | [8] windy in true, then the play decision is: | | NO > plot(py[6]) > plot(py, tp_args = list(FUN = function(i) c("Play decision:", + toupper(i)))) > nodeprune(py, 2) [1] root | [2] outlook in sunny: * | [3] outlook in overcast: yes | [4] outlook in rainy | | [5] windy in false: yes | | [6] windy in true: no > nodeprune(py, c(2, 6)) [1] root | [2] outlook in sunny: * | [3] outlook in overcast: yes | [4] outlook in rainy: * > sp_h <- partysplit(3, breaks = 75) > class(sp_h) [1] "partysplit" > unclass(sp_h) $varid [1] 3 $breaks [1] 75 $index NULL $right [1] TRUE $prob NULL $info NULL > character_split(sp_h, data = WeatherPlay) $name [1] "humidity" $levels [1] "<= 75" "> 75" > kidids_split(sp_h, data = WeatherPlay) [1] 2 2 2 2 2 1 1 2 1 2 1 2 1 2 > as.numeric(!(WeatherPlay$humidity <= 75)) + 1 [1] 2 2 2 2 2 1 1 2 1 2 1 2 1 2 > sp_o2 <- partysplit(1, index = c(1, 1, 2)) > character_split(sp_o2, data = WeatherPlay) $name [1] "outlook" $levels [1] "sunny, overcast" "rainy" > table(kidids_split(sp_o2, data = WeatherPlay), WeatherPlay$outlook) sunny overcast rainy 1 5 4 0 2 0 0 5 > unclass(sp_o2) $varid [1] 1 $breaks NULL $index [1] 1 1 2 $right [1] TRUE $prob NULL $info NULL > sp_o <- partysplit(1, index = 1:3) > character_split(sp_o, data = WeatherPlay) $name [1] "outlook" $levels [1] "sunny" "overcast" "rainy" > sp_t <- partysplit(2, breaks = c(69.5, 78.8), index = c(1, + 2, 1)) > character_split(sp_t, data = WeatherPlay) $name [1] "temperature" $levels [1] "(-Inf,69.5] | (78.8, Inf]" "(69.5,78.8]" > table(kidids_split(sp_t, data = WeatherPlay), cut(WeatherPlay$temperature, + breaks = c(-Inf, 69.5, 78.8, Inf))) (-Inf,69.5] (69.5,78.8] (78.8, Inf] 1 4 0 4 2 0 6 0 > n1 <- partynode(id = 1) > is.terminal(n1) [1] TRUE > print(n1) [1] root * > n1 <- partynode(id = 1, split = sp_o, kids = lapply(2:4, + partynode)) > print(n1, data = WeatherPlay) [1] root | [2] outlook in sunny * | [3] outlook in overcast * | [4] outlook in rainy * > fitted_node(n1, data = WeatherPlay) [1] 2 2 3 4 4 4 3 2 2 4 2 3 3 4 > kidids_node(n1, data = WeatherPlay) [1] 1 1 2 3 3 3 2 1 1 3 1 2 2 3 > t1 <- party(n1, data = WeatherPlay) > t1 [1] root | [2] outlook in sunny: * | [3] outlook in overcast: * | [4] outlook in rainy: * > party(n1, data = WeatherPlay[0, ]) [1] root | [2] outlook in sunny: * | [3] outlook in overcast: * | [4] outlook in rainy: * > t2 <- party(n1, data = WeatherPlay, fitted = data.frame(`(fitted)` = fitted_node(n1, + data = WeatherPlay), `(response)` = WeatherPlay$play, ch .... [TRUNCATED] > t2 <- as.constparty(t2) > t2 Model formula: play ~ outlook + temperature + humidity + windy Fitted party: [1] root | [2] outlook in sunny: no (n = 5, err = 40.0%) | [3] outlook in overcast: yes (n = 4, err = 0.0%) | [4] outlook in rainy: yes (n = 5, err = 40.0%) Number of inner nodes: 1 Number of terminal nodes: 3 > plot(t2, tnex = 1.5) > nd <- data.frame(outlook = factor(c("overcast", "sunny"), + levels = levels(WeatherPlay$outlook))) > predict(t2, newdata = nd, type = "response") 1 2 yes no Levels: yes no > predict(t2, newdata = nd, type = "prob") yes no 1 1.0 0.0 2 0.4 0.6 > predict(t2, newdata = nd, type = "node") 1 2 3 2 *** Run successfully completed *** > proc.time() user system elapsed 1.502 0.068 1.564 partykit/vignettes/partykit.Rnw0000644000176200001440000010150114172230001016454 0ustar liggesusers\documentclass[nojss]{jss} %\VignetteIndexEntry{partykit: A Toolkit for Recursive Partytioning} %\VignetteDepends{partykit} %\VignetteKeywords{recursive partitioning, regression trees, classification trees, decision trees} %\VignettePackage{partykit} %% packages \usepackage{amstext} \usepackage{amsfonts} \usepackage{amsmath} \usepackage{thumbpdf} \usepackage{rotating} %% need no \usepackage{Sweave} %% additional commands \newcommand{\squote}[1]{`{#1}'} \newcommand{\dquote}[1]{``{#1}''} \newcommand{\fct}[1]{\texttt{#1()}} \newcommand{\class}[1]{\squote{\texttt{#1}}} %% for internal use \newcommand{\fixme}[1]{\emph{\marginpar{FIXME} (#1)}} \newcommand{\readme}[1]{\emph{\marginpar{README} (#1)}} \hyphenation{Qua-dra-tic} \title{\pkg{partykit}: A Toolkit for Recursive Partytioning} \Plaintitle{partykit: A Toolkit for Recursive Partytioning} \author{Achim Zeileis\\Universit\"at Innsbruck \And Torsten Hothorn\\Universit\"at Z\"urich} \Plainauthor{Achim Zeileis, Torsten Hothorn} \Abstract{ The \pkg{partykit} package provides a flexible toolkit with infrastructure for learning, representing, summarizing, and visualizing a wide range of tree-structured regression and classification models. The functionality encompasses: (a)~Basic infrastructure for \emph{representing} trees (inferred by any algorithm) so that unified \code{print}/\code{plot}/\code{predict} methods are available. (b)~Dedicated methods for trees with \emph{constant fits} in the leaves (or terminal nodes) along with suitable coercion functions to create such tree models (e.g., by \pkg{rpart}, \pkg{RWeka}, PMML). (c)~A reimplementation of \emph{conditional inference trees} (\code{ctree}, originally provided in the \pkg{party} package). (d)~An extended reimplementation of \emph{model-based recursive partitioning} (\code{mob}, also originally in \pkg{party}) along with dedicated methods for trees with parametric models in the leaves. This vignette gives a brief overview of the package and discusses in detail the generic infrastructure for representing trees (a). Items~(b)--(d) are discussed in the remaining vignettes in the package. } \Keywords{recursive partitioning, regression trees, classification trees, decision trees} \Address{ Achim Zeileis \\ Department of Statistics \\ Faculty of Economics and Statistics \\ Universit\"at Innsbruck \\ Universit\"atsstr.~15 \\ 6020 Innsbruck, Austria \\ E-mail: \email{Achim.Zeileis@R-project.org} \\ URL: \url{http://eeecon.uibk.ac.at/~zeileis/} \\ Torsten Hothorn\\ Institut f\"ur Epidemiologie, Biostatistik und Pr\"avention \\ Universit\"at Z\"urich \\ Hirschengraben 84\\ CH-8001 Z\"urich, Switzerland \\ E-mail: \email{Torsten.Hothorn@R-project.org}\\ URL: \url{http://user.math.uzh.ch/hothorn/} } \begin{document} \SweaveOpts{eps=FALSE, keep.source=TRUE, eval = TRUE} <>= suppressWarnings(RNGversion("3.5.2")) options(width = 70) library("partykit") set.seed(290875) @ \section{Overview} \label{sec:overview} In the more than fifty years since \cite{Morgan+Sonquist:1963} published their seminal paper on ``automatic interaction detection'', a wide range of methods has been suggested that is usually termed ``recursive partitioning'' or ``decision trees'' or ``tree(-structured) models'' etc. Particularly influential were the algorithms CART \citep[classification and regression trees,][]{Breiman+Friedman+Olshen:1984}, C4.5 \citep{Quinlan:1993}, QUEST/GUIDE \citep{Loh+Shih:1997,Loh:2002}, and CTree \citep{Hothorn+Hornik+Zeileis:2006} among many others \citep[see][for a recent overview]{Loh:2014}. Reflecting the heterogeneity of conceptual algorithms, a wide range of computational implementations in various software systems emerged: Typically the original authors of an algorithm also provide accompanying software but many software systems, e.g., including \pkg{Weka} \citep{Witten+Frank:2005} or \proglang{R} \citep{R}, also provide collections of various types of trees. Within \proglang{R} the list of prominent packages includes \pkg{rpart} \citep[implementing the CART algorithm]{rpart}, \pkg{mvpart} \citep[for multivariate CART]{mvpart}, \pkg{RWeka} \citep[containing interfaces to J4.8, M5', LMT from \pkg{Weka}]{RWeka}, and \pkg{party} \citep[implementing CTree and MOB]{party} among many others. See the CRAN task view ``Machine Learning'' \citep{ctv} for an overview. All of these algorithms and software implementations have to deal with very similar challenges. However, due to the fragmentation of the communities in which the corresponding research is published -- ranging from statistics over machine learning to various applied fields -- many discussions of the algorithms do not reuse established theoretical results and terminology. Similarly, there is no common ``language'' for the software implementations and different solutions are provided by different packages (even within \proglang{R}) with relatively little reuse of code. The \pkg{partykit} tries to address the latter point and improve the computational situation by providing a common unified infrastructure for recursive partytioning in the \proglang{R} system for statistical computing. In particular, \pkg{partykit} provides tools for representing fitted trees along with printing, plotting, and computing predictions. The design principles are: \begin{itemize} \item One `agnostic' base class (\class{party}) which can encompass an extremely wide range of different types of trees. \item Subclasses for important types of trees, e.g., trees with constant fits (\class{constparty}) or with parametric models (\class{modelparty}) in each terminal node (or leaf). \item Nodes are recursive objects, i.e., a node can contain child nodes. \item Keep the (learning) data out of the recursive node and split structure. \item Basic printing, plotting, and predicting for raw node structure. \item Customization via suitable panel or panel-generating functions. \item Coercion from existing object classes in \proglang{R} (\code{rpart}, \code{J48}, etc.) to the new class. \item Usage of simple/fast \proglang{S}3 classes and methods. \end{itemize} In addition to all of this generic infrastructure, two specific tree algorithms are implemented in \pkg{partykit} as well: \fct{ctree} for conditional inference trees \citep{Hothorn+Hornik+Zeileis:2006} and \fct{mob} for model-based recursive partitioning \citep{Zeileis+Hothorn+Hornik:2008}. This vignette (\code{"partykit"}) introduces the basic \class{party} class and associated infrastructure while three further vignettes discuss the tools built on top of it: \code{"constparty"} covers the eponymous class for constant-fit trees along with suitable coercion functions, and \code{"ctree"} and \code{"mob"} discuss the new \fct{ctree} and \fct{mob} implementations, respectively. Each of the vignettes can be viewed within \proglang{R} via \code{vignette(}\emph{``name''}\code{, package = "partykit")}. Normal users reading this vignette will typically be interested only in the motivating example in Section~\ref{sec:intro} while the remaining sections are intended for programmers who want to build infrastructure on top of \pkg{partykit}. \section{Motivating example} \label{sec:intro} \subsection{Data} To illustrate how \pkg{partykit} can be used to represent trees, we employ a simple artificial data set taken from \cite{Witten+Frank:2005}. It concerns the conditions suitable for playing some unspecified game: % <>= data("WeatherPlay", package = "partykit") WeatherPlay @ % To represent the \code{play} decision based on the corresponding weather condition variables one could use the tree displayed in Figure~\ref{fig:weather-plot}. For now, it is ignored how this tree was inferred and it is simply assumed to be given. \setkeys{Gin}{width=0.8\textwidth} \begin{figure}[t!] \centering <>= py <- party( partynode(1L, split = partysplit(1L, index = 1:3), kids = list( partynode(2L, split = partysplit(3L, breaks = 75), kids = list( partynode(3L, info = "yes"), partynode(4L, info = "no"))), partynode(5L, info = "yes"), partynode(6L, split = partysplit(4L, index = 1:2), kids = list( partynode(7L, info = "yes"), partynode(8L, info = "no"))))), WeatherPlay) plot(py) @ \caption{\label{fig:weather-plot} Decision tree for \code{play} decision based on weather conditions in \code{WeatherPlay} data.} \end{figure} \setkeys{Gin}{width=\textwidth} To represent this tree (or recursive partition) in \pkg{partykit}, two basic building blocks are used: splits of class \class{partysplit} and nodes of class \class{partynode}. The resulting recursive partition can then be associated with a data set in an object of class \class{party}. \subsection{Splits} First, we employ the \fct{partysplit} function to create the three splits in the ``play tree'' from Figure~\ref{fig:weather-plot}. The function takes the following arguments \begin{Code} partysplit(varid, breaks = NULL, index = NULL, ..., info = NULL) \end{Code} where \code{varid} is an integer id (column number) of the variable used for splitting, e.g., \code{1L} for \code{outlook}, \code{3L} for \code{humidity}, \code{4L} for \code{windy} etc. Then, \code{breaks} and \code{index} determine which observations are sent to which of the branches, e.g., \code{breaks = 75} for the humidity split. Apart from further arguments not shown above (and just comprised under `\code{...}'), some arbitrary information can be associated with a \class{partysplit} object by passing it to the \code{info} argument. The three splits from Figure~\ref{fig:weather-plot} can then be created via % <>= sp_o <- partysplit(1L, index = 1:3) sp_h <- partysplit(3L, breaks = 75) sp_w <- partysplit(4L, index = 1:2) @ % For the numeric \code{humidity} variable the \code{breaks} are set while for the factor variables \code{outlook} and \code{windy} the information is supplied which of the levels should be associated with which of the branches of the tree. \subsection{Nodes} Second, we use these splits in the creation of the whole decision tree. In \pkg{partykit} a tree is represented by a \class{partynode} object which is recursive in that it may have ``kids'' that are again \class{partynode} objects. These can be created with the function \begin{Code} partynode(id, split = NULL, kids = NULL, ..., info = NULL) \end{Code} where \code{id} is an integer identifier of the node number, \code{split} is a \class{partysplit} object, and \code{kids} is a list of \class{partynode} objects. Again, there are further arguments not shown (\code{...}) and arbitrary information can be supplied in \code{info}. The whole tree from Figure~\ref{fig:weather-plot} can then be created via % <>= pn <- partynode(1L, split = sp_o, kids = list( partynode(2L, split = sp_h, kids = list( partynode(3L, info = "yes"), partynode(4L, info = "no"))), partynode(5L, info = "yes"), partynode(6L, split = sp_w, kids = list( partynode(7L, info = "yes"), partynode(8L, info = "no"))))) @ % where the previously created \class{partysplit} objects are used as splits and the nodes are simply numbered (depth first) from~1 to~8. For the terminal nodes of the tree there are no \code{kids} and the corresponding \code{play} decision is stored in the \code{info} argument. Printing the \class{partynode} object reflects the recursive structure stored. % <>= pn @ % However, the displayed information is still rather raw as it has not yet been associated with the \code{WeatherPlay} data set. \subsection{Trees (or recursive partitions)} Therefore, in a third step the recursive tree structure stored in \code{pn} is coupled with the corresponding data in a \class{party} object. % <>= py <- party(pn, WeatherPlay) print(py) @ % Now, Figure~\ref{fig:weather-plot} can easily be created by % <>= plot(py) @ % In addition to \fct{print} and \fct{plot}, the \fct{predict} method can now be applied, yielding the predicted terminal node IDs. % <>= predict(py, head(WeatherPlay)) @ % In addition to the \class{partynode} and the \class{data.frame}, the function \fct{party} takes several further arguments \begin{Code} party(node, data, fitted = NULL, terms = NULL, ..., info = NULL) \end{Code} i.e., \code{fitted} values, a \code{terms} object, arbitrary additional \code{info}, and again some further arguments comprised in \code{...}. \subsection{Methods and other utilities} The main idea about the \class{party} class is that tedious tasks such as \fct{print}, \fct{plot}, \fct{predict} do not have to be reimplemented for every new kind of decision tree but can simply be reused. However, in addition to these three basic tasks (as already illustrated above) developers of tree model software also need further basic utiltities for working with trees: e.g., functions for querying or subsetting the tree and for customizing printed/plotted output. Below, various utilities provided by the \pkg{partykit} package are introduced. For querying the dimensions of the tree, three basic functions are available: \fct{length} gives the number of kid nodes of the root node, \fct{depth} the depth of the tree and \fct{width} the number of terminal nodes. % <>= length(py) width(py) depth(py) @ % As decision trees can grow to be rather large, it is often useful to inspect only subtrees. These can be easily extracted using the standard \code{[} or \code{[[} operators: % <>= py[6] @ % The resulting object is again a full valid \class{party} tree and can hence be printed (as above) or plotted (via \code{plot(py[6])}, see the left panel of Figure~\ref{fig:plot-customization}). Instead of using the integer node IDs for subsetting, node labels can also be used. By default thise are just (character versions of) the node IDs but other names can be easily assigned: % <>= py2 <- py names(py2) names(py2) <- LETTERS[1:8] py2 @ % The function \fct{nodeids} queries the integer node IDs belonging to a \class{party} tree. By default all IDs are returned but optionally only the terminal IDs (of the leaves) can be extracted. % <>= nodeids(py) nodeids(py, terminal = TRUE) @ % Often functions need to be applied to certain nodes of a tree, e.g., for extracting information. This is accomodated by a new generic function \fct{nodeapply} that follows the style of other \proglang{R} functions from the \code{apply} family and has methods for \class{party} and \class{partynode} objects. Furthermore, it needs a set of node IDs (often computed via \fct{nodeids}) and a function \code{FUN} that is applied to each of the requested \class{partynode} objects, typically for extracting/formatting the \code{info} of the node. % <>= nodeapply(py, ids = c(1, 7), FUN = function(n) n$info) nodeapply(py, ids = nodeids(py, terminal = TRUE), FUN = function(n) paste("Play decision:", n$info)) @ % Similar to the functions applied in a \fct{nodeapply}, the \fct{print}, \fct{predict}, and \fct{plot} methods can be customized through panel function that format certain parts of the tree (such as header, footer, node, etc.). Hence, the same kind of panel function employed above can also be used for predictions: <>= predict(py, FUN = function(n) paste("Play decision:", n$info)) @ As a variation of this approach, an extended formatting with multiple lines can be easily accomodated by supplying a character vector in every node: % <>= print(py, terminal_panel = function(n) c(", then the play decision is:", toupper(n$info))) @ % The same type of approach can also be used in the default \fct{plot} method (with the main difference that the panel function operates on the \code{info} directly rather than on the \class{partynode}). % <>= plot(py, tp_args = list(FUN = function(i) c("Play decision:", toupper(i)))) @ % See the right panel of Figure~\ref{fig:plot-customization} for the resulting graphic. Many more elaborate panel functions are provided in \pkg{partykit}, especially for not only showing text in the visualizations but also statistical graphics. Some of these are briefly illustrated in this and the other package vignettes. Programmers that want to write their own panel functions are advised to inspect the corresponding \proglang{R} source code to see how flexible (but sometimes also complicated) these panel functions are. \setkeys{Gin}{width=0.48\textwidth} \begin{figure}[t!] \centering <>= plot(py[6]) @ <>= <> @ \caption{\label{fig:plot-customization} Visualization of subtree (left) and tree with custom text in terminal nodes (right).} \end{figure} \setkeys{Gin}{width=\textwidth} Finally, an important utility function is \fct{nodeprune} which allows to prune \class{party} trees. It takes a vector of node IDs and prunes all of their kids, i.e., making all the indicated node IDs terminal nodes. <>= nodeprune(py, 2) nodeprune(py, c(2, 6)) @ Note that for the pruned versions of this particular \class{party} tree, the new terminal nodes are displayed with a \code{*} rather than the play decision. This is because we did not store any play decisions in the \code{info} of the inner nodes of \code{py}. We could have of course done so initially, or could do so now, or we might want to do so automatically. For the latter, we would have to know how predictions should be obtained from the data and this is briefly discussed at the end of this vignette and in more detail in \code{vignette("constparty", package = "partykit")}. \section{Technical details} \subsection{Design principles} To facilitate reading of the subsequent sections, two design principles employed in the creation of \pkg{partykit} are briefly explained. % \begin{enumerate} \item Many helper utilities are encapsulated in functions that follow a simple naming convention. To extract/compute some information \emph{foo} from splits, nodes, or trees, \pkg{partykit} provides \emph{foo}\code{_split}, \emph{foo}\code{_node}, \emph{foo}\code{_party} functions (that are applicable to \class{partysplit}, \class{partynode}, and \class{party} objects, repectively). An example for the information \emph{foo} might be \code{kidids} or \code{info}. Hence, in the printing example above using \code{info_node(n)} rather than \code{n$info} for a node \code{n} would have been the preferred syntax; at least when programming new functionality on top of \pkg{partykit}. \item As already illustrated above, printing and plotting relies on \emph{panel functions} that visualize and/or format certain aspects of the resulting display, e.g., that of inner nodes, terminal nodes, headers, footers, etc. Furthermore, arguments like \code{terminal_panel} can also take \emph{panel-generating functions}, i.e., functions that produce a panel function when applied to the \class{party} object. \end{enumerate} \subsection{Splits} \label{sec:splits} \subsubsection{Overview} A split is basically a function that maps data -- or more specifically a partitioning variable -- to daugther nodes. Objects of class \class{partysplit} are designed to represent such functions and are set up by the \fct{partysplit} constructor. For example, a binary split in the numeric partitioning variable \code{humidity} (the 3rd variable in \code{WeatherPlay}) at the breakpoint \code{75} can be created (as above) by % <>= sp_h <- partysplit(3L, breaks = 75) class(sp_h) @ % The internal structure of class \class{partysplit} contains information about the partitioning variable, the splitpoints (or cutpoints or breakpoints), the handling of splitpoints, the treatment of observations with missing values and the kid nodes to send observations to: % <>= unclass(sp_h) @ % Here, the splitting rule is \code{humidity} $\le 75$: % <>= character_split(sp_h, data = WeatherPlay) @ % This representation of splits is completely abstract and, most importantly, independent of any data. Now, data comes into play when we actually want to perform splits: % <>= kidids_split(sp_h, data = WeatherPlay) @ % For each observation in \code{WeatherPlay} the split is performed and the number of the kid node to send this observation to is returned. Of course, this is a very complicated way of saying % <>= as.numeric(!(WeatherPlay$humidity <= 75)) + 1 @ \subsubsection{Mathematical notation} To explain the splitting strategy more formally, we employ some mathematical notation. \pkg{partykit} considers a split to represent a function $f$ mapping an element $x = (x_1, \dots, x_p)$ of a $p$-dimensional sample space $\mathcal{X}$ into a set of $k$ daugther nodes $\mathcal{D} = \{d_1, \dots, d_k\}$. This mapping is defined as a composition $f = h \circ g$ of two functions $g: \mathcal{X} \rightarrow \mathcal{I}$ and $h: \mathcal{I} \rightarrow \mathcal{D}$ with index set $\mathcal{I} = \{1, \dots, l\}, l \ge k$. Let $\mu = (-\infty, \mu_1, \dots, \mu_{l - 1}, \infty)$ denote the split points ($(\mu_1, \dots, \mu_{l - 1})$ = \code{breaks}). We are interested to split according to the information contained in the $i$-th element of $x$ ($i$ = \code{varid}). For numeric $x_i$, the split points are also numeric. If $x_i$ is a factor at levels $1, \dots, K$, the default split points are $\mu = (-\infty, 1, \dots, K - 1, \infty)$. The function $g$ essentially determines, which of the intervals (defined by $\mu$) the value $x_i$ is contained in ($I$ denotes the indicator function here): \begin{eqnarray*} x \mapsto g(x) = \sum_{j = 1}^l j I_{\mathcal{A}(j)}(x_i) \end{eqnarray*} where $\mathcal{A}(j) = (\mu_{j - 1}, \mu_j]$ for \code{right = TRUE} except $\mathcal{A}(l) = (\mu_{l - 1}, \infty)$. If \code{right = FALSE}, then $\mathcal{A}(j) = [\mu_{j - 1}, \mu_j)$ except $\mathcal{A}(1) = (-\infty, \mu_1)$. Note that for a categorical variable $x_i$ and default split points, $g$ is simply the identity. Now, $h$ maps from the index set $\mathcal{I}$ into the set of daugther nodes: \begin{eqnarray*} f(x) = h(g(x)) = d_{\sigma_{g(x)}} \end{eqnarray*} where $\sigma = (\sigma_1, \dots, \sigma_l) \in \{1, \dots, k\}^l$ (\code{index}). By default, $\sigma = (1, \dots, l)$ and $k = l$. If $x_i$ is missing, then $f(x)$ is randomly drawn with $\mathbb{P}(f(x) = d_j) = \pi_j, j = 1, \dots, k$ for a discrete probability distribution $\pi = (\pi_1, \dots, \pi_k)$ over the $k$ daugther nodes (\code{prob}). In the simplest case of a binary split in a numeric variable $x_i$, there is only one split point $\mu_1$ and, with $\sigma = (1, 2)$, observations with $x_i \le \mu_1$ are sent to daugther node $d_1$ and observations with $x_i > \mu_1$ to $d_2$. However, this representation of splits is general enough to deal with more complicated set-ups like surrogate splits, where typically the index needs modification, for example $\sigma = (2, 1)$, categorical splits, i.e., there is one data structure for both ordered and unordered splits, multiway splits, and functional splits. The latter can be implemented by defining a new artificial splitting variable $x_{p + 1}$ by means of a potentially very complex function of $x$ later used for splitting. \subsubsection{Further examples} Consider a split in a categorical variable at three levels where the first two levels go to the left daugther node and the third one to the right daugther node: % <>= sp_o2 <- partysplit(1L, index = c(1L, 1L, 2L)) character_split(sp_o2, data = WeatherPlay) table(kidids_split(sp_o2, data = WeatherPlay), WeatherPlay$outlook) @ % The internal structure of this object contains the \code{index} slot that maps levels to kid nodes. % <>= unclass(sp_o2) @ % This mapping is also useful with splits in ordered variables or when representing multiway splits: % <>= sp_o <- partysplit(1L, index = 1L:3L) character_split(sp_o, data = WeatherPlay) @ % For a split in a numeric variable, the mapping to daugther nodes can also be changed by modifying \code{index}: % <>= sp_t <- partysplit(2L, breaks = c(69.5, 78.8), index = c(1L, 2L, 1L)) character_split(sp_t, data = WeatherPlay) table(kidids_split(sp_t, data = WeatherPlay), cut(WeatherPlay$temperature, breaks = c(-Inf, 69.5, 78.8, Inf))) @ \subsubsection{Further comments} The additional argument \code{prop} can be used to specify a discrete probability distribution over the daugther nodes that is used to map observations with missing values to daugther nodes. Furthermore, the \code{info} argument and slot can take arbitrary objects to be stored with the split (for example split statistics). Currently, no specific structure of the \code{info} is used. Programmers that employ this functionality in their own functions/packages should access the elements of a \class{partysplit} object by the corresponding accessor function (and not just the \code{$} operator as the internal structure might be changed/extended in future release). \subsection{Nodes} \label{sec:nodes} \subsubsection{Overview} Inner and terminal nodes are represented by objects of class \class{partynode}. Each node has a unique identifier \code{id}. A node consisting only of such an identifier (and possibly additional information in \code{info}) is a terminal node: % <>= n1 <- partynode(id = 1L) is.terminal(n1) print(n1) @ % Inner nodes have to have a primary split \code{split} and at least two daugther nodes. The daugther nodes are objects of class \class{partynode} itself and thus represent the recursive nature of this data structure. The daugther nodes are pooled in a list \code{kids}. In addition, a list of \class{partysplit} objects offering surrogate splits can be supplied in argument \code{surrogates}. These are used in case the variable needed for the primary split has missing values in a particular data set. The IDs in a \class{partynode} should be numbered ``depth first'' (sometimes also called ``infix'' or ``pre-order traversal''). This simply means that the root node has identifier 1; the first kid node has identifier 2, whose kid (if present) has identifier 3 and so on. If other IDs are desired, then one can simply set \fct{names} (see above) for the tree; however, internally the depth-first numbering needs to be used. Note that the \fct{partynode} constructor also allows to create \class{partynode} objects with other ID schemes as this is necessary for growing the tree. If one wants to assure the a given \class{partynode} object has the correct IDs, one can simply apply \fct{as.partynode} once more to assure the right order of IDs. Finally, let us emphasize that \class{partynode} objects are not directly connected to the actual data (only indirectly through the associated \class{partysplit} objects). \subsubsection{Examples} Based on the binary split \code{sp_h} defined in the previous section, we set up an inner node with two terminal daugther nodes and print this stump (the data is needed because neither split nor nodes contain information about variable names or levels): % <>= n1 <- partynode(id = 1L, split = sp_o, kids = lapply(2L:4L, partynode)) print(n1, data = WeatherPlay) @ % Now that we have defined this simple tree, we want to assign observations to terminal nodes: % <>= fitted_node(n1, data = WeatherPlay) @ % Here, the \code{id}s of the terminal node each observations falls into are returned. Alternatively, we could compute the position of these daugther nodes in the list \code{kids}: % <>= kidids_node(n1, data = WeatherPlay) @ % Furthermore, the \code{info} argument and slot takes arbitrary objects to be stored with the node (predictions, for example, but we will handle this issue later). The slots can be extracted by means of the corresponding accessor functions. \subsubsection{Methods} A number of methods is defined for \class{partynode} objects: \fct{is.partynode} checks if the argument is a valid \class{partynode} object. \fct{is.terminal} is \code{TRUE} for terminal nodes and \code{FALSE} for inner nodes. The subset method \code{[} returns the \class{partynode} object corresponding to the \code{i}-th kid. The \fct{as.partynode} and \fct{as.list} methods can be used to convert flat list structures into recursive \class{partynode} objects and vice versa. As pointed out above, \fct{as.partynode} applied to \class{partynode} objects also renumbers the recursive nodes starting with root node identifier \code{from}. Furthermore, many of the methods defined for the class \class{party} illustrated above also work for plain \class{partynode} objects. For example, \fct{length} gives the number of kid nodes of the root node, \fct{depth} the depth of the tree and \fct{width} the number of terminal nodes. \subsection{Trees} \label{sec:trees} Although tree structures can be represented by \class{partynode} objects, a tree is more than a number of nodes and splits. More information about (parts of the) corresponding data is necessary for high-level computations on trees. \subsubsection{Trees and data} First, the raw node/split structure needs to be associated with a corresponding data set. % <>= t1 <- party(n1, data = WeatherPlay) t1 @ % Note that the \code{data} may have zero rows (i.e., only contain variable names/classes but not the actual data) and all methods that do not require the presence of any learning data still work fine: % <>= party(n1, data = WeatherPlay[0, ]) @ \subsubsection{Response variables and regression relationships} Second, for decision trees (or regression and classification trees) more information is required: namely, the response variable and its fitted values. Hence, a \class{data.frame} can be supplied in \code{fitted} that has at least one variable \code{(fitted)} containing the terminal node numbers of data used for fitting the tree. For representing the dependence of the response on the partitioning variables, a \code{terms} object can be provided that is leveraged for appropriately preprocessing new data in predictions. Finally, any additional (currently unstructured) information can be stored in \code{info} again. % <>= t2 <- party(n1, data = WeatherPlay, fitted = data.frame( "(fitted)" = fitted_node(n1, data = WeatherPlay), "(response)" = WeatherPlay$play, check.names = FALSE), terms = terms(play ~ ., data = WeatherPlay), ) @ % The information that is now contained in the tree \code{t2} is sufficient for all operations that should typically be performed on constant-fit trees. For this type of trees there is also a dedicated class \class{constparty} that provides some further convenience methods, especially for plotting and predicting. If a suitable \class{party} object like \code{t2} is already available, it just needs to be coerced: % <>= t2 <- as.constparty(t2) t2 @ % \setkeys{Gin}{width=0.6\textwidth} \begin{figure}[t!] \centering <>= plot(t2, tnex = 1.5) @ \caption{\label{fig:constparty-plot} Constant-fit tree for \code{play} decision based on weather conditions in \code{WeatherPlay} data.} \end{figure} \setkeys{Gin}{width=\textwidth} % As pointed out above, \class{constparty} objects have enhanced \fct{plot} and \fct{predict} methods. For example, \code{plot(t2)} now produces stacked bar plots in the leaves (see Figure~\ref{fig:constparty-plot}) as \code{t2} is a classification tree For regression and survival trees, boxplots and Kaplan-Meier curves are employed automatically, respectively. As there is information about the response variable, the \fct{predict} method can now produce more than just the predicted node IDs. The default is to predict the \code{"response"}, i.e., a factor for a classification tree. In this case, class probabilities (\code{"prob"}) are also available in addition to the majority votings. % <>= nd <- data.frame(outlook = factor(c("overcast", "sunny"), levels = levels(WeatherPlay$outlook))) predict(t2, newdata = nd, type = "response") predict(t2, newdata = nd, type = "prob") predict(t2, newdata = nd, type = "node") @ More details on how \class{constparty} objects and their methods work can be found in the corresponding \code{vignette("constparty", package = "partykit")}. \section{Summary} This vignette (\code{"partykit"}) introduces the package \pkg{partykit} that provides a toolkit for computing with recursive partytions, especially decision/regression/classification trees. In this vignette, the basic \class{party} class and associated infrastructure are discussed: splits, nodes, and trees with functions for printing, plotting, and predicting. Further vignettes in the package discuss in more detail the tools built on top of it. \bibliography{party} \end{document} partykit/vignettes/constparty.Rnw0000644000176200001440000007155714172230001017034 0ustar liggesusers\documentclass[nojss]{jss} %\VignetteIndexEntry{Constant Partying: Growing and Handling Trees with Constant Fits} %\VignetteDepends{partykit, rpart, RWeka, pmml, datasets} %\VignetteKeywords{recursive partitioning, regression trees, classification trees, decision trees} %\VignettePackage{partykit} %% packages \usepackage{amstext} \usepackage{amsfonts} \usepackage{amsmath} \usepackage{thumbpdf} \usepackage{rotating} %% need no \usepackage{Sweave} %% additional commands \newcommand{\squote}[1]{`{#1}'} \newcommand{\dquote}[1]{``{#1}''} \newcommand{\fct}[1]{{\texttt{#1()}}} \newcommand{\class}[1]{\dquote{\texttt{#1}}} \newcommand{\fixme}[1]{\emph{\marginpar{FIXME} (#1)}} %% further commands \renewcommand{\Prob}{\mathbb{P} } \renewcommand{\E}{\mathbb{E}} \newcommand{\V}{\mathbb{V}} \newcommand{\Var}{\mathbb{V}} \hyphenation{Qua-dra-tic} \title{Constant Partying: Growing and Handling Trees with Constant Fits} \author{Torsten Hothorn\\Universit\"at Z\"urich \And Achim Zeileis\\Universit\"at Innsbruck} \Plainauthor{Torsten Hothorn, Achim Zeileis} \Abstract{ This vignette describes infrastructure for regression and classification trees with simple constant fits in each of the terminal nodes. Thus, all observations that are predicted to be in the same terminal node also receive the same prediction, e.g., a mean for numeric responses or proportions for categorical responses. This class of trees is very common and includes all traditional tree variants (AID, CHAID, CART, C4.5, FACT, QUEST) and also more recent approaches like CTree. Trees inferred by any of these algorithms could in principle be represented by objects of class \class{constparty} in \pkg{partykit} that then provides unified methods for printing, plotting, and predicting. Here, we describe how one can create \class{constparty} objects by (a)~coercion from other \proglang{R} classes, (b)~parsing of XML descriptions of trees learned in other software systems, (c)~learning a tree using one's own algorithm. } \Keywords{recursive partitioning, regression trees, classification trees, decision trees} \Address{ Torsten Hothorn\\ Institut f\"ur Epidemiologie, Biostatistik und Pr\"avention \\ Universit\"at Z\"urich \\ Hirschengraben 84\\ CH-8001 Z\"urich, Switzerland \\ E-mail: \email{Torsten.Hothorn@R-project.org}\\ URL: \url{http://user.math.uzh.ch/hothorn/}\\ Achim Zeileis\\ Department of Statistics \\ Faculty of Economics and Statistics \\ Universit\"at Innsbruck \\ Universit\"atsstr.~15 \\ 6020 Innsbruck, Austria \\ E-mail: \email{Achim.Zeileis@R-project.org}\\ URL: \url{http://eeecon.uibk.ac.at/~zeileis/} } \begin{document} \setkeys{Gin}{width=\textwidth} \SweaveOpts{engine=R, eps=FALSE, keep.source=TRUE, eval=TRUE} <>= suppressWarnings(RNGversion("3.5.2")) options(width = 70) library("partykit") set.seed(290875) @ \section{Classes and methods} \label{sec:classes} This vignette describes the handling of trees with constant fits in the terminal nodes. This class of regression models includes most classical tree algorithms like AID \citep{Morgan+Sonquist:1963}, CHAID \citep{Kass:1980}, CART \citep{Breiman+Friedman+Olshen:1984}, FACT \citep{Loh+Vanichsetakul1:988}, QUEST \citep{Loh+Shih:1997}, C4.5 \citep{Quinlan:1993}, CTree \citep{Hothorn+Hornik+Zeileis:2006} etc. In this class of tree models, one can compute simple predictions for new observations, such as the conditional mean in a regression setup, from the responses of those learning sample observations in the same terminal node. Therefore, such predictions can easily be computed if the following pieces of information are available: the observed responses in the learning sample, the terminal node IDs assigned to the observations in the learning sample, and potentially associated weights (if any). In \pkg{partykit} it is easy to create a \class{party} object that contains these pieces of information, yielding a \class{constparty} object. The technical details of the \class{party} class are discussed in detail in Section~3.4 of \code{vignette("partykit", package = "partykit")}. In addition to the elements required for any \class{party}, a \class{constparty} needs to have: variables \code{(fitted)} and \code{(response)} (and \code{(weights)} if applicable) in the \code{fitted} data frame along with the \code{terms} for the model. If such a \class{party} has been created, its properties can be checked and coerced to class \class{constparty} by the \fct{as.constparty} function. Note that with such a \class{constparty} object it is possible to compute all kinds of predictions from the subsample in a given terminal node. For example, instead the mean response the median (or any other quantile) could be employed. Similarly, for a categorical response the predicted probabilities (i.e., relative frequencies) can be computed or the corresponding mode or a ranking of the levels etc. In case the full response from the learning sample is not available but only the constant fit from each terminal node, then a \class{constparty} cannot be set up. Specifically, this is the case for trees saved in the XML format PMML \citep[Predictive Model Markup Language,][]{DMG:2014} that does not provide the full learning sample. To also support such constant-fit trees based on simpler information \pkg{partykit} provides the \class{simpleparty} class. Inspired by the PMML format, this requires that the \code{info} of every node in the tree provides list elements \code{prediction}, \code{n}, \code{error}, and \code{distribution}. For classification trees these should contain the following node-specific information: the predicted single predicted factor, the learning sample size, the misclassification error (in \%), and the absolute frequencies of all levels. For regression trees the contents should be: the predicted mean, the learning sample size, the error sum of squares, and \code{NULL}. The function \fct{as.simpleparty} can also coerce \class{constparty} trees to \class{simpleparty} trees by computing the above summary statistics from the full response associated with each node of the tree. The remainder of this vignette consists of the following parts: In Section~\ref{sec:coerce} we assume that the trees were fitted using some other software (either within or outside of \proglang{R}) and we describe how these models can be coerced to \class{party} objects using either the \class{constparty} or \class{simpleparty} class. Emphasize is given to displaying such trees in textual and graphical ways. Subsequently, in Section~\ref{sec:mytree}, we show a simple classification tree algorithm can be easily implemented using the \pkg{partykit} tools, yielding a \class{constparty} object. Section~\ref{sec:prediction} shows how to compute predictions in both scenarios before Section~\ref{sec:conclusion} finally gives a brief conclusion. \section{Coercing tree objects} \label{sec:coerce} For the illustrations, we use the Titanic data set from package \pkg{datasets}, consisting of four variables on each of the $2201$ Titanic passengers: gender (male, female), age (child, adult), and class (1st, 2nd, 3rd, or crew) set up as follows: <>= data("Titanic", package = "datasets") ttnc <- as.data.frame(Titanic) ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] names(ttnc)[2] <- "Gender" @ The response variable describes whether or not the passenger survived the sinking of the ship. \subsection{Coercing rpart objects} We first fit a classification tree by means of the the \fct{rpart} function from package \pkg{rpart} \citep{rpart} to this data set (make sure to set \code{model = TRUE}; otherwise \code{model.frame.rpart} will return the \code{rpart} object and not the data): <>= library("rpart") (rp <- rpart(Survived ~ ., data = ttnc, model = TRUE)) @ The \class{rpart} object \code{rp} can be coerced to a \class{constparty} by \fct{as.party}. Internally, this transforms the tree structure of the \class{rpart} tree to a \class{partynode} and combines it with the associated learning sample as described in Section~\ref{sec:classes}. All of this is done automatically by <>= (party_rp <- as.party(rp)) @ Now, instead of the print method for \class{rpart} objects the print method for \code{constparty} objects creates a textual display of the tree structure. In a similar way, the corresponding \fct{plot} method produces a graphical representation of this tree, see Figure~\ref{party_plot}. \begin{figure}[p!] \centering <>= plot(rp) text(rp) @ <>= plot(party_rp) @ \caption{\class{rpart} tree of Titanic data plotted using \pkg{rpart} (top) and \pkg{partykit} (bottom) infrastructure. \label{party_plot}} \end{figure} By default, the \fct{predict} method for \class{rpart} objects computes conditional class probabilities. The same numbers are returned by the \fct{predict} method for \Sexpr{class(party_rp)[1L]} objects with \code{type = "prob"} argument (see Section~\ref{sec:prediction} for more details): <>= all.equal(predict(rp), predict(party_rp, type = "prob"), check.attributes = FALSE) @ Predictions are computed based on the \code{fitted} slot of a \class{constparty} object <>= str(fitted(party_rp)) @ which contains the terminal node numbers and the response for each of the training samples. So, the conditional class probabilities for each terminal node can be computed via <>= prop.table(do.call("table", fitted(party_rp)), 1) @ Optionally, weights can be stored in the \code{fitted} slot as well. \subsection{Coercing J48 objects} The \pkg{RWeka} package \citep{RWeka} provides an interface to the \pkg{Weka} machine learning library and we can use the \fct{J48} function to fit a J4.8 tree to the Titanic data <>= if (require("RWeka")) { j48 <- J48(Survived ~ ., data = ttnc) } else { j48 <- rpart(Survived ~ ., data = ttnc) } print(j48) @ This object can be coerced to a \class{party} object using <>= (party_j48 <- as.party(j48)) @ and, again, the print method from the \pkg{partykit} package creates a textual display. Note that, unlike the \class{rpart} trees, this tree includes multiway splits. The \fct{plot} method draws this tree, see Figure~\ref{J48_plot}. \begin{sidewaysfigure} \centering <>= plot(party_j48) @ \caption{\class{J48} tree of Titanic data plotted using \pkg{partykit} infrastructure. \label{J48_plot}} \end{sidewaysfigure} The conditional class probabilities computed by the \fct{predict} methods implemented in packages \pkg{RWeka} and \pkg{partykit} are equivalent: <>= all.equal(predict(j48, type = "prob"), predict(party_j48, type = "prob"), check.attributes = FALSE) @ In addition to \fct{J48} \pkg{RWeka} provides several other tree learners, e.g., \fct{M5P} implementing M5' and \fct{LMT} implementing logistic model trees, respectively. These can also be coerced using \fct{as.party}. However, as these are not constant-fit trees this yields plain \class{party} trees with some character information stored in the \code{info} slot. \subsection{Importing trees from PMML files} The previous two examples showed how trees learned by other \proglang{R} packages can be handled in a unified way using \pkg{partykit}. Additionally, \pkg{partykit} can also be used to import trees from any other software package that supports the PMML (Predictive Model Markup Language) format. As an example, we used \proglang{SPSS} to fit a QUEST tree to the Titanic data and exported this from \proglang{SPSS} in PMML format. This file is shipped along with the \pkg{partykit} package and we can read it as follows: <>= ttnc_pmml <- file.path(system.file("pmml", package = "partykit"), "ttnc.pmml") (ttnc_quest <- pmmlTreeModel(ttnc_pmml)) @ % \begin{figure}[t!] \centering <>= plot(ttnc_quest) @ \caption{QUEST tree for Titanic data, fitted using \proglang{SPSS} and exported via PMML. \label{PMML-Titanic-plot1}} \end{figure} % The object \code{ttnc_quest} is of class \class{simpleparty} and the corresponding graphical display is shown in Figure~\ref{PMML-Titanic-plot1}. As explained in Section~\ref{sec:classes}, the full learning data are not part of the PMML description and hence one can only obtain and display the summarized information provided by PMML. In this particular case, however, we have the learning data available in \proglang{R} because we had exported the data from \proglang{R} to begin with. Hence, for this tree we can augment the \class{simpleparty} with the full learning sample to create a \class{constparty}. As \proglang{SPSS} had reordered some factor levels we need to carry out this reordering as well" <>= ttnc2 <- ttnc[, names(ttnc_quest$data)] for(n in names(ttnc2)) { if(is.factor(ttnc2[[n]])) ttnc2[[n]] <- factor( ttnc2[[n]], levels = levels(ttnc_quest$data[[n]])) } @ % Using this data all information for a \class{constparty} can be easily computed: % <>= ttnc_quest2 <- party(ttnc_quest$node, data = ttnc2, fitted = data.frame( "(fitted)" = predict(ttnc_quest, ttnc2, type = "node"), "(response)" = ttnc2$Survived, check.names = FALSE), terms = terms(Survived ~ ., data = ttnc2) ) ttnc_quest2 <- as.constparty(ttnc_quest2) @ This object is plotted in Figure~\ref{PMML-Titanic-plot2}. \begin{figure}[t!] \centering <>= plot(ttnc_quest2) @ \caption{QUEST tree for Titanic data, fitted using \proglang{SPSS}, exported via PMML, and transformed into a \class{constparty} object. \label{PMML-Titanic-plot2}} \end{figure} Furthermore, we briefly point out that there is also the \proglang{R} package \pkg{pmml} \citep{pmml}, part of the \pkg{rattle} project \citep{rattle}, that allows to export PMML files for \pkg{rpart} trees from \proglang{R}. For example, for the \class{rpart} tree for the Titanic data: <>= library("pmml") tfile <- tempfile() write(toString(pmml(rp)), file = tfile) @ Then, we can simply read this file and inspect the resulting tree <>= (party_pmml <- pmmlTreeModel(tfile)) all.equal(predict(party_rp, newdata = ttnc, type = "prob"), predict(party_pmml, newdata = ttnc, type = "prob"), check.attributes = FALSE) @ Further example PMML files created with \pkg{rattle} are the Data Mining Group web page, e.g., \url{http://www.dmg.org/pmml_examples/rattle_pmml_examples/AuditTree.xml} or \url{http://www.dmg.org/pmml_examples/rattle_pmml_examples/IrisTree.xml}. \section{Growing a simple classification tree} \label{sec:mytree} Although the \pkg{partykit} package offers an extensive toolbox for handling trees along with implementations of various tree algorithms, it does not offer unified infrastructure for \emph{growing} trees. However, once you know how to estimate splits from data, it is fairly straightforward to implement trees. Consider a very simple CHAID-style algorithm (in fact so simple that we would advise \emph{not to use it} for any real application). We assume that both response and explanatory variables are factors, as for the Titanic data set. First we determine the best explanatory variable by means of a global $\chi^2$ test, i.e., splitting up the response into all levels of each explanatory variable. Then, for the selected explanatory variable we search for the binary best split by means of $\chi^2$ tests, i.e., we cycle through all potential split points and assess the quality of the split by comparing the distributions of the response in the so-defined two groups. In both cases, we select the split variable/point with lowest $p$-value from the $\chi^2$ test, however, only if the global test is significant at Bonferroni-corrected level $\alpha = 0.01$. This strategy can be implemented based on the data (response and explanatory variables) and some case weights as follows (\code{response} is just the name of the response and \code{data} is a data frame with all variables): <>= findsplit <- function(response, data, weights, alpha = 0.01) { ## extract response values from data y <- factor(rep(data[[response]], weights)) ## perform chi-squared test of y vs. x mychisqtest <- function(x) { x <- factor(x) if(length(levels(x)) < 2) return(NA) ct <- suppressWarnings(chisq.test(table(y, x), correct = FALSE)) pchisq(ct$statistic, ct$parameter, log = TRUE, lower.tail = FALSE) } xselect <- which(names(data) != response) logp <- sapply(xselect, function(i) mychisqtest(rep(data[[i]], weights))) names(logp) <- names(data)[xselect] ## Bonferroni-adjusted p-value small enough? if(all(is.na(logp))) return(NULL) minp <- exp(min(logp, na.rm = TRUE)) minp <- 1 - (1 - minp)^sum(!is.na(logp)) if(minp > alpha) return(NULL) ## for selected variable, search for split minimizing p-value xselect <- xselect[which.min(logp)] x <- rep(data[[xselect]], weights) ## set up all possible splits in two kid nodes lev <- levels(x[drop = TRUE]) if(length(lev) == 2) { splitpoint <- lev[1] } else { comb <- do.call("c", lapply(1:(length(lev) - 2), function(x) combn(lev, x, simplify = FALSE))) xlogp <- sapply(comb, function(q) mychisqtest(x %in% q)) splitpoint <- comb[[which.min(xlogp)]] } ## split into two groups (setting groups that do not occur to NA) splitindex <- !(levels(data[[xselect]]) %in% splitpoint) splitindex[!(levels(data[[xselect]]) %in% lev)] <- NA_integer_ splitindex <- splitindex - min(splitindex, na.rm = TRUE) + 1L ## return split as partysplit object return(partysplit(varid = as.integer(xselect), index = splitindex, info = list(p.value = 1 - (1 - exp(logp))^sum(!is.na(logp))))) } @ In order to actually grow a tree on data, we have to set up the recursion for growing a recursive \class{partynode} structure: <>= growtree <- function(id = 1L, response, data, weights, minbucket = 30) { ## for less than 30 observations stop here if (sum(weights) < minbucket) return(partynode(id = id)) ## find best split sp <- findsplit(response, data, weights) ## no split found, stop here if (is.null(sp)) return(partynode(id = id)) ## actually split the data kidids <- kidids_split(sp, data = data) ## set up all daugther nodes kids <- vector(mode = "list", length = max(kidids, na.rm = TRUE)) for (kidid in 1:length(kids)) { ## select observations for current node w <- weights w[kidids != kidid] <- 0 ## get next node id if (kidid > 1) { myid <- max(nodeids(kids[[kidid - 1]])) } else { myid <- id } ## start recursion on this daugther node kids[[kidid]] <- growtree(id = as.integer(myid + 1), response, data, w) } ## return nodes return(partynode(id = as.integer(id), split = sp, kids = kids, info = list(p.value = min(info_split(sp)$p.value, na.rm = TRUE)))) } @ A very rough sketch of a formula-based user-interface sets-up the data and calls \fct{growtree}: <>= mytree <- function(formula, data, weights = NULL) { ## name of the response variable response <- all.vars(formula)[1] ## data without missing values, response comes last data <- data[complete.cases(data), c(all.vars(formula)[-1], response)] ## data is factors only stopifnot(all(sapply(data, is.factor))) if (is.null(weights)) weights <- rep(1L, nrow(data)) ## weights are case weights, i.e., integers stopifnot(length(weights) == nrow(data) & max(abs(weights - floor(weights))) < .Machine$double.eps) ## grow tree nodes <- growtree(id = 1L, response, data, weights) ## compute terminal node number for each observation fitted <- fitted_node(nodes, data = data) ## return rich constparty object ret <- party(nodes, data = data, fitted = data.frame("(fitted)" = fitted, "(response)" = data[[response]], "(weights)" = weights, check.names = FALSE), terms = terms(formula)) as.constparty(ret) } @ The call to the constructor \fct{party} sets-up a \class{party} object with the tree structure contained in \code{nodes}, the training samples in \code{data} and the corresponding \code{terms} object. Class \class{constparty} inherits all slots from class \class{party} and has an additional \code{fitted} slot for storing the terminal node numbers for each sample in the training data, the response variable(s) and case weights. The \code{fitted} slot is a \class{data.frame} containing three variables: The fitted terminal node identifiers \code{"(fitted)"}, an integer vector of the same length as \code{data}; the response variables \code{"(response)"} as a vector (or \code{data.frame} for multivariate responses) with the same number of observations; and optionally a vector of weights \code{"(weights)"}. The additional \code{fitted} slot allows to compute arbitrary summary measures for each terminal node by simply subsetting the \code{"(response)"} and \code{"(weights)"} slots by \code{"(fitted)"} before computing (weighted) means, medians, empirical cumulative distribution functions, Kaplan-Meier estimates or whatever summary statistic might be appropriate for a certain response. The \fct{print}, \fct{plot}, and \fct{predict} methods for class \class{constparty} work this way with suitable defaults for the summary statistics depending on the class of the response(s). We now can fit this tree to the Titanic data; the \fct{print} method provides us with a first overview on the resulting model <>= (myttnc <- mytree(Survived ~ Class + Age + Gender, data = ttnc)) @ % \begin{figure}[t!] \centering <>= plot(myttnc) @ \caption{Classification tree fitted by the \fct{mytree} function to the \code{ttnc} data. \label{plottree}} \end{figure} % Of course, we can immediately use \code{plot(myttnc)} to obtain a graphical representation of this tree, the result is given in Figure~\ref{plottree}. The default behavior for trees with categorical responses is simply inherited from \class{constparty} and hence we readily obtain bar plots in all terminal nodes. As the tree is fairly large, we might be interested in pruning the tree to a more reasonable size. For this purpose the \pkg{partykit} package provides the \fct{nodeprune} function that can prune back to nodes with selected IDs. As \fct{nodeprune} (by design) does not provide a specific pruning criterion, we need to determine ourselves which nodes to prune. Here, one idea could be to impose significance at a higher level than the default $10^{-2}$ -- say $10^{-5}$ to obtain a strongly pruned tree. Hence we use \fct{nodeapply} to extract the minimal Bonferroni-corrected $p$-value from all inner nodes: % <>= nid <- nodeids(myttnc) iid <- nid[!(nid %in% nodeids(myttnc, terminal = TRUE))] (pval <- unlist(nodeapply(myttnc, ids = iid, FUN = function(n) info_node(n)$p.value))) @ Then, the pruning of the nodes with the larger $p$-values can be simply carried out by % <>= myttnc2 <- nodeprune(myttnc, ids = iid[pval > 1e-5]) @ % The corresponding visualization is shown in Figure~\ref{prunetree}. \setkeys{Gin}{width=0.85\textwidth} \begin{figure}[t!] \centering <>= plot(myttnc2) @ \caption{Pruned classification tree fitted by the \fct{mytree} function to the \code{ttnc} data. \label{prunetree}} \end{figure} \setkeys{Gin}{width=\textwidth} The accuracy of the tree built using the default options could be assessed by the bootstrap, for example. Here, we want to compare our tree for the Titanic survivor data with a simple logistic regression model. First, we fit this simple GLM and compute the (in-sample) log-likelihood: <>= logLik(glm(Survived ~ Class + Age + Gender, data = ttnc, family = binomial())) @ For our tree, we set-up $25$ bootstrap samples <>= bs <- rmultinom(25, nrow(ttnc), rep(1, nrow(ttnc)) / nrow(ttnc)) @ and implement the log-likelihood of a binomal model <>= bloglik <- function(prob, weights) sum(weights * dbinom(ttnc$Survived == "Yes", size = 1, prob[,"Yes"], log = TRUE)) @ What remains to be done is to iterate over all bootstrap samples, to refit the tree on the bootstrap sample and to evaluate the log-likelihood on the out-of-bootstrap samples based on the trees' predictions (details on how to compute predictions are given in the next section): <>= f <- function(w) { tr <- mytree(Survived ~ Class + Age + Gender, data = ttnc, weights = w) bloglik(predict(tr, newdata = ttnc, type = "prob"), as.numeric(w == 0)) } apply(bs, 2, f) @ We see that the in-sample log-likelihood of the linear logistic regression model is much smaller than the out-of-sample log-likelihood found for our tree and thus we can conclude that our tree-based approach fits data the better than the linear model. \section{Predictions} \label{sec:prediction} As argued in Section~\ref{sec:classes} arbitrary types of predictions can be computed from \class{constparty} objects because the full empirical distribution of the response in the learning sample nodes is available. All of these can be easily computed in the \fct{predict} method for \class{constparty} objects by supplying a suitable aggregation function. However, as certain types of predictions are much more commonly used, these are available even more easily by setting a \code{type} argument. \begin{table}[b!] \centering \begin{tabular}{llll} \hline Response class & \code{type = "node"} & \code{type = "response"} & \code{type = "prob"} \\ \hline \class{factor} & terminal node number & majority class & class probabilities \\ \class{numeric} & terminal node number & mean & ECDF \\ \class{Surv} & terminal node number & median survival time & Kaplan-Meier \\ \hline \end{tabular} \caption{Overview on type of predictions computed by the \fct{predict} method for \class{constparty} objects. For multivariate responses, combinations thereof are returned. \label{predict-type}} \end{table} The prediction \code{type} can either be \code{"node"}, \code{"response"}, or \code{"prob"} (see Table~\ref{predict-type}). The idea is that \code{"response"} always returns a prediction of the same class as the original response and \code{"prob"} returns some object that characterizes the entire empirical distribution. Hence, for different response classes, different types of predictions are produced, see Table~\ref{predict-type} for an overview. Additionally, for \class{numeric} responses \code{type = "quantile"} and \code{type = "density"} is available. By default, these return functions for computing predicted quantiles and probability densities, respectively, but optionally these functions can be directly evaluated \code{at} given values and then return a vector/matrix. Here, we illustrate all different predictions for all possible combinations of the explanatory factor levels. <>= nttnc <- expand.grid(Class = levels(ttnc$Class), Gender = levels(ttnc$Gender), Age = levels(ttnc$Age)) nttnc @ The corresponding predicted nodes, modes, and probability distributions are: <>= predict(myttnc, newdata = nttnc, type = "node") predict(myttnc, newdata = nttnc, type = "response") predict(myttnc, newdata = nttnc, type = "prob") @ Furthermore, the \fct{predict} method features a \code{FUN} argument that can be used to compute customized predictions. If we are, say, interested in the rank of the probabilities for the two classes, we can simply specify a function that implements this feature: <>= predict(myttnc, newdata = nttnc, FUN = function(y, w) rank(table(rep(y, w)))) @ The user-supplied function \code{FUN} takes two arguments, \code{y} is the response and \code{w} is a vector of weights (case weights in this situation). Of course, it would have been easier to do these computations directly on the conditional class probabilities (\code{type = "prob"}), but the approach taken here for illustration generalizes to situations where this is not possible, especially for numeric responses. \section{Conclusion} \label{sec:conclusion} The classes \class{constparty} and \class{simpleparty} introduced here can be used to represent trees with constant fits in the terminal nodes, including most of the traditional tree variants. For a number of implementations it is possible to convert the resulting trees to one of these classes, thus offering unified methods for handling constant-fit trees. User-extensible methods for printing and plotting these trees are available. Also, computing non-standard predictions, such as the median or empirical cumulative distribution functions, is easily possible within this framework. With the infrastructure provided in \pkg{partykit} it is rather straightforward to implement a new (or old) tree algorithm and therefore a prototype implementation of fancy ideas for improving trees is only a couple lines of \proglang{R} code away. \bibliography{party} \end{document} partykit/vignettes/mob.Rnw0000644000176200001440000024212114172230001015366 0ustar liggesusers\documentclass[nojss]{jss} \usepackage{amsmath,thumbpdf} \shortcites{mvtnorm} %% commands \newcommand{\ui}{\underline{i}} \newcommand{\oi}{\overline{\imath}} \newcommand{\argmin}{\operatorname{argmin}\displaylimits} \newcommand{\fixme}[1]{\emph{\marginpar{FIXME} (#1)}} \newcommand{\class}[1]{`\texttt{#1}'} %% neet no \usepackage{Sweave} \SweaveOpts{engine=R, eps=FALSE, keep.source=TRUE} <>= suppressWarnings(RNGversion("3.5.2")) library("partykit") options(prompt = "R> ", continue = "+ ", digits = 4, useFancyQuotes = FALSE) @ %\VignetteIndexEntry{Parties, Models, Mobsters: A New Implementation of Model-Based Recursive Partitioning in R} %\VignetteDepends{AER,Formula,mlbench,sandwich,strucchange,survival,TH.data,vcd,psychotools,psychotree} %\VignetteKeywords{parametric models, object-orientation, recursive partitioning} %\VignettePackage{partykit} \author{Achim Zeileis\\Universit\"at Innsbruck \And Torsten Hothorn\\Universit\"at Z\"urich} \Plainauthor{Achim Zeileis, Torsten Hothorn} \title{Parties, Models, Mobsters: A New Implementation of Model-Based Recursive Partitioning in \proglang{R}} \Plaintitle{Parties, Models, Mobsters: A New Implementation of Model-Based Recursive Partitioning in R} \Shorttitle{Model-Based Recursive Partitioning in \proglang{R}} \Keywords{parametric models, object-orientation, recursive partitioning} \Abstract{ MOB is a generic algorithm for \underline{mo}del-\underline{b}ased recursive partitioning \citep{Zeileis+Hothorn+Hornik:2008}. Rather than fitting one global model to a dataset, it estimates local models on subsets of data that are ``learned'' by recursively partitioning. It proceeds in the following way: (1)~fit a parametric model to a data set, (2)~test for parameter instability over a set of partitioning variables, (3)~if there is some overall parameter instability, split the model with respect to the variable associated with the highest instability, (4)~repeat the procedure in each of the resulting subsamples. It is discussed how these steps of the conceptual algorithm are translated into computational tools in an object-oriented manner, allowing the user to plug in various types of parametric models. For representing the resulting trees, the \proglang{R} package \pkg{partykit} is employed and extended with generic infrastructure for recursive partitions where nodes are associated with statistical models. Compared to the previously available implementation in the \pkg{party} package, the new implementation supports more inference options, is easier to extend to new models, and provides more convenience features. } \Address{ Achim Zeileis \\ Department of Statistics \\ Faculty of Economics and Statistics \\ Universit\"at Innsbruck \\ Universit\"atsstr.~15 \\ 6020 Innsbruck, Austria \\ E-mail: \email{Achim.Zeileis@R-project.org} \\ URL: \url{http://eeecon.uibk.ac.at/~zeileis/} \\ Torsten Hothorn\\ Institut f\"ur Epidemiologie, Biostatistik und Pr\"avention \\ Universit\"at Z\"urich \\ Hirschengraben 84\\ CH-8001 Z\"urich, Switzerland \\ E-mail: \email{Torsten.Hothorn@R-project.org}\\ URL: \url{http://user.math.uzh.ch/hothorn/}\\ } \begin{document} \section{Overview} To implement the model-based recursive partitioning (MOB) algorithm of \cite{Zeileis+Hothorn+Hornik:2008} in software, infrastructure for three aspects is required: (1)~statistical ``\emph{models}'', (2)~recursive ``\emph{party}''tions, and (3)~``\emph{mobsters}'' carrying out the MOB algorithm. Along with \cite{Zeileis+Hothorn+Hornik:2008}, an implementation of all three steps was provided in the \pkg{party} package \citep{party} for the \proglang{R} system for statistical computing \citep{R}. This provided one very flexible \code{mob()} function combining \pkg{party}'s \proglang{S}4 classes for representing trees with binary splits and the \proglang{S}4 model wrapper functions from \pkg{modeltools} \citep{modeltools}. However, while this supported many applications of interest, it was somewhat limited in several directions: (1)~The \proglang{S}4 wrappers for the models were somewhat cumbersome to set up. (2)~The tree infrastructure was originally designed for \code{ctree()} and somewhat too narrowly focused on it. (3)~Writing new ``mobster'' interfaces was not easy because of using unexported \proglang{S}4 classes. Hence, a leaner and more flexible interface (based on \proglang{S}3 classes) is now provided in \pkg{partykit} \citep{partykit}: (1)~New models are much easier to provide in a basic version and customization does not require setting up an additional \proglang{S}4 class-and-methods layer anymore. (2)~The trees are built on top of \pkg{partykit}'s flexible `\code{party}' objects, inheriting many useful methods and providing new ones dealing with the fitted models associated with the tree's nodes. (3)~New ``mobsters'' dedicated to specific models, e.g., \code{lmtree()} and \code{glmtree()} for MOBs of (generalized) linear models, are readily provided. The remainder of this vignette is organized as follows: Section~\ref{sec:algorithm} very briefly reviews the original MOB algorithm of \cite{Zeileis+Hothorn+Hornik:2008} and also highlights relevant subsequent work. Section~\ref{sec:implementation} introduces the new \code{mob()} function in \pkg{partykit} in detail, discussing how all steps of the MOB algorithm are implemented and which options for customization are available. For illustration logistic-regression-based recursive partitioning is applied to the Pima Indians diabetes data set from the UCI machine learning repository \citep{mlbench2}. Section~\ref{sec:illustration} and~\ref{sec:mobster} present further illustrative examples \citep[including replications from][]{Zeileis+Hothorn+Hornik:2008} before Section~\ref{sec:conclusion} provides some concluding remarks. \section{MOB: Model-based recursive partitioning} \label{sec:algorithm} First, the theory underling the MOB (model-based recursive partitioning) is briefly reviewed; a more detailed discussion is provided by \cite{Zeileis+Hothorn+Hornik:2008}. To fix notation, consider a parametric model $\mathcal{M}(Y, \theta)$ with (possibly vector-valued) observations $Y$ and a $k$-dimensional vector of parameters $\theta$. This model could be a (possibly multivariate) normal distribution for $Y$, a psychometric model for a matrix of responses $Y$, or some kind of regression model when $Y = (y, x)$ can be split up into a dependent variable $y$ and regressors $x$. An example for the latter could be a linear regression model $y = x^\top \theta$ or a generalized linear model (GLM) or a survival regression. Given $n$ observations $Y_i$ ($i = 1, \dots, n$) the model can be fitted by minimizing some objective function $\sum_{i = 1}^n \Psi(Y_i, \theta)$, e.g., a residual sum of squares or a negative log-likelihood leading to ordinary least squares (OLS) or maximum likelihood (ML) estimation, respectively. If a global model for all $n$ observations does not fit well and further covariates $Z_1, \dots, Z_\ell$ are available, it might be possible to partition the $n$ observations with respect to these variables and find a fitting local model in each cell of the partition. The MOB algorithm tries to find such a partition adaptively using a greedy forward search. The reasons for looking at such local models might be different for different types of models: First, the detection of interactions and nonlinearities in regression relationships might be of interest just like in standard classification and regression trees \citep[see e.g.,][]{Zeileis+Hothorn+Hornik:2008}. Additionally, however, this approach allows to add explanatory variables to models that otherwise do not have regressors or where the link between the regressors and the parameters of the model is inclear \citep[this idea is pursued by][]{Strobl+Wickelmaier+Zeileis:2011}. Finally, the model-based tree can be employed as a thorough diagnostic test of the parameter stability assumption (also termed measurement invariance in psychometrics). If the tree does not split at all, parameter stability (or measurement invariance) cannot be rejected while a tree with splits would indicate in which way the assumption is violated \citep[][employ this idea in psychometric item response theory models]{Strobl+Kopf+Zeileis:2015}. The basic idea is to grow a tee in which every node is associated with a model of type $\mathcal{M}$. To assess whether splitting of the node is necessary a fluctuation test for parameter instability is performed. If there is significant instability with respect to any of the partitioning variables $Z_j$, the node is splitted into $B$ locally optimal segments (the currenct version of the software has $B = 2$ as the default and as the only option for numeric/ordered variables) and then the procedure is repeated in each of the $B$ children. If no more significant instabilities can be found, the recursion stops. More precisely, the steps of the algorithm are % \begin{enumerate} \item Fit the model once to all observations in the current node. \item Assess whether the parameter estimates are stable with respect to every partitioning variable $Z_1, \dots, Z_\ell$. If there is some overall instability, select the variable $Z_j$ associated with the highest parameter instability, otherwise stop. \item Compute the split point(s) that locally optimize the objective function $\Psi$. \item Split the node into child nodes and repeat the procedure until some stopping criterion is met. \end{enumerate} % This conceptual framework is extremely flexible and allows to adapt it to various tasks by choosing particular models, tests, and methods in each of the steps: % \begin{enumerate} \item \emph{Model estimation:} The original MOB introduction \citep{Zeileis+Hothorn+Hornik:2008} discussed regression models: OLS regression, GLMs, and survival regression. Subsequently, \cite{Gruen+Kosmidis+Zeileis:2012} have also adapted MOB to beta regression for limited response variables. Furthermore, MOB provides a generic way of adding covariates to models that otherwise have no regressors: this can either serve as a check whether the model is indeed independent from regressors or leads to local models for subsets. Both views are of interest when employing MOB to detect parameter instabilities in psychometric models for item responses such as the Bradley-Terry or the Rasch model \citep[see][respectively]{Strobl+Wickelmaier+Zeileis:2011,Strobl+Kopf+Zeileis:2015}. \item \emph{Parameter instability tests:} To assess the stability of all model parameters across a certain partitioning variable, the general class of score-based fluctuation tests proposed by \cite{Zeileis+Hornik:2007} is employed. Based on the empirical score function observations (i.e., empirical estimating functions or contributions to the gradient), ordered with respect to the partitioning variable, the fluctuation or instability in the model's parameters can be tested. From this general framework the Andrews' sup\textit{LM} test is used for assessing numerical partitioning variables and a $\chi^2$ test for categorical partitioning variables (see \citealp{Zeileis:2005} and \citealp{Merkle+Zeileis:2013} for unifying views emphasizing regression and psychometric models, respectively). Furthermore, the test statistics for ordinal partitioning variables suggested by \cite{Merkle+Fan+Zeileis:2014} have been added as further options (but are not used by default as the simulation of $p$-values is computationally demanding). \item \emph{Partitioning:} As the objective function $\Psi$ is additive, it is easy to compute a single optimal split point (or cut point or break point). For each conceivable split, the model is estimated on the two resulting subsets and the resulting objective functions are summed. The split that optimizes this segmented objective function is then selected as the optimal split. For optimally splitting the data into $B > 2$ segments, the same idea can be used and a full grid search can be avoided by employing a dynamic programming algorithms \citep{Hawkins:2001,Bai+Perron:2003} but at the moment the latter is not implemented in the software. Optionally, however, categorical partitioning variables can be split into all of their categories (i.e., in that case $B$ is set to the number of levels without searching for optimal groupings). \item \emph{Pruning:} For determining the optimal size of the tree, one can either use a pre-pruning or post-pruning strategy. For the former, the algorithm stops when no significant parameter instabilities are detected in the current node (or when the node becomes too small). For the latter, one would first grow a large tree (subject only to a minimal node size requirement) and then prune back splits that did not improve the model, e.g., judging by information criteria such as AIC or BIC \citep[see e.g.,][]{Su+Wang+Fan:2004}. Currently, pre-pruning is used by default (via Bonferroni-corrected $p$-values from the score-based fluctuation tests) but AIC/BIC-based post-pruning is optionally available (especially for large data sets where traditional significance levels are not useful). \end{enumerate} % In the following it is discussed how most of the options above are embedded in a common computational framework using \proglang{R}'s facilities for model estimation and object orientation. \section[A new implementation in R]{A new implementation in \proglang{R}} \label{sec:implementation} This section introduces a new implementation of the general model-based recursive partitioning (MOB) algorithm in \proglang{R}. Along with \cite{Zeileis+Hothorn+Hornik:2008}, a function \code{mob()} had been introduced to the \pkg{party} package \citep{party} which continues to work but it turned out to be somewhat unflexible for certain applications/extensions. Hence, the \pkg{partykit} package \citep{partykit} provides a completely rewritten (and not backward compatible) implementation of a new \code{mob()} function along with convenience interfaces \code{lmtree()} and \code{glmtree()} for fitting linear model and generalized linear model trees, respectively. The function \code{mob()} itself is intended to be the workhorse function that can also be employed to quickly explore new models -- whereas \code{lmtree()} and \code{glmtree()} will be the typical user interfaces facilitating applications. The new \code{mob()} function has the following arguments: \begin{Code} mob(formula, data, subset, na.action, weights, offset, fit, control = mob_control(), ...) \end{Code} All arguments in the first line are standard for modeling functions in \proglang{R} with a \code{formula} interface. They are employed by \code{mob()} to do some data preprocessing (described in detail in Section~\ref{sec:formula}) before the \code{fit} function is used for parameter estimation on the preprocessed data. The \code{fit} function has to be set up in a certain way (described in detail in Section~\ref{sec:fit}) so that \code{mob()} can extract all information that is needed in the MOB algorithm for parameter instability tests (see Section~\ref{sec:sctest}) and partitioning/splitting (see Section~\ref{sec:split}), i.e., the estimated parameters, the associated objective function, and the score function contributions. A list of \code{control} options can be set up by the \code{mob_control()} function, including options for pruning (see Section~\ref{sec:prune}). Additional arguments \code{...} are passed on to the \code{fit} function. The result is an object of class `\code{modelparty}' inheriting from `\code{party}'. The \code{info} element of the overall `\code{party}' and the individual `\code{node}'s contain various informations about the models. Details are provided in Section~\ref{sec:object}. Finally, a wide range of standard (and some extra) methods are available for working with `\code{modelparty}' objects, e.g., for extracting information about the models, for visualization, computing predictions, etc. The standard set of methods is introduced in Section~\ref{sec:methods}. However, as will be discussed there, it may take some effort by the user to efficiently compute certain pieces of information. Hence, convenience interfaces such as \code{lmtree()} or \code{glmtree()} can alleviate these obstacles considerably, as illustrated in Section~\ref{sec:interface}. \subsection{Formula processing and data preparation} \label{sec:formula} The formula processing within \code{mob()} is essentially done in ``the usual way'', i.e., there is a \code{formula} and \code{data} and optionally further arguments such as \code{subset}, \code{na.action}, \code{weights}, and \code{offset}. These are processed into a \code{model.frame} from which the response and the covariates can be extracted and passed on to the actual \code{fit} function. As there are possibly three groups of variables (response, regressors, and partitioning variables), the \pkg{Formula} package \citep{Formula} is employed for processing these three parts. Thus, the formula can be of type \verb:y ~ x1 + ... + xk | z1 + ... + zl: where the variables on the left of the \code{|} specify the data $Y$ and the variables on the right specify the partitioning variables $Z_j$. As pointed out above, the $Y$ can often be split up into response (\code{y} in the example above) and regressors (\code{x1}, \dots, \code{xk} in the example above). If there are no regressors and just constant fits are employed, then the formula can be specified as \verb:y ~ 1 | z1 + ... + zl:. So far, this formula representation is really just a specification of groups of variables and does not imply anything about the type of model that is to be fitted to the data in the nodes of the tree. The \code{mob()} function does not know anything about the type of model and just passes (subsets of) the \code{y} and \code{x} variables on to the \code{fit} function. Only the partitioning variables \code{z} are used internally for the parameter instability tests (see Section~\ref{sec:sctest}). As different \code{fit} functions will require the data in different formats, \code{mob_control()} allows to set the \code{ytype} and \code{xtype}. The default is to assume that \code{y} is just a single column of the model frame that is extracted as a \code{ytype = "vector"}. Alternatively, it can be a \code{"data.frame"} of all response variables or a \code{"matrix"} set up via \code{model.matrix()}. The options \code{"data.frame"} and \code{"matrix"} are also available for \code{xtype} with the latter being the default. Note that if \code{"matrix"} is used, then transformations (e.g., logs, square roots etc.) and dummy/interaction codings are computed and turned into columns of a numeric matrix while for \code{"data.frame"} the original variables are preserved. By specifying the \code{ytype} and \code{xtype}, \code{mob()} is also provided with the information on how to correctly subset \code{y} and \code{x} when recursively partitioning data. In each step, only the subset of \code{y} and \code{x} pertaining to the current node of the tree is passed on to the \code{fit} function. Similarly, subsets of \code{weights} and \code{offset} are passed on (if specified). \subsubsection*{Illustration} For illustration, we employ the popular benchmark data set on diabetes among Pima Indian women that is provided by the UCI machine learning repository \citep{mlbench2} and available in the \pkg{mlbench} package \citep{mlbench}: % <>= data("PimaIndiansDiabetes", package = "mlbench") @ % Following \cite{Zeileis+Hothorn+Hornik:2008} we want to fit a model for \code{diabetes} employing the plasma glucose concentration \code{glucose} as a regressor. As the influence of the remaining variables on \code{diabetes} is less clear, their relationship should be learned by recursive partitioning. Thus, we employ the following formula: % <>= pid_formula <- diabetes ~ glucose | pregnant + pressure + triceps + insulin + mass + pedigree + age @ % Before passing this to \code{mob()}, a \code{fit} function is needed and a logistic regression function is set up in the following section. \subsection{Model fitting and parameter estimation} \label{sec:fit} The \code{mob()} function itself does not actually carry out any parameter estimation by itself, but assumes that one of the many \proglang{R} functions available for model estimation is supplied. However, to be able to carry out the steps of the MOB algorithm, \code{mob()} needs to able to extract certain pieces of information: especially the estimated parameters, the corresponding objective function, and associated score function contributions. Also, the interface of the fitting function clearly needs to be standardized so that \code{mob()} knows how to invoke the model estimation. Currently, two possible interfaces for the \code{fit} function can be employed: % \begin{enumerate} \item The \code{fit} function can take the following inputs \begin{Code} fit(y, x = NULL, start = NULL, weights = NULL, offset = NULL, ..., estfun = FALSE, object = FALSE) \end{Code} where \code{y}, \code{x}, \code{weights}, \code{offset} are (the subset of) the preprocessed data. In \code{start} starting values for the parameter estimates may be supplied and \code{...} is passed on from the \code{mob()} function. The \code{fit} function then has to return an output list with the following elements: \begin{itemize} \item \code{coefficients}: Estimated parameters $\hat \theta$. \item \code{objfun}: Value of the minimized objective function $\sum_i \Psi(y_i, x_, \hat \theta)$. \item \code{estfun}: Empirical estimating functions (or score function contributions) $\Psi'(y_i, x_i, \hat \theta)$. Only needed if \code{estfun = TRUE}, otherwise optionally \code{NULL}. \item \code{object}: A model object for which further methods could be available (e.g., \code{predict()}, or \code{fitted()}, etc.). Only needed if \code{object = TRUE}, otherwise optionally \code{NULL}. \end{itemize} By making \code{estfun} and \code{object} optional, the fitting function might be able to save computation time by only optimizing the objective function but avoiding further computations (such as setting up covariance matrix, residuals, diagnostics, etc.). \item The \code{fit} function can also of a simpler interface with only the following inputs: \begin{Code} fit(y, x = NULL, start = NULL, weights = NULL, offset = NULL, ...) \end{Code} The meaning of all arguments is the same as above. However, in this case \code{fit} needs to return a classed model object for which methods to \code{coef()}, \code{logLik()}, and \code{estfun()} \citep[see][and the \pkg{sandwich} package]{sandwich} are available for extracting the parameter estimates, the maximized log-likelihood, and associated empirical estimating functions (or score contributions), respectively. Internally, a function of type (1) is set up by \code{mob()} in case a function of type (2) is supplied. However, as pointed out above, a function of type (1) might be useful to save computation time. \end{enumerate} % In either case the \code{fit} function can, of course, choose to ignore any arguments that are not applicable, e.g., if the are no regressors \code{x} in the model or if starting values or not supported. The \code{fit} function of type (2) is typically convenient to quickly try out a new type of model in recursive partitioning. However, when writing a new \code{mob()} interface such as \code{lmtree()} or \code{glmtree()}, it will typically be better to use type (1). Similarly, employing supporting starting values in \code{fit} is then recommended to save computation time. \subsubsection*{Illustration} For recursively partitioning the \code{diabetes ~ glucose} relationship (as already set up in the previous section), we employ a logistic regression model. An interface of type (2) can be easily set up: % <>= logit <- function(y, x, start = NULL, weights = NULL, offset = NULL, ...) { glm(y ~ 0 + x, family = binomial, start = start, ...) } @ % Thus, \code{y}, \code{x}, and the starting values are passed on to \code{glm()} which returns an object of class `\code{glm}' for which all required methods (\code{coef()}, \code{logLik()}, and \code{estfun()}) are available. Using this \code{fit} function and the \code{formula} already set up above the MOB algorithm can be easily applied to the \code{PimaIndiansDiabetes} data: % <>= pid_tree <- mob(pid_formula, data = PimaIndiansDiabetes, fit = logit) @ % The result is a logistic regression tree with three terminal nodes that can be easily visualized via \code{plot(pid_tree)} (see Figure~\ref{fig:pid_tree}) and printed: <>= pid_tree @ % The tree finds three groups of Pima Indian women: \begin{itemize} \item[\#2] Women with low body mass index that have on average a low risk of diabetes, however this increases clearly with glucose level. \item[\#4] Women with average and high body mass index, younger than 30 years, that have a higher avarage risk that also increases with glucose level. \item[\#5] Women with average and high body mass index, older than 30 years, that have a high avarage risk that increases only slowly with glucose level. \end{itemize} Note that the example above is used for illustration here and \code{glmtree()} is recommended over using \code{mob()} plus manually setting up a \code{logit()} function. The same tree structure can be found via: % <>= pid_tree2 <- glmtree(diabetes ~ glucose | pregnant + pressure + triceps + insulin + mass + pedigree + age, data = PimaIndiansDiabetes, family = binomial) @ % However, \code{glmtree()} is slightly faster as it avoids many unnecessary computations, see Section~\ref{sec:interface} for further details. \begin{figure}[p!] \centering \setkeys{Gin}{width=0.8\textwidth} <>= plot(pid_tree) @ \caption{\label{fig:pid_tree} Logistic-regression-based tree for the Pima Indians diabetes data. The plots in the leaves report the estimated regression coefficients.} \setkeys{Gin}{width=\textwidth} <>= plot(pid_tree2, tp_args = list(ylines = 1, margins = c(1.5, 1.5, 1.5, 2.5))) @ \caption{\label{fig:pid_tree2} Logistic-regression-based tree for the Pima Indians diabetes data. The plots in the leaves give spinograms for \code{diabetes} versus \code{glucose}.} \end{figure} Here, we only point out that \code{plot(pid_tree2)} produces a nicer visualization (see Figure~\ref{fig:pid_tree2}). As $y$ is \code{diabetes}, a binary variable, and $x$ is \code{glucose}, a numeric variable, a spinogram is chosen automatically for visualization (using the \pkg{vcd} package, \citealp{vcd}). The x-axis breaks in the spinogram are the five-point summary of \code{glucose} on the full data set. The fitted lines are the mean predicted probabilities in each group. \subsection{Testing for parameter instability} \label{sec:sctest} In each node of the tree, first the parametric model is fitted to all observations in that node (see Section~\ref{sec:fit}). Subsequently it is of interest to find out whether the model parameters are stable over each particular ordering implied by the partitioning variables $Z_j$ or whether splitting the sample with respect to one of the $Z_j$ might capture instabilities in the parameters and thus improve the fit. The tests used in this step belong to the class of generalized M-fluctuation tests \citep{Zeileis:2005,Zeileis+Hornik:2007}. Depending on the class of each of the partitioning variables in \code{z} different types of tests are chosen by \code{mob()}: \begin{enumerate} \item For numeric partitioning variables (of class `\code{numeric}' or `\code{integer}') the sup\textit{LM}~statistic is used which is the maximum over all single-split \textit{LM} statistics. Associated $p$-values can be obtained from a table of critical values \citep[based on][]{Hansen:1997} stored within the package. If there are ties in the partitioning variable, the sequence of \textit{LM} statistics (and hence their maximum) is not unique and hence the results by default may depend to some degree on the ordering of the observations. To explore this, the option \code{breakties = TRUE} can be set in \code{mob_control()} which breaks ties randomly. If there are are only few ties, the influence is often negligible. If there are many ties (say only a dozen unique values of the partitioning variable), then the variable may be better treated as an ordered factor (see below). \item For categorical partitioning variables (of class `\code{factor}'), a $\chi^2$~statistic is employed which captures the fluctuation within each of the categories of the partitioning variable. This is also an \textit{LM}-type test and is asymptotically equivalent to the corresponding likelihood ratio test. However, it is somewhat cheaper to compute the \textit{LM} statistic because the model just has to be fitted once in the current node and not separately for each category of each possible partitioning variable. See also \cite{Merkle+Fan+Zeileis:2014} for a more detailed discussion. \item For ordinal partitioning variables (of class `\code{ordered}' inheriting from `\code{factor}') the same $\chi^2$ as for the unordered categorical variables is used by default \citep[as suggested by][]{Zeileis+Hothorn+Hornik:2008}. Although this test is consistent for any parameter instabilities across ordered variables, it does not exploit the ordering information. Recently, \cite{Merkle+Fan+Zeileis:2014} proposed an adapted max\textit{LM} test for ordered variables and, alternatively, a weighted double maximum test. Both are optionally availble in the new \code{mob()} implementation by setting \code{ordinal = "L2"} or \code{ordinal = "max"} in \code{mob_control()}, respectively. Unfortunately, computing $p$-values from both tests is more costly than for the default \code{ordinal = "chisq"}. For \code{"L2"} suitable tables of critical values have to be simulated on the fly using \code{ordL2BB()} from the \pkg{strucchange} package \citep{strucchange}. For \code{"max"} a multivariate normal probability has to be computed using the \pkg{mvtnorm} package \citep{mvtnorm}. \end{enumerate} All of the parameter instability tests above can be computed in an object-oriented manner as the ``\code{estfun}'' has to be available for the fitted model object. (Either by computing it in the \code{fit} function directly or by providing a \code{estfun()} extractor, see Section~\ref{sec:fit}.) All tests also require an estimate of the corresponding variance-covariance matrix of the estimating functions. The default is to compute this using an outer-product-of-gradients (OPG) estimator. Alternatively, the corrsponding information matrix or sandwich matrix can be used if: (a)~the estimating functions are actually maximum likelihood scores, and (b)~a \code{vcov()} method (based on an estimate of the information) is provided for the fitted model objects. The corresponding option in \code{mob_control()} is to set \code{vcov = "info"} or \code{vcov = "sandwich"} rather than \code{vcov = "opg"} (the default). For each of the $j = 1, \dots, \ell$ partitioning variables in \code{z} the test selected in the control options is employed and the corresponding $p$-value $p_j$ is computed. To adjust for multiple testing, the $p$ values can be Bonferroni adjusted (which is the default). To determine whether there is some overall instability, it is checked whether the minial $p$-value $p_{j^*} = \min_{j = 1, \dots, \ell} p_j$ falls below a pre-specified significance level $\alpha$ (by default $\alpha = 0.05$) or not. If there is significant instability, the variable $Z_{j^*}$ associated with the minimal $p$-value is used for splitting the node. \subsubsection*{Illustration} In the logistic-regression-based MOB \code{pid_tree} computed above, the parameter instability tests can be extracted using the \code{sctest()} function from the \pkg{strucchange} package (for \underline{s}tructural \underline{c}hange \underline{test}). In the first node, the test statistics and Bonferroni-corrected $p$-values are: % <>= library("strucchange") sctest(pid_tree, node = 1) @ % Thus, the body \code{mass} index has the lowest $p$-value and is highly significant and hence used for splitting the data. In the second node, no further significant parameter instabilities can be detected and hence partitioning stops in that branch. % <>= sctest(pid_tree, node = 2) @ % In the third node, however, there is still significant instability associated with the \code{age} variable and hence partitioning continues. % <>= sctest(pid_tree, node = 3) @ % Because no further instabilities can be found in the fourth and fifth node, the recursive partitioning stops there. \subsection{Splitting} \label{sec:split} In this step, the observations in the current node are split with respect to the chosen partitioning variable $Z_{j^*}$ into $B$ child nodes. As pointed out above, the \code{mob()} function currently only supports binary splits, i.e., $B = 2$. For deterimining the split point, an exhaustive search procedure is adopted: For each conceivable split point in $Z_{j^*}$, the two subset models are fit and the split associated with the minimal value of the objective function $\Psi$ is chosen. Computationally, this means that the \code{fit} function is applied to the subsets of \code{y} and \code{x} for each possibly binary split. The ``\code{objfun}'' values are simply summed up (because the objective function is assumed to be additive) and its minimum across splits is determined. In a search over a numeric partitioning variable, this means that typically a lot of subset models have to be fitted and often these will not vary a lot from one split to the next. Hence, the parameter estimates ``\code{coefficients}'' from the previous split are employed as \code{start} values for estimating the coefficients associated with the next split. Thus, if the \code{fit} function makes use of these starting values, the model fitting can often be speeded up. \subsubsection*{Illustration} For the Pima Indians diabetes data, the split points found for \code{pid_tree} are displayed both in the print output and the visualization (see Figure~\ref{fig:pid_tree} and~\ref{fig:pid_tree2}). \subsection{Pruning} \label{sec:prune} By default, the size of \code{mob()} trees is determined only by the significance tests, i.e., when there is no more significant parameter instability (by default at level $\alpha = 0.05$) the tree stops growing. Additional stopping criteria are only the minimal node size (\code{minsize}) and the maximum tree depth (\code{maxdepth}, by default infinity). However, for very large sample size traditional significance levels are typically not useful because even tiny parameter instabilities can be detected. To avoid overfitting in such a situation, one would either have to use much smaller significance levels or add some form of post-pruning to reduce the size of the tree afterwards. Similarly, one could wish to first grow a very large tree (using a large $\alpha$ level) and then prune it afterwards, e.g., using some information criterion like AIC or BIC. To accomodate such post-pruning strategies, \code{mob_control()} has an argument \code{prune} that can be a \code{function(objfun, df, nobs)} that either returns \code{TRUE} if a node should be pruned or \code{FALSE} if not. The arguments supplied are a vector of objective function values in the current node and the sum of all child nodes, a vector of corresponding degrees of freedom, and the number of observations in the current node and in total. For example if the objective function used is the negative log-likelihood, then for BIC-based pruning the \code{prune} function is: \code{(2 * objfun[1] + log(nobs[1]) * df[1]) < (2 * objfun[2] + log(nobs[2]) * df[2])}. As the negative log-likelihood is the default objective function when using the ``simple'' \code{fit} interface, \code{prune} can also be set to \code{"AIC"} or \code{"BIC"} and then suitable functions will be set up internally. Note, however, that for other objective functions this strategy is not appropriate and the functions would have to be defined differently (which \code{lmtree()} does for example). In the literature, there is no clear consensus as to how many degrees of freedom should be assigned to the selection of a split point. Hence, \code{mob_control()} allows to set \code{dfsplit} which by default is \code{dfsplit = TRUE} and then \code{as.integer(dfsplit)} (i.e., 1 by default) degrees of freedom per split are used. This can be modified to \code{dfsplit = FALSE} (or equivalently \code{dfsplit = 0}) or \code{dfsplit = 3} etc.\ for lower or higher penalization of additional splits. \subsubsection*{Illustration} With $n = \Sexpr{nrow(PimaIndiansDiabetes)}$ observations, the sample size is quite reasonable for using the classical significance level of $\alpha = 0.05$ which is also reflected by the moderate tree size with three terminal nodes. However, if we wished to explore further splits, a conceivable strategy could be the following: % <>= pid_tree3 <- mob(pid_formula, data = PimaIndiansDiabetes, fit = logit, control = mob_control(verbose = TRUE, minsize = 50, maxdepth = 4, alpha = 0.9, prune = "BIC")) @ This first grows a large tree until the nodes become too small (minimum node size: 50~observations) or the tree becomes too deep (maximum depth 4~levels) or the significance levels come very close to one (larger than $\alpha = 0.9$). Here, this large tree has eleven nodes which are subsequently pruned based on whether or not they improve the BIC of the model. For this data set, the resulting BIC-pruned tree is in fact identical to the pre-pruned \code{pid_tree} considered above. \subsection[Fitted `party' objects]{Fitted `\texttt{party}' objects} \label{sec:object} The result of \code{mob()} is an object of class `\code{modelparty}' inheriting from `\code{party}'. See the other vignettes in the \pkg{partykit} package \citep{partykit} for more details of the general `\code{party}' class. Here, we just point out that the main difference between a `\code{modelparty}' and a plain `\code{party}' is that additional information about the data and the associated models is stored in the \code{info} elements: both of the overall `\code{party}' and the individual `\code{node}'s. The details are exemplified below. \subsubsection*{Illustration} In the \code{info} of the overall `\code{party}' the following information is stored for \code{pid_tree}: % <>= names(pid_tree$info) @ % The \code{call} contains the \code{mob()} call. The \code{formula} and \code{Formula} are virtually the same but are simply stored as plain `\code{formula}' and extended `\code{Formula}' \citep{Formula} objects, respectively. The \code{terms} contain separate lists of terms for the \code{response} (and regressor) and the \code{partitioning} variables. The \code{fit}, \code{control} and \code{dots} are the arguments that were provided to \code{mob()} and \code{nreg} is the number of regressor variables. Furthermore, each \code{node} of the tree contains the following information: % <>= names(pid_tree$node$info) @ % The \code{coefficients}, \code{objfun}, and \code{object} are the results of the \code{fit} function for that node. In \code{nobs} and \code{p.value} the number of observations and the minimal $p$-value are provided, respectively. Finally, \code{test} contains the parameter instability test results. Note that the \code{object} element can also be suppressed through \code{mob_control()} to save memory space. \subsection{Methods} \label{sec:methods} There is a wide range of standard methods available for objects of class `\code{modelparty}'. The standard \code{print()}, \code{plot()}, and \code{predict()} build on the corresponding methods for `\code{party}' objects but provide some more special options. Furthermore, methods are provided that are typically available for models with formula interfaces: \code{formula()} (optionally one can set \code{extended = TRUE} to get the `\code{Formula}'), \code{getCall()}, \code{model.frame()}, \code{weights()}. Finally, there is a standard set of methods for statistical model objects: \code{coef()}, \code{residuals()}, \code{logLik()} (optionally setting \code{dfsplit = FALSE} suppresses counting the splits in the degrees of freedom, see Section~\ref{sec:prune}), \code{deviance()}, \code{fitted()}, and \code{summary()}. Some of these methods rely on reusing the corresponding methods for the individual model objects in the terminal nodes. Functions such as \code{coef()}, \code{print()}, \code{summary()} also take a \code{node} argument that can specify the node IDs to be queried. Two methods have non-standard arguments to allow for additional flexibility when dealing with model trees. Typically, ``normal'' users do not have to use these arguments directly but they are very flexible and facilitate writing convenience interfaces such as \code{glmtree()} (see Section~\ref{sec:interface}). \begin{itemize} \item The \code{predict()} method has the following arguments: \code{predict(object, newdata = NULL, type = "node", ...)}. The argument \code{type} can either be a function or a character string. More precisely, if \code{type} is a function it should be a \code{function (object, newdata = NULL, ...)} that returns a vector or matrix of predictions from a fitted model \code{object} either with or without \code{newdata}. If \code{type} is a character string, such a function is set up internally as \code{predict(object, newdata = newdata, type = type, ...)}, i.e., it relies on a suitable \code{predict()} method being available for the fitted models associated with the `\code{party}' object. \item The \code{plot()} method has the following arguments: \code{plot(x, terminal_panel = NULL, FUN = NULL)}. This simply calls the \code{plot()} method for `\code{party}' objects with a custom panel function for the terminal panels. By default, \code{node_terminal} is used to include some short text in each terminal node. This text can be set up by \code{FUN} with the default being the number of observations and estimated parameters. However, more elaborate terminal panel functions can be written, as done for the convenience interfaces. \end{itemize} Finally, two \proglang{S}3-style functions are provided without the corresponding generics (as these reside in packages that \pkg{partykit} does not depend on). The \code{sctest.modelparty} can be used in combination with the \code{sctest()} generic from \pkg{strucchange} as illustrated in Section~\ref{sec:sctest}. The \code{refit.modelparty} function extracts (or refits if necessary) the fitted model objects in the specified nodes (by default from all nodes). \subsubsection*{Illustration} The \code{plot()} and \code{print()} methods have already been illustrated for the \code{pid_tree} above. However, here we add that the \code{print()} method can also be used to show more detailed information about particular nodes instead of showing the full tree: % <>= print(pid_tree, node = 3) @ % Information about the model and coefficients can for example be extracted by: % <>= coef(pid_tree) coef(pid_tree, node = 1) ## IGNORE_RDIFF_BEGIN summary(pid_tree, node = 1) ## IGNORE_RDIFF_END @ % As the coefficients pertain to a logistic regression, they can be easily interpreted as odds ratios by taking the \code{exp()}: % <<>>= exp(coef(pid_tree)[,2]) @ % <>= risk <- round(100 * (exp(coef(pid_tree)[,2])-1), digits = 1) @ % i.e., the odds increase by \Sexpr{risk[1]}\%, \Sexpr{risk[2]}\% and \Sexpr{risk[3]}\% with respect to glucose in the three terminal nodes. Log-likelihoods and information criteria are available (which by default also penalize the estimation of splits): <>= logLik(pid_tree) AIC(pid_tree) BIC(pid_tree) @ % Mean squared residuals (or deviances) can be extracted in different ways: <>= mean(residuals(pid_tree)^2) deviance(pid_tree)/sum(weights(pid_tree)) deviance(pid_tree)/nobs(pid_tree) @ % Predicted nodes can also be easily obtained: % <>= pid <- head(PimaIndiansDiabetes) predict(pid_tree, newdata = pid, type = "node") @ % More predictions, e.g., predicted probabilities within the nodes, can also be obtained but require some extra coding if only \code{mob()} is used. However, with the \code{glmtree()} interface this is very easy as shown below. Finally, several methods for `\code{party}' objects are, of course, also available for `\code{modelparty}' objects, e.g., querying width and depth of the tree: % <>= width(pid_tree) depth(pid_tree) @ % Also subtrees can be easily extracted: % <>= pid_tree[3] @ % The subtree is again a completely valid `\code{modelparty}' and hence it could also be visualized via \code{plot(pid_tree[3])} etc. \subsection{Extensions and convenience interfaces} \label{sec:interface} As illustrated above, dealing with MOBs can be carried out in a very generic and object-oriented way. Almost all information required for dealing with recursively partitioned models can be encapsulated in the \code{fit()} function and \code{mob()} does not require more information on what type of model is actually used. However, for certain tasks more detailed information about the type of model used or the type of data it can be fitted to can (and should) be exploited. Notable examples for this are visualizations of the data along with the fitted model or model-based predictions in the leaves of the tree. To conveniently accomodate such specialized functionality, the \pkg{partykit} provides two convenience interfaces \code{lmtree()} and \code{glmtree()} and encourages other packages to do the same (e.g., \code{raschtree()} and \code{bttree()} in \pkg{psychotree}). Furthermore, such a convenience interface can avoid duplicated formula processing in both \code{mob()} plus its \code{fit} function. Specifically, \code{lmtree()} and \code{glmtree()} interface \code{lm.fit()}, \code{lm.wfit()}, and \code{glm.fit()}, respectively, and then provide some extra computations to return valid fitted `\code{lm}' and `\code{glm}' objects in the nodes of the tree. The resulting `\code{modelparty}' object gains an additional class `\code{lmtree}'/`\code{glmtree}' to dispatch to its enhanced \code{plot()} and \code{predict()} methods. \subsubsection*{Illustration} The \code{pid_tree2} object was already created above with \code{glmtree()} (instead of \code{mob()} as for \code{pid_tree}) to illustrate the enhanced plotting capabilities in Figure~\ref{fig:pid_tree2}. Here, the enhanced \code{predict()} method is used to obtain predicted means (i.e., probabilities) and associated linear predictors (on the logit scale) in addition to the previously available predicted nods IDs. % <<>>= predict(pid_tree2, newdata = pid, type = "node") predict(pid_tree2, newdata = pid, type = "response") predict(pid_tree2, newdata = pid, type = "link") @ \section{Illustrations} \label{sec:illustration} In the remainder of the vignette, further empirical illustrations of the MOB method are provided, including replications of the results from \cite{Zeileis+Hothorn+Hornik:2008}: \begin{enumerate} \item An investigation of the price elasticity of the demand for economics journals across covariates describing the type of journal (e.g., its price, its age, and whether it is published by a society, etc.) \item Prediction of house prices in the well-known Boston Housing data set, also taken from the UCI machine learning repository. \item Explore how teaching ratings and beauty scores of professors are associated and how this association changes across further explanatory variables such as age, gender, and native speaker status of the professors. \item Assessment of differences in the preferential treatment of women/children (``women and children first'') across subgroups of passengers on board of the ill-fated maiden voyage of the RMS Titanic. \item Modeling of breast cancer survival by capturing heterogeneity in certain (treatment) effects across patients. \item Modeling of paired comparisons of topmodel candidates by capturing heterogeneity in their attractiveness scores across participants in a survey. \end{enumerate} More details about several of the underlying data sets, previous studies exploring the data, and the results based on MOB can be found in \cite{Zeileis+Hothorn+Hornik:2008}. Here, we focus on using the \pkg{partykit} package to replicate the analysis and explore the resulting trees. The first three illustrations employ the \code{lmtree()} convenience function, the fourth is based on logistic regression using \code{glmtree()}, and the fifth uses \code{survreg()} from \pkg{survival} \citep{survival} in combination with \code{mob()} directly. The sixth and last illustration is deferred to a separate section and shows in detail how to set up new ``mobster'' functionality from scratch. \subsection{Demand for economic journals} The price elasticity of the demand for 180~economic journals is assessed by an OLS regression in log-log form: The dependent variable is the logarithm of the number of US library subscriptions and the regressor is the logarithm of price per citation. The data are provided by the \pkg{AER} package \citep{AER} and can be loaded and transformed via: % <>= data("Journals", package = "AER") Journals <- transform(Journals, age = 2000 - foundingyear, chars = charpp * pages) @ % Subsequently, the stability of the price elasticity across the remaining variables can be assessed using MOB. Below, \code{lmtree()} is used with the following partitioning variables: raw price and citations, age of the journal, number of characters, and whether the journal is published by a scientific society or not. A minimal segment size of 10~observations is employed and by setting \code{verbose = TRUE} detailed progress information about the recursive partitioning is displayed while growing the tree: % <>= j_tree <- lmtree(log(subs) ~ log(price/citations) | price + citations + age + chars + society, data = Journals, minsize = 10, verbose = TRUE) @ % \begin{figure}[t!] \centering \setkeys{Gin}{width=0.75\textwidth} <>= plot(j_tree) @ \caption{\label{fig:Journals} Linear-regression-based tree for the journals data. The plots in the leaves show linear regressions of log(subscriptions) by log(price/citation).} \end{figure} % The resulting tree just has one split and two terminal nodes for young journals (with a somewhat larger price elasticity) and old journals (with an even lower price elasticity), respectively. Figure~\ref{fig:Journals} can be obtained by \code{plot(j_tree)} and the corresponding printed representation is shown below. % <>= j_tree @ % Finally, various quantities of interest such as the coefficients, standard errors and test statistics, and the associated parameter instability tests could be extracted by the following code. The corresponding output is suppressed here. % <>= coef(j_tree, node = 1:3) summary(j_tree, node = 1:3) sctest(j_tree, node = 1:3) @ \subsection{Boston housing data} The Boston housing data are a popular and well-investigated empirical basis for illustrating nonlinear regression methods both in machine learning and statistics. We follow previous analyses by segmenting a bivariate linear regression model for the house values. The data set is available in package \pkg{mlbench} and can be obtained and transformed via: % <>= data("BostonHousing", package = "mlbench") BostonHousing <- transform(BostonHousing, chas = factor(chas, levels = 0:1, labels = c("no", "yes")), rad = factor(rad, ordered = TRUE)) @ % It provides $n = \Sexpr{NROW(BostonHousing)}$ observations of the median value of owner-occupied homes in Boston (in USD~1000) along with $\Sexpr{NCOL(BostonHousing)}$ covariates including in particular the number of rooms per dwelling (\code{rm}) and the percentage of lower status of the population (\code{lstat}). A segment-wise linear relationship between the value and these two variables is very intuitive, whereas the shape of the influence of the remaining covariates is rather unclear and hence should be learned from the data. Therefore, a linear regression model for median value explained by \verb:rm^2: and \verb:log(lstat): is employed and partitioned with respect to all remaining variables. Choosing appropriate transformations of the dependent variable and the regressors that enter the linear regression model is important to obtain a well-fitting model in each segment and we follow in our choice the recommendations of \cite{Breiman+Friedman:1985}. Monotonic transformations of the partitioning variables do not affect the recursive partitioning algorithm and hence do not have to be performed. However, it is important to distinguish between numerical and categorical variables for choosing an appropriate parameter stability test. The variable \code{chas} is a dummy indicator variable (for tract bounds with Charles river) and thus needs to be turned into a factor. Furthermore, the variable \code{rad} is an index of accessibility to radial highways and takes only 9 distinct values. Hence, it is most appropriately treated as an ordered factor. Note that both transformations only affect the parameter stability test chosen (step~2), not the splitting procedure (step~3). % Note that with splittry = 0 (according to old version of mob) there is no % split in dis <>= bh_tree <- lmtree(medv ~ log(lstat) + I(rm^2) | zn + indus + chas + nox + age + dis + rad + tax + crim + b + ptratio, data = BostonHousing) bh_tree @ % The corresponding visualization is shown in Figure~\ref{fig:BostonHousing}. It shows partial scatter plots of the dependent variable against each of the regressors in the terminal nodes. Each scatter plot also shows the fitted values, i.e., a projection of the fitted hyperplane. \setkeys{Gin}{width=\textwidth} \begin{figure}[p!] \centering <>= plot(bh_tree) @ \includegraphics[width=18cm,keepaspectratio,angle=90]{mob-BostonHousing-plot} \caption{\label{fig:BostonHousing} Linear-regression-based tree for the Boston housing data. The plots in the leaves give partial scatter plots for \code{rm} (upper panel) and \code{lstat} (lower panel).} \end{figure} From this visualization, it can be seen that in the nodes~4, 6, 7 and 8 the increase of value with the number of rooms dominates the picture (upper panel) whereas in node~9 the decrease with the lower status population percentage (lower panel) is more pronounced. Splits are performed in the variables \code{tax} (poperty-tax rate) and \code{ptratio} (pupil-teacher ratio). For summarizing the quality of the fit, we could compute the mean squared error, log-likelihood or AIC: % <>= mean(residuals(bh_tree)^2) logLik(bh_tree) AIC(bh_tree) @ \subsection{Teaching ratings data} \cite{Hamermesh+Parker:2005} investigate the correlation of beauty and teaching evaluations for professors. They provide data on course evaluations, course characteristics, and professor characteristics for 463 courses for the academic years 2000--2002 at the University of Texas at Austin. It is of interest how the average teaching evaluation per course (on a scale 1--5) depends on a standardized measure of beauty (as assessed by a committee of six persons based on photos). \cite{Hamermesh+Parker:2005} employ a linear regression, weighted by the number of students per course and adjusting for several further main effects: gender, whether or not the teacher is from a minority, a native speaker, or has tenure, respectively, and whether the course is taught in the upper or lower division. Additionally, the age of the professors is available as a regressor but not considered by \cite{Hamermesh+Parker:2005} because the corresponding main effect is not found to be significant in either linear or quadratic form. Here, we employ a similar model but use the available regressors differently. The basic model is again a linear regression for teaching rating by beauty, estimated by weighted least squares (WLS). All remaining explanatory variables are \emph{not} used as regressors but as partitioning variables because we argue that it is unclear how they influence the correlation between teaching rating and beauty. Hence, MOB is used to adaptively incorporate these further variables and determine potential interactions. First, the data are loaded from the \pkg{AER} package \citep{AER} and only the subset of single-credit courses is excluded. % <>= data("TeachingRatings", package = "AER") tr <- subset(TeachingRatings, credits == "more") @ % The single-credit courses include elective modules that are quite different from the remaining courses (e.g., yoga, aerobics, or dance) and are hence omitted from the main analysis. WLS estimation of the null model (with only an intercept) and the main effects model is carried out in a first step: % <>= tr_null <- lm(eval ~ 1, data = tr, weights = students) tr_lm <- lm(eval ~ beauty + gender + minority + native + tenure + division, data = tr, weights = students) @ % Then, the model-based tree can be estimated with \code{lmtree()} using only \code{beauty} as a regressor and all remaining variables for partitioning. For WLS estimation, we set \code{weights = students} and \code{caseweights = FALSE} because the weights are only proportionality factors and do not signal exactly replicated observations \citep[see][for a discussion of the different types of weights]{Lumley:2020}. % <>= (tr_tree <- lmtree(eval ~ beauty | minority + age + gender + division + native + tenure, data = tr, weights = students, caseweights = FALSE)) @ % \begin{figure}[t!] \setkeys{Gin}{width=\textwidth} <>= plot(tr_tree) @ \caption{\label{fig:tr_tree} WLS-based tree for the teaching ratings data. The plots in the leaves show scatterplots for teaching rating by beauty score.} \end{figure} % The resulting tree can be visualized by \code{plot(tr_tree)} and is shown in Figure~\ref{fig:tr_tree}. This shows that despite age not having a significant main effect \citep[as reported by][]{Hamermesh+Parker:2005}, it clearly plays an important role: While the correlation of teaching rating and beauty score is rather moderate for younger professors, there is a clear correlation for older professors (with the cutoff age somewhat lower for female professors). % <>= coef(tr_lm)[2] coef(tr_tree)[, 2] @ % Th $R^2$ of the tree is also clearly improved over the main effects model: % <>= 1 - c(deviance(tr_lm), deviance(tr_tree))/deviance(tr_null) @ \subsection{Titanic survival data} To illustrate how differences in treatment effects can be captured by MOB, the Titanic survival data is considered: The question is whether ``women and children first'' is applied in the same way for all subgroups of the passengers of the Titanic. Or, in other words, whether the effectiveness of preferential treatment for women/children differed across subgroups. The \code{Titanic} data is provided in base \proglang{R} as a contingency table and transformed here to a `\code{data.frame}' for use with \code{glmtree()}: % <>= data("Titanic", package = "datasets") ttnc <- as.data.frame(Titanic) ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] names(ttnc)[2] <- "Gender" ttnc <- transform(ttnc, Treatment = factor( Gender == "Female" | Age == "Child", levels = c(FALSE, TRUE), labels = c("Male&Adult", "Female|Child"))) @ % The data provides factors \code{Survived} (yes/no), \code{Class} (1st, 2nd, 3rd, crew), \code{Gender} (male, female), and \code{Age} (child, adult). Additionally, a factor \code{Treatment} is added that distinguishes women/children from male adults. To investigate how the preferential treatment effect (\code{Survived ~ Treatment}) differs across the remaining explanatory variables, the following logistic-regression-based tree is considered. The significance level of \code{alpha = 0.01} is employed here to avoid overfitting and separation problems in the logistic regression. % <>= ttnc_tree <- glmtree(Survived ~ Treatment | Class + Gender + Age, data = ttnc, family = binomial, alpha = 0.01) ttnc_tree @ % \begin{figure}[t!] \setkeys{Gin}{width=\textwidth} <>= plot(ttnc_tree, tp_args = list(ylines = 1, margins = c(1.5, 1.5, 1.5, 2.5))) @ \caption{\label{fig:ttnc_tree} Logistic-regression-based tree for the Titanic survival data. The plots in the leaves give spinograms for survival status versus preferential treatment (women or children).} \end{figure} % This shows that the treatment differs strongly across passengers classes, see also the result of \code{plot(ttnc_tree)} in Figure~\ref{fig:ttnc_tree}. The treatment effect is much lower in the 3rd class where women/children still have higher survival rates than adult men but the odds ratio is much lower compared to all remaining classes. The split between the 2nd and the remaining two classes (1st, crew) is due to a lower overall survival rate (intercepts of \Sexpr{round(coef(ttnc_tree)[2, 1], digits = 2)} and \Sexpr{round(coef(ttnc_tree)[3, 1], digits = 2)}, respectively) while the odds ratios associated with the preferential treatment are rather similar (\Sexpr{round(coef(ttnc_tree)[2, 2], digits = 2)} and \Sexpr{round(coef(ttnc_tree)[3, 2], digits = 2)}, respectively). Another option for assessing the class effect would be to immediately split into all four classes rather than using recursive binary splits. This can be obtained by setting \code{catsplit = "multiway"} in the \code{glmtree()} call above. This yields a tree with just a single split but four kid nodes. \subsection{German breast cancer data} To illustrate that the MOB approach can also be used beyond (generalized) linear regression models, it is employed in the following to analyze censored survival times among German women with positive node breast cancer. The data is available in the \pkg{TH.data} package and the survival time is transformed from days to years: % <>= data("GBSG2", package = "TH.data") GBSG2$time <- GBSG2$time/365 @ % For regression a parametric Weibull regression based on the \code{survreg()} function from the \pkg{survival} package \citep{survival} is used. A fitting function for \code{mob()} can be easily set up: % <>= library("survival") wbreg <- function(y, x, start = NULL, weights = NULL, offset = NULL, ...) { survreg(y ~ 0 + x, weights = weights, dist = "weibull", ...) } @ % As the \pkg{survreg} package currently does not provide a \code{logLik()} method for `\code{survreg}' objects, this needs to be added here: % <>= logLik.survreg <- function(object, ...) structure(object$loglik[2], df = sum(object$df), class = "logLik") @ % Without the \code{logLik()} method, \code{mob()} would not know how to extract the optimized objective function from the fitted model. With the functions above available, a censored Weibull-regression-tree can be fitted: The dependent variable is the censored survival time and the two regressor variables are the main risk factor (number of positive lymph nodes) and the treatment variable (hormonal therapy). All remaining variables are used for partitioning: age, tumor size and grade, progesterone and estrogen receptor, and menopausal status. The minimal segment size is set to 80. % <>= gbsg2_tree <- mob(Surv(time, cens) ~ horTh + pnodes | age + tsize + tgrade + progrec + estrec + menostat, data = GBSG2, fit = wbreg, control = mob_control(minsize = 80)) @ % \begin{figure}[p!] \centering \setkeys{Gin}{width=0.6\textwidth} <>= plot(gbsg2_tree) @ \caption{\label{fig:GBSG2} Censored Weibull-regression-based tree for the German breast cancer data. The plots in the leaves report the estimated regression coefficients.} \setkeys{Gin}{width=\textwidth} <>= gbsg2node <- function(mobobj, col = "black", linecol = "red", cex = 0.5, pch = NULL, jitter = FALSE, xscale = NULL, yscale = NULL, ylines = 1.5, id = TRUE, xlab = FALSE, ylab = FALSE) { ## obtain dependent variable mf <- model.frame(mobobj) y <- Formula::model.part(mobobj$info$Formula, mf, lhs = 1L, rhs = 0L) if(isTRUE(ylab)) ylab <- names(y)[1L] if(identical(ylab, FALSE)) ylab <- "" if(is.null(ylines)) ylines <- ifelse(identical(ylab, ""), 0, 2) y <- y[[1L]] ## plotting character and response if(is.null(pch)) pch <- y[,2] * 18 + 1 y <- y[,1] y <- as.numeric(y) pch <- rep(pch, length.out = length(y)) if(jitter) y <- jitter(y) ## obtain explanatory variables x <- Formula::model.part(mobobj$info$Formula, mf, lhs = 0L, rhs = 1L) xnam <- colnames(x) z <- seq(from = min(x[,2]), to = max(x[,2]), length = 51) z <- data.frame(a = rep(sort(x[,1])[c(1, NROW(x))], c(51, 51)), b = z) names(z) <- names(x) z$x <- model.matrix(~ ., data = z) ## fitted node ids fitted <- mobobj$fitted[["(fitted)"]] if(is.null(xscale)) xscale <- range(x[,2]) + c(-0.1, 0.1) * diff(range(x[,2])) if(is.null(yscale)) yscale <- range(y) + c(-0.1, 0.1) * diff(range(y)) ## panel function for scatter plots in nodes rval <- function(node) { ## node index nid <- id_node(node) ix <- fitted %in% nodeids(mobobj, from = nid, terminal = TRUE) ## dependent variable y <- y[ix] ## predictions yhat <- if(is.null(node$info$object)) { refit.modelparty(mobobj, node = nid) } else { node$info$object } yhat <- predict(yhat, newdata = z, type = "quantile", p = 0.5) pch <- pch[ix] ## viewport setup top_vp <- viewport(layout = grid.layout(nrow = 2, ncol = 3, widths = unit(c(ylines, 1, 1), c("lines", "null", "lines")), heights = unit(c(1, 1), c("lines", "null"))), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_scatterplot", nid, sep = "")) pushViewport(top_vp) grid.rect(gp = gpar(fill = "white", col = 0)) ## main title top <- viewport(layout.pos.col = 2, layout.pos.row = 1) pushViewport(top) mainlab <- paste(ifelse(id, paste("Node", nid, "(n = "), ""), info_node(node)$nobs, ifelse(id, ")", ""), sep = "") grid.text(mainlab) popViewport() plot_vp <- viewport(layout.pos.col = 2, layout.pos.row = 2, xscale = xscale, yscale = yscale, name = paste("node_scatterplot", nid, "plot", sep = "")) pushViewport(plot_vp) ## scatterplot grid.points(x[ix,2], y, gp = gpar(col = col, cex = cex), pch = pch) grid.lines(z[1:51,2], yhat[1:51], default.units = "native", gp = gpar(col = linecol)) grid.lines(z[52:102,2], yhat[52:102], default.units = "native", gp = gpar(col = linecol, lty = 2)) grid.xaxis(at = c(ceiling(xscale[1]*10), floor(xscale[2]*10))/10) grid.yaxis(at = c(ceiling(yscale[1]), floor(yscale[2]))) if(isTRUE(xlab)) xlab <- xnam[2] if(!identical(xlab, FALSE)) grid.text(xlab, x = unit(0.5, "npc"), y = unit(-2, "lines")) if(!identical(ylab, FALSE)) grid.text(ylab, y = unit(0.5, "npc"), x = unit(-2, "lines"), rot = 90) grid.rect(gp = gpar(fill = "transparent")) upViewport() upViewport() } return(rval) } class(gbsg2node) <- "grapcon_generator" plot(gbsg2_tree, terminal_panel = gbsg2node, tnex = 2, tp_args = list(xscale = c(0, 52), yscale = c(-0.5, 8.7))) @ \caption{\label{fig:GBSG2-scatter} Censored Weibull-regression-based tree for the German breast cancer data. The plots in the leaves depict censored (hollow) and uncensored (solid) survival time by number of positive lymph nodes along with fitted median survival for patients with (dashed line) and without (solid line) hormonal therapy.} \end{figure} % Based on progesterone receptor, a tree with two leaves is found: % <>= gbsg2_tree coef(gbsg2_tree) logLik(gbsg2_tree) @ % The visualization produced by \code{plot(gbsg2_tree)} is shown in Figure~\ref{fig:GBSG2}. A nicer graphical display using a scatter plot (with indication of censoring) and fitted regression curves is shown in Figure~\ref{fig:GBSG2-scatter}. This uses a custom panel function whose code is too long and elaborate to be shown here. Interested readers are referred to the \proglang{R} code underlying the vignette. The visualization shows that for higher progesterone receptor levels: (1)~survival times are higher overall, (2)~the treatment effect of hormonal therapy is higher, and (3)~the negative effect of the main risk factor (number of positive lymph nodes) is less severe. \section{Setting up a new mobster} \label{sec:mobster} To conclude this vignette, we present another illustration that shows how to set up new mobster functionality from scratch. To do so, we implement the Bradley-Terry tree suggested by \cite{Strobl+Wickelmaier+Zeileis:2011} ``by hand''. The \pkg{psychotree} package already provides an easy-to-use mobster called \code{bttree()} but as an implementation exercise we recreate its functionality here. The only inputs required are a suitable data set with paired comparisons (\code{Topmodel2007} from \pkg{psychotree}) and a parametric model for paired comparison data (\code{btmodel()} from \pkg{psychotools}, implementing the Bradley-Terry model). The latter optionally computes the empirical estimating functions and already comes with a suitable extractor method. <>= data("Topmodel2007", package = "psychotree") library("psychotools") @ % The Bradley-Terry (or Bradley-Terry-Luce) model is a standard model for paired comparisons in social sciences. It parametrizes the probability $\pi_{ij}$ for preferring some object $i$ over another object $j$ in terms of corresponding ``ability'' or ``worth'' parameters $\theta_i$: \begin{eqnarray*} \pi_{ij}\phantom{)} & = & \frac{\theta_i}{\theta_i + \theta_j} \\ \mathsf{logit}(\pi_{ij}) & = & \log(\theta_i) - \log(\theta_j) \end{eqnarray*} This model can be easily estimated by maximum likelihood as a logistic or log-linear GLM. This is the approach used internally by \code{btmodel()}. The \code{Topmodel2007} data provide paired comparisons of attractiveness among the six finalists of the TV show \emph{Germany's Next Topmodel~2007}: Barbara, Anni, Hana, Fiona, Mandy, Anja. The data were collected in a survey with 192~respondents at Universit{\"a}t T{\"u}bingen and the available covariates comprise gender, age, and familiarty with the TV~show. The latter is assess by three by yes/no questions: (1)~Do you recognize the women?/Do you know the show? (2)~Did you watch it regularly? (3)~Did you watch the final show?/Do you know who won? To fit the Bradley-Terry tree to the data, the available building blocks just have to be tied together. First, we set up the basic/simple model fitting interface described in Section~\ref{sec:fit}: % @ <>= btfit1 <- function(y, x = NULL, start = NULL, weights = NULL, offset = NULL, ...) btmodel(y, ...) @ % The function \code{btfit1()} simply calls \code{btmodel()} ignoring all arguments except \code{y} as the others are not needed here. No more processing is required because \class{btmodel} objects come with a \code{coef()}, \code{logLik()}, and \code{estfun()} method. Hence, we can call \code{mob()} now specifying the response and the partitioning variable (and no regressors because there are no regressors in this model). % <>= bt1 <- mob(preference ~ 1 | gender + age + q1 + q2 + q3, data = Topmodel2007, fit = btfit1) @ % An alternative way to fit the exact same tree somewhat more quickly would be to employ the extended interface described in Section~\ref{sec:fit}: % <>= btfit2 <- function(y, x = NULL, start = NULL, weights = NULL, offset = NULL, ..., estfun = FALSE, object = FALSE) { rval <- btmodel(y, ..., estfun = estfun, vcov = object) list( coefficients = rval$coefficients, objfun = -rval$loglik, estfun = if(estfun) rval$estfun else NULL, object = if(object) rval else NULL ) } @ % Still \code{btmodel()} is employed for fitting the model but the quantities \code{estfun} and \code{vcov} are only computed if they are really required. This may save some computation time -- about 20\% on the authors' machine at the time of writing -- when computing the tree: % <>= bt2 <- mob(preference ~ 1 | gender + age + q1 + q2 + q3, data = Topmodel2007, fit = btfit2) @ % The speed-up is not huge but comes almost for free: just a few additional lines of code in \code{btfit2()} are required. For other models where it is more costly to set up a full model (with variance-covariance matrix, predictions, residuals, etc.) larger speed-ups are also possible. Both trees, \code{bt1} and \code{bt2}, are equivalent (except for the details of the fitting function). Hence, in the following we only explore \code{bt2}. However, the same code can be applied to \code{bt1} as well. Many tools come completely for free and are inherited from the general \class{modelparty}/\class{party}. For example, both printing (\code{print(bt2)}) and plotting (\code{plot(bt2)}) shows the estimated parameters in the terminal nodes which can also be extracted by the \code{coef()} method: <>= bt2 coef(bt2) @ The corresponding visualization is shown in the upper panel of Figure~\ref{fig:topmodel-plot1}. In all cases, the estimated coefficients on the logit scale omitting the fixed zero reference level (Anja) are reported. To show the corresponding worth parameters $\theta_i$ including the reference level, one can simply provide a small panel function \code{worthf()}. This applies the \code{worth()} function from \pkg{psychotools} to the fitted-model object stored in the \code{info} slot of each node, yielding the lower panel in Figure~\ref{fig:topmodel-plot1}. % <>= worthf <- function(info) paste(info$object$labels, format(round(worth(info$object), digits = 3)), sep = ": ") plot(bt2, FUN = worthf) @ % \begin{figure}[p!] \centering <>= plot(bt2) @ \vspace*{0.5cm} <>= <> @ \caption{\label{fig:topmodel-plot1} Bradley-Terry-based tree for the topmodel attractiveness data. The default plot (upper panel) reports the estimated coefficients on the log scale while the adapted plot (lower panel) shows the corresponding worth parameters.} \end{figure} % To show a graphical display of these worth parameters rather than printing their numerical values, one can use a simply glyph-style plot. A simply way to generate these is to use the \code{plot()} method for \class{btmodel} objects from \pkg{partykit} and \code{nodeapply} this to all terminal nodes (see Figure~\ref{fig:topmodel-plot2}): % <>= par(mfrow = c(2, 2)) nodeapply(bt2, ids = c(3, 5, 6, 7), FUN = function(n) plot(n$info$object, main = n$id, ylim = c(0, 0.4))) @ % \begin{figure}[t!] \centering <>= <> @ \caption{\label{fig:topmodel-plot2} Worth parameters in the terminal nodes of the Bradley-Terry-based tree for the topmodel attractiveness data.} \end{figure} % Alternatively, one could set up a proper panel-generating function in \pkg{grid} that allows to create the glyphs within the terminal nodes of the tree (see Figure~\ref{fig:topmodel-plot3}). As the code for this panel-generating function \code{node_btplot()} is too complicated to display within the vignette, we refer interested readers to the underlying code. Given this panel-generating function Figure~\ref{fig:topmodel-plot3} can be generated with <>= plot(bt2, drop = TRUE, tnex = 2, terminal_panel = node_btplot(bt2, abbreviate = 1, yscale = c(0, 0.5))) @ \begin{figure}[t!] \centering <>= ## visualization function node_btplot <- function(mobobj, id = TRUE, worth = TRUE, names = TRUE, abbreviate = TRUE, index = TRUE, ref = TRUE, col = "black", linecol = "lightgray", cex = 0.5, pch = 19, xscale = NULL, yscale = NULL, ylines = 1.5) { ## node ids node <- nodeids(mobobj, terminal = FALSE) ## get all coefficients cf <- partykit:::apply_to_models(mobobj, node, FUN = function(z) if(worth) worth(z) else coef(z, all = FALSE, ref = TRUE)) cf <- do.call("rbind", cf) rownames(cf) <- node ## get one full model mod <- partykit:::apply_to_models(mobobj, node = 1L, FUN = NULL) if(!worth) { if(is.character(ref) | is.numeric(ref)) { reflab <- ref ref <- TRUE } else { reflab <- mod$ref } if(is.character(reflab)) reflab <- match(reflab, mod$labels) cf <- cf - cf[,reflab] } ## reference if(worth) { cf_ref <- 1/ncol(cf) } else { cf_ref <- 0 } ## labeling if(is.character(names)) { colnames(cf) <- names names <- TRUE } ## abbreviation if(is.logical(abbreviate)) { nlab <- max(nchar(colnames(cf))) abbreviate <- if(abbreviate) as.numeric(cut(nlab, c(-Inf, 1.5, 4.5, 7.5, Inf))) else nlab } colnames(cf) <- abbreviate(colnames(cf), abbreviate) if(index) { x <- 1:NCOL(cf) if(is.null(xscale)) xscale <- range(x) + c(-0.1, 0.1) * diff(range(x)) } else { x <- rep(0, length(cf)) if(is.null(xscale)) xscale <- c(-1, 1) } if(is.null(yscale)) yscale <- range(cf) + c(-0.1, 0.1) * diff(range(cf)) ## panel function for bt plots in nodes rval <- function(node) { ## node index id <- id_node(node) ## dependent variable setup cfi <- cf[id,] ## viewport setup top_vp <- viewport(layout = grid.layout(nrow = 2, ncol = 3, widths = unit(c(ylines, 1, 1), c("lines", "null", "lines")), heights = unit(c(1, 1), c("lines", "null"))), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_btplot", id, sep = "")) pushViewport(top_vp) grid.rect(gp = gpar(fill = "white", col = 0)) ## main title top <- viewport(layout.pos.col = 2, layout.pos.row = 1) pushViewport(top) mainlab <- paste(ifelse(id, paste("Node", id, "(n = "), ""), info_node(node)$nobs, ifelse(id, ")", ""), sep = "") grid.text(mainlab) popViewport() ## actual plot plot_vpi <- viewport(layout.pos.col = 2, layout.pos.row = 2, xscale = xscale, yscale = yscale, name = paste("node_btplot", id, "plot", sep = "")) pushViewport(plot_vpi) grid.lines(xscale, c(cf_ref, cf_ref), gp = gpar(col = linecol), default.units = "native") if(index) { grid.lines(x, cfi, gp = gpar(col = col, lty = 2), default.units = "native") grid.points(x, cfi, gp = gpar(col = col, cex = cex), pch = pch, default.units = "native") grid.xaxis(at = x, label = if(names) names(cfi) else x) } else { if(names) grid.text(names(cfi), x = x, y = cfi, default.units = "native") else grid.points(x, cfi, gp = gpar(col = col, cex = cex), pch = pch, default.units = "native") } grid.yaxis(at = c(ceiling(yscale[1] * 100)/100, floor(yscale[2] * 100)/100)) grid.rect(gp = gpar(fill = "transparent")) upViewport(2) } return(rval) } class(node_btplot) <- "grapcon_generator" plot(bt2, drop = TRUE, tnex = 2, terminal_panel = node_btplot(bt2, abbreviate = 1, yscale = c(0, 0.5))) @ \caption{\label{fig:topmodel-plot3} Bradley-Terry-based tree for the topmodel attractiveness data with visualizations of the worth parameters in the terminal nodes.} \end{figure} Finally, to illustrate how different predictions can be easily computed, we set up a small data set with three new individuals: % <>= tm <- data.frame(age = c(60, 25, 35), gender = c("male", "female", "female"), q1 = "no", q2 = c("no", "no", "yes"), q3 = "no") tm @ % For these we can easily compute (1)~the predicted node ID, (2)~the corresponding worth parameters, (3)~the associated ranks. <>= tm predict(bt2, tm, type = "node") predict(bt2, tm, type = function(object) t(worth(object))) predict(bt2, tm, type = function(object) t(rank(-worth(object)))) @ This completes the tour of fitting, printing, plotting, and predicting the Bradley-Terry tree model. Convenience interfaces that employ code like shown above can be easily defined and collected in new packages such as \pkg{psychotree}. \section{Conclusion} \label{sec:conclusion} The function \code{mob()} in the \pkg{partykit} package provides a new flexible and object-oriented implementation of the general algorithm for model-based recursive partitioning using \pkg{partykit}'s recursive partytioning infrastructure. New model fitting functions can be easily provided, especially if standard extractor functions (such as \code{coef()}, \code{estfun()}, \code{logLik()}, etc.) are available. The resulting model trees can then learned, visualized, investigated, and employed for predictions. To gain some efficiency in the computations and to allow for further customization (in particular specialized visualization and prediction methods), convenience interfaces \code{lmtree()} and \code{glmtree()} are provided for recursive partitioning based on (generalized) linear models. \bibliography{party} \end{document} partykit/vignettes/party.bib0000644000176200001440000006537114172230001015750 0ustar liggesusers @article{Kass:1980, author = {Gordon V. Kass}, title = {An Exploratory Technique for Investigating Large Quantities of Categorical Data}, journal = {Applied Statistics}, year = {1980}, volume = 29, number = 2, pages = {119--127}, } @Book{Quinlan:1993, author = {John R. 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Witten and Eibe Frank}, year = {2005}, edition = {2nd}, publisher = {Morgan Kaufmann}, address = {San Francisco}, } @Article{Theussl+Zeileis:2009, author = {Stefan Theu{\ss}l and Achim Zeileis}, title = {Collaborative Software Development Using \proglang{R}-{F}orge}, journal = {The \proglang{R} Journal}, year = {2009}, volume = {1}, number = {1}, pages = {9--14}, month = {May}, url = {http://journal.R-project.org/} } @Manual{R, title = {\proglang{R}: {A} Language and Environment for Statistical Computing}, author = {{\proglang{R} Core Team}}, organization = {\proglang{R} Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2013}, url = {http://www.R-project.org/} } @Manual{mvtnorm, title = {\pkg{mvtnorm}: Multivariate Normal and $t$~Distributions}, author = {Alan Genz and Frank Bretz and Tetsuhisa Miwa and Xuefei Mi and Friedrich Leisch and Fabian Scheipl and Torsten Hothorn}, year = {2015}, note = {\proglang{R}~package version~1.0-3}, url = {http://CRAN.R-project.org/package=mvtnorm}, } @Manual{partykit, title = {\pkg{partykit}: A Toolkit for Recursive Partytioning}, author = {Torsten Hothorn and Achim Zeileis}, year = {2015}, note = {\proglang{R} package version 1.0-3}, url = {http://CRAN.R-project.org/package=partykit} } @Manual{party, title = {\pkg{party}: A Laboratory for Recursive Partytioning}, author = {Torsten Hothorn and Kurt Hornik and Carolin Strobl and Achim Zeileis}, year = {2015}, note = {\proglang{R} package version 1.0-23}, url = {http://CRAN.R-project.org/package=party} } @Manual{psychotree, title = {\pkg{psychotree}: Recursive Partitioning Based on Psychometric Models}, author = {Achim Zeileis and Carolin Strobl and Florian Wickelmaier and Basil {Abou El-Komboz} and Julia Kopf}, year = {2014}, note = {\proglang{R}~package version~0.14-0}, url = {http://CRAN.R-project.org/package=psychotree} } @Manual{C50, title = {\pkg{C50}: {C5.0} Decision Trees and Rule-Based Models}, author = {Max Kuhn and Steve Weston and Nathan Coulter and John R. Quinlan}, year = {2014}, note = {\proglang{R} package version 0.1.0-19}, url = {http://CRAN.R-project.org/package=C50} } @Manual{mvpart, title = {\pkg{mvpart}: Multivariate Partitioning}, author = {Glenn De'ath}, year = {2014}, note = {\proglang{R} package version 1.6-2}, url = {http://CRAN.R-project.org/package=mvpart} } @Manual{survival, title = {\pkg{survival}: A Package for Survival Analysis in \proglang{S}}, author = {Terry M. Therneau}, year = {2015}, note = {\proglang{R} package version 2.38-3}, url = {http://CRAN.R-project.org/package=survival}, } @TechReport{rpart, author = {Terry M. Therneau and Elizabeth J. Atkinson}, title = {An Introduction to Recursive Partitioning Using the \pkg{rpart} Routine}, year = {1997}, type = {Technical Report}, number = {61}, institution = {Section of Biostatistics, Mayo Clinic, Rochester}, url = {http://www.mayo.edu/hsr/techrpt/61.pdf} } @Article{evtree, author = {Thomas Grubinger and Achim Zeileis and Karl-Peter Pfeiffer}, title = {\pkg{evtree}: Evolutionary Learning of Globally Optimal Classification and Regression Trees in \proglang{R}}, journal = {Journal of Statistical Software}, year = {2014}, volume = {61}, number = {1}, month = {1--29}, doi = {10.18637/jss.v061.i01} } @Article{RWeka, author = {Kurt Hornik and Christian Buchta and Achim Zeileis}, title = {Open-Source Machine Learning: \proglang{R} Meets \pkg{Weka}}, journal = {Computational Statistics}, year = {2009}, volume = {24}, number = {2}, pages = {225--232}, } @Article{Formula, author = {Achim Zeileis and Yves Croissant}, title = {Extended Model Formulas in \proglang{R}: Multiple Parts and Multiple Responses}, journal = {Journal of Statistical Software}, year = {2010}, volume = {34}, number = {1}, pages = {1--13}, doi = {10.18637/jss.v034.i01} } @Article{sandwich, author = {Achim Zeileis}, title = {Object-Oriented Computation of Sandwich Estimators}, year = {2006}, journal = {Journal of Statistical Software}, volume = {16}, number = {9}, pages = {1--16}, doi = {10.18637/jss.v016.i09} } @Article{strucchange, author = {Achim Zeileis and Friedrich Leisch and Kurt Hornik and Christian Kleiber}, title = {\pkg{strucchange}: {A}n \proglang{R} Package for Testing for Structural Change in Linear Regression Models}, journal = {Journal of Statistical Software}, year = {2002}, volume = {7}, number = {2}, pages = {1--38}, doi = {10.18637/jss.v007.i02} } @Article{vcd, author = {David Meyer and Achim Zeileis and Kurt Hornik}, title = {The Strucplot Framework: Visualizing Multi-Way Contingency Tables with \pkg{vcd}}, journal = {Journal of Statistical Software}, year = {2006}, volume = {17}, number = {3}, pages = {1--48}, doi = {10.18637/jss.v017.i03} } @Book{AER, title = {Applied Econometrics with \proglang{R}}, author = {Christian Kleiber and Achim Zeileis}, year = {2008}, publisher = {Springer-Verlag}, address = {New York}, url = {http://CRAN.R-project.org/package=AER} } @Manual{modeltools, title = {\pkg{modeltools}: Tools and Classes for Statistical Models}, author = {Torsten Hothorn and Friedrich Leisch and Achim Zeileis}, year = {2013}, note = {\proglang{R} package version 0.2-21}, url = {http://CRAN.R-project.org/package=modeltools} } @Manual{mlbench, title = {\pkg{mlbench}: Machine Learning Benchmark Problems}, author = {Friedrich Leisch and Evgenia Dimitriadou}, year = {2012}, note = {\proglang{R} package version 2.1-1}, url = {http://CRAN.R-project.org/package=mlbench} } @Manual{pmml, title = {\pkg{pmml}: Generate PMML for Various Models}, author = {Graham Williams and Tridivesh Jena and Michael Hahsler and {Zementis Inc.} and Hemant Ishwaran and Udaya B. Kogalur and Rajarshi Guha}, year = {2014}, note = {\proglang{R} package version 1.4.2}, url = {http://CRAN.R-project.org/package=pmml}, } @Book{rattle, title = {Data Mining with \pkg{rattle} and \proglang{R}: The Art of Excavating Data for Knowledge Discovery}, author = {Graham Williams}, year = {2011}, publisher = {Springer-Verlag}, address = {New York}, url = {http://CRAN.R-project.org/package=rattle}, } @Misc{mlbench2, author = {K. Bache and M. Lichman}, year = {2013}, title = {{UCI} Machine Learning Repository}, url = {http://archive.ics.uci.edu/ml/}, institution = {University of California, Irvine, School of Information and Computer Sciences} } @Misc{ctv, author = {Torsten Hothorn}, title = {{CRAN} Task View: Machine Learning \& Statistical Learning}, year = {2014}, note = {Version~2014-08-30}, url = {https://CRAN.R-project.org/view=MachineLearning}, } @Misc{DMG:2014, author = {{Data Mining Group}}, title = {Predictive Model Markup Language}, year = {2014}, note = {Version~4.2}, url = {http://www.dmg.org/} } @Article{Friendly+Symanzik+Onder:2019, author = {Michael Friendly and J\"urgen Symanzik and Ortac Onder}, title = {Visualising the {T}itanic Disaster}, journal = {Significance}, year = {2019}, volume = {16}, number = {1}, pages = {14--19}, doi = {10.1111/j.1740-9713.2019.01229.x} } @Misc{Lumley:2020, author = {Thomas Lumley}, title = {Weights in Statistics}, year = {2020}, note = {Biased and Inefficient -- Blog post on 2020-08-04}, url = {https://notstatschat.rbind.io/2020/08/04/weights-in-statistics/} } partykit/data/0000755000176200001440000000000014172230001013020 5ustar liggesuserspartykit/data/WeatherPlay.rda0000644000176200001440000000054114172230001015735 0ustar liggesusers‹SQnƒ0 ¶–ªÕ¤Ý£;; µå7¢AER…Њ¿­gÚÊØТ )Ø~~±N>Ã't!”Ð¥A¨©]‹ê—¡×\¯ÅŽ3uàÒKYEˆù®![Û¥¶+ ív öíåÌxƒ/)?ñ´ÐÞ°Ô.Ê<¯ ˜‰—+&%Kšä Ž¥¬À2÷â1‹”ڻ䕻qIó¸_ìµ³þ,àð<ˆ°>àÁud±äýè»…>°!îÃú—aÿÝHߘ‡õPÇûŽ©$ýã˜Âh7^Z“n¢ ÞŽ9fiÁ!°”,yG4‘øtôw)SmŸI4þbV¼—æâ?2†&gÇ cø*J• ñ áBñìÈ%S¥ÄožÊ,Ù' /§}Nò=Ö±ýQ}æRœ×Ø«™m¬®ëŸ ÉΞ)¶Ž¥ÞÒÉ&·_Êʪpartykit/data/HuntingSpiders.rda0000644000176200001440000000111514172230001016454 0ustar liggesusers‹¥VM›0œ@¤VU{íoàÐßÐCÏíe¯a³HEê©?¶¿£©éú-—mˆjÉx«†¾€¢5öè§Šï5Y×–õÌ¢.Ov¦h‡ªzq:TMfªC Eo›<ë ûòS5m–õöÜÔýÌÂäy1S<šƒQo }1ÂoâÎÔGÈç¦ë Û⺿”'¼ÐO…=taÌòÊtˆ”û£éMöh]8óÔ6— as®~¸Çõzýé–_ãü »m= partykit/src/0000755000176200001440000000000014723350653012720 5ustar liggesuserspartykit/src/rfweights.c0000644000176200001440000000620414657366332015077 0ustar liggesusers #include "rfweights.h" SEXP R_rfweights (SEXP fdata, SEXP fnewdata, SEXP weights, SEXP scale) { SEXP ans; double *dans; int *id, *ind, *iweights, *tnsize; int Ntree = LENGTH(fdata), Ndata, Nnewdata; int OOB = LENGTH(fnewdata) == 0; if (TYPEOF(fdata) != VECSXP) error("fdata is not a list"); if (LENGTH(fdata) == 0) return(R_NilValue); if (TYPEOF(weights) != VECSXP) error("weights is not a list"); if (TYPEOF(scale) != LGLSXP || LENGTH(scale) != 1) error("scale is not a scalar logical"); if (LENGTH(weights) == 0) return(R_NilValue); Ndata = LENGTH(VECTOR_ELT(fdata, 0)); if (OOB) { Nnewdata = Ndata; fnewdata = fdata; } else { if (LENGTH(fnewdata) == 0) return(R_NilValue); if (TYPEOF(fnewdata) != VECSXP) error("fnewdata is not a list"); Nnewdata = LENGTH(VECTOR_ELT(fnewdata, 0)); } PROTECT(ans = allocMatrix(REALSXP, Ndata, Nnewdata)); dans = REAL(ans); for (int i = 0; i < Ndata * Nnewdata; i++) dans[i] = 0.0; /* sum of weights for each terminal node id because trees can be very large (terminal node size = 1) we only once allocate Ndata integers */ tnsize = R_Calloc(Ndata, int); for (int i = 0; i < Ndata; i++) tnsize[i] = 1; for (int b = 0; b < Ntree; b++) { if (TYPEOF(VECTOR_ELT(weights, b)) != INTSXP) error("some elements of weights are not integer"); if (LENGTH(VECTOR_ELT(weights, b)) != Ndata) error("some elements of weights have incorrect length"); if (TYPEOF(VECTOR_ELT(fnewdata, b)) != INTSXP) error("some elements of fnewdata are not integer"); if (LENGTH(VECTOR_ELT(fnewdata, b)) != Nnewdata) error("some elements of fnewdata have incorrect length"); if (TYPEOF(VECTOR_ELT(fdata, b)) != INTSXP) error("some elements of fdata are not integer"); if (LENGTH(VECTOR_ELT(fdata, b)) != Ndata) error("some elements of fdata have incorrect length"); iweights = INTEGER(VECTOR_ELT(weights, b)); ind = INTEGER(VECTOR_ELT(fnewdata, b)); id = INTEGER(VECTOR_ELT(fdata, b)); if (LOGICAL(scale)[0]) { /* reset to zero */ for (int i = 0; i < Ndata; i++) tnsize[i] = 0; /* sum of weights in each terminal node id */ for (int i = 0; i < Ndata; i++) tnsize[id[i] - 1] += iweights[i]; } /* else: tnsize == 1 */ for (int j = 0; j < Nnewdata; j++) { if (OOB & (iweights[j] > 0)) continue; for (int i = 0; i < Ndata; i++) { /* checking tnsize[id[i] - 1] > 0 is a precaution because partykit::cforest prunes-off empty terminal nodes in honest trees */ if (id[i] == ind[j] && tnsize[id[i] - 1] > 0) dans[j * Ndata + i] += (double) iweights[i] / tnsize[id[i] - 1]; } } } R_Free(tnsize); UNPROTECT(1); return(ans); } partykit/src/partykit-init.c0000644000176200001440000000103214172227777015700 0ustar liggesusers #include #include #include "rfweights.h" #define CALLDEF(name, n) {#name, (DL_FUNC) &name, n} #define REGCALL(name) R_RegisterCCallable("partykit", #name, (DL_FUNC) &name) static const R_CallMethodDef callMethods[] = { CALLDEF(R_rfweights, 4), {NULL, NULL, 0} }; void attribute_visible R_init_partykit ( DllInfo *dll ) { R_registerRoutines(dll, NULL, callMethods, NULL, NULL); R_useDynamicSymbols(dll, FALSE); R_forceSymbols(dll, TRUE); REGCALL(R_rfweights); } partykit/src/rfweights.h0000644000176200001440000000021014172227777015074 0ustar liggesusers #include #include #include SEXP R_rfweights (SEXP fdata, SEXP fnewdata, SEXP weights, SEXP scale); partykit/src/partykit-win.def0000644000176200001440000000006014172227777016046 0ustar liggesusers LIBRARY partykit.dll EXPORTS R_init_partykit partykit/NAMESPACE0000644000176200001440000001170014402335717013345 0ustar liggesusers useDynLib(partykit, .registration = TRUE) import("stats") import("graphics") import("grid") import("Formula") import("libcoin") import("inum") import("mvtnorm") importFrom("survival", "survfit" ) importFrom("rpart", "prune" ) importFrom("grDevices", "gray.colors" ) importFrom("utils", "capture.output", "head", "tail", "setTxtProgressBar", "txtProgressBar" ) export( ## core infrastructure "party", "partynode", "partysplit", ## internal tree growing infrastructure "extree_data", "extree_fit", ## new ctree implementation "ctree", "ctree_control", "sctest.constparty", "varimp.constparty", ## new mob implementation "mob", "mob_control", "refit.modelparty", ## mobsters "lmtree", "glmtree", ## new cforest implementation "cforest", "predict.cforest", "varimp", "gettree", "varimp.cforest", "gettree.cforest", ## as/is class generics "as.party", "as.partynode", "as.constparty", "as.simpleparty", "is.constparty", "is.partynode", "is.simpleparty", ## new generics "is.terminal", "nodeapply", "nodeids", "width", "nodeprune", ## exported methods (to facilitate re-use) "plot.party", "predict.party", "print.party", "plot.modelparty", "predict.modelparty", "print.modelparty", "sctest.modelparty", "prune.modelparty", "prune.lmtree", "nodeprune.party", ## workhorse infrastructure "breaks_split", "character_split", "formatinfo_node", "data_party", "data_party.default", "edge_simple", "fitted_node", "id_node", "index_split", "info_node", "info_split", "kidids_node", "kidids_split", "kids_node", "predict_party", "predict_party.default", "prob_split", "right_split", "split_node", "surrogates_node", "varid_split", ## visualization tools "node_barplot", "node_bivplot", "node_boxplot", "node_surv", "node_ecdf", "node_mvar", "node_inner", "node_party", "node_terminal", ## coercion methods for (non-imported) external classes "as.party.Weka_tree", "as.party.rpart", "as.party.XMLNode", "as.simpleparty.XMLNode", ## misc infrastructure "pmmlTreeModel", "get_paths", "model_frame_rpart" ) ## methods for class party S3method("[", "party") S3method("[[", "party") S3method("as.simpleparty", "party") S3method("depth", "party") S3method("formula", "party") S3method("getCall", "party") S3method("getCall", "constparties") S3method("length", "party") S3method("model.frame", "party") S3method("names", "party") S3method("names<-", "party") S3method("nodeapply", "party") S3method("nodeids", "party") S3method("predict", "party") S3method("width", "party") S3method("nodeprune", "party") S3method("nodeprune", "partynode") S3method("nodeprune", "default") S3method("print", "party") S3method("plot", "party") S3method("data_party", "default") S3method("predict_party", "default") S3method("[[", "extree_data") S3method("model.frame", "extree_data") ## methods for class partynode S3method("[", "partynode") S3method("[[", "partynode") S3method("as.list", "partynode") S3method("as.partynode", "partynode") S3method("depth", "partynode") S3method("is.terminal", "partynode") S3method("length", "partynode") S3method("nodeapply", "partynode") S3method("nodeids", "partynode") S3method("print", "partynode") S3method("width", "partynode") ## methods for class constparty S3method("as.simpleparty", "constparty") S3method("plot", "constparty") S3method("predict_party", "constparty") S3method("print", "constparty") S3method("varimp", "constparty") ## methods for class simpleparty S3method("as.simpleparty", "simpleparty") S3method("plot", "simpleparty") S3method("predict_party", "simpleparty") S3method("print", "simpleparty") ## methods for class modelparty S3method("coef", "modelparty") S3method("deviance", "modelparty") S3method("fitted", "modelparty") S3method("formula", "modelparty") S3method("getCall", "modelparty") S3method("logLik", "modelparty") S3method("model.frame", "modelparty") S3method("nobs", "modelparty") S3method("residuals", "modelparty") S3method("summary", "modelparty") S3method("weights", "modelparty") S3method("predict", "modelparty") S3method("print", "modelparty") S3method("plot", "modelparty") S3method("prune", "modelparty") ## methods for class lmtree S3method("plot", "lmtree") S3method("predict", "lmtree") S3method("print", "lmtree") S3method("prune", "lmtree") ## methods for class glmtree S3method("plot", "glmtree") S3method("predict", "glmtree") S3method("print", "glmtree") ## methods for class cforest S3method("predict", "cforest") S3method("varimp", "cforest") S3method("gettree", "cforest") S3method("model.frame", "cforest") ## misc methods S3method("as.partynode", "list") S3method("as.party", "Weka_tree") S3method("as.party", "XMLNode") S3method("as.simpleparty", "XMLNode") S3method("as.party", "rpart") ## conditional registration of strucchange methods if(getRversion() >= "3.6.0") { S3method(strucchange::sctest, "constparty") S3method(strucchange::sctest, "modelparty") } partykit/inst/0000755000176200001440000000000014723350653013106 5ustar liggesuserspartykit/inst/ULGcourse-2020/0000755000176200001440000000000014172227777015347 5ustar liggesuserspartykit/inst/ULGcourse-2020/code_tree.R0000644000176200001440000001137714172227777017434 0ustar liggesusers## ---- Data ------------------------------------------------------------------- ## Titanic survival data from base R data("Titanic", package = "datasets") ## turn four-way contingency table into long data frame ttnc <- as.data.frame(Titanic) ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] names(ttnc)[2] <- "Gender" ## wage determinants data from "Applied Econometrics with R" data("CPS1985", package = "AER") ## ---- Motivational tree examples --------------------------------------------- ## Titanic survival: CTree library("partykit") ct_ttnc <- ctree(Survived ~ Gender + Age + Class, data = ttnc, alpha = 0.01) plot(ct_ttnc) ## Wage determinants: CTree ct_cps <- ctree(log(wage) ~ education + experience + age + ethnicity + gender + union, data = CPS1985, alpha = 0.01) plot(ct_cps) ## Wage determinants: MOB (based on lm) mob_cps <- lmtree(log(wage) ~ education | experience + age + ethnicity + gender + union, data = CPS1985) plot(mob_cps) ## ---- Determine first split using classical statistical inference ------------ ## Titanic survival ## - Gender plot(Survived ~ Gender, data = ttnc) tab <- xtabs(~ Survived + Gender, data = ttnc) chisq.test(tab) ## - Age plot(Survived ~ Age, data = ttnc) tab <- xtabs(~ Survived + Age, data = ttnc) chisq.test(tab) ## - Class plot(Survived ~ Class, data = ttnc) tab <- xtabs(~ Survived + Class, data = ttnc) chisq.test(tab) ## Wage determinants ## - education plot(log(wage) ~ education, data = CPS1985) cor.test(~ log(wage) + education, data = CPS1985) ## - gender plot(log(wage) ~ gender, data = CPS1985) t.test(log(wage) ~ gender, data = CPS1985) ## ---- Conditional inference trees -------------------------------------------- ## Refit CTree from motivation section library("partykit") ct_ttnc <- ctree(Survived ~ Gender + Age + Class, data = ttnc) plot(ct_ttnc) print(ct_ttnc) ## Predictions ndm <- data.frame(Gender = "Male", Age = "Adult", Class = c("1st", "2nd", "3rd")) predict(ct_ttnc, newdata = ndm, type = "node") predict(ct_ttnc, newdata = ndm, type = "response") predict(ct_ttnc, newdata = ndm, type = "prob") ## Women and children first? ndf <- data.frame(Gender = "Female", Age = "Adult", Class = c("1st", "2nd", "3rd")) ndc <- data.frame(Gender = "Male", Age = "Child", Class = c("1st", "2nd", "3rd")) cbind( Male = predict(ct_ttnc, newdata = ndm, type = "prob")[, 2], Female = predict(ct_ttnc, newdata = ndf, type = "prob")[, 2], Child = predict(ct_ttnc, newdata = ndc, type = "prob")[, 2] ) ## Refined tree (allowing small subgroups for children) ct_ttnc2 <- ctree(Survived ~ Gender + Age + Class, data = ttnc, alpha = 0.01, minbucket = 5, minsplit = 15, maxdepth = 4) plot(ct_ttnc2) ## New predictions predict(ct_ttnc2, newdata = ndc, type = "prob") ## Fitted class labels and nodes from the tree ttnc$Fit <- predict(ct_ttnc2, type = "response") ttnc$Group <- factor(predict(ct_ttnc2, type = "node")) ## Confusion matrix xtabs(~ Fit + Survived, data = ttnc) ## Group-specific survival proportions tab <- xtabs(~ Group + Survived, data = ttnc) prop.table(tab, 1) ## ROC analysis ## - Set up predictions library("ROCR") pred <- prediction(predict(ct_ttnc, type = "prob")[, 2], ttnc$Survived) ## - Accurcacies plot(performance(pred, "acc")) ## - ROC curve plot(performance(pred, "tpr", "fpr")) abline(0, 1, lty = 2) ## ---- Recursive partitioning ------------------------------------------------- ## Fit RPart/CART tree to Titanic survival data library("rpart") rp_ttnc <- rpart(Survived ~ Gender + Age + Class, data = ttnc) ## Display from rpart package plot(rp_ttnc) text(rp_ttnc) print(rp_ttnc) ## Leverage display from partykit package py_ttnc <- as.party(rp_ttnc) plot(py_ttnc) print(py_ttnc) ## Results from pruning and cross-validation rp_ttnc$cptable ## Prune tree (suboptimally here) prune(rp_ttnc, cp = 0.1) ## ---- Model-based recursive partitioning ------------------------------------- ## Add preferential treatment variable to data ttnc <- transform(ttnc, Treatment = factor(Gender == "Female" | Age == "Child", levels = c(FALSE, TRUE), labels = c("Male&Adult", "Female|Child") ) ) ## Fit and display model-based tree estimating heterogenous treatment effects mob_ttnc <- glmtree(Survived ~ Treatment | Class + Gender + Age, data = ttnc, family = binomial, alpha = 0.01) plot(mob_ttnc) print(mob_ttnc) ## ---- Evolutionary learning of globally optimal trees ------------------------ ## Package and random seed for reproducibility library("evtree") set.seed(1) ## Fit and display tree ev_ttnc <- evtree(Survived ~ Gender + Age + Class, data = ttnc) plot(ev_ttnc) ev_ttnc ## ---- ggplot2 visualizations ------------------------------------------------- ## Load package and set theme library("ggparty") theme_set(theme_minimal()) ## Trees from above autoplot(ct_ttnc2) autoplot(ct_cps) autoplot(py_ttnc) autoplot(ev_ttnc) partykit/inst/ULGcourse-2020/airport_20200412.jpg0000644000176200001440000022217714172227777020516 0ustar liggesusersÿØÿàJFIFÿáhExifII*12i‡BShotwell 0.28.4  ®  Ÿÿá ôhttp://ns.adobe.com/xap/1.0/ ÿÛC     ÿÛC   ÿÀŸ®"ÿÄ ÿĵ}!1AQa"q2‘¡#B±ÁRÑð$3br‚ %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyzƒ„…†‡ˆ‰Š’“”•–—˜™š¢£¤¥¦§¨©ª²³´µ¶·¸¹ºÂÃÄÅÆÇÈÉÊÒÓÔÕÖרÙÚáâãäåæçèéêñòóôõö÷øùúÿÄ ÿĵw!1AQaq"2B‘¡±Á #3RðbrÑ $4á%ñ&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz‚ƒ„…†‡ˆ‰Š’“”•–—˜™š¢£¤¥¦§¨©ª²³´µ¶·¸¹ºÂÃÄÅÆÇÈÉÊÒÓÔÕÖרÙÚâãäåæçèéêòóôõö÷øùúÿÚ 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00000 n 0000000212 00000 n 0000000292 00000 n 0000006845 00000 n trailer << /Size 10 /Info 1 0 R /Root 2 0 R >> startxref 7102 %%EOF partykit/inst/ULGcourse-2020/slides_forest.Rnw0000644000176200001440000024515214172227777020715 0ustar liggesusers\documentclass[11pt,t,usepdftitle=false,aspectratio=169]{beamer} \usetheme[nototalframenumber,license]{uibk} \title{Random Forests} \subtitle{Supervised Learning: Algorithmic Modeling} \author{Lisa Schlosser, Achim Zeileis} %% forest header image \renewcommand{\headerimage}[1]{% \IfStrEqCase{#1}{% {1}{% \gdef\myheaderimageid{#1}% \gdef\myheaderimageposition{nw}% \gdef\myheaderimage{forest.jpg}% }}[% \gdef\myheaderimageid{1}% \gdef\myheaderimageposition{nw}% \gdef\myheaderimage{forest.jpg}% ]% } \headerimage{1} %% custom subsection slides \setbeamercolor*{subsectionfade}{use={normal text},parent={normal text},fg=structure.fg!30!normal text.bg} \AtBeginSubsection[]{% \begin{frame}[c] \begin{center} \usebeamercolor[fg]{subsectionfade} \Large \insertsection \\[2ex] \usebeamercolor[fg]{structure} \huge\bfseries\insertsubsection \end{center} \end{frame} } \usepackage[utf8]{inputenc} \setbeamertemplate{caption}{\insertcaption} %% includes a replacement for \usepackage{Sweave} %\usepackage{Sweave} \usepackage{changepage} \usepackage{amsmath,tikz} \usepackage{calc} \usepackage{graphicx} \usetikzlibrary{positioning,shapes,arrows,decorations.pathreplacing,calc,automata,mindmap,trees,tikzmark,decorations.pathreplacing} \usepackage{xcolor} \usepackage{changepage} %\usepackage[cal=boondoxo]{mathalfa} %\graphicspath{{plots/}} \newcommand{\argmax}{\operatorname{argmax}\displaylimits} \newcommand{\argmin}{\operatorname{argmin}\displaylimits} %% colors \definecolor{HighlightOrange}{rgb}{0.9490196,0.5725490,0.0000000} \definecolor{HighlightBlue}{rgb}{0.4784314,0.7490196,0.9803922} \definecolor{forestred}{RGB}{206,73,81} \definecolor{treegreen}{RGB}{0,143,0} \definecolor{lightblue}{RGB}{34,151,230} \definecolor{lightorange}{RGB}{255,165,0} \SweaveOpts{engine=R, eps=FALSE, keep.source=TRUE} <>= options(prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE, width = 70) set.seed(7) invisible(.Call(grDevices:::C_palette, grDevices::hcl( h = c(0, 5, 125, 245, 195, 315, 65, 0), c = c(0, 100, 90, 85, 63, 105, 90, 0), l = c(0, 55, 75, 60, 82, 48, 80, 65) ))) library("partykit") library("Formula") library("latex2exp") library("lattice") library("MASS") library("colorspace") library("disttree") library("latex2exp") library("gamlss") library("crch") library("RainTyrol") library("ggplot2") theme_set(theme_bw(base_size = 18)) library(colorspace) ## HCL palette pal <- hcl(c(10, 128, 260, 290, 50), 100, 50) names(pal) <- c("forest", "tree", "gamlss", "gamboostLSS", "EMOS") pallight <- hcl(c(10, 128, 260, 290, 70), 100, 50, alpha = 0.25) names(pallight) <- c("forest", "tree", "gamlss", "gamboostLSS", "EMOS") transpgray <- rgb(0.190,0.190,0.190, alpha = 0.2) lightblue <- "#2297E6" lightorange <- "#FFA500" @ <>= ## Reg. Tree set.seed(7) nobs <- 200 kappa <- 12 x <- c(1:nobs)/nobs ytrue <- numeric(length = length(x)) for(i in 1:(nobs)) ytrue[i] <- if(x[i]<1/3) 0.5 else 1+(1-plogis(kappa*(2*(x[i]-0.2)-1))) y <- ytrue + rnorm(nobs,0,0.3) # more points for precise illustration of true function x100 <- c(1:(100*nobs))/(100*nobs) ytrue <- ytree <- ytree2 <- ytree3 <- ytree4 <- yforest <- numeric(length = length(x100)) for(i in 1:(nobs*100)) ytrue[i] <- if(x100[i]<1/3) 0.5 else 1+(1-plogis(kappa*(2*(x100[i]-0.2)-1))) for(i in 1:(nobs*100)) ytree[i] <- if(x100[i]<1/3) 0.5 else {if(x100[i]<2/3) 2 else 1} for(i in 1:(nobs*100)) ytree2[i] <- if(x100[i]<0.31) 0.47 else {if(x100[i]<0.69) 1.9 else 1.1} for(i in 1:(nobs*100)) ytree3[i] <- if(x100[i]<0.34) 0.52 else {if(x100[i]<0.54) 2.2 else {if(x100[i]<0.74) 1.74 else 0.9}} for(i in 1:(nobs*100)) ytree4[i] <- if(x100[i]<0.32) 0.51 else {if(x100[i]<0.63) 1.8 else 1.15} for(i in 1:(nobs*100)) yforest[i] <- if(x100[i]<=0.33) 0.52 else {if(x100[i]<=0.34) 1.5 else {if(x100[i]<=0.54) 2 else {if(x100[i]<=0.63) 1.9 else {if(x100[i]<=0.69) 1.6 else {if(x100[i]<=0.74) 1.3 else 1}}}}} @ \begin{document} \section{Random forests} \subsection{Motivation} \begin{frame}[fragile] \frametitle{Motivation} {\bf Idea:} \\ \begin{itemize} \item Combine an ensemble of trees. \item A single tree can capture non-linear and non-additive effects and select covariates and possible interactions automatically. \item Combining trees to a forest model allows for an approximation of smooth effects. \item A forest can regularize and stabilize the model. \end{itemize} %\bigskip \end{frame} \begin{frame} \frametitle{Motivation} \vspace{0.2cm} \begin{minipage}{0.4\textwidth} \only<1>{\textbf{Tree model:\\}}\only<2-12>{\textbf{Subsampling:\\}}\only<13->{\textbf{Forest model:\\}} \vspace{-0.4cm} %\vspace{-0.8cm} \begin{center} \only<1>{ %\vspace{0.2cm} \resizebox{0.63\textwidth}{!}{ \begin{tikzpicture} \node[ellipse, fill=HighlightBlue!70, align=center] (n0) at (2, 3) {}; 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%\visible<4>{ \begin{scope} \clip (-1,4.3) -- (4,4.3) -- (4,2.7) -- (-2,2.7) -- (-2,4.3) -- (0,4.3); %\clip (1,3.5) ellipse (3 and 0.8); \pgfmathsetseed{7} \foreach \p in {1,...,200} {\fill[gray] (1+3*rand,3.5+0.8*rand) circle (0.04);} \end{scope} %} %%% color points %\visible<5-6>{ %\begin{scope} %\clip (-1,4.3) -- (4,4.3) -- (4,2.7) -- (-2,2.7) -- (-2,4.3) -- (0,4.3); %\pgfmathsetseed{7} %\foreach \p in {1,...,100} {\fill[treegreen] (1+3*rand,3.5+0.8*rand) circle (0.07);} %\end{scope} %} \visible<3->{ \node[ellipse, draw=treegreen, align=center, minimum width=80pt, minimum height = 40pt, line width = 3pt] (subset1) at (0.1, 3.5) {}; } %\visible<7-8>{ %\begin{scope} %\clip (-1,4.3) -- (4,4.3) -- (4,2.7) -- (-2,2.7) -- (-2,4.3) -- (0,4.3); %\pgfmathsetseed{7} %\foreach \p in {1,...,49} {\fill[gray] (1+3*rand,3.5+0.8*rand) circle (0.04);} %\foreach \p in {50,...,150} {\fill[lightblue] (1+3*rand,3.5+0.8*rand) circle (0.07);} %\end{scope} %} \visible<5->{ \node[ellipse, draw = lightblue, align=center, minimum width=100pt, minimum height = 30pt, line width = 3pt] (subset2) at (1.2, 3.6) {}; } %\visible<9-10>{ %\begin{scope} %\clip (-1,4.3) -- (4,4.3) -- (4,2.7) -- (-2,2.7) -- (-2,4.3) -- (0,4.3); %\pgfmathsetseed{7} %\foreach \p in {1,...,99} {\fill[gray] (1+3*rand,3.5+0.8*rand) circle (0.04);} %\foreach \p in {100,...,200} {\fill[lightorange] (1+3*rand,3.5+0.8*rand) circle (0.07);} %\end{scope} %} \visible<7->{ \node[ellipse, draw = lightorange, align=center, minimum width=120pt, minimum height = 25pt, line width = 3pt] (subset3) at (1.6, 3.3) {}; } \visible<4->{ \node[ellipse, fill=treegreen, align=center] (n00) at (-1, 2) {}; \node[ellipse, fill=treegreen, align=center] (n01) at (-1.25, 1.25) {}; \draw[-, line width=1pt] (n00) -- (n01); \node[rectangle, fill=treegreen, align=center] (n02) at (-1.5, 0.5) {}; \draw[-, line width=1pt] (n01) -- (n02); \node[rectangle, fill=treegreen, align=center] (n03) at (-1, 0.5) {}; \draw[-, line width=1pt] (n01) -- (n03); \node[rectangle, fill=treegreen, align=center] (n04) at (-0.5, 0.5) {}; \draw[-, line width=1pt] (n00) -- (n04); } \visible<6->{ \node[ellipse, fill=lightblue, align=center] (n10) at (1, 2) {}; 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\draw[-, line width=1pt] (n22) -- (n23); \node[rectangle, fill=lightorange, align=center] (n24) at (3.5, 0.5) {}; \draw[-, line width=1pt] (n22) -- (n24); } \visible<10->{ \node[ellipse, draw = black, align=center, minimum width=15pt, minimum height = 15pt, line width = 2pt] (B1) at (-1.5, 0.5) {}; \node[ellipse, align=center, line width = 3pt, text=treegreen] (Y1) at (-1.5, -0.5) {\LARGE $\hat{y}_1$}; } \visible<11->{ \node[ellipse, draw = black, align=center, minimum width=15pt, minimum height = 15pt, line width = 2pt] (B2) at (1.25, 0.5) {}; \node[ellipse, align=center, line width = 3pt, text=lightblue] (Y2) at (1.25, -0.5) {\LARGE $\hat{y}_2$}; } \visible<12->{ \node[ellipse, draw = black, align=center, minimum width=15pt, minimum height = 15pt, line width = 2pt] (B2) at (3.5, 0.5) {}; \node[ellipse, align=center, line width = 3pt, text=lightorange] (Y3) at (3.5, -0.5) {\LARGE $\hat{y}_3$};(3.5, 0.5) } \end{tikzpicture} } } \end{center} \end{minipage} \hspace{0.7cm} \begin{minipage}{0.36\textwidth} %\begin{center} %\vspace{0.1cm} \only<1-2>{ %\vspace{0.01cm} <>= par(mar=c(3,3,2,0)) #par(mar=c(3,3,2,5.5)) plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19) box(lwd=5) #lines(x = x, y = ytrue, col = "gray", lwd=5, main = "") lines(x = x100, y = ytree, col = pal["forest"], lwd=7) mtext(text = "X", side = 1, cex = 2.5, line = 2) mtext(text = "Y", side = 2, cex = 2.5, line = 1) @ } \only<3>{ %\vspace{0.01cm} %\hspace{-0.1cm} <>= par(mar=c(3,3,2,0)) #par(mar=c(3,3,2,5.5)) plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19) box(lwd=5) mtext(text = "X", side = 1, cex = 2.5, line = 2) mtext(text = "Y", side = 2, cex = 2.5, line = 1) @ } \only<4-5>{ %\vspace{0.01cm} %\hspace{-0.1cm} <>= <> lines(x = x100, y = ytree2, col = pal["tree"], lwd=7) @ } \only<6-7>{ %\vspace{0.01cm} %\hspace{-0.1cm} <>= <> lines(x = x100, y = ytree3, col = lightblue, lwd=7) @ } \only<8>{ %\vspace{0.01cm} %\hspace{-0.1cm} <>= <> lines(x = x100, y = ytree4, col = lightorange, lwd=7) @ } \only<9-12>{ <>= par(mar=c(3,3,2,0)) #par(mar=c(3,3,2,5.5)) plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19) box(lwd=5) lines(x = x100, y = ytree2, col = pal["tree"], lwd=7) lines(x = x100, y = ytree3, col = lightblue, lwd=7) lines(x = x100, y = ytree4, col = lightorange, lwd=7) lines(x = c(0.6,0.6), y = c(-1, 1.8), type = "l", lty = 2, lwd = 4) mtext(text = "Y", side = 2, cex = 2.5, line = 1) mtext(text = "x", side = 1, cex = 4, line = 2, at=0.6) @ } \only<13->{ <>= par(mar=c(3,3,2,0)) plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19) box(lwd=5) lines(x = x100, y = yforest, col = pal["forest"], lwd=7) lines(x = c(0.6,0.6), y = c(-1, 1.8), type = "l", lty = 2, lwd = 4) mtext(text = "x", side = 1, cex = 4, line = 2, at=0.6) mtext(text = "Y", side = 2, cex = 2.5, line = 1) @ } \end{minipage} \vspace{0.5cm} \only<13->{ $\hat{y}= \frac{1}{3} (\hat{y}_1 + \hat{y}_2 + \hat{y}_3)$ } \vspace{0.3cm} \visible<14->{ for $\hat{y}_t$ being the average response value in the segment $\mathcal{B}^t_x$ which the observed covariate $x$ is assigned to in the $t$-th tree with learning data $\{(y_i,x_i)\}_{i=1,\ldots,n}$: \vspace{0.3cm} $\hat{y}_t= \frac{1}{|\mathcal{B}^t_x|} \sum_{i: x_i \in \mathcal{B}^t_x} y_i$ \visible<15->{ $\ =\ \sum_{i=1}^n \frac{I(x_i \in \mathcal{B}^t_x)}{|\mathcal{B}^t_x|} \cdot y_i$ } \visible<16->{ $\ =\ \sum_{i=1}^n w_i(x) \cdot y_i$ } } \end{frame} \subsection{Aggregation of trees\\ \&\\ random sampling} \begin{frame} \frametitle{Aggregation of trees} {\bf Simple tree model:} Obtain the predicted response $\hat{y}$ for an observed covariate~$x$ by averaging over observations in the terminal node~$\mathcal{B}_x$: $$ \hat{y}= \frac{1}{|\mathcal{B}_x|} \sum_{i: x_i \in \mathcal{B}_x} y_i \visible<2->{ \ =\ \sum_{i=1}^n w_i(x) \cdot y_i$$ } \visible<3->{ $$\ =\ \argmin_{\mu} \sum_{i=1}^n w_i(x) \cdot (y_i - \mu)^2$$ } \visible<4->{ {\bf Model-based tree:} Obtain the predicted model parameter(s) $\hat{\theta}$ for an observed covariate~$x$ by optimizing a loss function for all observations in the terminal node~$\mathcal{B}_x$: $$ \hat{\theta}= \argmin_{\theta} \sum_{i: x_i \in \mathcal{B}_x} loss(\theta; y_i) \ =\ \argmin_{\theta} \sum_{i=1}^n w_i(x) \cdot loss(\theta; y_i)$$ } % {\bf Note:} The model-based approach allows for fitting complex models but also includes the specific case of averaging over all observations which corresponds to minimizing the residual sum of squares $\sum (y_i - \theta)^2$. \end{frame} \begin{frame} \frametitle{Aggregation of trees} {\bf Strategy:} Combine T trees to a forest model by employing tree-based weights. The predicted model parameter (vector) $\hat{\theta}$ is the argument %of the parameter space $\Theta$ that minimizes the weighted sum of a loss function evaluated for learning data $\{(y_i,x_i)\}_{i=1,\ldots,n}$: \vspace{-0.2cm} \[ \hat{\theta}(x) = \argmin_{\theta} \sum_{i=1}^n w_i(x) \cdot loss(\theta; y_i) \] \medskip \only<2-4>{ \vspace{0.13cm} \textbf{Weights:} \vspace{-1.14cm} \begin{eqnarray*} w^{\text{base}}_i(x) & = & 1 \\[0.2cm] \visible<3-4>{ w^{\text{tree}}_i(x) & = & \frac{I(x_i \in \mathcal{B}_x)}{\left|\mathcal{B}_x\right|} \\[0.1cm] \visible<4>{ w^{\text{forest}}_i(x) & = & \frac{1}{T} \sum_{t=1}^T \frac{I(x_i \in \mathcal{B}^t_x)}{\left|\mathcal{B}^t_x\right|} \end{eqnarray*} }}} \end{frame} \begin{frame} \frametitle{Random sampling} {\bf Idea:} Build each tree on a different subset of the full data set. \medskip {\bf Sampling observations:} \begin{itemize} \item Bootstrapping: resampling with replacement, usually ``n out of n''. \item Subsampling: draw a subset without replacement (typically of the size of 63.2\% of the full data set; for large data sets a smaller fraction can be advantageous). \end{itemize} \bigskip {\bf Sampling covariates:}\\ \smallskip In order to reduce the correlation among trees random input variable sampling is employed, i.e., for each split only a subset of covariates is selected randomly and provided as possible split variables (typical sampling size: $\sqrt{\text{\#Var}}$). \end{frame} \begin{frame} \frametitle{Hyperparameter selection} Apart from the size and type of sampling two further control parameters have to be set for a forest model: \begin{itemize} \item {\bf Number of trees:} A high number of trees allows for a more stable model and for a better approximation of smooth effects, however, at the cost of higher computational effort. \item {\bf Size of the trees:} The size of each single tree can be controlled by setting stopping criteria such as a minimal number of observations in a node, maximum tree depth or a significance level if a statistical test is employed in the tree algorithm. However, in a forest model each tree is usually built as large as possible which can lead to overfitting for a single tree, but this is compensated by aggregating the trees to a forest model. \end{itemize} \end{frame} <>= data("CPS1985", package = "AER") @ \begin{frame}[fragile] \frametitle{Example: wages} \textbf{Data:} Random sample from the May 1985 US Current Population Survey. A data frame containing \Sexpr{nrow(CPS1985)} observations on \Sexpr{ncol(CPS1985)} variables. \bigskip \begin{tabular}{ll} \hline Variable & Description\\ \hline \code{wage} & Wage (in US dollars per hour). \\ \code{education} & Education (in years). \\ \code{experience} & Potential work experience (in years, \code{age - education - 6}). \\ \code{age} & Age (in years). \\ \code{ethnicity} & Factor: Caucasian, Hispanic, Other. \\ \code{gender} & Factor: Male, Female. \\ \code{union} & Factor. Does the individual work on a union job? \\ \hline \end{tabular} \bigskip \textbf{Model formula:} \code{log(wage) ~ education + experience + age + ethnicity + gender + union}. \end{frame} <>= set.seed(4) f <- log(wage) ~ education + experience + age + ethnicity + gender + union ct_cps <- ctree(f, data = CPS1985, alpha = 0.01) cf <- cforest(f, data = CPS1985, ntree = 5) #, control =ctree_control(maxdepth = 5)) vimp <- varimp(cf , risk = "loglik") @ \begin{frame}[fragile] \frametitle{Example: wages} Single tree model: \setkeys{Gin}{width=0.99\textwidth} <>= plot(ct_cps) @ \end{frame} \begin{frame}[fragile] \frametitle{Example: wages} Forest model - tree I: \setkeys{Gin}{width=0.99\textwidth} <>= #par(mfrow=c(2,2)) plot(party(cf[[1]][[1]], data = CPS1985[,c("wage", "education", "experience", "age", "ethnicity", "gender", "union")]), drop_terminal = TRUE) @ \end{frame} \begin{frame}[fragile] \frametitle{Example: wages} Forest model - tree II: \setkeys{Gin}{width=0.99\textwidth} <>= #par(mfrow=c(2,2)) plot(party(cf[[1]][[2]], data = CPS1985[,c("wage", "education", "experience", "age", "ethnicity", "gender", "union")]), drop_terminal = TRUE) @ \end{frame} \begin{frame}[fragile] \frametitle{Example: wages} Forest model - tree III: \setkeys{Gin}{width=0.99\textwidth} <>= #par(mfrow=c(2,2)) plot(party(cf[[1]][[3]], data = CPS1985[,c("wage", "education", "experience", "age", "ethnicity", "gender", "union")]), drop_terminal = TRUE) @ \end{frame} \begin{frame}[fragile] \frametitle{Example: wages} Forest model - tree IV: \setkeys{Gin}{width=0.99\textwidth} <>= #par(mfrow=c(2,2)) plot(party(cf[[1]][[4]], data = CPS1985[,c("wage", "education", "experience", "age", "ethnicity", "gender", "union")]), drop_terminal = TRUE) @ \end{frame} \begin{frame}[fragile] \frametitle{Example: wages} \vspace{-0.5cm} \setkeys{Gin}{width=0.94\textwidth} <>= nd <- data.frame(education = 13.02, #c(2:18), experience = 17.82, age = c((18:64)/1), #36.83, ethnicity = "cauc", region = "other", gender = "male", occupation = "worker", sector = "other", union = "no", married = "yes") { par(mfrow = c(2,2)) set.seed(74) cf <- cforest(f, data = CPS1985, ntree = 2) predwage <- cbind(c((18:64)/1), predict(cf, newdata = nd)) colnames(predwage) <- c("age", "predicted log(wage)") plot(x = predwage[,"age"], y = exp(predwage[,"predicted log(wage)"]), type = 'l', ylab = "predicted wage", xlab = "age", main = "Forest with 2 trees") cf <- cforest(f, data = CPS1985, ntree = 4) predwage <- cbind(c((18:64)/1), predict(cf, newdata = nd)) colnames(predwage) <- c("age", "predicted log(wage)") plot(x = predwage[,"age"], y = exp(predwage[,"predicted log(wage)"]), type = 'l', ylab = "predicted wage", xlab = "age", main = "Forest with 4 trees") lines(x = predwage[,"age"], y = exp(predwage[,"predicted log(wage)"]), type = 'l', col = "gray") cf <- cforest(f, data = CPS1985, ntree = 20) predwage <- cbind(c((18:64)/1), predict(cf, newdata = nd)) colnames(predwage) <- c("age", "predicted log(wage)") plot(x = predwage[,"age"], y = exp(predwage[,"predicted log(wage)"]), type = 'l', ylab = "predicted wage", xlab = "age", main = "Forest with 20 trees") cf <- cforest(f, data = CPS1985, ntree = 200) predwage <- cbind(c((18:64)/1), predict(cf, newdata = nd)) colnames(predwage) <- c("age", "predicted log(wage)") plot(x = predwage[,"age"], y = exp(predwage[,"predicted log(wage)"]), type = 'l', ylab = "predicted wage", xlab = "age", main = "Forest with 200 trees") } @ \end{frame} \begin{frame} \frametitle{Variable importance} {\bf Problem:} In a single tree model the effect of each covariate can easily be investigated based on a simple illustration of the tree structure. However, in a forest model this would require to investigate each tree on its own including its specific setting (induced by random sampling). \bigskip {\bf Idea:} Asses the influence of a covariate on the forest model by \begin{itemize} \item permuting the selected covariate and evaluating the resulting change in performance of the model (mean decrease in accuracy, measured for example based on the employed loss function) or \item calculating the total decrease in node impurities from splitting in the selected covariate (measured for example by the Gini index for classification trees or the RMSE for regression trees), \end{itemize} averaged over all trees. \bigskip %\bigskip % {\bf Implementations:} % \begin{itemize} % \item \fct{importance} in the R package randomForest. % \item \fct{importance.ranger} in the R package ranger. % \item \fct{varimp} in the R package partykit. % \end{itemize} % \only<2->{ % \setkeys{Gin}{width=0.5\textwidth} % <>= % par(mar = c(4,5.5,0,2)) % barplot(sort(vimp, decreasing = FALSE), % horiz = TRUE, las = 1, axes = FALSE, % xlab = "Variable importance: mean decrease in log-likelihood") % axis(1, at = seq(0,1,0.02), las = 1, mgp=c(0,1,0)) % @ % Depending on the fitted model the corresponding objective function can be employed as \emph{risk function} to measure accuracy by calculating importance scores (e.g., log-likelihood, number of misclassifications, \ldots).\\ % To measure impurity, for example, the Gini index can be employed for classification trees or the RMSE for regression trees. %} \end{frame} \begin{frame} \frametitle{Example: wages} Evaluation of variable importance in the fitted forest model: \bigskip \setkeys{Gin}{width=0.57\textwidth} <>= par(mar = c(4,5.4,1,2)) barplot(sort(vimp, decreasing = FALSE), horiz = TRUE, las = 1, axes = FALSE, xlab = "Variable importance: mean decrease in log-likelihood") axis(1, at = seq(0,1,0.02), las = 1, mgp=c(0,1,0)) @ \end{frame} \subsection{Implementations} \begin{frame}[fragile] \frametitle{R software for forest models} {\bf randomForest:} \begin{itemize} \item R package for classic random forests. \item Based on implementations of CART. \item First implementation of random forests in R. \end{itemize} % \medskip % % <>= % randomForest(formula, data=NULL, ..., subset, na.action=na.fail) % randomForest(x, y=NULL, ...) % @ % % \medskip % % Optional control arguments: % \begin{itemize} % \item \code{ntree}: nr. of trees, % \item \code{mtry}: nr. of randomly sampled split variable candidates, % \item \code{replace}: type of subsetting, % \item \code{sampsize}: size of drawn subsamples, % \item \code{nodesize}: minimum size of terminal nodes, % \item \code{maxnodes}: maximum number of terminal nodes, % \item \ldots % \end{itemize} \medskip {\bf ranger}: \begin{itemize} \item RANdom forest GEneRator. \item R package providing a fast implementation of classic random forests. \end{itemize} \medskip {\bf partykit:} \begin{itemize} \item R package offering a toolkit for unbiased recursive partitioning. \item Provides the forest-building function \fct{cforest}, based on conditional inference trees (CTree). \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{R software for forest models} {\bf ranger}: <>= library("ranger") rf <- ranger(log(wage) ~ education + experience + age + ethnicity + gender + union, data = CPS1985) @ Optional control arguments: \begin{itemize} \item \code{num.trees}: number of trees, \item \code{mtry}: number of randomly sampled split variable candidates, \item \code{replace}: sample with replacement, \item \code{sample.fraction}: fraction of observations to sample, \item \code{min.node.size}: minimal size of terminal nodes, \item \code{max.depth}: maximal tree depth, \item \code{splitrule}: splitting rule, \item \ldots \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{R software for forest models} {\bf ranger}: <>= newdata <- data.frame(education = 13, experience = 17, age = 36, ethnicity = "cauc", region = "other", gender = "male", occupation = "worker", sector = "other", union = "no", married = "yes") pred_rf <- predict(rf, data = newdata) pred_rf$predictions exp(pred_rf$predictions) rf <- ranger(log(wage) ~ education + experience + age + ethnicity + gender + union, data = CPS1985, importance = "impurity") importance(rf) @ \end{frame} \begin{frame}[fragile] \frametitle{R software for forest models} {\bf partykit:} <>= library("partykit") cf <- cforest(log(wage) ~ education + experience + age + ethnicity + gender + union, data = CPS1985) @ \only<1>{ Optional forest-specific control arguments: \begin{itemize} \item \code{ytrafo}: transformation function applied to the response, \item \code{ntree}: number of trees, \item \code{mtry}: number of randomly sampled split variable candidates, \item \code{perturb}: type and size of subsetting, \item \ldots \end{itemize} %\vspace{0.9cm} } \only<2->{ Optional tree-specific arguments handed over via \fct{ctree\_control}: \begin{itemize} \item \code{minsplit}: minimum number of observations to perform a split, \item \code{minbucket}: minimum number of observations in a node after splitting, \item \code{maxdepth}: maximum depth of the tree, \item \code{alpha}: significance level for split variable selection, \item \ldots \end{itemize} } % \only<3>{ % % <>= % cf <- cforest(log(wage) ~ education + experience + age + ethnicity + gender + union, % data = CPS1985, control = ctree_control(minsplit = 20)) % @ % } \end{frame} \begin{frame}[fragile] \frametitle{R software for forest models} {\bf partykit:} <>= library("partykit") cf <- cforest(log(wage) ~ education + experience + age + ethnicity + gender + union, data = CPS1985) @ Optional tree-specific arguments handed over via \fct{ctree\_control}: \begin{itemize} \item \code{minsplit}: minimum number of observations to perform a split, \item \code{minbucket}: minimum number of observations in a node after splitting, \item \code{maxdepth}: maximum depth of the tree, \item \code{alpha}: significance level for split variable selection, \item \ldots \end{itemize} <>= cf <- cforest(log(wage) ~ education + experience + age + ethnicity + gender + union, data = CPS1985, control = ctree_control(minsplit = 20)) @ \end{frame} \begin{frame}[fragile] \frametitle{R software for forest models} {\bf partykit:} <>= newdata <- data.frame(education = 13, experience = 17, age = 36, ethnicity = "cauc", region = "other", gender = "male", occupation = "worker", sector = "other", union = "no", married = "yes") pred_cf <- predict(cf, newdata = newdata) pred_cf exp(pred_cf) varimp(cf) @ \end{frame} \begin{frame} \frametitle{R software for forest models} \textbf{Further R packages:} % \begin{itemize} \item grf: generalized random forests, \item disttree: distributional forests, based on partykit, \item circtree: circular distributional forests, based on partykit, \item model4you: model-based random forests for personalized treatment effects, \item randomSurvivalForest: random forests for the analysis of right-censored survival data, \item \ldots \end{itemize} \end{frame} \subsection{Distributional forests} \begin{frame}%[fragile] \frametitle{Motivation} \vspace{-0.41cm} \begin{figure}[!htb] \minipage{0.285\textwidth} \begin{center} <>= nobs <- 200 ## GLM set.seed(7) x <- c(1:nobs)/nobs ytrue <- 1+x*1.5 y <- ytrue + rnorm(nobs,0,0.3) @ \visible<2->{ <>= par(mar=c(2,0,2,0)) plot(y=y , x=x, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19) box(lwd=5) lines(x = x, y = ytrue, col = pal["forest"], lwd = 7, main = "") @ } \end{center} \endminipage \visible<3->{{\LARGE$\rightarrow$}} \minipage{0.285\textwidth} \begin{center} <>= ## GAM set.seed(7) x <- c(1:nobs)/nobs x <- 2*(x-0.5) ytrue <- x^3 y <- ytrue + rnorm(nobs,0,0.3) @ \visible<3->{ <>= par(mar=c(2,0,2,0)) plot(y=y , x=x, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19) box(lwd=5) lines(x = x, y = ytrue, col = pal["forest"], lwd = 7, main = "") @ } \end{center} \endminipage \visible<4->{{\LARGE$\rightarrow$}} \minipage{0.285\textwidth} \begin{center} <>= ## GAMLSS set.seed(7) x <- c(1:nobs)/nobs x <- 2*(x-0.5) ytrue <- x^3 var <- exp(-(2*x)^2)/2 y <- ytrue + rnorm(nobs, 0, 0.1 + var) @ \visible<4->{ <>= par(mar=c(2,0,2,0)) plot(x, y, xaxt = "n", yaxt = "n", ann = FALSE, type = "n") polygon(c(x, rev(x)), c(ytrue + 0.1 + var, rev(ytrue - 0.1 - var)), col = pallight["forest"], border = "transparent") lines(x, ytrue, col = pal["forest"], lwd=7) points(x, y, col = "slategray", pch = 19) box(lwd = 5) @ } \end{center} \endminipage \vspace{0.5cm} \minipage{0.25\textwidth} \begin{center} \visible<2->{ LM, GLM\\ \vspace{0.5cm} \code{lm}\\ \code{glm}\\ \vspace{1.5cm}} \end{center} \endminipage \hspace{1.1cm} \minipage{0.25\textwidth} \begin{center} \visible<3->{ GAM\\ \vspace{0.5cm} \code{mgcv}\\ \code{VGAM}\\ \vspace{1.5cm}} \end{center} \endminipage \hspace{1.1cm} \minipage{0.25\textwidth} \begin{center} \visible<4->{ GAMLSS\\ \vspace{0.5cm} \code{gamlss}\\ \code{mgcv}\\ \code{VGAM}\\ \code{gamboostLSS}\\ \code{bamlss}} \end{center} \endminipage \end{figure} \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \vspace{-0.41cm} \begin{figure}[!htb] \minipage{0.285\textwidth} \begin{center} <>= ## Reg. Tree set.seed(7) kappa <- 12 x <- c(1:nobs)/nobs ytrue <- ytree <- yforest <- numeric(length = length(x)) for(i in 1:nobs) ytrue[i] <- if(x[i]<1/3) 0.5 else 1+(1-plogis(kappa*(2*(x[i]-0.2)-1))) y <- ytrue + rnorm(nobs,0,0.3) for(i in 1:nobs) ytree[i] <- if(x[i]<1/3) 0.5 else {if(x[i]<2/3) 2 else 1} @ \visible<1->{ <>= par(mar=c(2,0,2,0)) plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19) box(lwd=5) #lines(x = x, y = ytrue, col = "gray", lwd=5, main = "") lines(x = x, y = ytree, col = pal["forest"], lwd=7) @ } \end{center} \endminipage \visible<2->{{\LARGE$\rightarrow$}} \minipage{0.285\textwidth} \begin{center} <>= ## Random Forest for(i in 1:nobs) yforest[i] <- if(x[i]<0.27) 0.5 else { if(x[i]<0.39) 0.5 + 1.5*(plogis((x[i]-0.33)/6*700)) else 1+(1-plogis(kappa*(2*(x[i]-0.2)-1)))} @ \visible<2->{ <>= par(mar=c(2,0,2,0)) plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19) box(lwd=5) #lines(x = x, y = ytrue, col = "gray", lwd=5, main = "") lines(x = x, y = yforest, col = pal["forest"], lwd=7, main = "") @ } \end{center} \endminipage \visible<3->{{\LARGE$\rightarrow$}} \minipage{0.285\textwidth} \begin{center} \visible<3->{ <>= par(mar=c(2,0,2,0)) plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, type = "n") box(lwd=5) text(x = mean(range(x)), y = mean(range(y)), "?", cex = 12) @ } \end{center} \endminipage \minipage{0.285\textwidth} \begin{center} \vspace{0.0cm} \visible<1->{ Regression tree\\ \vspace{0.3cm} \resizebox{0.2\textwidth}{!}{ \begin{tikzpicture} \node[ellipse, fill=HighlightBlue!70, align=center] (n0) at (1, 2) {}; \node[rectangle, fill=HighlightOrange!70, align=center] (n1) at (0.5, 1) {}; \draw[-, line width=1pt] (n0) -- (n1); \node[ellipse, fill=HighlightBlue!70, align=center] (n2) at (1.5, 1) {}; \draw[-, line width=1pt] (n0) -- (n2); \node[rectangle, fill=HighlightOrange!70, align=center] (n3) at (1, 0) {}; \draw[-, line width=1pt] (n2) -- (n3); \node[rectangle, fill=HighlightOrange!70, align=center] (n4) at (2, 0) {}; \draw[-, line width=1pt] (n2) -- (n4); \end{tikzpicture}} \vspace{0.2cm}\\ \code{rpart}\\ \code{party(kit)}\\ \vspace{1cm}} \end{center} \endminipage \hspace{0.65cm} \minipage{0.285\textwidth} \begin{center} \vspace{-0.4cm} \visible<2->{ Random forest\\ \vspace{0.4cm} \resizebox{0.6\textwidth}{!}{ \begin{tikzpicture} \node[ellipse, fill=HighlightBlue!70, align=center] (n00) at (1, 2) {}; \node[rectangle, fill=HighlightOrange!70, align=center] (n01) at (0.5, 1) {}; \draw[-, line width=1pt] (n00) -- (n01); \node[rectangle, fill=HighlightOrange!70, align=center] (n02) at (1.5, 1) {}; \draw[-, line width=1pt] (n00) -- (n02); \node[ellipse, fill=HighlightBlue!70, align=center] (n10) at (3, 2) {}; \node[ellipse, fill=HighlightBlue!70, align=center] (n11) at (2.5, 1) {}; \draw[-, line width=1pt] (n10) -- (n11); \node[ellipse, fill=HighlightBlue!70, align=center] (n12) at (3.5, 1) {}; \draw[-, line width=1pt] (n10) -- (n12); \node[rectangle, fill=HighlightOrange!70, align=center] (n13) at (2, 0) {}; \draw[-, line width=1pt] (n11) -- (n13); \node[rectangle, fill=HighlightOrange!70, align=center] (n14) at (2.8, 0) {}; \draw[-, line width=1pt] (n11) -- (n14); \node[rectangle, fill=HighlightOrange!70, align=center] (n15) at (3.2, 0) {}; \draw[-, line width=1pt] (n12) -- (n15); \node[rectangle, fill=HighlightOrange!70, align=center] (n16) at (4, 0) {}; \draw[-, line width=1pt] (n12) -- (n16); \node[ellipse, fill=HighlightBlue!70, align=center] (n20) at (5, 2) {}; \node[rectangle, fill=HighlightOrange!70, align=center] (n21) at (4.5, 1) {}; \draw[-, line width=1pt] (n20) -- (n21); \node[ellipse, fill=HighlightBlue!70, align=center] (n22) at (5.5, 1) {}; \draw[-, line width=1pt] (n20) -- (n22); \node[rectangle, fill=HighlightOrange!70, align=center] (n23) at (5, 0) {}; \draw[-, line width=1pt] (n22) -- (n23); \node[rectangle, fill=HighlightOrange!70, align=center] (n24) at (6, 0) {}; \draw[-, line width=1pt] (n22) -- (n24); \end{tikzpicture} } \vspace{0.3cm}\\ \code{randomForest}\\ \code{ranger}\\ \code{party(kit)}} \end{center} \endminipage \hspace{0.65cm} \minipage{0.285\textwidth} \begin{center} \vspace{0.15cm} \visible<3->{ Distributional trees and forests\\ \vspace{1.15cm} \code{disttree}\\ based on \code{partykit}\\ \vspace{1cm}} \end{center} \endminipage \end{figure} \end{frame} \begin{frame} \frametitle{Building blocks} %\vspace{0.5cm} \begin{minipage}{0.79\textwidth} \vspace{-0.5cm} \textbf{Distributional modeling:} \begin{itemize} \vspace{-0.05cm} \item Specify the complete probability distribution \\ \vspace{-0.05cm} (location, scale, shape, \dots). \end{itemize} \smallskip \textbf{Tree:} \begin{itemize} \vspace{-0.05cm} \item Capture non-linear and non-additive effects. \vspace{-0.1cm} \item Automatic selection of covariates and interactions. %detection of steps and abrupt changes. %(data driven) \end{itemize} \smallskip \textbf{Forest:} \begin{itemize} \vspace{-0.05cm} \item Smoother effects. \vspace{-0.1cm} \item Stabilization and regularization of the model. \end{itemize} \bigskip \bigskip $\Rightarrow$ \textbf{Synthesis:} Distributional Trees and Forests \end{minipage} <>= ## GAMLSS set.seed(7) nobs <- 200 x_g <- c(1:nobs)/nobs x_g <- 2*(x_g-0.5) ytrue_g <- x_g^3 var_g <- exp(-(1.74*x_g)^2)/2.5 y_g <- ytrue_g + rnorm(nobs, 0, 0.1 + var_g) @ <>= ## Reg. Tree set.seed(7) kappa <- 12 x <- c(1:nobs)/nobs ytrue <- ytree <- yforest <- var <- numeric(length = length(x)) for(i in 1:nobs) ytrue[i] <- if(x[i]<1/3) 0.5 else 1+(1-plogis(kappa*(2*(x[i]-0.2)-1))) for(i in 1:nobs) var[i] <- if(x[i]<1/3) 0.1 else 0.6 *(4/3 - x[i]) y <- ytrue + rnorm(nobs, 0, 0.1 + var) for(i in 1:nobs) ytree[i] <- if(x[i]<1/3) 0.5 else {if(x[i]<2/3) 2 else 1} @ <>= ## Random Forest for(i in 1:nobs) yforest[i] <- if(x[i]<0.27) 0.5 else { if(x[i]<0.39) 0.5 + 1.5*(plogis((x[i]-0.33)/6*700)) else 1+(1-plogis(kappa*(2*(x[i]-0.2)-1)))} @ \begin{minipage}{0.2\textwidth} \vspace{-0.05cm} <>= par(mar=c(1,0,1,0)) plot(x_g, y_g, xaxt = "n", yaxt = "n", ann = FALSE, type = "n") polygon(c(x_g, rev(x_g)), c(ytrue_g + 0.1 + var_g, rev(ytrue_g - 0.1 - var_g)), col = pallight["forest"], border = "transparent") lines(x_g, ytrue_g, col = pal["forest"], lwd=10) points(x_g, y_g, col = "slategray", pch = 19) box(lwd = 5) @ \vspace{0.15cm} <>= par(mar=c(1,0,1,0)) plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19, ylim = c(min(y), max(y))) #lines(x = x, y = ytrue, col = "gray", lwd=5, main = "") lines(x = x, y = ytree, col = pal["forest"], lwd=10) box(lwd=5) @ \vspace{0.15cm} <>= par(mar=c(1,0,1,0)) plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19, ylim = c(min(y), max(y))) #lines(x = x, y = ytrue, col = "gray", lwd=5, main = "") lines(x = x, y = yforest, col = pal["forest"], lwd=10, main = "") box(lwd=5) @ \vspace{0.15cm} <>= par(mar=c(1,0,1,0)) #plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19) #box(lwd=5) #lines(x = x, y = ytrue, col = "gray", lwd=5, main = "") #lines(x = x, y = yforest, col = pal["forest"], lwd=7, main = "") plot(x = x, y = y, xaxt="n", yaxt="n", ann=FALSE, col = "slategray", pch = 19, ylim = c(min(y), max(y))) polygon(c(x, rev(x)), c(yforest + 0.1 + var, rev(yforest - (0.1 + var))), # c(ytrue_g + 0.1 + var_g, rev(ytrue_g - 0.1 - var_g)) col = pallight["forest"], border = "transparent") box(lwd=5) lines(x = x, y = yforest, col = pal["forest"], lwd=10) @ \end{minipage} \end{frame} <>= set.seed(54) nobs <- 500 x <- runif(nobs, 0, 1) mu <- sigma <- ytrue <- numeric(length = nobs) for(i in 1:nobs) sigma[i] <- if(x[i]<=0.4) 1 else 3 for(i in 1:nobs) mu[i] <- if(x[i]<= 0.4|| x[i]>0.8) 4 else 12 y <- rnorm(nobs, mean = mu, sd = sigma) ytrue <- mu data <- data.frame(cbind(y,x, ytrue)) alldata <- cbind(data, mu, sigma) odata <- alldata[order(alldata["x"]),] @ <>= data <- data.frame(x = numeric(0), x = numeric(0), x = numeric(0)) names(data) <- c("x","x","x") fig <- party( partynode(1L, split = partysplit(2L, breaks = 0.4), kids = list( partynode(2L, info = c( "n = 200", " True parameters: ", expression(mu == '4'), expression(sigma == '1') )), partynode(3L, split = partysplit(3L, breaks = 0.8), kids = list( partynode(4L, info = c( "n = 200", " True parameters: ", expression(mu == '12'), expression(sigma == '3') )), partynode(5L, info = c( "n = 100", " True parameters: ", expression(mu == '4'), expression(sigma == '3') )))))), data ) node_inner_ext <- function (obj, id = TRUE, pval = TRUE, abbreviate = FALSE, fill = "white", gp = gpar()) { meta <- obj$data nam <- names(obj) extract_label <- function(node) { if (is.terminal(node)) return(rep.int("", 2L)) varlab <- character_split(split_node(node), meta)$name if (abbreviate > 0L) varlab <- abbreviate(varlab, as.integer(abbreviate)) if (pval) { nullna <- function(x) is.null(x) || is.na(x) pval <- suppressWarnings(try(!nullna(info_node(node)$p.value), silent = TRUE)) pval <- if (inherits(pval, "try-error")) FALSE else pval } if (pval) { pvalue <- node$info$p.value plab <- ifelse(pvalue < 10^(-3L), paste("p <", 10^(-3L)), paste("p =", round(pvalue, digits = 3L))) } else { plab <- "" } return(c(varlab, plab)) } maxstr <- function(node) { lab <- extract_label(node) klab <- if (is.terminal(node)) "" else unlist(lapply(kids_node(node), maxstr)) lab <- c(lab, klab) lab <- unlist(lapply(lab, function(x) strsplit(x, "\n"))) lab <- lab[which.max(nchar(lab))] if (length(lab) < 1L) lab <- "" return(lab) } nstr <- maxstr(node_party(obj)) if (nchar(nstr) < 6) nstr <- "aAAAAa" rval <- function(node) { node_vp <- viewport(x = unit(0.5, "npc"), y = unit(0.5, "npc"), width = unit(1, "strwidth", nstr) * 1.3, height = unit(3, "lines"), name = paste("node_inner", id_node(node), sep = ""), gp = gp) pushViewport(node_vp) xell <- c(seq(0, 0.2, by = 0.01), seq(0.2, 0.8, by = 0.05), seq(0.8, 1, by = 0.01)) yell <- sqrt(xell * (1 - xell)) xell <- xell*1.11 - 0.055 # to adapt size of the ellipse to the size with p-value lab <- extract_label(node) fill <- rep(fill, length.out = 2L) grid.polygon(x = unit(c(xell, rev(xell)), "npc"), y = unit(c(yell, -yell) + 0.5, "npc"), gp = gpar(fill = fill[1])) grid.text(lab[1L], y = unit(1.5 + 0.5, # to adapt position of x to its position with p-value "lines")) #grid.text(lab[1L], y = unit(1.5 + 0.5 * (lab[2L] != ""), # "lines")) grid.text(lab[2L], y = unit(1, "lines")) if (id) { nodeIDvp <- viewport(x = unit(0.5, "npc"), y = unit(1, "npc"), width = max(unit(1, "lines"), unit(1.3, "strwidth", nam[id_node(node)])), height = max(unit(1, "lines"), unit(1.3, "strheight", nam[id_node(node)]))) pushViewport(nodeIDvp) grid.rect(gp = gpar(fill = fill[2])) grid.text(nam[id_node(node)]) popViewport() } upViewport() } return(rval) } class(node_inner_ext) <- "grapcon_generator" @ \begin{frame}[fragile] \frametitle{Distributional trees} \vspace*{-0.12cm} \begin{center} DGP: $\; Y\ |\ X = x \; \sim \; \mathcal{N}(\mu(x), \sigma^2(x))$ \vspace*{-0.21cm} \setkeys{Gin}{width=0.58\linewidth} <>= par(mar=c(5.1,4.1,2.4,1.1)) plot(y=odata$y, x=odata$x, ylab = "y", xlab = "x", col = "gray") lines(x = odata$x, y = odata$mu, col = pal["forest"], lwd = 2.5, main = "") polygon(c(odata$x, rev(odata$x)), c(odata$mu + odata$sigma, rev(odata$mu - odata$sigma)), col = pallight["forest"], border = "transparent") legend("topleft", expression(mu %+-% sigma), bty = "n") @ \end{center} \end{frame} % \begin{frame} % \frametitle{Distributional trees} % \vspace*{-0.12cm} % \begin{center} % DGP: $\; Y\ |\ X = x \; \sim \; \mathcal{N}(\mu(x), \sigma^2(x))$ % % \vspace*{-0.21cm} % \setkeys{Gin}{width=0.5\linewidth} % <>= % paltrees <- rgb(c(0.97, 0.64, 1), c(0.70, 0.83, 1), c(0.30, 0.99, 1)) % plot(fig, inner_panel = node_inner_ext, % tp_args = list(FUN = identity, width = 18, fill = paltrees[c(1, 3)]), % ip_args = list(fill = paltrees[c(2, 3)]), % drop_terminal = TRUE, tnex = 1.7) % @ % \end{center} % \end{frame} <>= set.seed(7) nobs <- 500 x <- runif(nobs, 0, 1) mu <- sigma <- ytrue <- numeric(length = nobs) for(i in 1:nobs) sigma[i] <- if(x[i]<=0.4) 1 else 3 for(i in 1:nobs) mu[i] <- if(x[i]<= 0.4|| x[i]>0.8) 4 else 12 y <- rnorm(nobs, mean = mu, sd = sigma) #y <- rcnorm(nobs, mean = mu, sd = sigma, left = 0) ytrue <- mu data <- data.frame(cbind(y,x, ytrue)) tree <- disttree(y ~ x, data = data, family = NO(), type.tree = "mob") #tree <- disttree(y ~ x, data = data, family = dist_list_cens_normal) @ \begin{frame}[fragile] \frametitle{Distributional trees} \begin{center} \vspace*{-0.12cm} Model: \code{disttree(y ~ x)}\\ \vspace*{-0.2cm} \setkeys{Gin}{width=0.5\linewidth} <>= # function for output in terminal panels FUN <- function (x) { cf <- x$coefficients cf <- matrix(cf, ncol = 1, dimnames = list(names(cf), "")) c(sprintf("n = %s", x$nobs), "Estimated parameters:", parse(text = paste0("mu == '", format(round(cf[1], 2), nsmall = 2), "'")), parse(text = paste0("sigma == '", format(round(cf[2], 2), nsmall = 2), "'"))) } paltrees <- rgb(c(0.97, 0.64, 1), c(0.70, 0.83, 1), c(0.30, 0.99, 1)) ## plot version using FUN and tree of class 'disttree' plot(tree, drop = TRUE, tnex = 1.7, FUN = FUN, tp_args = list(fill = paltrees[c(1, 3)], width = 18), ip_args = list(fill = paltrees[c(2, 3)])) @ \end{center} \end{frame} \begin{frame}[fragile] \frametitle{Distributional trees} \begin{center} \vspace*{-0.12cm} Model: \code{disttree(y ~ x)}\\ \vspace*{-0.2cm} \setkeys{Gin}{width=0.5\linewidth} <>= plot(as.constparty(tree), tnex = 1.7, drop = TRUE, tp_args = list(fill = paltrees[c(1, 3)], ylines = 1.5), ip_args = list(fill = paltrees[c(2, 3)])) @ \end{center} \end{frame} \begin{frame}[fragile] \frametitle{Distributional trees} \begin{center} \vspace*{-0.12cm} Model: \code{disttree(y ~ x)}\\ \vspace*{-0.2cm} \setkeys{Gin}{width=0.5\linewidth} <>= node_density <- function (tree, xscale = NULL, yscale = NULL, horizontal = FALSE, main = "", xlab = "", ylab = "Density", id = TRUE, rug = TRUE, fill = paltrees[c(1, 3)], col = "black", lwd = 0.5, ...) { yobs <- tree$data[,as.character(tree$info$formula[[2]])] ylines <- 1.5 if (is.null(xscale)) xscale <- c(-5.1,22.5) if (is.null(yscale)) yscale <- c(-0.05,0.45) xr <- xscale yr <- yscale if (horizontal) { yyy <- xscale xscale <- yscale yscale <- yyy } rval <- function(node) { yrange <- seq(from = -20, to = 90)/4 ydens <- node$info$object$ddist(yrange) top_vp <- viewport(layout = grid.layout(nrow = 2, ncol = 3, widths = unit(c(ylines, 1, 1), c("lines", "null", "lines")), heights = unit(c(1, 1), c("lines", "null"))), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_density",node$id, sep = "")) pushViewport(top_vp) grid.rect(gp = gpar(fill = "white", col = 0)) top <- viewport(layout.pos.col = 2, layout.pos.row = 1) pushViewport(top) mainlab <- paste(ifelse(id, paste("Node", node$id, "(n = "), "n = "), node$info$nobs, ifelse(id, ")", ""), sep = "") grid.text(mainlab) popViewport() plot <- viewport(layout.pos.col = 2, layout.pos.row = 2, xscale = xscale, yscale = yscale, name = paste("node_density", node$id, "plot", sep = "")) pushViewport(plot) yd <- ydens xd <- yrange if (horizontal) { yyy <- xd xd <- yd yd <- yyy yyy <- xr xr <- yr yr <- yyy rxd <- rep(0, length(xd)) ryd <- rev(yd) } else { rxd <- rev(xd) ryd <- rep(0, length(yd)) } if (rug) { nodeobs <- node$info$object$y if (horizontal) { grid.rect(x = xscale[1], y = nodeobs , height = 0, width = xscale[1], default.units = "native", just = c("right", "bottom"), gp = gpar(lwd = 2, col = gray(0, alpha = 0.18))) } else { grid.rect(x = nodeobs, y = yscale[1], width = 0, height = abs(yscale[1]), default.units = "native", just = c("center", "bottom"), gp = gpar(lwd = 2, col = gray(0, alpha = 0.18))) #grid.lines(x = xr, y = yr, gp = gpar(col = "lightgray"), # default.units = "native") #grid.lines(x = xr, y = yr, gp = gpar(col = "lightgray"), # default.units = "native") } } grid.polygon(x = c(xd, rxd), y = c(yd, ryd), default.units = "native", gp = gpar(col = "black", fill = fill, lwd = lwd)) #grid.lines(x = xd, y = yd, default.units = "native", # gp = gpar(col = col, lwd = lwd)) grid.xaxis() grid.yaxis() grid.rect(gp = gpar(fill = "transparent")) upViewport(2) } return(rval) } class(node_density) <- "grapcon_generator" plot(tree, tnex = 1.7, drop = TRUE, terminal_panel = node_density, tp_args = list(fill = paltrees[c(1, 3)]), ip_args = list(fill = paltrees[c(2, 3)])) @ \end{center} \end{frame} %\begin{frame} %\frametitle{Distributional trees} %\center %\vspace*{-1cm} %\setkeys{Gin}{width=0.8\linewidth} %\includegraphics{tree_box} %\end{frame} \begin{frame} \frametitle{Learning distributional trees and forests} \begin{minipage}{0.7\textwidth} {\bf Tree:} \begin{enumerate} \item<3-> Fit global distributional model $\mathcal{D}(Y; \theta)$: \\ % to the whole data set:\\ Estimate $\hat{\theta}$ via maximum likelihood \\ $\hat{\theta} = \argmax_{\theta \in \Theta} \sum_{i=1}^n \ell(\theta; y_i)$ \item<8-> Test for associations/instabilities of the \\ scores $\frac{\partial \ell}{\partial \theta}(\hat{\theta};y_i)$ and each possible split variable $X_j$. \end{enumerate} \end{minipage} \begin{minipage}{0.23\textwidth} %\vspace{-0.1cm} \begin{tikzpicture} \visible<2-3>{ \node[ellipse, fill=HighlightBlue!70, align=center, scale = 0.7, minimum width=60pt, minimum height = 30pt] (n0) at (0.8, 1.7) {$Y$}; } \visible<4>{ \node[ellipse, fill=HighlightBlue!70, align=center, scale = 0.7, minimum width=60pt, minimum height = 30pt] (n0) at (0.8, 1.7) {$\mathcal{D}(Y;\hat{\theta}$)}; } \visible<5>{ \node[inner sep=0pt] (density_all) at (0.8, 1.7) {\includegraphics[width=0.7\textwidth]{density_all}}; } \visible<6->{ \node[inner sep=0pt] (density_all) at (0.8, 1.7) {\includegraphics[width=0.7\textwidth]{density_all_hist}}; } \visible<7-9>{ \node[rectangle, fill=HighlightOrange!70, align=center, scale = 0.7, minimum width=50pt, minimum height = 20pt] (n1) at (0, 0.2) {?}; \node[rectangle, fill=HighlightOrange!70, align=center, scale = 0.7, minimum width=50pt, minimum height = 20pt] (n2) at (1.6, 0.2) {?}; \draw[-, gray, line width=0.5pt] (0.7, 1.16) -- (n1); \draw[-, gray, line width=0.5pt] (0.9, 1.16) -- (n2); } \visible<10-11>{ \node[rectangle, fill=HighlightOrange!70, align=center, scale = 0.7, minimum width=50pt, minimum height = 20pt] (n1) at (0, 0.2) {$Y_1$}; \node[rectangle, fill=HighlightOrange!70, align=center, scale = 0.7, minimum width=50pt, minimum height = 20pt] (n2) at (1.6, 0.2) {$Y_2$}; \draw[-, gray, line width=0.5pt] (0.7, 1.16) -- (n1) node [midway, left] {\scriptsize $X \leq p$}; \draw[-, gray, line width=0.5pt] (0.9, 1.16) -- (n2) node [midway, right] {\scriptsize $X > p$}; } \visible<12>{ \node[rectangle, fill=HighlightOrange!70, align=center, scale = 0.7, minimum width=50pt, minimum height = 20pt] (n1) at (0, 0.2) {$\mathcal{D}(Y_1;\hat{\theta}_1$)}; \node[rectangle, fill=HighlightOrange!70, align=center, scale = 0.7, minimum width=50pt, minimum height = 20pt] (n2) at (1.6, 0.2) {$\mathcal{D}(Y_2;\hat{\theta}_2$)}; } \visible<12->{ \draw[-, gray, line width=0.5pt] (0.7, 1.16) -- (n1) node [midway, left] {\scriptsize $X \leq p$}; \draw[-, gray, line width=0.5pt] (0.9, 1.16) -- (n2) node [midway, right] {\scriptsize $X > p$}; } \visible<13->{ \node[inner sep=0pt] (density_1_hist) at (-0.2,-0.04) {\includegraphics[width=0.6\textwidth]{density_2_hist}}; } \visible<13->{ \node[inner sep=0pt] (density_2_hist) at (1.8,-0.04) {\includegraphics[width=0.6\textwidth]{density_1_hist}}; } \end{tikzpicture} \end{minipage} \vspace{0.1cm} %\begin{adjustwidth}{-0.0em}{-1em} \begin{enumerate} \setcounter{enumi}{2} \item<9-> Split along the covariate $X$ with strongest association or instability \\ and at breakpoint $p$ with highest improvement in log-likelihood. \item<11-> Repeat steps 1--3 recursively until some stopping criterion \\ is met, yielding $B$ subgroups $\mathcal{B}_b$ with $b = 1, \dots, B$. \end{enumerate} %\end{adjustwidth} \vspace{0.4cm} \visible<14->{ {\bf Forest:} Ensemble of $T$ trees. \begin{itemize} \item Bootstrap or subsamples. \item Random input variable sampling. \end{itemize} } \end{frame} \begin{frame}[fragile] \frametitle{Weather forecasting} \textbf{Goal:} \medskip \begin{center} \begin{tikzpicture} \draw[->] (0.4,0)--(0.9,0); \draw[] (1,-0.4) rectangle (2.5,0.4); \node[font=\scriptsize] at (1.75,0) {nature}; \draw[->] (2.6,0)--(3.1,0); \visible<1>{% \node[] at (0.0,0) {X}; \node[] at (3.5,0) {Y};} \visible<2->{% \node[inner sep=0pt] (today) at (-2.3,-0.4) {\includegraphics[width=.365\textwidth]{airport_20200412.jpg}}; \node[font=\scriptsize] at (-2.3,-2.4) {2020-04-12}; \node[inner sep=0pt] (future) at (5.8,-0.4) {\includegraphics[width=.365\textwidth]{airport_20200413.jpg}}; \node[font=\scriptsize] at (5.8,-2.4) {2020-04-13};} \end{tikzpicture} \end{center} %% https://innsbruck-airport.panomax.com/ \only<1-2>{% \textbf{Data:} \begin{itemize} \item X: State of the atmosphere now (temperature, precipitation, wind, \dots). \item Y: State of the atmosphere in the future (hours, days, weeks, \dots). \end{itemize}}% \only<3->{% \textbf{Two stages:} \begin{itemize} \item Physical model: Numerical weather prediction (NWP). \item Statistical model: Model output statistics (MOS). \end{itemize}} \end{frame} % \begin{frame}[fragile] % \frametitle{Weather forecasting} % % \textbf{Numerical weather prediction (NWP):} % \begin{itemize} % \item Based on a physical model. % \item Massive numerical simulation of atmospheric processes. % \item Here: Global model on a $50\times 50 \text{ km}^2$ grid. % \end{itemize} % % \medskip % % \textbf{Problem:} Uncertain initial conditions, unresolved processes. % % \medskip % % \textbf{Solution:} Ensemble of simulation runs under perturbed conditions. % % \end{frame} % % % % <>= % library("zoo") % % Sys.setenv("TZ"="UTC") % % # ------------------------------------------------------------------- % # GFS ensemble forecast % # ------------------------------------------------------------------- % % GFS <- read.table("Data/GENS_00_innsbruck_20200412.dat", header = TRUE) % init <- min(as.POSIXct(GFS$timestamp-GFS$step*3600,origin="1970-01-01")) % title <- sprintf("%s\n%s", % "Global Forecast System (GFS) Ensemble Forecast for Innsbruck, Airport", % sprintf("Forecast initialized %s", strftime(init, "%Y-%m-%d %H:%M UTC"))) % % # observations % load("Data/STAGEobs_tawes_11121_defense.rda") % #load("Data/STAGEobs_tawes_11121.rda") % # "2018-03-14 00:00:00" in line 321 (first entry for temperature) % # "2018-03-13 06:00:00" in line 317 (first entry for rain -> aggregated to 24h sums) % # "2018-03-23 00:00:00" in line 357 % % getZoo <- function( x, variable ) { % x <- subset( x, varname == variable ) % if ( nrow(x) == 0 ) stop("Ups, variable seems not to exist at all!") % # Else create zoo % x <- zoo( subset(x,select=-c(varname,timestamp,step)), % as.POSIXct(x$timestamp,origin="1970-01-01") ) % x % } % GFS_t2m <- getZoo( GFS, "tmp2m" ) - 273.15 % # temperature bias: model simulates temperature for height 1675 (~1070 m higher than true height) % # => add 10.7 degrees to account for bias (approx. 1 degree / 100 m) % # Custom bias % GFS_t2m <- GFS_t2m + 6.5 % % # Subsetting obs % obs <- subset(obs, index(obs) %in% index(GFS_t2m)) % % GFS_t2m <- merge(GFS_t2m, obs = obs[, grep("tl", names(obs))]) % ###GFS_t2m$obs <- obs[,"obs$tl"] % # first value of rain is 18 hours later than temperature % #(both start at 6:00 but rain is cumulated over 24 hours) % # -> drop first 3 values of temperature % GFS_t2m <- GFS_t2m[-c(1:3),] % % GFS_rain <- getZoo( GFS, "apcpsfc" ) % GFS_rain$obs <- obs[,"rr6"] % # precipitaion sums over 24 hours (00:00 UTC - 00:00 UTC +1day) % GFS_rain24 <- GFS_rain[c((1:10)*4),] % for(i in 1:NROW(GFS_rain24)){ % GFS_rain24[i,] <- colSums(GFS_rain[c((4*i-3):(4*i)),]) % } % % % # Two POSIXct vectors for the axis % main <- seq(min(as.POSIXct(as.Date(index(GFS_t2m)))),max(index(GFS_t2m)),by=86400) % minor <- seq(min(index(GFS_t2m)),max(index(GFS_t2m)),by=3*3600) % % # GFS_t2m_mean <- rowMeans(GFS_t2m) % GFS_t2m_mean <- GFS_t2m % GFS_t2m_mean[,1] <- rowMeans(GFS_t2m[,-NCOL(GFS_t2m)]) % GFS_t2m_mean <- GFS_t2m_mean[,1] % % # GFS_rain_mean <- rowMeans(GFS_rain) % GFS_rain24_mean <- GFS_rain24 % GFS_rain24_mean[,1] <- rowMeans(GFS_rain24[,-NCOL(GFS_rain24)]) % GFS_rain24_mean <- GFS_rain24_mean[,1] % @ % % <>= % par(mar=c(0.4,0,0.2,0), oma=c(6,3.2,5,4)) % layout( matrix(1:2,ncol=1) ) % plot(GFS_t2m[,1], screen=1, xaxs="i", xaxt="n", ylim = range(GFS_t2m, na.rm = TRUE)*1.05, col = "slategray" ) % abline(v = main, lty = 2 ) % mtext(side = 3, line = 1, cex = 1.2, font = 2, title ) % mtext(side = 2, line = 2.3, cex = 1, font = 1, text = "Temperature [°C]" ) % @ % % <>= % plot(GFS_rain24[,1], screen=1, xaxs="i", xaxt="n", yaxs="i", ylim=range(GFS_rain24, na.rm = TRUE)*c(0,1.05), col = "slategray" ) % abline(v = main, lty = 2 ) % mtext(side = 2, line = 2.3, cex = 1, font = 1, text = "Rain [mm/6h]" ) % axis(side = 1, at = main + 42300, strftime(main,"%b %d"), % line = 0, col.ticks=NA, col.axis="gray30", col = NA ) % @ % % \begin{frame}[fragile] % \frametitle{Weather forecasting} % % \vspace{-0.6cm} % \setkeys{Gin}{width=0.95\linewidth} % \begin{center} % \only<1>{% % <>= % <> % <> % @ % }% % \only<2>{% % <>= % <> % lines(GFS_t2m[,3], col = "slategray") % <> % lines(GFS_rain24[,3], col = "slategray") % @ % }% % \only<3>{% % <>= % <> % lines(GFS_t2m[,2], col = "slategray") % lines(GFS_t2m[,3], col = "slategray") % <> % lines(GFS_rain24[,2], col = "slategray") % lines(GFS_rain24[,3], col = "slategray") % @ % }% % \only<4>{% % <>= % <> % for(j in 2:(NCOL(GFS_t2m) - 1)) lines(GFS_t2m[,j], col = "slategray") % <> % for(j in 2:(NCOL(GFS_rain24) - 1)) lines(GFS_rain24[,j], col = "slategray") % @ % }% % \only<5>{% % <>= % <> % for(j in 2:(NCOL(GFS_t2m) - 1)) lines(GFS_t2m[,j], col = "slategray") % lines(GFS_t2m[,"obs"], col = 2, lwd = 2.3) % <> % for(j in 2:(NCOL(GFS_rain24) - 1)) lines(GFS_rain24[,j], col = "slategray") % lines(GFS_rain24[,"obs"], col = 2, lwd = 2.3) % @ % }% % \end{center} % % \end{frame} \begin{frame}[fragile] \frametitle{Weather forecasting: precipitation} \textbf{Goal:} Predict daily precipitation amount in Tyrol. %complex terrain. \bigskip \pause \textbf{Observation data:} National Hydrographical Service. \begin{itemize} \item Daily 24h precipitation sums from July over 28 years (1985--2012). \item 95 observation stations in Tyrol. \end{itemize} \bigskip \pause \textbf{Numerical weather prediction:} Global Ensemble Forecast System. \begin{itemize} \item Model outputs: Precipitation, temperature, air pressure, convective available potential energy, downwards short wave radiation flux, \dots \item 80 covariates based on ensemble min/max/mean/standard deviation. \end{itemize} \bigskip \pause \textbf{Distribution assumption:} Power-transformed Gaussian, censored at 0. \[ (\text{precipitation})^\frac{1}{1.6} \sim \textit{c}\mathcal{N}(\mu,\sigma^2) \] \end{frame} %% \begin{frame} %% \frametitle{Weather forecasting: precipitation} %% %% \textbf{Base variables:} %% \begin{itemize} %% \item Total precipitation. %% \item Convective available potential energy. %% \item Downwards short wave radiation flux (``sunshine''). %% \item Mean sea level pressure. %% \item Preciptable water. %% \item 2m maximum temperature. %% \item Total column-integrated condensate. %% \item Temperature. %% \item Temperature differences in altitude. %% \end{itemize} %% %% \medskip %% %% \textbf{Variations:} 80 covariates based on ensemble min/max/mean/standard deviation. %% %% \end{frame} <>= if(file.exists("Data/Axams_pred.rda") & file.exists("Data/Axams_testdata.rda")){ load("Data/Axams_pred.rda") load("Data/Axams_testdata.rda") } else { ##### # load observations and covariates data("RainAxams") # tree and forest formula { dt.formula <- df.formula <- robs ~ tppow_mean + tppow_sprd + tppow_min + tppow_max + tppow_mean0612 + tppow_mean1218 + tppow_mean1824 + tppow_mean2430 + tppow_sprd0612 + tppow_sprd1218 + tppow_sprd1824 + tppow_sprd2430 + capepow_mean + capepow_sprd + capepow_min + capepow_max + capepow_mean0612 + capepow_mean1218 + capepow_mean1224 + capepow_mean1230 + capepow_sprd0612 + capepow_sprd1218 + capepow_sprd1224 + capepow_sprd1230 + dswrf_mean_mean + dswrf_mean_max + dswrf_sprd_mean + dswrf_sprd_max + msl_mean_mean + msl_mean_min + msl_mean_max + msl_sprd_mean + msl_sprd_min + msl_sprd_max + pwat_mean_mean + pwat_mean_min + pwat_mean_max + pwat_sprd_mean + pwat_sprd_min + pwat_sprd_max + tmax_mean_mean + tmax_mean_min + tmax_mean_max + tmax_sprd_mean + tmax_sprd_min + tmax_sprd_max + tcolc_mean_mean + tcolc_mean_min + tcolc_mean_max + tcolc_sprd_mean + tcolc_sprd_min + tcolc_sprd_max + t500_mean_mean + t500_mean_min + t500_mean_max + t700_mean_mean + t700_mean_min + t700_mean_max + t850_mean_mean + t850_mean_min + t850_mean_max + t500_sprd_mean + t500_sprd_min + t500_sprd_max + t700_sprd_mean + t700_sprd_min + t700_sprd_max + t850_sprd_mean + t850_sprd_min + t850_sprd_max + tdiff500850_mean + tdiff500850_min + tdiff500850_max + tdiff700850_mean + tdiff700850_min + tdiff700850_max + tdiff500700_mean + tdiff500700_min + tdiff500700_max + msl_diff } # learning data: 24 years (1985 - 2008, both inlcuded) # testing data: 4 successive years (2009, 2010, 2011, 2012) learndata <- RainAxams[RainAxams$year < 2009,] testdata <- RainAxams[RainAxams$year %in% c(2009, 2010, 2011, 2012),] save(file = "Data/Axams_testdata.rda", testdata) ############################################################## # fitting the models set.seed(7) df <- distforest(df.formula, data = learndata, family = dist_list_cens_normal, ntree = 100, censtype = "left", censpoint = 0, control = disttree_control(teststat = "quad", testtype = "Univ", type.tree = "ctree", intersplit = TRUE, mincriterion = 0, minsplit = 50, minbucket = 20), mtry = 27) #### prepare data for plot of estimated density functions # predictions for one day (in each of the four years) # (19th of July 2011 is missing) pday <- 24 # 2 (hohe Beobachtung zu niedrig geschaetzt), 4, 15, evtl. auch 7, 8, 23 (eine 0-Beobachtung und 2 sehr aehnliche), pdays <- if(pday<19) c(pday, pday + 31, pday + 62, pday + 92) else c(pday, pday + 31, pday + 61, pday + 92) pdf <- predict(df, newdata = testdata[pdays,], type = "parameter") pdf$pdays <- pdays save(file = "Data/Axams_pred.rda", pdf) } pdays <- pdf$pdays pday <- pdays[1] df_mu <- pdf$mu df_sigma <- pdf$sigma # plot predicted distributions together with observations set.seed(7) x <- c(0.01, sort(runif(500,0.01,8))) y1 <- crch::dcnorm(x, mean = df_mu[1], sd = df_sigma[1], left = 0) y2 <- crch::dcnorm(x, mean = df_mu[2], sd = df_sigma[2], left = 0) y3 <- crch::dcnorm(x, mean = df_mu[3], sd = df_sigma[3], left = 0) y4 <- crch::dcnorm(x, mean = df_mu[4], sd = df_sigma[4], left = 0) # switch x-axis back to untransformed scale # x <- x^(1.6) # point mass (slightly shifted) pm1 <- c(0.05, crch::dcnorm(-1, mean = df_mu[1], sd = df_sigma[1], left = 0)) # 0.15 pm2 <- c(0.01, crch::dcnorm(-1, mean = df_mu[2], sd = df_sigma[2], left = 0)) # 0.05 pm3 <- c(-0.03, crch::dcnorm(-1, mean = df_mu[3], sd = df_sigma[3], left = 0)) # -0.05 pm4 <- c(-0.07, crch::dcnorm(-1, mean = df_mu[4], sd = df_sigma[4], left = 0)) # -0.15 # predictions pred1 <- c(testdata[pdays,"robs"][1], # ^(1.6), crch::dcnorm(testdata[pdays,"robs"][1], mean = df_mu[1], sd = df_sigma[1], left = 0)) pred2 <- c(testdata[pdays,"robs"][2], # ^(1.6), crch::dcnorm(testdata[pdays,"robs"][2], mean = df_mu[2], sd = df_sigma[2], left = 0)) pred3 <- c(testdata[pdays,"robs"][3], # ^(1.6), crch::dcnorm(testdata[pdays,"robs"][3], mean = df_mu[3], sd = df_sigma[3], left = 0)) pred4 <- c(testdata[pdays,"robs"][4], # ^(1.6), crch::dcnorm(testdata[pdays,"robs"][4], mean = df_mu[4], sd = df_sigma[4], left = 0)) #legendheight lh1 <- crch::dcnorm(0.01, mean = df_mu[1], sd = df_sigma[1], left = 0) lh2 <- crch::dcnorm(0.01, mean = df_mu[2], sd = df_sigma[2], left = 0) lh3 <- crch::dcnorm(0.01, mean = df_mu[3], sd = df_sigma[3], left = 0) lh4 <- crch::dcnorm(0.01, mean = df_mu[4], sd = df_sigma[4], left = 0) @ \begin{frame}[fragile] \frametitle{Weather forecasting: precipitation} \textbf{Application for one station:} Axams. \begin{itemize} %\vspace{-0.05cm} \item Learn forest model on data from 24 years (1985--2008). %\vspace{-0.05cm} \item Evaluate on 4 years (2009--2012). Here: July \Sexpr{24}. \end{itemize} \vspace*{-0.4cm} \begin{center} \setkeys{Gin}{width=0.54\textwidth} <>= par(mar = c(4, 4, 1, 1)) plot(x = x, y = y1, type = "l", col = 2, ylab = "Density", lwd = 2, # xlab = expression(Total~precipitation~"["~mm~"/"~"24h"~"]"), xlab = expression(Total~precipitation~"["~mm^(1/1.6)~"/"~"24h"~"]"), ylim = c(0,max(y1, y2, y3, y4, pm1, pm2, pm3, pm4) + 0.01), xlim = c(-1.5,8)) # xlim = c(-2,28)) lines(x = x, y = y2, type = "l", lwd = 2, col = 4) lines(x = x, y = y3, type = "l", lwd = 2, col = 3) lines(x = x, y = y4, type = "l", lwd = 2, col = 6) legend('topright', c("Predicted distribution", "Point mass at censoring point", "Observation"), bty = "n", col = "black", lty = c(1, NA, NA), pch = c(NA, 19, 4), cex = 1) # plot point mass lines(x = c(pm1[1], pm1[1]), y = c(pm1[2], 0), col = 2, type = "l", lwd = 2) lines(x = c(pm2[1], pm2[1]), y = c(pm2[2], 0), col = 4, type = "l", lwd = 2) lines(x = c(pm3[1], pm3[1]), y = c(pm3[2], 0), col = 3, type = "l", lwd = 2) lines(x = c(pm4[1], pm4[1]), y = c(pm4[2], 0), col = 6, type = "l", lwd = 2) points(x = pm1[1], y = pm1[2], col = 2, pch = 19, cex = 1.4) points(x = pm2[1], y = pm2[2], col = 4, pch = 19, cex = 1.4) points(x = pm3[1], y = pm3[2], col = 3, pch = 19, cex = 1.4) points(x = pm4[1], y = pm4[2], col = 6, pch = 19, cex = 1.4) # plot predictions points(x = pred1[1], y = pred1[2], col = 2, pch = 4, cex = 1.4, lwd = 2) points(x = pred2[1], y = pred2[2], col = 4, pch = 4, cex = 1.4, lwd = 2) points(x = pred3[1], y = pred3[2], col = 3, pch = 4, cex = 1.4, lwd = 2) points(x = pred4[1], y = pred4[2], col = 6, pch = 4, cex = 1.4, lwd = 2) lines(x = c(pred1[1], pred1[1]), y = c(pred1[2], 0), col = "darkgray", type = "l", lty = 2, lwd = 2) lines(x = c(pred2[1], pred2[1]), y = c(pred2[2], 0), col = "darkgray", type = "l", lty = 2, lwd = 2) lines(x = c(pred3[1], pred3[1]), y = c(pred3[2], 0), col = "darkgray", type = "l", lty = 2, lwd = 2) lines(x = c(pred4[1], pred4[1]), y = c(pred4[2], 0), col = "darkgray", type = "l", lty = 2, lwd = 2) # add labels text(x = -0.8, y = lh1, labels = "2009", col = 2, cex = 1) # -1.7 text(x = -0.8, y = lh2, labels = "2010", col = 4, cex = 1) # -1.7 text(x = -0.8, y = lh3, labels = "2011", col = 3, cex = 1) # -1.7 text(x = -0.8, y = lh4, labels = "2012", col = 6, cex = 1) # -1.7 @ \end{center} \only<2>{ \vspace{-0.5cm} {\small Replication: \texttt{demo("RainAxams", package = "disttree")}} } \end{frame} % \begin{frame}[fragile] % \frametitle{Weather forecasting: precipitation} % % \textbf{Application for one station:} Axams. % \begin{itemize} % %\vspace{-0.05cm} % \item Learn forest model on data from 24 years. % %\vspace{-0.05cm} % \item Evaluate on 4 years. % %\vspace{-0.05cm} % \item 10 times 7-fold cross validation. % \end{itemize} % % \bigskip % % \textbf{Benchmark:} Against other heteroscedastic censored Gaussian models. % \begin{itemize} % \item \emph{Ensemble MOS:} Linear predictors using only total precipitation. % \item \emph{Prespecified GAMLSS:} Variable selection based on expert knowledge. % \item \emph{Boosted GAMLSS:} Automatic variable selection. % \end{itemize} % % \bigskip % % \textbf{Evaluation:} Continuous ranked probability skill score. % % %% \vspace{0.1cm} % %% \begin{table}[t!] % %% \footnotesize % %% % %% \hskip-0.4cm\begin{tabular}{ l l l } % %% \hline % %% Model & Type & Variable Selection \\ % %% \hline % %% \vspace{-0.15cm} % %% \textbf{Distributional forest} & recursive & automatic \\ % %% & partitioning & \\ % %% \vspace{-0.15cm} % %% \textbf{Prespecified GAMLSS} & spline & based on expert \\ % %% & in each & knowledge \\ % %% \vspace{-0.15cm} % %% \textbf{Boosted GAMLSS} & spline & automatic \\ % %% & in each & \\ % %% \vspace{-0.15cm} % %% \textbf{EMOS} & linear & total precipitation mean \\ % %% & & and standard deviation \\ % %% \hline % %% \end{tabular} % %% \end{table} % % \end{frame} % % % % % <>= % #### cross validation rain % if(file.exists("Data/crps_cross.rda")){ % load("Data/crps_cross.rda") % } else { % % nrep_cross <- 10 % seed <- 7 % % res_cross <- mclapply(1:nrep_cross, % function(i){ % % set.seed(seed*i) % % # randomly split data in 7 parts each including 4 years % years <- 1985:2012 % testyears <- list() % for(j in 1:7){ % testyears[[j]] <- sample(years, 4, replace = FALSE) % years <- years[!(years %in% testyears[[j]])] % } % % #crps <- matrix(nrow = 7, ncol = 7) % reslist <- list() % for(k in 1:7){ % test <- testyears[[k]] % train <- c(1985:2012)[!c(1985:2012) %in% test] % % res <- evalmodels(station = "Axams", % train = train, % test = test, % gamboost_cvr = TRUE) % % #crps[k,] <- res$crps % reslist[[k]] <- res % } % % #colnames(crps) <- names(res$crps) % return(reslist) % }, % mc.cores = detectCores() - 1 % ) % % # extract CRPS % crps_cross <- matrix(nrow = nrep_cross, ncol = 7) % # loop over all repetitions % for(i in 1:length(res_cross)){ % #loop over all 7 folds (for 7 methods) % crps_cross_int <- matrix(nrow = length(res_cross[[1]]), ncol = 7) % for(j in 1:length(res_cross[[1]])){ % crps_cross_int[j,] <- res_cross[[i]][[j]]$crps % } % crps_cross[i,] <- colMeans(crps_cross_int, na.rm = TRUE) % } % colnames(crps_cross) <- names(res_cross[[1]][[1]]$crps) % % save(crps_cross, file = "Data/crps_cross.rda") % } % @ % % % % % \begin{frame}[fragile] % \frametitle{Weather forecasting: precipitation} % \begin{center} % \vspace*{-0.2cm} % \setkeys{Gin}{width=0.65\textwidth} % <>= % #par(mar = c(2.5,2,1,2)) % boxplot(1 - crps_cross[,c(2,3,4)] / crps_cross[,6], ylim = c(-0.005, 0.065), % names = c("Distributional forest", "Prespecified GAMLSS", "Boosted GAMLSS"), % main = "Cross validation (with reference model EMOS)", % cex.main=1.4, % cex.lab=1.2, % ylab = "CRPS skill score", col = "lightgray") % abline(h = 0, col = pal["EMOS"], lwd = 2) % @ % \end{center} % \end{frame} % \begin{frame}[fragile] % \frametitle{Weather forecasting: precipitation} % %\vspace{0.2cm} % \textbf{Application for all 95 stations:} % \begin{itemize} % \item Learn forest model on data from 24 years (1985--2008). % \item Evaluate on 4 years (2009--2012). % \item Benchmark against other heteroscedastic censored Gaussian models. % \end{itemize} % % \end{frame} % % % <>= % #### prediction over all stations 24 - 4 % if(file.exists("Data/crps_24to4_all.rda")){ % load("Data/crps_24to4_all.rda") % } else { % % data("StationsTyrol") % stations <- StationsTyrol$name % test <- 2009:2012 % train <- 1985:2008 % % % res_24to4_all <- mclapply(1:length(stations), % function(i){ % % set.seed(7) % % res <- evalmodels(station = stations[i], % train = train, % test = test, % gamboost_cvr = TRUE) % % return(res) % }, % mc.cores = detectCores() - 1 % ) % % # extract crps % crps_24to4_all <- matrix(nrow = length(stations), ncol = 7) % # loop over all stations % for(i in 1:length(stations)){ % crps_24to4_all[i,] <- res_24to4_all[[i]]$crps % } % % colnames(crps_24to4_all) <- names(res_24to4_all[[1]]$crps) % rownames(crps_24to4_all) <- stations % % save(crps_24to4_all, file = "Data/crps_24to4_all.rda") % } % % % # skill score % s <- 1 - crps_24to4_all[, 2:4]/crps_24to4_all[,6] % colnames(s) <- c("Distributional forest", "Prespecified GAMLSS", "Boosted GAMLSS") % % % ## prepare data for map which shows where distforest performed better than gamlss or gamboostLSS based on the crps % % crps_map <- crps_24to4_all[,c("distforest", "gamlss", "gamboostLSS", "emos_log")] % % # best method % bst <- apply(crps_map, 1, which.min) % % # distance of forest to best other method % dst <- crps_map[,1] - crps_map[cbind(1:nrow(crps_map), apply(crps_map[, -1], 1, which.min) + 1)] % % # breaks/groups % brk <- c(-0.1, -0.05, -0.005, 0.005, 0.05, 0.1) % #brk <- c(-0.1, -0.05, -0.01, 0.01, 0.05, 0.1) % grp <- cut(dst, breaks = brk) % % # HCL colors (relatively flashy, essentially CARTO Tropic) % clr <- colorspace::diverging_hcl(5, h = c(130, 320), c = 70, l = c(50, 90), power = 1.3) % % % library("raster") # dem (digital elevation model) % library("sp") # gadm www.gadm.org/country % % data("StationsTyrol", package = "RainTyrol") % data("MapTyrol", package = "RainTyrol") % # data(MapTyrol_border, package = "RainTyrol") % # Create SpatialPointsDataFrame from station list % sp <- SpatialPointsDataFrame(subset(StationsTyrol, % select=c(lon,lat)), % data = subset(StationsTyrol, % select = -c(lon,lat)), % proj4string = crs(MapTyrol$RasterLayer)) % @ % % % \begin{frame}[fragile] % \frametitle{Weather forecasting: precipitation} % \begin{center} % \vspace*{-0.5cm} % % \setkeys{Gin}{width=0.84\textwidth} % <>= % % ## plot map of Tyrol with all 95 observations % layout(cbind(1, 2), width = c(9, 1)) % par(mar = c(5,4,4,0.1)) % raster::image(MapTyrol$RasterLayer, col = rev(gray.colors(100)), % main="Stations in Tyrol", ylab = "Latitude", xlab = "Longitude", % xlim = c(9.8,13.2), % ylim = c(46.6, 47.87)) % plot(MapTyrol$SpatialPolygons, add = TRUE) % points(sp[70,], pch = 19, col = "black", cex = 1.85) % points(sp, pch = c(21, 24, 25, 22)[bst], bg = clr[grp], col = "black", las = 1, cex = 1.5) % legend(x = 9.8, y = 47.815, pch = c(21, 24, 25, 22), legend = c("Distributional forest", "Prespecified GAMLSS", "Boosted GAMLSS", "EMOS"), cex = 1, bty = "n") % text(x = 10.3, y = 47.82, labels = "Models with lowest CRPS") % mtext("CRPS\ndifference", side=4, las = TRUE, at = c(x = 13.5, y = 47.76), line = 0.3) % par(mar = c(0.5,0.2,0.5,2.3)) % ## legend % plot(0, 0, type = "n", axes = FALSE, xlab = "", ylab = "", % xlim = c(0, 1), ylim = c(-0.2, 0.2), xaxs = "i", yaxs = "i") % rect(0, brk[-6], 0.5, brk[-1], col = rev(clr)) % axis(4, at = brk, las = 1, mgp=c(0,-0.5,-1)) % % % @ % \end{center} % \end{frame} % % % % \begin{frame}[fragile] % \frametitle{Weather forecasting: precipitation} % \begin{center} % \vspace*{-0.5cm} % % \setkeys{Gin}{width=0.47\textwidth} % <>= % % ## plot map of Tyrol with all 95 observations % layout(cbind(1, 2), width = c(9, 1)) % par(mar = c(5,4,4,0.1)) % raster::image(MapTyrol$RasterLayer, col = rev(gray.colors(100)), % main="Stations in Tyrol", ylab = "Latitude", xlab = "Longitude", % xlim = c(9.8,13.2), % ylim = c(46.6, 47.87)) % plot(MapTyrol$SpatialPolygons, add = TRUE) % points(sp[70,], pch = 19, col = "black", cex = 1.85) % points(sp, pch = c(21, 24, 25, 22)[bst], bg = clr[grp], col = "black", las = 1, cex = 1.5) % legend(x = 9.8, y = 47.815, pch = c(21, 24, 25, 22), legend = c("Distributional forest", "Prespecified GAMLSS", "Boosted GAMLSS", "EMOS"), cex = 1, bty = "n") % text(x = 10.3, y = 47.82, labels = "Models with lowest CRPS") % mtext("CRPS\ndifference", side=4, las = TRUE, at = c(x = 13.5, y = 47.76), line = 0.3) % par(mar = c(0.5,0.2,0.5,2.3)) % ## legend % plot(0, 0, type = "n", axes = FALSE, xlab = "", ylab = "", % xlim = c(0, 1), ylim = c(-0.2, 0.2), xaxs = "i", yaxs = "i") % rect(0, brk[-6], 0.5, brk[-1], col = rev(clr)) % axis(4, at = brk, las = 1, mgp=c(0,-0.5,-1)) % % % @ % \end{center} % \vspace{-0.2cm} % \textbf{Conclusions:} % \begin{itemize} % \item Distributional forests provide an easy-to-apply alternative to already existing methods. % \item Do not require expert knowledge for pre-specifications. % \item Competitive performance: mainly en par or even slightly better. % \end{itemize} % % \end{frame} \subsection{References} \begin{frame} \frametitle{References} \vspace{-0.2cm} \scriptsize Breiman L (2001). \dquote{Random {Forests}.} \emph{Machine Learning}, \textbf{45}(1), 5--32. \doi{10.1023/A:1010933404324} \medskip Breiman L, Cutler A (2004). \dquote{Random Forests.}, \url{https://www.stat.berkeley.edu/~breiman/RandomForests} (Accessed: 2018-02-22) \medskip %Hothorn T, Zeileis A (2017). % \dquote{Transformation Forests.} % \emph{arXiv 1701.02110}, arXiv.org E-Print Archive. % \url{http://arxiv.org/abs/1701.02110} % %\smallskip Hothorn T, Hornik K, Zeileis A (2006). \dquote{Unbiased Recursive Partitioning: A Conditional Inference Framework.} \emph{Journal of Computational and Graphical Statistics}, \textbf{15}(3), 651--674. \doi{10.1198/106186006X133933} \medskip Hothorn T, Zeileis A (2015). \dquote{{partykit}: A Modular Toolkit for Recursive Partytioning in \textsf{R}.} \emph{Journal of Machine Learning Research}, \textbf{16}, 3905--3909. \url{http://www.jmlr.org/papers/v16/hothorn15a.html} \medskip Liaw A, Wiener M (2002). \dquote{Classification and Regression by randomForest.} \emph{R News}, \textbf{2}(3), 18--22. \url{https://CRAN.R-project.org/doc/Rnews/} \medskip Wright M N, Ziegler A (2017). \dquote{{ranger}: A Fast Implementation of Random Forests for High Dimensional Data in {C++} and {R}.} \emph{Journal of Statistical Software}, \textbf{77}{1}, 1--17. \doi{10.18637/jss.v077.i01} \medskip % Zeileis A, Hothorn T, Hornik K (2008). % \dquote{Model-Based Recursive Partitioning.} % \emph{Journal of Computational and Graphical Statistics}, % \textbf{17}(2), 492--514. % \doi{10.1198/106186008X319331} % % \medskip Athey S, Tibshirani J, Wager S (2019). \dquote{Generalized Random Forests.} \emph{Annals of Statistics}, \textbf{47}{2}, 1148--1178. \doi{10.1214/18-AOS1709"} \medskip Schlosser L, Hothorn T, Stauffer R, Zeileis A (2019). \dquote{Distributional Regression Forests for Probabilistic Precipitation Forecasting in Complex Terrain.} \emph{The Annals of Applied Statistics}, \textbf{13}(3), 1564--1589. \doi{10.1214/19-AOAS1247} \end{frame} \end{document} partykit/inst/ULGcourse-2020/Makefile0000644000176200001440000000301614723350654017000 0ustar liggesusers# --------------------------------------------------------------------------- # List of Files to be processed RNW_SOURCES=slides_tree slides_forest # --------------------------------------------------------------------------- .PHONY: clean distclean all: slides slides: $(RNW_SOURCES:=.pdf) clean scripts: $(RNW_SOURCES:=.R) handouts: $(RNW_SOURCES:=_1x1.pdf) clean # --------------------------------------------------------------------------- # Generic rules for creating files 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/Type /Encoding /BaseEncoding /WinAnsiEncoding /Differences [ 45/minus 96/quoteleft 144/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent /dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron /space] >> endobj xref 0 10 0000000000 65535 f 0000000021 00000 n 0000000163 00000 n 0000003829 00000 n 0000003912 00000 n 0000004013 00000 n 0000004046 00000 n 0000000212 00000 n 0000000292 00000 n 0000006741 00000 n trailer << /Size 10 /Info 1 0 R /Root 2 0 R >> startxref 6998 %%EOF partykit/inst/ULGcourse-2020/exercises/0000755000176200001440000000000014172227777017341 5ustar liggesuserspartykit/inst/ULGcourse-2020/exercises/exercise_forest_wage.Rmd0000644000176200001440000000702214172227777024202 0ustar liggesusers--- title: "Exercise: Wage" output: html_document --- ```{r, include = FALSE} file <- "data/CPS1985.rds" stopifnot(file.exists(file)) data <- readRDS(file) head(data) ``` In this exercise we will use the CPS1985 data set, a random sample from the May 1985 US Current Population Survey. The data set provides information on the hourly wage in US dollars of 534 individuals together with 10 additional variables such as education, age and experience. Simply download the file `r xfun::embed_file(file, text = "CPS1985.rds")` by clicking or download it from the source which also provides more detailed information on the data set. We can import/read this file using `data <- readRDS(...)`. The file contains the following information: * `wage`: wage in US dollars per hour (numeric). * `education`: education in years (numeric). * `experience`: potential work experience in years; age - education - 6 (numeric). * `age`: age in years (numeric). * `ethnicity`: Caucasian, Hispanic, other (factor). * `gender`: male or female (factor). * `union`: Does the individual work on a union job? (factor). # The Tasks We would like to find out how wage depends on the provided additional attributes. Our response variable is the logarithm of the numeric variable `wage`. As covariates we use the additional variables `education`, `experience`, `age`, `ethnicity`, `gender` and `union`. Apply the forest-building function `cforest` to build a forest model as described in the following points: * Load the data set `"CPS1985.rds"`. * Build a forest model with 50 trees. * Predict the hourly log(wage) for a 37-year old hispanic female with 10 years of experience and 17 years of education who is not working on a union job. Does the prediction change if she was working on a union job? * Which covariates have the highest influence on the model? * Separate the data set into a learning set (2/3 of the full data) and a testing set (1/3 of the full data). Build a forest on the learning data set and predict the log(wage) on the testing data set. Evaluate the performance by calculating the root-mean-squared error (RMSE) on the testing data. How do parameters such as the number of trees influence the performance? * Apply the function `ranger` to build a forest model using the same parameters and compare it to the cforest model, e.g., based on predictions, the RMSE on the testing data or variable importance. ```{r, include = FALSE} f <- log(wage) ~ education + experience + age + ethnicity + gender + union library("partykit") set.seed(4) cf <- cforest(formula = f, data = data, ntree = 50) newworker <- data.frame(education = 17, experience = 10, age = 37, ethnicity = "hispanic", gender = "female", union = "no") predict(cf, newdata = newworker) newworker2 <- newworker newworker2$union <- "yes" predict(cf, newdata = newworker2) ``` ```{r, include = FALSE} set.seed(4) trainid <- sample(1:NROW(data), size = 356, replace = FALSE) train <- data[trainid,] test <- data[-trainid,] ``` ```{r, include = FALSE} set.seed(4) library("ranger") rf <- ranger(f, data = train, num.trees = 50) cf <- cforest(f, data = train, ntree = 50) pred_cf <- predict(cf, newdata = test) rmse_cf <- sqrt(sum((log(test$wage) - pred_cf)^2)) pred_rf <- predict(rf, data = test)$prediction rmse_rf <- sqrt(sum((log(test$wage) - pred_rf)^2)) varimp(cf) rf <- ranger(f, data = train, num.trees = 50, importance = "impurity") importance(rf) ```partykit/inst/ULGcourse-2020/exercises/exercise_forest_german_credit.Rmd0000644000176200001440000001602214172227777026062 0ustar liggesusers--- title: "Exercise: South German Credit" output: html_document --- ```{r, include = FALSE} file <- "data/german.rds" stopifnot(file.exists(file)) data <- readRDS(file) head(data) ``` In this exercise we will use the 'South German Credit' data set. It contains a classification of the credit risk of 1000 individuals into 'good' and 'bad' together with 20 additional attributes. Simply download the file `r xfun::embed_file(file, text = "german.rds")` by clicking or download it from the corresponding homepage which also provides more detailed information on the data set. We can import/read this file using `data <- readRDS(...)`. The file contains the following information: * `status`: status of the debtor's checking account with the bank (factor). * `duration`: credit duration in months (integer). * `credit_history`: history of compliance with previous or concurrent credit contracts (factor). * `purpose`: purpose for which the credit is needed (factor). * `amount`: credit amount in DM (integer). * `savings`: debtor's savings (factor). * `employment_duration`: duration of debtor's employment with current employer (factor; discretized quantitative). * `installment_rate`: credit installments as a percentage of debtor's disposable income (ordered factor; discretized quantitative). * `personal_status_sex`: combined information on sex and marital status (factor; sex cannot be recovered from the variable, because male singles and female non-singles are coded with the same code (2); female widows cannot be easily classified, because the code table does not list them in any of the female categories). * `other_debtors`: Is there another debtor or a guarantor for the credit? (factor). * `present_residence`: length of time (in years) the debtor lives in the present residence (ordered factor; discretized quantitative). * `property`: the debtor's most valuable property, i.e. the highest possible code is used. Code 2 is used, if codes 3 or 4 are not applicable and there is a car or any other relevant property that does not fall under variable `savings` (factor). * `age`: age in years (integer). * `other_installment_plans`: installment plans from providers other than the credit-giving bank (factor). * `housing`: type of housing the debtor lives in (factor) * `number_credits`: number of credits including the current one the debtor has (or had) at this bank (ordered factor, discretized quantitative). * `job`: quality of debtor's job (ordinal) * `people_liable`: number of persons who financially depend on the debtor (i.e., are entitled to maintenance) (factor, discretized quantitative). * `telephone`: Is there a telephone landline registered on the debtor's name? (factor; remember that the data are from the 1970s) * `foreign_worker`: Is the debtor a foreign worker? (factor) * `credit_risk`: Has the credit contract been complied with (good) or not (bad)? (factor) # The Tasks We would like to find out how the credit risk of a person depends on the provided additional attributes of the person and the considered credit itself. Therefore, our response in this case is the binary variable `credit_risk`, as covariates we have 20 additional variables (17 categorical, 3 numeric). Apply the forest-building function `cforest` to build a forest model as described in the following points: * Load the data set `"german.rds"`. * Build a forest model with 50 trees. * Predict the credit risk of a new client who doesn't have a checking account, has never taken a credit before, is a 40-year-old married male who is a skilled employee working in a business in his home town for already 6 years now, and who plans to take one credit of 5000 DM for repairs in his own house where he moved in 3 years ago. The credit duration is one year, the installment rate is 15 %. There is no information provided on his savings and no registered telephone number on the client's name. There are no other installment plans or other debtors and there is no other person depending financially on the client. Does it have an impact on the prediction if he plans to spend the money on furniture? * Which covariates have the highest influence on the model? * Separate the data set into a learning set (2/3 of the full data) and a testing set (1/3 of the full data). Build a forest on the learning data set and predict the credit risk on the testing data set. Assess the performance by evaluating the number of misclassifications on the testing data. How do parameters such as the number of trees influence the performance? * Apply the function `ranger` to build a forest model using the same parameters and compare it to the cforest model, e.g., based on predictions, the number of misclassifications on the testing data or variable importance. ```{r, include = FALSE} # data <- readRDS("data/german.rds") f <- credit_risk ~ status + duration + credit_history + purpose + amount + savings + employment_duration + installment_rate + personal_status_sex + other_debtors + present_residence + property + age + other_installment_plans + housing + number_credits + job + people_liable + telephone + foreign_worker library("partykit") cf <- cforest(formula = f, data = data, ntree = 50) newclient <- data.frame(status = "no checking account", duration = 12, credit_history = "no credits taken/all credits paid back duly", purpose = "repairs", amount = 5000, savings = "unknown/no savings account", employment_duration = "4 <= ... < 7 yrs", installment_rate = "< 20", personal_status_sex = "male : married/widowed", other_debtors = "none", present_residence = "1 <= ... < 4 yrs", property = "real estate", age = 40, other_installment_plans = "none", housing = "own", number_credits = "1", job = "skilled employee/official", people_liable = "0 to 2", telephone = "no", foreign_worker = "no" ) newclient2 <- newclient newclient2$purpose <- "furniture/equipment" predict(cf, newdata = newclient) predict(cf, newdata = newclient2) ``` ```{r, include = FALSE} set.seed(4) trainid <- sample(1:NROW(data), size = 667, replace = FALSE) train <- data[trainid,] test <- data[-trainid,] ``` ```{r, include = FALSE} library("ranger") library("caret") rf <- ranger(formula = f, data = train, num.trees = 50) rf$confusion.matrix rf <- ranger(formula = f, data = train, num.trees = 500) rf$confusion.matrix rf <- ranger(formula = f, data = train, num.trees = 50) pred_cf <- predict(cf, newdata = test) confusionMatrix(pred_cf, test$credit_risk) pred_rf <- predict(rf, data = test)$prediction confusionMatrix(pred_rf, test$credit_risk) varimp(cf) rf <- ranger(f, data = train, num.trees = 50, importance = "impurity") importance(rf) ```partykit/inst/ULGcourse-2020/exercises/exercise_titanic.Rmd0000644000176200001440000001070614172227777023333 0ustar liggesusers--- title: "Exercise: Titanic" output: html_document --- ```{r, include = FALSE} file <- "data/titanic.rds" stopifnot(file.exists(file)) data <- readRDS(file) head(data) ``` In this exercise we will use the 'titanic' data set. As the data set presented on the slides, this version describes the survival status of individual passengers on the Titanic, however, it provides additional information on the passengers given by 10 covriates but does not include information on the crew. Simply download the file `r xfun::embed_file(file, text = "titanic.rds")` by clicking or download it from OpenOLAT or from the corresponding homepage which also provides more detailed information on the data set. We can import/read this file using `data <- readRDS(...)`. The file contains the following information: * `name`: passenger's name (character). * `gender.`: 'male' or 'female' (factor) . * `age`: age in years (numeric). * `class`: passenger class or the type of service aboard for crew members (factor). * `embarked`: place of embarkment (factor; C = Cherbourg, Q = Queenstown, S = Southampthon). * `country`: home country (factor). * `ticketno`: ticket number (integer; NA for crew members). * `fare`: ticket price (numeric; NA for crew members, musicians and employees of the shipyard company). * `sibsp`: number if siblings/spouses aboard (ordered factor). * `parch`: number of parents/children aboard (ordered factor). * `survived`: Did the passenger survive? (factor). # The Tasks We would like to find out how the survival status of a passenger on the Titanic depends on the provided additional attributes. By employing a tree model we are looking for a separation into homogeneous subgroups based on the additional information. Our response in this case is the binary variable `survived`, as covariates we use the additional variables `gender`, `age`, `class`, `embarked`, `fare`, `sibsp` and `parch`. Apply the CTree algorithm to build the tree models described in the following steps: * Load the data set `"titanic.rds"`. * Build a tree using pre-pruning with a significance level of 0.01, with a maximum depth of 5 levels and the segment size of terminal nodes not being smaller than 20. * Evaluate the performance on the learning data by calculating the corresponding confusion matrix. How large is the misclassification rate? * Predict the survival status of a 30-years-old female passenger, travelling with her husband and her two parents who all embarked in Southampton and paid 25 Pounds each for a 2nd class ticket. Does the prediction change if she had a ticket for the 3rd class? * Separate the data set into a learning set (2/3 of the full data) and a testing set (1/3 of the full data). Note that for observations in the test data which include NAs predictions can not be made. Build a tree on the learning data set and predict the survival status on the testing data set. Evaluate the performance based on the number of misclassifications. How do parameters such as a minimal segment size or the significance level applied for pre-pruning influence the performance? ```{r, include = FALSE} formula <- survived ~ gender + age + class + embarked + fare + sibsp + parch library("partykit") ct <- ctree(formula, data = data) ct <- ctree(formula, data = data, control = ctree_control(alpha = 0.01, minbucket = 20, maxdepth = 5)) library("caret") caret::confusionMatrix(data$survived, predict(ct, newdata = data)) newpassenger <- data.frame(gender = "female", age = 30, class = "2nd", embarked = "S", fare = 25, sibsp = "1", parch = "2") predict(ct, newdata = newpassenger) newpassenger2 <- newpassenger newpassenger2$class <- "3rd" predict(ct, newdata = newpassenger2) ``` ```{r, include = FALSE, echo = FALSE, out.width = "100%", fig.width = 10, fig.height = 5} plot(ct) ``` ```{r, include = FALSE} set.seed(4) trainid <- sample(1:NROW(data), size = 1471, replace = FALSE) train <- data[trainid,] test <- data[-trainid,] test <- na.omit(test) ctrain <- ctree(formula, data = train) predtest <- predict(ctrain, newdata = test) library("caret") caret::confusionMatrix(test$survived, predtest) ctrain <- ctree(formula, data = train, control = ctree_control(alpha = 0.01)) plot(ctrain) predtest <- predict(ctrain, newdata = test) caret::confusionMatrix(test$survived, predtest) ``` partykit/inst/ULGcourse-2020/exercises/exercise_german_credit.Rmd0000644000176200001440000001627714172227777024514 0ustar liggesusers--- title: "Exercise: South German Credit" output: html_document --- ```{r, include = FALSE} file <- "data/german.rds" stopifnot(file.exists(file)) data <- readRDS(file) head(data) ``` In this exercise we will use the 'South German Credit' data set. It contains a classification of the credit risk of 1000 individuals into 'good' and 'bad' together with 20 additional attributes. Simply download the file `r xfun::embed_file(file, text = "german.rds")` by clicking or download it from the corresponding homepage which also provides more detailed information on the data set. We can import/read this file using `data <- readRDS(...)`. The file contains the following information: * `status`: status of the debtor's checking account with the bank (factor). * `duration`: credit duration in months (integer). * `credit_history`: history of compliance with previous or concurrent credit contracts (factor). * `purpose`: purpose for which the credit is needed (factor). * `amount`: credit amount in DM (integer). * `savings`: debtor's savings (factor). * `employment_duration`: duration of debtor's employment with current employer (factor; discretized quantitative). * `installment_rate`: credit installments as a percentage of debtor's disposable income (ordered factor; discretized quantitative). * `personal_status_sex`: combined information on sex and marital status (factor; sex cannot be recovered from the variable, because male singles and female non-singles are coded with the same code (2); female widows cannot be easily classified, because the code table does not list them in any of the female categories). * `other_debtors`: Is there another debtor or a guarantor for the credit? (factor). * `present_residence`: length of time (in years) the debtor lives in the present residence (ordered factor; discretized quantitative). * `property`: the debtor's most valuable property, i.e. the highest possible code is used. Code 2 is used, if codes 3 or 4 are not applicable and there is a car or any other relevant property that does not fall under variable `savings` (factor). * `age`: age in years (integer). * `other_installment_plans`: installment plans from providers other than the credit-giving bank (factor). * `housing`: type of housing the debtor lives in (factor) * `number_credits`: number of credits including the current one the debtor has (or had) at this bank (ordered factor, discretized quantitative). * `job`: quality of debtor's job (ordinal) * `people_liable`: number of persons who financially depend on the debtor (i.e., are entitled to maintenance) (factor, discretized quantitative). * `telephone`: Is there a telephone landline registered on the debtor's name? (factor; remember that the data are from the 1970s) * `foreign_worker`: Is the debtor a foreign worker? (factor) * `credit_risk`: Has the credit contract been complied with (good) or not (bad)? (factor) # The Tasks We would like to find out how the credit risk of a person depends on the provided additional attributes of the person and the considered credit itself. By employing a tree model we are looking for a separation into homogeneous subgroups based on the additional information. Our response in this case is the binary variable `credit_risk`, as covariates we have 20 additional variables (17 categorical, 3 numeric). Apply the CTree algorithm to build the tree models described in the following steps: * Load the data set `"german.rds"`. * Build a tree using pre-pruning with a significance level of 0.04, with a maximum depth of 4 levels and the segment size of terminal nodes not being smaller than 15. * Evaluate the performance on the learning data by calculating the corresponding confusion matrix. How large is the misclassification rate? * Predict the credit risk of a new client who doesn't have a checking account, has never taken a credit before, is a 35-year-old married male who is a skilled employee working in a business in his home town for already 5 years now, and who plans to take one credit of 4000 DM for repairs in his own house where he moved in 2 years ago. The credit duration is 24 months, the installment rate is 30 %. There is no information provided on his savings and no registered telephone number on the client's name. There are no other installment plans or other debtors and there is no other person depending financially on the client. Does it have an impact on the prediction if the duration is reduced to only 12 months? * Separate the data set into a learning set (2/3 of the full data) and a testing set (1/3 of the full data). Build a tree on the learning data set and predict the credit risk on the testing data set. Evaluate the performance based on the number of misclassifications. How do parameters such as a minimal segment size or the significance level applied for pre-pruning influence the performance? ```{r, include = FALSE} # data <- readRDS("data/german.rds") formula <- credit_risk ~ status + duration + credit_history + purpose + amount + savings + employment_duration + installment_rate + personal_status_sex + other_debtors + present_residence + property + age + other_installment_plans + housing + number_credits + job + people_liable + telephone + foreign_worker library("partykit") ct <- ctree(formula, data = data) ct <- ctree(formula, data = data, control = ctree_control(alpha = 0.04, minbucket = 15, maxdepth = 4)) library("caret") caret::confusionMatrix(data$credit_risk, predict(ct, newdata = data)) newclient <- data.frame(status = "no checking account", duration = 24, credit_history = "no credits taken/all credits paid back duly", purpose = "repairs", amount = 4000, savings = "unknown/no savings account", employment_duration = "4 <= ... < 7 yrs", installment_rate = "25 <= ... < 35", personal_status_sex = "male : married/widowed", other_debtors = "none", present_residence = "1 <= ... < 4 yrs", property = "real estate", age = 35, other_installment_plans = "none", housing = "own", number_credits = "1", job = "skilled employee/official", people_liable = "0 to 2", telephone = "no", foreign_worker = "no" ) predict(ct, newdata = newclient) newclient2 <- newclient newclient2$duration <- 12 predict(ct, newdata = newclient2) ``` ```{r, include = FALSE, echo = FALSE, out.width = "100%", fig.width = 10, fig.height = 5} plot(ct) ``` ```{r, include = FALSE} set.seed(4) trainid <- sample(1:NROW(data), size = 667, replace = FALSE) train <- data[trainid,] test <- data[-trainid,] ctrain <- ctree(formula, data = train) predtest <- predict(ctrain, newdata = test) library("caret") caret::confusionMatrix(test$credit_risk, predtest) ctrain <- ctree(formula, data = train, control = ctree_control(alpha = 0.01)) plot(ctrain) predtest <- predict(ctrain, newdata = test) caret::confusionMatrix(test$credit_risk, predtest) ``` partykit/inst/ULGcourse-2020/exercises/data/0000755000176200001440000000000014172227777020252 5ustar liggesuserspartykit/inst/ULGcourse-2020/exercises/data/titanic.rds0000644000176200001440000011445514172227777022431 0ustar liggesusers‹í½ xÇq <$J¢A@€\QR6EÉ’lÙ²,á H€Ûq°ì‹hvh'¡’8Çg;qça%‘²;gÇŽc+>ÇsIœ8;‰s¹Ü#É]’Ë]ΗËÝåâ»ó_ÝÓU]];³»éË㿯9Øéš~TWWWUWW¿zŸçy-^Ë^H­ð§×úøìÈÝ/‡wáÇÚ<ïúw{{¼àïƒýóóaiétn2>“ë/U QiÃduAVT©$YÃÕ¥ äÎEå`µ`Žr€é¨\^‰â 7œ_÷ã¼9fAÊSˆò~nÒ7r'Þ?i Šå R¸° €ã~”`xÞS@mŠ~µœ;·ùñšUJ¶7• ¥MVË‚ÆüRÉ/˜ÂoíŸá¹»û‹wOVK›O'Ÿá©ò Ï-æƒg¸b 9Õ?û¥Lu˜¹þêRµ\ü à l >¸ùæ¼_(& “~5+—MQûûóPN’_•a…bˆLJósSA\΃˜†fY}ê—áÕ™ÜHì—–sS…°®€[UÈDàã€õôóëQŒHLÚ x J1Žzo1xÒ/åƒ8š ‹ÅPu°8ÄÓ/(¨­l>³&@g‹+0V¹éj>*.RŠ&·¿° A´Ñ[S°­¶”pü‡‹aÙŸ‡ÑÎÍùÅJ„ÈéD Ö.Þöc&CcP3VÍÃïÜl¬E±ÅBéÊÆ(47Å~X ÌíÆ–Ä_¨ú¹Á8— ¶UÝ ŠÊå0P ÏGâ0@TW å®Ce£A„kyÂ%¼?~á¹<ÔYö7J.ùÝÓ¯ÆÈýîsšê±ƒ~\„vâ°\>ä·@ê¶3Gñ33z$Õ[ íÄÑ Ôa?&¤žL²´Î„Kk0ÉtS —_6à'8x2˜óó~î,´ j^ŒÃ¼o o­…Tˆ.TÒL"DÀãµ€1€Bìΰ³Àm"×.W©ø4Â5Ð¥¥`Æ%7•à‹Òå0»¥€è‰¥SÓ–;èŸÉ<ÎÑy.«z‘R>ƒxË' 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liggesusers\documentclass[11pt,t,usepdftitle=false,aspectratio=169]{beamer} \usetheme[nototalframenumber,license]{uibk} \title{Classification and Regression Trees and Beyond} \subtitle{Supervised Learning: Algorithmic Modeling} \author{Lisa Schlosser, Achim Zeileis} %% forest header image \renewcommand{\headerimage}[1]{% \IfStrEqCase{#1}{% {1}{% \gdef\myheaderimageid{#1}% \gdef\myheaderimageposition{nw}% \gdef\myheaderimage{forest.jpg}% }}[% \gdef\myheaderimageid{1}% \gdef\myheaderimageposition{nw}% \gdef\myheaderimage{forest.jpg}% ]% } \headerimage{1} %% custom subsection slides \setbeamercolor*{subsectionfade}{use={normal text},parent={normal text},fg=structure.fg!30!normal text.bg} \AtBeginSubsection[]{% \begin{frame}[c] \begin{center} \usebeamercolor[fg]{subsectionfade} \Large \insertsection \\[2ex] \usebeamercolor[fg]{structure} \huge\bfseries\insertsubsection \end{center} \end{frame} } %% for \usepackage{Sweave} <>= transparent_png <- function(name, width, height, ...) { grDevices::png(filename = paste(name, "png", sep = "."), width = width, height = height, res = 100, units = "in", type = "quartz", bg = "transparent") } @ \SweaveOpts{engine=R, eps=FALSE, echo=FALSE, results=hide, keep.source=TRUE} <>= options(prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE, width = 70) library("rpart") library("partykit") library("coin") set.seed(7) @ <>= data("CPS1985", package = "AER") data("Titanic", package = "datasets") ttnc <- as.data.frame(Titanic) ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] names(ttnc)[2] <- "Gender" @ \begin{document} \section{Classification and regression trees and beyond} \subsection{Motivation} %\subsectionpage \begin{frame}[fragile] \frametitle{Motivation} \smallskip \textbf{Idea:} ``Divide and conquer.'' \begin{itemize} \item \emph{Goal:} Split the data into small(er) and (rather) homogenous subgroups. \item \emph{Inputs:} Explanatory variables (or covariates/regressors) used for splitting. \item \emph{Output:} Prediction for dependent (or target) variable(s). \end{itemize} \bigskip \pause \textbf{Formally:} \begin{itemize} \item Dependent variable $Y$ (possibly multivariate). \item Based on explanatory variables $X_1, \dots, X_m$. \item ``Learn'' subgroups of data by combining splits in $X_1, \dots, X_m$. \item Predict $Y$ with (simple) model in the subgroups, often simply the mean. \end{itemize} \bigskip \pause \textbf{Key features:} \begin{itemize} \item Predictive power in nonlinear regression relationships. \item Interpretability (enhanced by tree visualization), i.e., no ``black box''. \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \textbf{Example:} Survival (yes/no) on the Titanic. Women and children first? \begin{center} \setkeys{Gin}{width=0.9\textwidth} <>= ct_ttnc <- ctree(Survived ~ Gender + Age + Class, data = ttnc, alpha = 0.01) plot(ct_ttnc) @ \end{center} \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \textbf{Model formula:} \code{Survived ~ Gender + Age + Class}. \bigskip \textbf{Data:} Information on the survival of 2201~passengers on board the ill-fated maiden voyage of the RMS~Titanic in 1912. A data frame containing \Sexpr{nrow(ttnc)} observations on \Sexpr{ncol(ttnc)} variables. \bigskip \begin{tabular}{ll} \hline Variable & Description\\ \hline \code{Class} & Factor: 1st, 2nd, 3rd, or Crew.\\ \code{Gender} & Factor: Male, Female.\\ \code{Age} & Factor: Child, Adult.\\ \code{Survived} & Factor: No, Yes.\\ \hline \end{tabular} \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \textbf{Example:} Determinants of wages and returns to education. \begin{center} \setkeys{Gin}{width=0.99\textwidth} <>= ct_cps <- ctree(log(wage) ~ education + experience + age + ethnicity + gender + union, data = CPS1985, alpha = 0.01) plot(ct_cps) @ \end{center} \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \textbf{Model formula:} \code{log(wage) ~ education + experience + age + ethnicity + gender + union}. \bigskip \textbf{Data:} Random sample from the May 1985 US Current Population Survey. A data frame containing \Sexpr{nrow(CPS1985)} observations on \Sexpr{ncol(CPS1985)} variables. \bigskip \begin{tabular}{ll} \hline Variable & Description\\ \hline \code{wage} & Wage (in US dollars per hour). \\ \code{education} & Education (in years). \\ \code{experience} & Potential work experience (in years, \code{age - education - 6}). \\ \code{age} & Age (in years). \\ \code{ethnicity} & Factor: Caucasian, Hispanic, Other. \\ \code{gender} & Factor: Male, Female. \\ \code{union} & Factor. Does the individual work on a union job? \\ \hline \end{tabular} \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \textbf{Alternatively:} Linear regression tree. \begin{center} \setkeys{Gin}{width=0.9\textwidth} <>= mob_cps <- lmtree(log(wage) ~ education | experience + age + ethnicity + gender + union, data = CPS1985) plot(mob_cps) @ \end{center} \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \textbf{Model formula:} \code{log(wage) ~ education | experience + age + ethnicity + gender + union}. \bigskip \textbf{Model fit:} \begin{itemize} \item Not just a group-specific mean. \item But group-specific intercept and slope (i.e., returns to education). \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \textbf{Example:} Nowcasting (1--3 hours ahead) of wind direction at Innsbruck Airport. \setkeys{Gin}{width=0.87\linewidth} \begin{center} \includegraphics{circtree_ibk.pdf} \end{center} \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \textbf{Data:} 41,979 data points for various weather observations. \begin{itemize} \item Dependent variable: Wind direction 1--3 hours ahead. \item Explanatory variables: Current weather observations including wind direction, wind speed, temperature, (reduced) air pressure, relative humidity. \item Circular response in $[0^{\circ}, 360^{\circ})$ with $0^{\circ} = 360^{\circ}$. \end{itemize} \bigskip \textbf{Model fit:} Circular distribution (von Mises), fitted by maximum likelihood. \end{frame} % \begin{frame}[fragile] % \frametitle{Motivation} % {\small Wage data: \quad $log(wage) \; \sim \; education + experience + ethnicity + region + parttime$} % \begin{center} % \setkeys{Gin}{width=0.99\textwidth} % <>= % data("CPS1988", package = "AER") % ## ctree % plot(ctree(log(wage)~education+experience+ethnicity+region+parttime,data=CPS1988, % control = ctree_control(alpha = 0.01, minsplit = 7000))) % @ % \end{center} % \end{frame} % \begin{frame}[fragile] % \frametitle{Motivation} % {\small Boston housing: \quad $medv \; \sim \; lstat + crim + rm + age + black$} % \begin{center} % \setkeys{Gin}{width=0.99\textwidth} % <>= % data("Boston") % plot(ctree(medv~lstat + crim + rm + age + black, % data = Boston, control = ctree_control(alpha = 0.01, minsplit = 150))) % @ % \end{center} % \end{frame} \begin{frame}[fragile] \frametitle{Motivation} \textbf{Original idea:} Trees are purely algorithmic models without assumptions. \begin{itemize} \item Data-driven ``learning'' of homogenous subgroups. \item Simple constant fit in each group, e.g., an average or proportion. \end{itemize} \bigskip \pause \textbf{Subsequently:} Trees are well-suited for combination with classical models. \begin{itemize} \item Group-wise models, e.g., fitted by least squares or maximum likelihood. \item Model-based learning accounts for model differences across subgroups. \end{itemize} \bigskip \pause \textbf{Trade-off:} \begin{itemize} \item Assume simple model and learn larger tree \emph{vs.} \item More complex model and potentially smaller tree. \end{itemize} \end{frame} \subsection{Tree algorithm} \begin{frame}[fragile] \frametitle{Tree algorithm} \textbf{Base algorithm:} \begin{enumerate} \item Fit a model to the response $Y$. \item Assess association of $Y$ (or a corresponding transformation/goodness-of-fit measure) and each possible split variable $X_j$. \item Split sample along the $X_{j^{\ast}}$ with strongest association: Choose split point with highest improvement of the model fit. \item Repeat steps 1--3 recursively in the subsamples until some stopping criterion is met. \item \emph{Optionally:} Reduce size of the tree by pruning branches of splits that do not improve the model fit sufficiently. \end{enumerate} \end{frame} \begin{frame}[fragile] \frametitle{Tree algorithm} \textbf{Specific algorithms:} Many (albeit not all) can be derived from the base algorithm by combining suitable building blocks. \bigskip \pause \textbf{Models for $Y$:} Simple constant fits vs.\ more complex statistical models. \bigskip \pause \textbf{Goodness of fit:} Suitable measure depends on type of response variable(s) $Y$ and the corresponding model. \end{frame} \begin{frame}[fragile] \frametitle{Tree algorithm} \textbf{Goodness of fit:} \begin{itemize} \item Numeric response: \begin{itemize} \item $Y$ or ranks of $Y$. \item (Absolute) deviations $Y - \bar Y$. \item Residual sum of squares $\sum (Y - \hat{Y})^2$. \end{itemize} \pause \item Categorical response: \begin{itemize} \item Dummy variables for categories. \item Number of misclassifications. \item Gini impurity. \end{itemize} \pause \item Survival response: \begin{itemize} \item Log-rank scores. \end{itemize} \pause \item Parametric model: \begin{itemize} \item Residuals. \item Model scores (gradient contributions). \end{itemize} \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Tree algorithm} \textbf{Split variable selection:} Optimize some criterion over all $X_j$ ($j = 1, \dots, m$). \begin{itemize} \item Objective function (residual sum of squares, log-likelihood, misclassification rate, impurity, \dots). \item Test statistic or corresponding $p$-value. \end{itemize} \bigskip \pause \textbf{Split point selection:} Optimize some criterion over all (binary) splits in $X_{j^*}$. \begin{itemize} \item Objective function. \item Two-sample test statistic or corresponding $p$-value. \end{itemize} \bigskip \pause \textbf{Stopping criteria:} \begin{itemize} \item Constraints: Number of observations per node, tree depth, \dots \item Lack of improvement: Significance, information criteria, \dots \end{itemize} \end{frame} \subsection{Split variable selection} \begin{frame}[fragile] \frametitle{Split variable selection} \textbf{Idea:} \begin{itemize} \item Select variable $X_j$ ($j = 1, \dots, m$) most associated with heterogeneity in $Y$. \item Heterogeneity captured by goodness-of-fit measure. \item \emph{Often:} Maximum association over all possible binary splits. \item \emph{Alternatively:} Overall association. \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Split variable selection} \textbf{Potential bias:} Variables with many potential splits may yield greater association ``by chance'', e.g., continuous $X_j$ or categorical with many levels. \bigskip \pause \textbf{Unbiased recursive partitioning:} Accounts for potential random variation by employing $p$-values from appropriate statistical tests. \bigskip \pause \textbf{Possible tests:} Depend on scales of $Y$, $X_j$, and the adopted model. \begin{itemize} \item $\chi^2$ test, Pearson correlation test, two-sample t-test, ANOVA. \item Maximally-selected two-sample tests. \item Parameter instability tests. \item \dots \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Split variable selection} \textbf{Examples:} \begin{itemize} \item Titanic survival and wage determinants data. \item Selection of first split variable in root node. \item Employ classical statistical tests. \item Does not exactly match a particular tree algorithm but similar to CTree. \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Split variable selection} \textbf{Assess pairwise associations:} \code{Survived ~ Gender} (Titanic). \begin{minipage}[t]{0.43\linewidth} <>= plot(Survived ~ Gender, data = ttnc) @ \vspace{-0.7cm} <>= <> @ \end{minipage} \hfill \pause \begin{minipage}[t]{0.5\linewidth} <>= xtabs(~ Survived + Gender, data = ttnc) @ \end{minipage} \pause <>= chisq.test(xtabs(~ Survived + Gender, data = ttnc)) @ \end{frame} \begin{frame}[fragile] \frametitle{Split variable selection} \textbf{Assess pairwise associations:} \code{Survived ~ Age} (Titanic). \begin{minipage}[t]{0.43\linewidth} <>= plot(Survived ~ Age, data = ttnc) @ \vspace{-0.7cm} <>= <> @ \end{minipage} \hfill \pause \begin{minipage}[t]{0.5\linewidth} <>= xtabs(~ Survived + Age, data = ttnc) @ \end{minipage} <>= chisq.test(xtabs(~ Survived + Age, data = ttnc)) @ \end{frame} \begin{frame}[fragile] \frametitle{Split variable selection} \textbf{Assess pairwise associations:} \code{Survived ~ Class} (Titanic). \begin{minipage}[t]{0.43\linewidth} <>= plot(Survived ~ Class, data = ttnc) @ \vspace{-0.7cm} <>= <> @ \end{minipage} \hfill \pause \begin{minipage}[t]{0.5\linewidth} <>= xtabs(~ Survived + Class, data = ttnc) @ \end{minipage} <>= chisq.test(xtabs(~ Survived + Class, data = ttnc)) @ \end{frame} % % \begin{frame}[fragile] % \frametitle{Split variable selection} % \textbf{Compare pairwise associations} (Titanic): % Based on independence tests, e.g., $\chi^2$-test for categorical variables. % \vspace{0.4cm} % <>= % chisq_test(Survived ~ Gender, data = ttnc) % @ % % \vspace{0.2cm} % % <>= % chisq_test(Survived ~ Age, data = ttnc) % @ % % \vspace{0.7cm} % % $\Rightarrow$ Select the split variable showing the lowest $p$-value. % % \end{frame} \begin{frame}[fragile] \frametitle{Split variable selection} \begin{center} \setkeys{Gin}{width=0.95\textwidth} <>= <> @ \end{center} \end{frame} \begin{frame}[fragile] \frametitle{Split variable selection} \textbf{Assess pairwise associations:} \code{log(wage) ~ education} (Wages). \begin{minipage}[t]{0.39\linewidth} <>= plot(log(wage) ~ education, data = CPS1985) @ \vspace{-0.7cm} \setkeys{Gin}{width=\textwidth} <>= <> @ \end{minipage} \hfill \pause \begin{minipage}[t]{0.59\linewidth} <>= cor.test(~ log(wage) + education, data = CPS1985) @ <>= out <- capture.output(cor.test(~ log(wage) + education, data = CPS1985)) out <- gsub("alternative hypothesis: ", "alternative hypothesis:\n", out, fixed = TRUE) writeLines(out) @ \end{minipage} \end{frame} \begin{frame}[fragile] \frametitle{Split variable selection} \textbf{Assess pairwise associations:} \code{log(wage) ~ gender} (Wages). \begin{minipage}[t]{0.39\linewidth} <>= plot(log(wage) ~ gender, data = CPS1985) @ \vspace{-0.7cm} \setkeys{Gin}{width=\textwidth} <>= <> @ \end{minipage} \hfill \pause \begin{minipage}[t]{0.59\linewidth} <>= t.test(log(wage) ~ gender, data = CPS1985) @ <>= out <- capture.output(t.test(log(wage) ~ gender, data = CPS1985)) out <- gsub("alternative hypothesis: ", "alternative hypothesis:\n", out, fixed = TRUE) writeLines(out) @ \end{minipage} \end{frame} \begin{frame}[fragile] \frametitle{Split variable selection} \begin{center} \setkeys{Gin}{width=0.99\textwidth} <>= <> @ \end{center} \end{frame} \subsection{Split point selection \& pruning} \begin{frame}[fragile] \frametitle{Split point selection} \textbf{Idea:} \begin{itemize} \item Split $Y$ into most homogenous subgroups with respect to selected $X_{j^*}$. \item Homogeneity captured by goodness-of-fit measure. \item \emph{Often:} Consider only binary splits. \item Trivial for binary $X_{j^*}$. \item Otherwise typically exhaustive search over all binary splits. \item Possibly already done in split variable selection. \end{itemize} \bigskip \pause \textbf{Goodness-of-fit measure:} Depends on scale of $Y$ and the adopted model. \begin{itemize} \item Objective function (residual sum of squares, log-likelihood, misclassification rate, impurity, \dots). \item Two-sample test statistic or corresponding $p$-value. \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Split point selection} \textbf{Example:} \begin{itemize} \item Wage determinants data. \item Selection of best split point in education in root node. \item Residual sum of squares vs.\ normal log-likelihood. \item Two-sample ANOVA-type $\chi^2$ test and corresponding $p$-value. \end{itemize} \end{frame} <>= evalsplit <- function(sp) { m <- lm(log(wage) ~ factor(education <= sp), data = CPS1985) s <- independence_test(log(wage) ~ factor(education <= sp), data = CPS1985, teststat = "quadratic") c( rss = deviance(m), loglik = logLik(m), logpval = pchisq(statistic(s), df = 1, log = TRUE, lower.tail = FALSE), teststatistic = statistic(s) ) } sp <- head(sort(unique(CPS1985$education)), -1) eval <- sapply(sp, evalsplit) @ \begin{frame}[fragile] \frametitle{Split point selection} <>= par(mar = c(5, 3, 1, 3)) plot(sp, eval["loglik",], type = "n", xlab = "education", ylab = "", axes = FALSE) abline(v = 13, lty = 2, lwd = 1.5) lines(sp, eval["loglik", ], type = "o", col = 2, lwd = 1.5) axis(2, col.ticks = 2, col.axis = 2) par(new = TRUE) plot(sp, eval["teststatistic",], type = "o", col = 4, lwd = 1.5, xlab = "", ylab = "", axes = FALSE) axis(4, col.ticks = 4, col.axis = 4) axis(1) axis(1, at = 13) box() legend("topleft", c("Log-likelihood", "Test statistic"), col = c(2, 4), lwd = 1.5, pch = 1, bty = "n") @ \end{frame} \begin{frame}[fragile] \frametitle{Split point selection} <>= par(mar = c(5, 3, 1, 3)) plot(sp, eval["rss",], type = "n", xlab = "education", ylab = "", axes = FALSE) abline(v = 13, lty = 2, lwd = 1.5) lines(sp, eval["rss", ], type = "o", col = 2, lwd = 1.5) axis(2, col.ticks = 2, col.axis = 2) par(new = TRUE) plot(sp, eval["logpval",], type = "o", col = 4, lwd = 1.5, xlab = "", ylab = "", axes = FALSE) axis(4, col.ticks = 4, col.axis = 4) axis(1) axis(1, at = 13) box() legend("bottomleft", c("Residual sum of squares", "Log-p-value"), col = c(2, 4), lwd = 1.5, pch = 1, bty = "n") @ \end{frame} \begin{frame}[fragile] \frametitle{Split point selection} \begin{center} \setkeys{Gin}{width=0.99\textwidth} <>= <> @ \end{center} \end{frame} \begin{frame}[fragile] \frametitle{Pruning} \textbf{Goal:} Avoid overfitting. \medskip \textbf{Pre-pruning:} Internal stopping criterium. Stop splitting when there is no significant association to any of the possible split variables $X_j$. \medskip \textbf{Post-pruning:} Grow large tree and prune splits that do not improve the model fit (e.g., via cross-validation or information criteria). \end{frame} \begin{frame}[fragile] \frametitle{Pruning} \textbf{Pre-pruning:} \begin{itemize} \item[+] Does not require additional calculations as only already provided information from statistical test is used. \item[+] Computationally less expensive as trees are prevented from getting too large. \item[--] Performance depends on the power of the selected statistical test. \end{itemize} \vspace{0.4cm} \textbf{Post-pruning:} \begin{itemize} \item[+] Stable method to avoid overfitting, regardless of the power of the employed statistical test. \item[+] Can employ information criteria such as AIC or BIC for model-based partitioning. \item[--] Computationally more expensive as very large trees are grown and additional (out-of-bag) evaluations are required. \end{itemize} \end{frame} \subsection{Conditional inference trees} \begin{frame} \frametitle{Conditional inference trees} \textbf{CTree:} \begin{itemize} \item Employs general conditional inference (or permutation test) framework for association of $h(Y)$ vs.\ $g(X_j)$. \item Broadly applicable by choosing suitable transformations $h(\cdot)$ and $g(\cdot)$. \item \emph{Examples:} Univariate $Y$ of arbitrary scale, multivariate, model-based, etc. \item \emph{Default:} Pre-pruning based on direct asymptotic tests for split variable selection. Maximally-selected two-sample statistics for split point selection. \item \emph{Software:} R package \emph{partykit} (and previously: \emph{party}). \item \emph{Reference:} Hothorn, Hornik, Zeileis (2006). \end{itemize} \bigskip \textbf{Note:} CTree used in previous illustrations of classification and regression trees. \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \textbf{Illustration:} Titanic survival data. \bigskip \textbf{Data:} Preprocessing from four-way contingency table \code{Titanic} in base R. <>= data("Titanic", package = "datasets") ttnc <- as.data.frame(Titanic) ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] names(ttnc)[2] <- "Gender" @ \bigskip \textbf{CTree:} With default arguments. <>= library("partykit") ct_ttnc <- ctree(Survived ~ Gender + Age + Class, data = ttnc) plot(ct_ttnc) print(ct_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \setkeys{Gin}{width=0.9\linewidth} <>= plot(ct_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} <>= print(ct_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \textbf{Predictions:} Different types. <>= ndm <- data.frame(Gender = "Male", Age = "Adult", Class = c("1st", "2nd", "3rd")) predict(ct_ttnc, newdata = ndm, type = "node") predict(ct_ttnc, newdata = ndm, type = "response") predict(ct_ttnc, newdata = ndm, type = "prob") @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \textbf{Predictions:} Women and children first? <>= ndf <- data.frame(Gender = "Female", Age = "Adult", Class = c("1st", "2nd", "3rd")) ndc <- data.frame(Gender = "Male", Age = "Child", Class = c("1st", "2nd", "3rd")) cbind( Male = predict(ct_ttnc, newdata = ndm, type = "prob")[, 2], Female = predict(ct_ttnc, newdata = ndf, type = "prob")[, 2], Child = predict(ct_ttnc, newdata = ndc, type = "prob")[, 2] ) @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \textbf{Hyperparameters:} See \code{?ctree_control}. \begin{itemize} \item \code{alpha}: Significance level for pre-pruning in split variable selection. \item \code{minsplit}: Minimum number of observations in a node for splitting. \item \code{minbucket}: Minimum number of observations in a terminal node. \item \code{maxdepth}: Maximum depth of the tree. \item \code{multiway}: Use multiway splits for unordered factors with $> 2$ levels? \item \dots \end{itemize} \bigskip \pause \textbf{Example:} <>= ct_ttnc2 <- ctree(Survived ~ Gender + Age + Class, data = ttnc, alpha = 0.01, minbucket = 5, minsplit = 15, maxdepth = 4) plot(ct_ttnc2) @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \setkeys{Gin}{width=\linewidth} <>= plot(ct_ttnc2) @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \textbf{Predictions:} Male children in 1st and 2nd class are now in their own terminal nodes. <>= predict(ct_ttnc2, newdata = ndc, type = "prob") @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \textbf{Evaluations:} ``As usual.'' \begin{itemize} \item In-sample vs. out-of-sample. \item Scoring rules (e.g., misclassification rates or other loss functions). \item Confusion matrix. \item Receiver operator characteristic (ROC) curve. \item \dots \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \textbf{In-sample:} Augment learning data. <>= ttnc$Fit <- predict(ct_ttnc2, type = "response") ttnc$Group <- factor(predict(ct_ttnc2, type = "node")) @ \bigskip \textbf{Confusion matrix:} <>= xtabs(~ Fit + Survived, data = ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \textbf{Terminal nodes:} Recompute empirical survival rates. <>= tab <- xtabs(~ Group + Survived, data = ttnc) prop.table(tab, 1) @ \end{frame} \begin{frame}[fragile] \frametitle{Conditional inference trees} \textbf{More graphics:} \emph{ggplot2} support via \code{autoplot()} method from \emph{ggparty}. \setkeys{Gin}{width=0.9\linewidth} <>= library("ggparty") theme_set(theme_minimal()) autoplot(ct_ttnc2) @ \end{frame} \subsection{Recursive partitioning} \begin{frame} \frametitle{Recursive partitioning} \textbf{RPart:} \begin{itemize} \item Implements classic CART algorithm (classification and regression trees). \item Split variable and split point selection via exhaustive search based on objective functions. \item Hence biased towards split variables with many possible splits. \item Cross-validation-based post-pruning and no pre-pruning. \item \emph{Default:} Gini impurity for classification, residual sum of squares for regression. \item \emph{Software:} R package \emph{rpart}. Similar implementations in other languages (e.g., \emph{scikit-learn}). \item \emph{Reference:} Algorithm by Breiman \emph{et al.} (1984), open-source implementation by Therneau \& Atkinson (1997). \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Recursive partitioning} \textbf{R package:} Part of every standard R installation. \bigskip \textbf{Hyperparameters:} \code{?rpart.control}. \bigskip \textbf{RPart:} With default arguments. <>= library("rpart") rp_ttnc <- rpart(Survived ~ Gender + Age + Class, data = ttnc) plot(rp_ttnc) text(rp_ttnc) print(rp_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Recursive partitioning} \setkeys{Gin}{width=0.9\linewidth} <>= plot(rp_ttnc) text(rp_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Recursive partitioning} \setkeys{Gin}{width=0.9\linewidth} <>= print(rp_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Recursive partitioning} \textbf{Coercion:} \begin{itemize} \item \code{as.party()} method to coerce \code{rpart} objects to \code{constparty} objects. \item Based on generic infrastructure for recursive partitioning in \emph{partykit}. \item Enables unified interface (print, plot, predict, \dots). \end{itemize} \medskip <>= py_ttnc <- as.party(rp_ttnc) plot(py_ttnc) print(py_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Recursive partitioning} \setkeys{Gin}{width=0.9\linewidth} <>= plot(py_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Recursive partitioning} \setkeys{Gin}{width=0.9\linewidth} <>= print(py_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Recursive partitioning} \textbf{Post-pruning:} \begin{itemize} \item Cost-complexity pruning, similar to using information criteria. \item Complexity parameter \code{cp} controls trade-off between reduction of objective function and tree size. \item Carried out automatically during fitting. \item Additionally, ten-fold cross-validation carried out as well. \item Results in \code{rpart} object as \code{cptable}. \end{itemize} \bigskip \pause \textbf{Here:} Fitted object also has optimal cross-validation error (\code{xerror}). \medskip <>= rp_ttnc$cptable @ \end{frame} \begin{frame}[fragile] \frametitle{Recursive partitioning} \textbf{Example:} Employ complexity parameter \code{cp = 0.1} for illustration. \medskip <>= prune(rp_ttnc, cp = 0.1) @ \end{frame} \subsection{Model-based recursive partitioning} \begin{frame} \frametitle{Model-based recursive partitioning} \textbf{MOB:} \begin{itemize} \item Parametric model in subgroups (maximum likelihood, least squares, \dots). \item Split variable selection based on asymptotic parameter instability tests. \item Split point selection via exhaustive search based on objective function. \item Significance-based pre-pruning (default) and optionally post-pruning based on information criteria (AIC, BIC, \dots). \item \emph{Examples:} (Generalized) linear model tree, distributional trees, \dots \item \emph{Software:} R package \emph{partykit} (and previously: \emph{party}), various ``mobsters'' in extension packages. \item \emph{Hyperparameters:} \code{?mob\_control}. \item \emph{Reference:} Zeileis, Hothorn, Hornik (2008). \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Model-based recursive partitioning} \textbf{Example:} Investigate treatment heterogeneity for ``women and children first.'' \medskip <>= ttnc <- transform(ttnc, Treatment = factor(Gender == "Female" | Age == "Child", levels = c(FALSE, TRUE), labels = c("Male&Adult", "Female|Child") ) ) @ \bigskip \pause \textbf{Model:} Tree based on binary logit GLM for survival. \medskip <>= mob_ttnc <- glmtree(Survived ~ Treatment | Class + Gender + Age, data = ttnc, family = binomial, alpha = 0.01) plot(mob_ttnc) print(mob_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Model-based recursive partitioning} \setkeys{Gin}{width=0.83\textwidth} <>= plot(mob_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Model-based recursive partitioning} \vspace{-0.4cm} \small <>= mob_ttnc @ \end{frame} \subsection{Evolutionary learning of globally optimal trees} \begin{frame} \frametitle{Evolutionary learning of globally optimal trees} \textbf{EvTree:} \begin{itemize} \item \emph{Goal:} Globally optimal partition rather than locally optimal split in each step. \item NP-hard optimization problem, attempt solution via evolutionary learning. \item Based on so-called ``fitness'' function. \item Essentially a penalized objective function, similar to information criteria or cost-complexity. \item Thus, no additional pruning step. \item \emph{Software:} R package \emph{evtree} (leverages \emph{partykit}). \item \emph{Hyperparameters:} \code{?evtree\_control}. \item \emph{Reference:} Grubinger, Zeileis, Pfeiffer (2014). \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Evolutionary learning of globally optimal trees} \textbf{EvTree:} With default parameters. \medskip <>= library("evtree") set.seed(1) ev_ttnc <- evtree(Survived ~ Gender + Age + class, data = ttnc) plot(ev_ttnc) print(ev_ttnc) @ <>= library("evtree") if(file.exists("ev_ttnc.rds")) { ev_ttnc <- readRDS("ev_ttnc.rds") } else { set.seed(1) ev_ttnc <- evtree(Survived ~ Gender + Age + Class, data = ttnc) saveRDS(ev_ttnc, file = "ev_ttnc.rds") } @ \end{frame} \begin{frame}[fragile] \frametitle{Evolutionary learning of globally optimal trees} \setkeys{Gin}{width=0.72\textwidth} <>= plot(ev_ttnc) @ \end{frame} \begin{frame}[fragile] \frametitle{Evolutionary learning of globally optimal trees} <>= ev_ttnc @ \end{frame} \subsection{Other algorithms} \begin{frame} \frametitle{Other algorithms} \textbf{Furthermore:} Based on \emph{partykit}. \begin{itemize} \item \emph{model4you:} Model-based trees/forests with personalised treatment effects. \item \emph{disttree:} Distributional modeling with regression trees and random forests. \item \emph{circtree:} Circular distributional trees and forests. \item \emph{glmertree:} Generalized linear mixed-effects model trees. \item \emph{psychotree:} Psychometric model trees (Rasch, Bradley-Terry, \dots). \item \emph{stablelearner:} Stability assessment of trees (and other learners). \item \ldots \end{itemize} \end{frame} \begin{frame} \frametitle{Other algorithms} \textbf{Other R packages:} \begin{itemize} \item \emph{RWeka:} Interface to \emph{Weka} machine learning library, provided open-source implementations of C4.5 (J.48) and M5 (M5'), and LMT. \item \emph{C50:} C5.0 (successor to C4.5) decision trees and rule-based models. \item Many more: \emph{mvpart}, \emph{quint}, \emph{stima}, \dots. \end{itemize} \end{frame} \begin{frame} \frametitle{Other algorithms} \textbf{Beyond R:} \begin{itemize} \item Unbiased recursive partitioning software (standalone) by Loh and co-workers: \emph{QUEST}, \emph{GUIDE}, \dots \item In Python: \emph{scikit-learn} implements classical machine learning algorithms, very limited availability of statistical inference-based algorithms. \item \dots \end{itemize} \end{frame} \subsection{References} \begin{frame} \frametitle{References} \small Breiman L, Friedman JH, Olshen RA, Stone CJ (1984). \dquote{Classification and Regression Trees.} \emph{Wadsworth, California.}, \medskip Therneau T, Atkinson B (1997). \dquote{An Introduction to Recursive Partitioning Using the {rpart} Routine.} Technical Report~61, Section of Biostatistics, Mayo Clinic, Rochester. \url{http://www.mayo.edu/hsr/techrpt/61.pdf} \medskip % Breiman L (2001). % \dquote{Random {Forests}.} % \emph{Machine Learning}, % \textbf{45}(1), 5--32. % \doi{10.1023/A:1010933404324} % % \medskip Hothorn T, Hornik K, Zeileis A (2006). \dquote{Unbiased Recursive Partitioning: A Conditional Inference Framework.} \emph{Journal of Computational and Graphical Statistics}, \textbf{15}(3), 651--674. \doi{10.1198/106186006X133933} \medskip Zeileis A, Hothorn T, Hornik K (2008). \dquote{Model-Based Recursive Partitioning.} \emph{Journal of Computational and Graphical Statistics}, \textbf{17}(2), 492--514. \doi{10.1198/106186008X319331} \medskip Hothorn T, Zeileis A (2015). \dquote{{partykit}: A Modular Toolkit for Recursive Partytioning in \textsf{R}.} \emph{Journal of Machine Learning Research}, \textbf{16}, 3905--3909. \url{http://www.jmlr.org/papers/v16/hothorn15a.html} % medskip % % Schlosser L, Hothorn T, Stauffer R, Zeileis A (2019). % \dquote{Distributional Regression Forests for Probabilistic Precipitation Forecasting in Complex Terrain.} % \emph{The Annals of Applied Statistics}, \textbf{13}(3), 1564--1589. % \doi{10.1214/19-AOAS1247} % \medskip % Breiman L (2001). % \dquote{Statistical Modeling: The Two Cultures.} % \emph{Statistical Science}, % \textbf{16}(3), 199--231. % \doi{10.1214/ss/1009213726} \end{frame} \end{document} partykit/inst/ULGcourse-2020/Data/0000755000176200001440000000000014172227777016220 5ustar liggesuserspartykit/inst/ULGcourse-2020/Data/Axams_pred.rda0000644000176200001440000000035014172227777020771 0ustar liggesusers‹ r‰0æŠàb```f`fbV “54ÄMׂ… Èad`aà)(HI’Â`µ |@Ìâ ôK™Òz%Ž…ö’×ÿÛ¿Ò7ú©vJzÿ÷ ÑsŸv‡«clâ½Sõqµý_þŽo­Ù9ö¿ 6ˆOŸ)íÀöVäÇ%¸: 0pðn€Ð¡:– PœÄš—˜›Z d€dÊ-…Ig¦ç&Â8)‰•Åhpå—ëÁ áiÙûÿÿÿ?è6%ç$Ãl‚ r¥$–$ê¥õyÿ@/Fù½Ppartykit/inst/ULGcourse-2020/Data/GENS_00_innsbruck_20200416.dat0000644000176200001440000016114414172227777023010 0ustar liggesusers# ASCII output from GENSvis.py # Contains interpolated values from the # GFS ensemble on 1.000000 x 1.000000 degrees # The data in here are for station # 11120: INNSBRUCK # Station position: 11.3553 47.2589 # Used grid point 1: 12.0000 48.0000 # Used grid point 2: 12.0000 47.0000 # Used grid point 3: 11.0000 47.0000 # Used grid point 4: 11.0000 48.0000 varname timestamp step mem0 mem1 mem2 mem3 mem4 mem5 mem6 mem7 mem8 mem9 mem10 mem11 mem12 mem13 mem14 mem15 mem16 mem17 mem18 mem19 mem20 tmax2m 1587016800 6 274.664 274.738 274.526 274.712 274.552 274.621 274.490 274.490 274.859 274.543 274.647 274.750 274.664 274.773 274.664 274.681 274.681 274.581 274.690 274.590 274.590 tmax2m 1587038400 12 283.811 283.413 283.548 283.500 283.557 283.546 283.492 283.592 283.929 283.748 283.564 283.581 283.711 283.662 283.334 283.454 283.671 283.767 283.527 284.028 283.689 tmax2m 1587060000 18 283.907 283.801 284.050 283.568 284.002 283.929 283.719 284.024 284.007 283.833 283.971 283.649 283.754 283.928 283.969 284.088 283.651 283.811 283.792 283.863 283.664 tmax2m 1587081600 24 272.914 273.703 273.071 272.628 273.828 272.528 273.642 272.867 272.611 272.791 272.902 273.240 272.640 273.100 272.505 272.825 273.111 273.323 272.952 273.952 272.435 tmax2m 1587103200 30 276.829 276.881 276.700 276.813 276.907 276.903 276.677 276.813 276.887 276.856 276.856 276.720 276.839 276.855 276.839 276.970 276.878 276.896 276.777 276.664 276.794 tmax2m 1587124800 36 286.091 286.672 285.659 286.115 285.905 286.666 286.140 286.730 286.592 285.826 286.072 285.753 286.110 286.720 286.254 286.234 285.490 285.931 286.327 285.869 286.142 tmax2m 1587146400 42 286.960 286.607 286.562 287.070 286.344 287.471 286.106 287.282 287.418 286.972 287.179 286.545 286.953 287.315 287.496 286.582 286.310 286.843 287.337 287.084 287.324 tmax2m 1587168000 48 277.760 277.455 276.515 277.678 277.043 277.610 276.495 277.224 276.663 277.928 277.607 276.845 277.157 277.810 277.467 277.382 276.899 277.237 277.928 276.294 277.481 tmax2m 1587189600 54 278.333 278.187 278.250 278.176 278.401 278.264 278.184 278.321 278.435 278.099 278.323 277.855 278.229 278.157 278.341 278.080 278.068 278.285 278.282 278.395 278.271 tmax2m 1587211200 60 287.358 286.765 287.047 287.438 288.086 287.993 287.139 287.797 286.944 287.862 287.862 287.155 286.440 287.081 288.056 287.218 287.902 287.167 286.642 286.037 286.330 tmax2m 1587232800 66 287.045 286.944 286.858 287.129 287.649 287.531 287.037 287.393 286.492 287.545 287.740 286.982 286.727 286.730 287.492 286.987 287.805 287.212 286.483 286.143 286.922 tmax2m 1587254400 72 277.746 277.256 277.440 277.806 278.834 278.809 277.359 277.944 277.723 278.680 278.852 278.068 277.221 277.463 278.332 276.817 279.073 277.319 278.066 278.211 276.962 tmax2m 1587276000 78 278.733 278.709 278.433 278.637 279.276 278.750 278.475 278.450 278.315 278.875 279.047 278.684 277.858 278.503 278.821 278.386 279.128 279.098 279.058 277.733 278.555 tmax2m 1587297600 84 286.063 285.430 285.382 285.503 286.740 284.829 286.599 285.433 284.595 285.109 286.194 286.343 285.520 285.629 286.056 285.501 285.838 286.785 285.808 285.112 285.410 tmax2m 1587319200 90 286.249 285.395 285.344 285.560 286.546 284.479 286.605 285.463 284.701 285.345 286.547 286.343 285.791 286.033 285.941 285.443 285.731 286.880 285.745 285.597 285.602 tmax2m 1587340800 96 279.894 279.458 279.485 279.820 280.452 280.063 279.279 279.999 279.317 280.113 279.904 279.662 279.062 279.450 279.860 279.515 279.786 279.778 280.384 277.677 279.498 tmax2m 1587362400 102 278.230 276.944 277.828 278.355 278.900 277.866 278.494 278.484 277.427 277.668 279.273 278.409 277.734 278.334 278.243 277.529 277.980 278.664 278.572 276.851 277.578 tmax2m 1587384000 108 283.891 281.789 284.158 283.096 285.864 280.571 284.936 284.329 285.606 280.348 285.889 284.531 284.156 283.560 283.719 279.789 284.213 285.735 282.287 284.437 284.223 tmax2m 1587405600 114 283.342 282.503 283.646 283.018 285.345 279.938 285.177 284.163 285.280 279.976 285.458 284.322 283.736 283.188 283.470 279.539 284.108 286.319 282.086 284.523 284.418 tmax2m 1587427200 120 278.621 277.056 279.137 278.565 280.370 277.162 279.376 279.523 277.022 275.616 280.403 275.910 278.238 278.351 279.685 276.402 279.149 279.297 278.694 275.741 276.603 tmax2m 1587448800 126 275.880 274.859 276.044 275.052 278.812 274.530 276.987 276.868 275.551 273.145 277.790 273.193 275.520 274.377 276.995 273.647 276.511 277.051 276.509 273.544 274.915 tmax2m 1587470400 132 282.983 282.402 283.849 280.727 285.872 278.246 280.099 282.315 285.173 279.329 283.550 280.363 284.425 281.777 285.795 275.967 284.042 286.364 279.820 280.225 285.510 tmax2m 1587492000 138 283.165 282.569 283.793 280.953 285.888 278.667 279.784 282.454 285.707 279.546 282.841 279.699 284.620 282.308 285.478 276.378 284.088 286.925 279.791 279.437 286.318 tmax2m 1587513600 144 276.080 275.330 275.935 275.051 280.985 275.332 275.646 278.533 277.550 275.156 276.536 274.354 276.238 274.501 279.126 274.522 276.587 279.763 276.787 274.209 278.447 tmax2m 1587535200 150 274.274 273.167 274.399 271.944 277.576 271.887 272.162 275.132 277.060 272.452 273.542 270.982 274.743 273.190 275.922 271.017 274.169 278.917 273.822 270.690 278.228 tmax2m 1587556800 156 284.182 282.949 283.273 279.119 284.592 280.145 276.353 286.517 285.990 281.686 284.821 278.961 284.148 282.546 282.241 278.240 281.888 286.803 284.657 279.811 287.951 tmax2m 1587578400 162 284.049 283.205 283.399 279.113 284.704 280.767 276.622 286.893 286.235 282.139 284.539 279.313 284.100 282.605 282.061 278.517 281.864 286.545 285.314 280.280 288.251 tmax2m 1587600000 168 276.678 274.827 274.825 273.408 279.158 274.867 273.253 276.475 277.784 274.017 275.418 274.173 275.770 274.251 276.343 275.787 274.465 280.415 277.626 274.139 280.540 tmax2m 1587621600 174 274.241 273.476 273.506 270.823 276.299 272.098 270.890 276.934 276.942 274.064 275.661 271.764 275.204 272.676 273.294 273.087 271.764 279.440 277.019 271.883 277.841 tmax2m 1587643200 180 281.219 282.865 281.355 278.854 283.677 280.568 279.205 286.868 287.259 283.913 287.078 279.947 283.713 281.489 281.566 278.946 280.623 285.786 286.938 280.858 284.901 tmax2m 1587664800 186 281.109 283.060 281.501 278.822 283.483 281.141 279.939 286.750 287.275 283.987 287.203 279.753 284.067 281.828 281.258 279.054 281.014 285.743 286.866 280.573 285.005 tmax2m 1587686400 192 274.745 274.848 275.003 272.880 277.454 273.897 273.782 278.730 278.834 276.226 278.081 273.812 276.401 274.384 276.069 275.881 273.279 280.434 278.370 273.626 277.441 tmax2m 1587708000 198 273.945 274.017 275.712 272.775 276.387 272.672 273.640 277.719 278.599 276.520 277.544 272.135 271.938 274.289 275.482 274.217 272.400 279.514 275.502 273.413 272.455 tmax2m 1587729600 204 281.934 281.247 284.878 280.613 284.377 279.429 282.446 285.521 283.587 282.934 279.902 279.612 279.194 282.645 283.925 280.534 277.479 285.507 276.813 278.532 282.353 tmax2m 1587751200 210 282.160 281.274 285.275 280.807 284.069 279.270 282.477 285.663 283.288 282.413 279.284 279.847 279.592 282.307 284.481 281.378 277.877 286.067 277.280 277.493 283.305 tmax2m 1587772800 216 275.998 274.525 276.992 274.008 277.935 273.338 275.707 279.636 279.360 277.359 275.928 272.849 274.140 275.796 275.556 275.051 271.093 280.426 272.327 274.548 275.225 tmax2m 1587794400 222 273.696 272.440 276.164 271.523 275.880 270.377 275.030 278.254 277.390 275.836 273.307 273.969 273.926 272.688 275.742 275.977 268.951 277.345 269.864 273.230 274.795 tmax2m 1587816000 228 282.633 281.853 287.765 274.516 281.378 277.880 284.859 282.581 276.118 284.337 272.069 276.887 285.554 275.298 284.387 280.927 278.090 277.922 276.598 277.041 285.594 tmax2m 1587837600 234 282.893 282.220 287.896 275.295 281.178 278.422 284.616 283.175 275.647 284.264 271.969 276.559 286.155 275.447 284.406 281.126 278.742 277.792 276.319 277.553 286.308 tmax2m 1587859200 240 274.456 275.570 279.125 273.399 277.562 272.343 277.895 279.252 273.258 279.616 270.248 273.510 274.853 271.028 276.798 277.594 271.715 275.735 269.684 275.568 275.550 dd10m 1587016800 6 211.762 214.307 212.972 211.435 211.170 212.379 211.771 213.217 209.670 212.988 211.109 209.254 210.224 210.383 210.126 214.886 210.825 212.643 209.969 211.656 211.411 dd10m 1587038400 12 279.912 290.752 288.060 273.107 288.359 282.840 284.445 295.846 274.795 272.124 275.580 279.375 283.318 273.961 277.625 284.500 282.299 277.412 273.616 275.026 281.223 dd10m 1587060000 18 4.773 0.718 1.306 2.555 4.369 2.698 357.305 8.648 14.453 1.038 3.559 6.441 6.079 6.619 8.193 9.779 0.888 3.534 3.259 353.959 359.900 dd10m 1587081600 24 229.680 257.859 235.856 222.294 231.010 234.859 274.056 216.458 214.276 239.287 242.370 230.958 218.322 239.804 214.045 214.001 240.642 225.825 227.634 261.187 248.875 dd10m 1587103200 30 224.612 232.707 236.147 219.220 244.917 207.849 240.729 203.981 212.170 231.970 227.760 245.427 218.074 210.498 217.927 225.149 238.831 227.871 208.117 242.871 221.850 dd10m 1587124800 36 340.079 341.846 340.443 326.144 336.750 338.630 345.991 337.922 326.167 349.544 344.274 351.504 334.661 1.659 348.894 333.121 332.976 334.973 352.784 335.073 348.873 dd10m 1587146400 42 30.143 28.126 28.381 17.483 27.709 30.876 34.711 26.550 33.271 31.149 26.883 17.407 24.032 31.705 37.787 17.632 25.166 31.044 17.485 21.616 26.445 dd10m 1587168000 48 229.691 227.477 215.549 229.146 206.290 225.142 213.070 241.113 220.670 235.379 231.016 247.648 225.090 236.260 213.786 252.693 219.016 223.452 236.531 224.834 237.153 dd10m 1587189600 54 255.664 273.245 254.688 221.824 223.377 243.862 254.775 262.546 271.975 264.023 276.718 268.473 264.224 269.999 225.037 273.135 232.565 252.863 272.747 276.737 272.900 dd10m 1587211200 60 337.549 335.649 329.474 331.778 333.277 279.381 335.737 314.153 321.770 325.749 12.113 5.184 317.692 339.288 339.882 320.145 347.319 320.888 343.639 339.554 325.501 dd10m 1587232800 66 37.902 11.383 25.027 38.156 56.515 1.053 27.986 10.708 356.287 54.993 58.251 61.775 357.396 16.387 55.617 8.329 76.014 32.911 54.604 2.885 11.728 dd10m 1587254400 72 224.421 219.254 238.866 239.916 209.090 215.807 244.073 239.983 253.614 204.408 203.692 197.301 271.199 245.356 218.350 246.030 219.970 223.375 211.797 276.802 233.297 dd10m 1587276000 78 318.844 313.487 309.682 321.987 247.088 322.454 332.829 303.982 318.728 261.489 341.464 35.531 330.689 348.885 298.223 304.195 313.340 344.272 285.517 343.014 326.424 dd10m 1587297600 84 19.737 12.672 24.204 15.225 8.576 18.487 22.696 7.560 11.038 7.137 38.488 55.079 23.993 39.317 355.993 349.681 6.595 40.369 53.973 33.851 23.095 dd10m 1587319200 90 52.270 45.745 59.933 58.478 64.996 48.531 71.950 72.167 51.436 36.349 83.312 89.699 59.368 80.076 50.623 38.205 49.516 69.464 79.750 60.707 52.191 dd10m 1587340800 96 133.636 105.190 130.739 140.430 151.877 109.042 154.687 139.844 105.434 86.267 155.045 147.231 120.549 147.762 128.785 103.863 128.948 139.492 151.689 107.539 109.111 dd10m 1587362400 102 135.553 85.901 137.024 147.999 165.049 114.721 82.473 149.712 122.776 89.159 164.132 100.323 119.159 150.135 143.284 110.727 131.430 149.012 144.197 77.759 94.204 dd10m 1587384000 108 80.912 75.076 89.488 85.984 156.101 79.094 87.307 113.524 56.999 57.835 76.970 49.408 77.180 73.654 108.205 76.846 91.851 80.350 105.747 46.860 54.874 dd10m 1587405600 114 83.132 76.369 96.696 73.584 187.128 79.416 88.422 110.444 77.637 54.190 83.483 61.161 79.850 68.605 117.863 61.162 93.248 90.648 93.040 75.701 65.294 dd10m 1587427200 120 103.674 105.981 123.888 82.918 159.821 99.179 129.883 149.332 130.032 95.579 117.746 107.976 128.059 68.081 150.107 89.687 118.648 144.039 115.648 110.190 129.396 dd10m 1587448800 126 73.513 92.477 83.105 81.969 137.689 98.432 118.939 104.792 91.785 105.288 86.864 87.685 104.580 58.687 141.976 103.007 89.316 150.317 103.201 106.154 137.298 dd10m 1587470400 132 78.876 85.862 63.760 79.586 131.526 91.251 82.908 99.620 94.046 101.334 86.741 96.846 73.421 67.587 116.612 100.969 71.225 140.671 101.394 109.288 114.477 dd10m 1587492000 138 99.064 88.123 72.617 82.722 140.063 99.218 88.688 118.366 100.142 105.929 100.936 106.188 61.312 74.626 107.275 104.306 78.996 152.464 127.575 127.497 119.088 dd10m 1587513600 144 155.069 133.662 111.576 128.312 162.558 128.064 118.562 157.451 174.479 153.887 155.175 144.990 160.494 113.378 162.108 133.673 140.237 201.284 162.682 151.295 188.349 dd10m 1587535200 150 153.885 113.413 90.153 75.824 151.322 118.880 96.337 162.374 292.859 140.402 168.054 146.217 31.178 120.165 76.649 140.761 60.643 280.681 171.659 155.057 267.270 dd10m 1587556800 156 57.093 56.878 68.843 62.290 137.295 82.698 86.606 111.474 28.431 91.622 38.468 95.671 39.493 57.967 72.752 113.050 48.801 1.341 146.991 127.571 345.061 dd10m 1587578400 162 67.385 51.741 70.134 67.427 146.200 80.148 87.864 68.986 33.103 87.524 36.158 98.563 46.416 61.311 80.811 121.564 37.449 34.597 157.440 132.400 352.226 dd10m 1587600000 168 200.959 144.864 151.034 98.316 169.580 151.057 127.239 316.469 27.179 183.797 237.038 161.677 181.956 145.115 141.439 164.557 55.970 170.300 202.112 175.959 343.141 dd10m 1587621600 174 359.333 5.876 93.143 43.415 170.337 50.353 113.234 339.883 322.289 254.151 270.798 159.327 355.997 34.834 149.927 175.103 35.833 318.663 223.724 175.111 342.565 dd10m 1587643200 180 32.824 15.057 63.295 35.081 108.424 40.899 93.019 2.455 9.964 14.242 302.625 78.181 19.648 44.782 112.023 113.670 25.942 38.403 275.201 74.216 348.472 dd10m 1587664800 186 34.658 1.763 62.289 15.810 135.675 27.398 80.392 358.564 123.496 83.762 250.962 58.154 28.594 23.285 103.893 93.833 23.222 103.384 287.971 39.123 0.134 dd10m 1587686400 192 49.667 316.259 173.468 312.043 185.373 298.829 185.904 311.226 191.011 193.200 214.688 250.113 25.516 314.014 203.323 211.730 325.645 197.347 337.601 237.480 346.405 dd10m 1587708000 198 56.005 336.413 328.600 292.755 212.132 313.797 36.461 327.750 191.617 198.250 212.653 302.720 20.437 306.004 352.566 277.356 348.833 209.213 345.023 238.155 13.359 dd10m 1587729600 204 38.442 2.612 7.164 317.103 18.808 332.569 46.073 359.386 182.241 193.329 230.639 323.131 33.118 330.369 22.318 327.938 17.882 193.654 341.834 62.501 25.756 dd10m 1587751200 210 34.329 20.536 22.444 357.876 204.991 356.273 53.225 359.424 202.087 223.682 339.634 3.689 61.372 344.964 11.331 350.072 40.836 251.129 338.360 357.927 28.761 dd10m 1587772800 216 58.789 25.374 168.223 26.981 207.486 0.157 167.673 293.242 230.089 210.925 347.709 189.142 152.267 339.567 346.998 194.810 71.812 277.445 287.059 287.278 175.543 dd10m 1587794400 222 40.062 328.395 164.323 21.416 205.349 348.722 191.791 292.107 317.047 199.265 6.494 226.726 182.737 339.100 353.965 190.334 45.638 28.351 294.866 117.850 210.051 dd10m 1587816000 228 40.185 346.398 113.403 53.599 128.028 340.416 137.983 328.488 338.265 126.096 13.895 331.315 40.505 332.322 0.609 175.885 35.284 10.814 325.257 84.268 294.984 dd10m 1587837600 234 53.673 350.615 156.762 39.456 92.747 348.234 174.750 348.390 327.512 135.226 15.780 347.913 18.457 333.677 33.728 173.598 41.830 337.504 2.533 72.917 329.012 dd10m 1587859200 240 187.766 332.514 195.327 42.336 168.148 312.260 194.234 301.270 297.183 183.345 10.640 12.079 260.548 340.264 189.886 177.765 155.253 329.567 324.102 129.655 237.479 ff10m 1587016800 6 2.422 2.405 2.432 2.405 2.455 2.430 2.376 2.435 2.453 2.439 2.426 2.387 2.393 2.455 2.437 2.383 2.421 2.447 2.390 2.454 2.439 ff10m 1587038400 12 1.288 1.323 1.288 1.290 1.255 1.271 1.215 1.395 1.260 1.225 1.345 1.380 1.258 1.279 1.403 1.193 1.456 1.253 1.208 1.275 1.330 ff10m 1587060000 18 1.122 1.030 1.216 1.047 1.210 0.996 1.073 1.094 1.084 0.882 1.195 1.122 1.011 1.115 1.066 1.144 1.063 1.136 0.991 1.334 0.977 ff10m 1587081600 24 0.580 0.408 0.647 0.739 0.698 0.575 0.488 0.412 0.868 0.576 0.497 0.635 0.603 0.642 0.709 0.888 0.790 0.716 0.658 0.433 0.527 ff10m 1587103200 30 0.998 0.974 1.033 0.979 1.000 1.318 0.889 1.199 1.241 1.001 0.923 0.768 1.213 0.881 1.058 1.131 1.015 1.028 0.924 0.849 0.837 ff10m 1587124800 36 0.883 1.234 1.176 0.701 1.289 0.636 1.177 0.479 0.555 1.015 1.000 1.122 1.089 0.629 0.849 1.039 1.142 0.964 0.569 1.127 0.829 ff10m 1587146400 42 1.176 1.211 1.347 1.239 1.164 1.088 1.163 1.034 1.008 1.236 1.209 1.283 1.173 0.941 1.069 1.183 1.309 1.143 1.043 1.211 1.150 ff10m 1587168000 48 1.145 1.267 1.007 1.154 1.130 1.463 1.533 1.022 1.434 1.157 0.391 0.761 1.186 1.355 1.292 0.969 1.132 1.383 1.463 0.849 1.256 ff10m 1587189600 54 0.761 1.005 0.796 1.055 0.868 1.010 0.824 0.760 1.034 0.823 0.357 0.510 0.956 0.930 0.676 0.910 0.640 0.801 0.975 0.973 0.889 ff10m 1587211200 60 1.219 1.635 1.408 0.971 0.592 0.593 1.332 0.875 1.258 1.014 0.858 1.309 1.731 1.253 0.835 1.263 0.806 1.452 1.314 2.082 1.789 ff10m 1587232800 66 1.153 1.348 1.188 0.917 1.150 0.533 1.324 0.924 1.358 1.148 1.200 1.462 1.481 1.415 1.184 0.959 0.914 1.344 0.947 1.756 1.433 ff10m 1587254400 72 1.883 1.689 1.753 1.570 2.163 1.540 1.541 1.792 1.270 1.996 1.835 1.546 1.646 1.437 2.138 1.459 1.981 1.449 1.922 1.454 1.710 ff10m 1587276000 78 1.552 1.228 1.370 1.410 1.356 1.131 1.237 1.408 1.701 1.130 0.901 0.953 1.740 1.444 1.543 1.461 1.286 1.199 1.095 1.944 1.255 ff10m 1587297600 84 3.642 3.201 3.150 3.358 2.513 2.923 2.881 2.561 3.408 3.699 3.445 3.040 3.356 3.000 3.424 3.283 3.557 3.417 1.933 3.479 3.306 ff10m 1587319200 90 2.677 2.465 2.531 2.577 1.986 2.287 2.016 2.311 2.461 2.445 2.419 2.363 2.631 2.341 2.228 2.189 2.215 2.696 2.068 2.319 2.583 ff10m 1587340800 96 1.849 1.733 2.107 1.979 2.153 1.787 1.437 2.540 1.637 1.784 2.306 1.637 1.847 1.671 2.016 1.775 1.852 1.979 2.208 1.809 1.680 ff10m 1587362400 102 1.794 2.227 2.011 1.811 2.754 1.817 1.116 2.368 1.668 1.860 1.832 0.751 1.854 1.018 2.289 1.740 2.003 1.753 2.038 1.824 1.720 ff10m 1587384000 108 2.932 3.650 2.666 2.259 2.171 3.083 2.931 2.181 3.539 3.481 2.247 4.368 2.810 2.952 2.452 2.794 2.813 2.981 1.904 3.560 4.389 ff10m 1587405600 114 2.866 3.134 2.251 2.416 1.022 2.808 2.393 2.350 2.703 3.961 2.559 3.847 2.520 2.842 2.322 3.333 2.485 2.176 2.341 2.919 3.623 ff10m 1587427200 120 2.136 2.383 1.993 2.330 1.318 2.492 2.146 1.780 1.989 3.053 2.048 2.465 2.293 2.646 2.412 2.940 1.872 1.912 2.214 2.844 2.820 ff10m 1587448800 126 2.791 2.475 2.232 3.225 1.883 2.836 1.369 1.321 1.733 3.201 2.580 2.367 1.771 2.919 2.188 3.198 1.940 2.099 2.350 2.831 2.459 ff10m 1587470400 132 3.614 3.444 4.176 4.182 3.005 3.839 3.286 2.788 2.937 3.706 3.540 3.554 3.125 4.256 2.365 3.775 3.276 2.362 3.591 3.931 2.727 ff10m 1587492000 138 2.835 3.281 3.432 3.366 2.358 3.382 3.048 2.812 1.998 2.822 3.211 3.404 2.596 3.403 1.361 3.466 2.803 1.481 3.205 3.867 1.934 ff10m 1587513600 144 2.630 2.181 2.090 2.319 2.511 2.708 2.831 2.622 1.782 2.523 3.127 3.073 1.015 2.365 1.474 2.939 1.585 2.078 3.274 3.396 1.896 ff10m 1587535200 150 0.915 1.548 1.877 2.303 2.398 2.498 3.347 2.282 0.457 1.620 1.593 2.156 1.726 1.539 1.178 2.247 1.304 1.122 2.769 2.959 1.099 ff10m 1587556800 156 2.539 3.460 3.199 4.369 3.018 3.176 4.351 1.822 3.014 2.457 2.036 3.168 3.720 3.307 3.477 2.725 3.462 2.044 2.086 3.224 2.757 ff10m 1587578400 162 1.535 2.583 2.243 3.024 2.839 2.663 3.092 1.245 1.939 1.834 1.633 2.413 2.089 3.006 3.279 2.400 3.153 1.461 1.402 2.176 2.900 ff10m 1587600000 168 0.531 0.591 1.440 1.062 3.036 1.599 2.166 1.175 0.358 1.819 0.661 1.930 0.394 2.177 2.500 2.347 1.291 0.291 2.240 2.604 2.112 ff10m 1587621600 174 1.092 1.920 0.705 2.067 1.818 1.399 2.142 1.293 0.282 0.577 0.995 1.720 1.062 0.884 2.481 1.750 1.785 0.624 1.836 1.486 2.317 ff10m 1587643200 180 3.234 3.503 3.846 3.646 1.667 3.481 3.177 1.930 1.390 1.678 1.345 1.964 3.446 4.360 2.599 1.089 3.763 1.345 2.120 1.615 3.639 ff10m 1587664800 186 3.320 2.835 2.275 3.131 1.639 2.574 2.504 1.820 1.021 0.775 1.008 1.667 3.087 2.951 1.530 0.723 2.508 1.161 1.219 0.896 3.340 ff10m 1587686400 192 1.202 1.854 0.935 1.846 2.265 1.519 1.085 1.509 2.697 2.519 2.938 0.919 1.977 1.713 0.754 0.917 1.845 2.153 3.672 1.615 2.374 ff10m 1587708000 198 1.127 2.209 0.977 1.893 1.404 2.077 1.102 1.131 2.514 2.235 2.755 1.271 2.976 1.981 1.221 0.877 2.715 1.647 3.036 0.991 2.043 ff10m 1587729600 204 2.501 4.667 3.156 2.606 0.939 4.370 2.745 2.103 2.831 2.525 1.397 1.986 4.340 4.072 2.892 0.982 4.153 1.375 2.988 0.997 2.907 ff10m 1587751200 210 2.334 3.372 1.993 1.786 0.063 3.608 2.269 1.559 2.090 1.311 1.546 1.159 2.863 3.258 1.865 0.272 3.349 1.958 2.858 0.572 2.046 ff10m 1587772800 216 0.783 0.485 1.075 1.800 1.243 2.240 1.922 1.148 1.537 1.797 1.413 2.124 1.818 2.517 1.282 1.938 1.362 0.825 2.052 0.272 0.499 ff10m 1587794400 222 1.083 0.922 1.430 1.999 0.578 1.953 1.706 1.280 1.179 0.783 2.197 1.370 1.583 3.015 1.185 2.443 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0.026 0.000 0.000 4.577 1.813 0.029 0.158 2.104 8.623 0.328 7.199 5.471 0.000 1.428 0.004 2.389 0.000 7.880 0.519 0.964 0.003 apcpsfc 1587837600 234 0.122 0.018 1.697 3.385 6.126 0.139 0.978 3.532 8.508 1.262 6.704 10.060 0.005 1.556 0.209 1.953 0.000 13.346 1.668 2.581 0.128 apcpsfc 1587859200 240 0.003 0.335 0.051 3.038 5.990 0.083 0.785 0.673 5.914 0.031 3.234 8.924 0.000 1.468 0.225 0.460 0.000 8.404 0.238 0.726 0.023 tmp2m 1587016800 6 274.464 274.595 274.373 274.521 274.399 274.373 274.347 274.347 274.659 274.399 274.495 274.607 274.521 274.621 274.521 274.538 274.528 274.485 274.547 274.399 274.447 tmp2m 1587038400 12 282.248 282.379 282.366 282.169 282.370 282.227 282.331 282.401 282.181 282.112 282.134 282.012 282.344 282.152 282.188 282.504 282.183 282.379 282.082 282.169 282.175 tmp2m 1587060000 18 274.101 274.492 274.035 274.429 274.746 273.528 274.759 273.763 273.986 274.288 273.943 274.453 273.710 274.254 273.571 273.972 274.280 274.582 274.282 275.192 273.767 tmp2m 1587081600 24 271.229 271.772 271.104 270.871 271.581 271.230 271.719 271.283 271.141 271.288 271.145 271.395 271.184 271.264 271.083 271.530 271.285 271.289 271.293 271.103 271.032 tmp2m 1587103200 30 276.829 276.881 276.700 276.813 276.907 276.903 276.629 276.813 276.839 276.856 276.856 276.767 276.839 276.855 276.839 276.922 276.878 276.896 276.777 276.664 276.746 tmp2m 1587124800 36 286.091 285.833 285.633 286.067 285.539 286.619 285.566 286.683 286.544 285.778 286.072 285.753 286.110 286.672 286.206 286.208 285.437 285.904 286.327 285.869 286.095 tmp2m 1587146400 42 278.193 277.457 277.199 277.740 277.714 278.244 277.376 278.067 277.858 278.291 278.228 277.270 277.914 278.209 278.119 278.162 277.299 277.995 278.114 277.078 278.009 tmp2m 1587168000 48 274.484 275.464 274.177 274.597 274.540 275.298 274.830 274.371 274.802 274.879 274.143 274.176 274.717 274.696 275.056 274.584 274.435 275.240 275.185 274.547 275.532 tmp2m 1587189600 54 278.333 278.187 278.250 278.140 278.401 278.264 278.181 278.321 278.435 278.073 278.314 277.855 278.229 278.157 278.341 278.064 278.068 278.285 278.282 278.395 278.271 tmp2m 1587211200 60 287.184 286.765 286.574 287.237 287.921 287.931 286.970 287.618 286.685 287.693 287.735 286.919 286.313 287.028 287.681 287.070 287.776 286.940 286.642 286.037 286.330 tmp2m 1587232800 66 277.835 277.939 278.057 278.588 278.387 278.845 278.231 278.531 278.661 278.200 278.360 279.044 277.876 278.409 278.482 277.230 279.195 278.178 278.404 278.645 277.738 tmp2m 1587254400 72 276.448 275.665 275.934 276.243 277.275 276.653 275.658 276.176 275.455 277.513 277.207 276.424 275.708 275.974 276.996 275.825 276.886 275.741 276.552 275.617 275.708 tmp2m 1587276000 78 278.733 278.709 278.433 278.637 279.276 278.750 278.466 278.441 278.315 278.875 279.038 278.684 277.858 278.503 278.848 278.386 279.128 279.089 279.058 277.706 278.538 tmp2m 1587297600 84 286.053 285.368 285.356 285.503 286.582 284.710 286.456 285.203 284.548 285.100 286.194 286.200 285.520 285.612 285.971 285.474 285.630 286.785 285.639 285.112 285.401 tmp2m 1587319200 90 280.093 279.562 279.563 279.837 280.567 280.112 278.946 280.055 279.416 280.144 279.682 279.287 279.218 279.044 279.899 279.428 279.916 279.973 280.404 278.189 279.554 tmp2m 1587340800 96 276.397 276.408 276.271 277.040 278.430 277.153 277.610 277.466 274.346 276.730 278.032 277.723 275.559 277.493 276.979 275.977 275.604 277.061 278.488 273.981 276.291 tmp2m 1587362400 102 277.926 276.437 277.692 278.177 278.808 277.322 278.155 278.195 277.140 277.231 279.231 278.231 277.565 278.191 277.973 277.007 277.736 278.452 278.018 276.708 277.291 tmp2m 1587384000 108 283.298 281.789 283.797 283.001 285.587 279.978 284.936 284.202 285.267 279.989 285.767 284.409 283.759 283.486 283.401 279.635 283.825 285.396 282.029 284.437 284.223 tmp2m 1587405600 114 278.763 277.303 279.353 278.770 280.405 277.315 279.612 279.553 277.502 275.816 280.614 276.279 278.607 278.529 279.827 276.570 279.239 279.671 278.893 276.093 277.011 tmp2m 1587427200 120 275.744 274.353 275.809 275.022 278.203 274.490 276.896 276.622 274.192 272.957 277.914 272.390 275.407 274.613 276.565 273.466 276.436 276.545 276.461 272.254 273.365 tmp2m 1587448800 126 274.351 274.509 275.784 273.430 278.635 273.618 276.242 276.740 275.526 272.823 276.393 272.965 275.055 272.204 276.934 272.758 276.056 276.611 275.469 273.272 274.881 tmp2m 1587470400 132 282.983 282.376 283.849 280.727 285.824 278.246 280.046 282.315 285.173 279.329 283.248 280.046 284.442 281.729 285.699 275.967 284.016 286.364 279.767 279.546 285.510 tmp2m 1587492000 138 276.392 276.072 276.410 275.499 281.233 275.501 275.972 278.723 277.919 275.509 276.862 274.480 276.756 274.954 279.601 274.805 277.061 280.027 277.040 274.509 279.380 tmp2m 1587513600 144 272.834 270.667 272.590 271.495 276.219 271.295 272.288 273.570 273.388 270.798 272.492 270.133 271.345 270.430 274.925 270.314 272.823 274.859 272.488 269.985 273.811 tmp2m 1587535200 150 274.248 273.091 274.289 271.835 277.454 271.609 271.336 275.047 277.060 272.351 273.533 270.792 274.743 273.106 275.865 270.827 274.100 278.917 273.779 270.564 278.228 tmp2m 1587556800 156 284.182 282.949 283.273 279.119 284.592 280.145 276.353 286.517 285.990 281.686 284.615 278.913 284.148 282.546 282.241 278.240 281.766 286.459 284.631 279.811 287.951 tmp2m 1587578400 162 277.310 275.418 275.246 273.770 279.320 275.093 273.580 277.450 278.267 274.608 276.243 274.421 276.249 274.634 276.670 276.051 274.927 280.807 277.942 274.494 280.710 tmp2m 1587600000 168 271.930 269.723 272.189 269.211 274.749 269.731 268.615 273.148 272.444 270.141 271.065 269.793 270.774 270.318 273.064 272.414 269.022 278.193 273.447 269.110 276.759 tmp2m 1587621600 174 274.241 273.479 273.506 270.775 276.230 272.098 270.650 276.934 276.932 274.064 275.661 271.764 275.204 272.676 273.050 273.087 271.764 279.440 277.019 271.883 276.263 tmp2m 1587643200 180 281.219 282.697 281.355 278.802 283.582 280.568 278.871 286.851 287.255 283.913 287.061 279.938 283.591 281.489 281.566 278.680 280.596 285.776 286.707 280.810 284.853 tmp2m 1587664800 186 275.175 275.320 275.421 273.258 277.792 274.517 274.431 279.075 279.209 276.701 278.103 274.205 276.697 274.728 276.443 275.989 273.827 281.036 278.544 274.067 277.872 tmp2m 1587686400 192 270.075 270.912 270.238 270.294 271.840 269.816 269.036 275.980 277.220 274.306 276.603 267.706 269.956 271.053 270.349 271.403 269.707 276.950 274.972 269.946 270.793 tmp2m 1587708000 198 273.945 274.006 275.712 272.775 276.387 272.683 273.640 277.719 278.577 276.473 277.274 272.135 271.938 274.289 275.482 274.193 272.390 279.466 272.560 273.413 272.328 tmp2m 1587729600 204 281.934 281.220 284.830 280.513 284.129 279.348 282.446 285.495 282.990 282.389 279.419 279.574 279.194 282.645 283.925 280.477 277.479 285.433 276.813 277.390 282.353 tmp2m 1587751200 210 276.512 275.289 277.523 275.000 278.320 273.510 276.448 280.269 279.560 277.550 276.176 273.878 274.614 276.115 276.694 275.494 271.669 280.717 272.848 274.771 276.356 tmp2m 1587772800 216 269.278 268.153 271.290 271.131 274.057 269.188 271.465 275.069 277.458 273.119 273.273 270.263 269.226 272.526 269.941 272.096 267.320 277.242 267.550 271.373 269.624 tmp2m 1587794400 222 273.622 272.436 276.164 270.385 275.854 269.605 275.030 278.195 275.201 275.836 270.817 273.934 273.926 271.715 275.694 275.977 268.951 276.548 269.864 273.230 274.795 tmp2m 1587816000 228 282.585 281.725 287.765 274.516 281.330 277.806 284.345 282.481 275.600 284.167 271.968 276.623 285.554 275.298 284.335 280.712 278.090 277.604 276.245 277.014 285.594 tmp2m 1587837600 234 275.827 276.144 279.525 273.612 277.780 272.913 278.357 279.599 273.441 279.820 270.628 273.675 276.100 271.259 277.655 277.942 272.492 275.734 270.750 275.830 277.216 tmp2m 1587859200 240 271.366 270.564 274.151 271.061 275.232 268.002 274.511 275.676 270.614 275.850 268.037 270.525 269.359 268.706 272.227 275.515 266.599 274.295 266.830 272.990 272.372 tcdcclm 1587016800 6 2.014 0.825 2.544 2.709 3.373 3.132 3.689 2.123 3.527 2.175 1.902 1.220 2.589 2.301 2.185 3.506 2.178 1.012 1.763 2.975 2.930 tcdcclm 1587038400 12 2.790 3.395 2.871 4.129 2.462 2.805 2.948 3.019 2.784 2.520 2.847 2.518 2.780 2.506 3.370 2.204 2.609 2.665 3.323 2.653 2.704 tcdcclm 1587060000 18 5.362 5.562 5.208 6.658 5.700 3.513 6.175 3.881 5.362 5.786 4.749 5.196 4.912 5.132 4.490 4.490 5.941 6.164 5.301 6.115 5.723 tcdcclm 1587081600 24 3.690 6.167 0.952 1.816 5.301 1.994 6.420 3.339 2.448 5.054 2.162 5.599 2.812 3.655 2.210 1.331 3.400 3.977 4.867 2.941 2.234 tcdcclm 1587103200 30 2.306 1.775 2.199 3.630 3.285 2.877 4.319 3.002 2.077 2.905 1.976 3.895 3.093 1.721 2.133 2.371 2.421 3.644 3.238 1.394 3.157 tcdcclm 1587124800 36 2.621 2.271 2.432 2.414 1.465 3.068 1.150 3.787 2.988 2.708 2.399 0.721 1.957 2.646 2.693 2.422 3.498 1.419 2.331 2.118 2.225 tcdcclm 1587146400 42 3.182 2.523 2.403 3.847 1.436 4.468 2.088 4.794 4.595 3.631 4.460 1.811 2.969 3.735 3.701 3.425 3.249 3.022 3.270 2.443 4.405 tcdcclm 1587168000 48 3.141 5.587 2.731 3.635 4.012 4.626 2.621 3.431 3.829 4.638 3.220 2.845 3.965 3.490 5.170 2.676 2.046 4.304 4.462 4.473 5.693 tcdcclm 1587189600 54 4.997 6.145 5.565 4.550 4.824 5.588 4.945 5.894 6.132 3.667 4.519 3.675 5.636 4.084 5.853 3.067 3.128 5.989 5.766 5.504 6.433 tcdcclm 1587211200 60 4.129 3.254 5.500 5.076 5.209 4.258 5.172 4.706 5.662 2.903 5.042 4.298 4.851 4.252 4.538 3.564 3.769 4.093 3.552 5.657 4.656 tcdcclm 1587232800 66 4.919 4.755 4.934 5.909 5.613 6.098 4.527 6.166 5.994 4.955 5.237 4.202 4.126 6.069 5.834 5.223 5.768 4.750 5.548 4.388 4.049 tcdcclm 1587254400 72 5.791 3.941 6.166 6.373 7.268 7.478 3.859 4.566 5.345 7.786 7.530 4.584 3.798 7.392 6.836 7.149 5.789 4.924 5.010 2.326 5.428 tcdcclm 1587276000 78 4.411 6.202 4.600 4.244 6.795 7.097 3.670 3.531 3.847 7.206 6.798 5.615 0.919 5.866 7.197 5.936 6.937 2.692 4.325 1.933 5.438 tcdcclm 1587297600 84 1.613 6.700 1.577 1.180 4.906 5.642 1.091 3.151 1.986 5.641 4.517 3.319 1.774 4.240 4.511 2.470 3.339 2.123 3.169 3.488 3.971 tcdcclm 1587319200 90 3.711 4.257 4.603 5.611 6.307 7.049 1.875 6.745 2.584 6.683 1.699 2.620 3.877 4.840 5.814 4.487 2.180 3.146 7.220 2.305 3.531 tcdcclm 1587340800 96 6.215 5.149 5.021 7.123 7.743 7.655 6.488 6.919 4.371 7.257 4.264 3.901 6.085 4.990 7.508 5.763 4.557 6.127 7.262 4.998 5.067 tcdcclm 1587362400 102 5.843 5.338 4.952 7.071 6.862 7.097 7.804 7.768 3.011 6.160 7.303 5.612 5.593 5.381 7.074 5.967 3.835 6.164 7.077 4.917 5.061 tcdcclm 1587384000 108 6.234 5.719 5.029 6.616 7.511 7.328 6.598 7.864 3.327 5.606 7.325 2.755 4.987 5.658 6.805 6.681 6.334 5.530 7.029 1.802 2.771 tcdcclm 1587405600 114 5.665 4.966 5.044 6.663 7.899 7.679 5.210 7.667 0.520 5.474 7.353 0.552 5.696 6.064 7.168 6.127 6.380 2.956 7.355 0.351 0.303 tcdcclm 1587427200 120 5.195 4.956 5.837 6.037 7.057 7.615 5.885 7.760 2.883 5.510 6.613 2.042 6.160 6.281 6.341 6.201 5.888 3.374 7.139 1.210 1.009 tcdcclm 1587448800 126 4.116 3.764 3.651 5.201 6.523 5.833 5.842 6.541 3.611 4.903 5.319 4.738 3.779 3.078 6.158 6.305 3.963 3.325 5.829 3.142 3.282 tcdcclm 1587470400 132 0.997 2.406 1.210 2.797 6.805 5.478 5.767 5.880 0.455 3.557 2.721 2.896 1.175 0.118 4.310 6.593 1.812 0.378 5.656 2.768 0.340 tcdcclm 1587492000 138 0.545 3.584 0.181 3.603 6.356 5.597 5.743 5.676 0.191 5.094 4.873 5.706 0.577 0.126 5.036 6.184 3.117 0.149 5.788 5.649 0.875 tcdcclm 1587513600 144 3.371 1.114 1.239 3.947 4.882 4.048 5.576 5.609 0.218 3.384 4.426 4.927 0.174 0.181 4.035 5.172 3.675 0.388 2.716 4.698 1.374 tcdcclm 1587535200 150 1.363 0.174 4.120 2.001 5.879 3.117 5.666 2.693 0.212 0.684 2.275 0.751 0.149 2.645 4.217 2.655 4.822 0.694 0.692 1.231 3.426 tcdcclm 1587556800 156 0.983 0.098 0.403 1.886 6.754 1.143 5.595 1.164 0.111 1.334 2.803 2.262 0.098 3.643 5.197 4.570 5.677 3.717 0.090 0.136 5.247 tcdcclm 1587578400 162 3.942 0.059 3.086 4.108 7.233 3.676 5.890 0.378 2.273 3.585 1.548 5.253 0.059 6.043 5.956 5.784 5.637 5.916 0.187 0.869 6.610 tcdcclm 1587600000 168 2.556 0.111 5.556 4.811 7.676 3.658 5.408 0.111 0.639 0.589 0.577 4.026 0.119 4.717 5.276 5.784 1.273 6.494 1.444 0.313 5.889 tcdcclm 1587621600 174 1.827 0.160 6.361 2.015 7.621 0.657 3.838 0.342 2.477 0.761 0.453 3.300 3.464 0.793 4.476 4.483 0.164 6.598 3.433 0.983 4.447 tcdcclm 1587643200 180 2.281 1.200 4.687 0.499 6.850 0.178 5.171 0.132 4.208 1.393 1.811 2.732 5.950 0.046 2.392 5.317 2.167 5.874 4.393 4.254 3.726 tcdcclm 1587664800 186 4.736 0.377 2.377 1.426 5.263 0.602 5.431 2.833 5.447 3.170 7.399 5.635 5.129 2.496 5.251 6.489 3.541 5.618 7.654 5.748 4.544 tcdcclm 1587686400 192 2.870 0.613 0.080 3.334 4.614 0.979 2.014 5.132 4.476 5.115 7.870 3.342 4.045 4.663 1.713 6.283 4.583 5.280 7.913 5.109 5.425 tcdcclm 1587708000 198 1.813 0.344 0.706 5.682 4.056 0.310 0.770 3.277 5.368 5.488 7.620 1.467 1.850 1.871 0.337 2.384 3.278 4.613 7.028 3.503 3.991 tcdcclm 1587729600 204 1.015 0.822 4.827 3.971 5.285 2.921 0.527 1.918 6.234 3.884 7.794 1.264 0.328 5.375 0.913 2.481 5.200 4.872 5.333 4.979 0.279 tcdcclm 1587751200 210 3.019 1.712 0.816 5.580 5.119 4.949 2.822 5.732 7.053 4.346 7.736 2.855 0.321 4.982 0.712 2.360 4.474 5.860 3.775 6.766 3.945 tcdcclm 1587772800 216 0.763 2.573 0.066 6.254 6.244 6.235 1.368 4.314 7.668 2.983 7.475 2.744 1.356 6.668 1.035 3.691 5.364 6.960 1.418 7.432 1.773 tcdcclm 1587794400 222 0.411 5.068 0.080 7.867 5.267 4.356 2.700 5.936 7.827 2.182 7.863 5.085 2.841 7.679 2.085 5.593 2.074 7.177 2.229 6.105 0.305 tcdcclm 1587816000 228 0.262 3.364 0.130 7.786 4.417 1.471 4.497 7.030 7.681 2.939 7.818 6.731 1.413 6.923 1.021 5.716 0.550 7.397 3.200 6.598 0.606 tcdcclm 1587837600 234 0.552 6.198 1.348 7.631 6.192 2.476 5.200 6.223 7.778 5.419 7.932 7.512 1.328 5.750 1.828 5.674 0.430 7.843 6.656 7.368 2.258 tcdcclm 1587859200 240 0.193 5.932 0.805 7.620 6.761 2.857 5.387 5.490 7.905 5.823 7.646 7.860 0.887 6.696 2.207 5.257 0.623 7.901 4.229 7.198 1.997 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284.241 284.123 284.252 284.957 284.390 284.869 285.087 285.156 284.811 284.159 tmax2m 1586649600 48 277.979 277.956 277.760 278.242 278.177 278.321 277.758 277.784 277.796 278.279 278.119 277.783 277.749 277.845 278.175 277.910 278.114 278.065 278.119 277.938 278.227 tmax2m 1586671200 54 276.702 276.680 276.628 276.696 276.779 276.606 276.638 276.603 276.629 276.699 276.711 276.697 276.695 276.537 276.689 276.638 276.724 276.710 276.709 276.587 276.884 tmax2m 1586692800 60 284.543 284.405 284.518 285.034 284.626 284.597 284.828 283.189 284.548 285.006 284.361 284.205 284.420 284.537 284.718 284.507 284.822 284.620 284.886 284.016 285.152 tmax2m 1586714400 66 284.758 284.649 284.566 285.016 284.731 284.733 285.020 283.785 284.740 285.149 284.512 284.375 284.755 284.711 284.889 284.705 284.970 284.864 284.967 284.299 285.384 tmax2m 1586736000 72 277.347 277.195 277.524 276.515 277.524 276.766 277.714 277.143 277.193 277.271 277.527 277.503 277.491 276.914 277.424 277.411 277.445 277.643 277.990 277.566 277.357 tmax2m 1586757600 78 275.366 275.144 275.308 275.325 275.752 275.114 275.410 274.893 275.189 275.156 275.629 275.599 275.135 275.037 275.366 275.267 275.511 275.427 275.540 275.552 275.551 tmax2m 1586779200 84 283.140 283.841 284.100 283.550 283.298 284.175 283.097 283.912 284.039 284.304 284.348 283.264 282.622 283.989 283.176 282.831 282.324 282.602 283.061 282.868 282.434 tmax2m 1586800800 90 282.870 284.018 284.167 283.550 283.585 284.103 283.232 284.271 284.331 284.419 284.553 283.416 283.074 284.050 283.248 282.795 281.977 281.839 282.962 283.054 282.172 tmax2m 1586822400 96 276.010 276.227 276.325 276.460 276.222 276.450 276.704 275.577 276.654 277.642 277.394 275.660 275.365 275.218 276.865 276.782 275.762 275.314 276.376 276.958 276.285 tmax2m 1586844000 102 275.623 275.526 275.653 275.701 275.672 275.043 275.269 275.598 275.174 275.568 275.918 275.604 275.837 275.296 275.658 275.460 275.524 274.851 275.553 275.532 275.711 tmax2m 1586865600 108 281.867 282.132 281.369 282.183 279.873 282.178 279.638 279.461 279.701 281.188 280.717 283.775 280.905 279.314 282.570 279.322 283.357 277.977 283.119 280.517 280.583 tmax2m 1586887200 114 281.665 281.241 281.249 281.681 280.098 282.886 276.788 279.399 277.897 280.926 281.032 283.786 280.927 279.895 282.442 280.541 283.715 278.528 282.945 280.681 281.390 tmax2m 1586908800 120 276.031 276.098 276.065 276.394 275.811 276.762 269.426 275.793 272.296 277.055 276.386 277.460 275.495 274.942 276.781 275.263 276.898 274.789 276.210 276.303 275.392 tmax2m 1586930400 126 274.673 274.139 274.762 274.210 274.240 275.203 268.919 274.511 273.848 275.904 274.843 275.338 274.896 274.622 275.107 274.571 275.182 274.175 274.626 274.986 274.917 tmax2m 1586952000 132 283.398 284.017 283.467 281.439 281.586 285.006 277.328 282.867 283.308 284.684 283.973 283.890 284.176 283.849 283.953 283.679 284.872 282.694 282.823 282.943 284.047 tmax2m 1586973600 138 283.817 284.546 283.851 280.826 281.748 285.248 277.680 283.210 283.896 284.996 284.187 283.915 284.594 284.273 283.996 283.941 285.195 282.980 281.539 283.150 284.492 tmax2m 1586995200 144 277.857 278.067 277.992 276.357 276.739 278.486 272.663 277.856 276.386 278.655 277.923 276.842 277.717 277.594 277.981 276.996 279.210 276.844 276.901 277.367 278.316 tmax2m 1587016800 150 275.959 276.152 276.185 274.327 275.748 277.797 272.077 276.346 275.851 276.904 276.202 275.720 275.904 276.979 276.223 274.862 277.004 275.521 275.276 275.692 276.632 tmax2m 1587038400 156 282.147 286.980 284.237 277.372 285.682 284.517 280.240 286.739 285.744 287.269 285.923 285.208 286.020 287.149 284.098 283.020 282.974 284.128 278.883 282.231 285.958 tmax2m 1587060000 162 282.672 287.000 284.427 277.817 284.281 283.701 280.897 287.321 286.135 286.275 284.458 286.112 286.118 286.322 284.093 280.603 283.078 283.824 278.883 280.175 285.385 tmax2m 1587081600 168 277.634 279.565 278.659 276.177 278.552 278.446 274.901 280.206 279.039 279.845 279.081 279.190 278.064 279.723 279.319 275.667 278.702 278.496 276.878 276.299 279.967 tmax2m 1587103200 174 277.310 277.162 277.237 275.630 277.854 277.309 274.722 278.911 277.111 278.604 277.813 277.712 277.432 279.198 277.172 275.239 277.880 277.015 276.177 275.424 277.823 tmax2m 1587124800 180 287.690 283.500 288.376 282.852 288.589 287.198 282.704 284.844 287.005 289.584 289.143 288.141 283.791 288.681 284.560 285.175 287.764 287.910 281.011 283.878 287.563 tmax2m 1587146400 186 288.356 283.300 288.501 282.359 289.002 287.092 281.737 284.674 286.988 289.808 289.659 288.549 284.103 288.874 284.390 284.363 287.514 288.272 281.685 284.595 287.694 tmax2m 1587168000 192 280.064 277.625 281.293 277.917 281.926 279.918 276.713 279.952 280.739 281.827 281.447 279.903 277.445 280.734 279.330 278.417 281.368 279.903 277.604 276.870 279.088 tmax2m 1587189600 198 279.547 277.403 279.829 277.129 280.832 279.308 277.183 279.455 280.751 281.323 280.681 279.629 278.317 280.364 278.934 278.884 280.463 279.719 278.306 278.179 279.933 tmax2m 1587211200 204 290.345 283.585 292.469 288.487 289.684 289.551 287.164 282.191 289.634 291.554 291.366 290.382 289.071 291.842 291.006 289.966 291.603 290.105 289.452 289.304 292.439 tmax2m 1587232800 210 290.645 282.982 292.820 289.260 289.760 289.853 287.393 281.902 289.936 291.897 291.111 290.309 289.019 291.675 291.415 290.198 291.583 290.027 290.180 289.151 292.122 tmax2m 1587254400 216 282.385 278.628 283.859 281.866 283.097 283.912 280.932 279.679 281.899 284.143 283.865 281.863 280.667 283.941 284.375 282.306 283.303 283.816 281.408 279.508 282.620 tmax2m 1587276000 222 280.482 276.161 281.424 280.218 281.191 279.925 279.099 277.173 280.850 281.591 280.362 280.303 278.983 281.570 281.015 280.206 280.991 280.540 280.753 278.755 281.152 tmax2m 1587297600 228 286.479 288.926 289.686 286.512 290.128 287.882 289.637 287.600 289.956 290.731 290.179 284.041 287.416 291.336 291.099 288.473 288.498 286.528 292.032 286.061 292.808 tmax2m 1587319200 234 286.824 289.254 288.747 286.488 289.838 287.494 289.152 288.493 289.901 290.124 288.456 283.961 287.625 290.427 290.399 287.882 287.490 286.492 291.377 286.434 293.534 tmax2m 1587340800 240 281.743 281.324 282.515 280.977 283.094 282.521 282.677 280.009 282.837 282.700 282.112 280.164 280.454 282.776 284.076 282.255 282.212 282.321 282.890 279.124 284.383 dd10m 1586498400 6 184.254 184.614 180.916 180.190 183.314 180.251 189.118 178.854 186.898 190.673 175.300 186.118 187.141 189.588 188.906 179.520 186.199 185.025 181.418 186.894 186.336 dd10m 1586520000 12 33.660 32.408 33.885 56.524 48.667 36.099 27.975 41.848 30.527 21.470 33.643 25.241 40.197 47.338 19.450 35.342 25.773 44.932 42.890 42.086 31.949 dd10m 1586541600 18 36.288 33.425 34.942 40.921 47.735 36.721 36.340 43.726 37.285 33.608 42.488 32.063 35.167 29.373 27.401 35.206 33.750 31.565 29.237 37.671 43.421 dd10m 1586563200 24 358.172 12.218 11.586 212.408 210.735 221.023 323.066 336.449 13.344 6.926 317.013 14.639 305.488 14.034 27.975 2.556 3.617 72.241 24.619 186.876 267.867 dd10m 1586584800 30 15.374 17.249 15.796 292.541 279.214 22.726 0.471 16.662 11.889 19.832 11.093 6.957 9.696 11.982 24.226 15.685 9.053 16.557 10.667 321.029 11.902 dd10m 1586606400 36 39.451 39.540 41.990 41.566 51.095 52.418 31.078 28.220 34.066 47.861 34.320 31.991 31.257 41.517 59.364 38.807 47.938 44.005 41.038 37.639 38.586 dd10m 1586628000 42 89.926 85.188 91.096 92.650 98.987 103.610 79.871 76.400 79.889 107.192 87.213 82.246 77.390 96.101 109.863 85.303 95.315 91.401 96.605 83.129 91.341 dd10m 1586649600 48 189.175 189.577 188.391 188.722 189.614 189.607 187.722 188.218 188.014 192.200 187.297 186.966 191.297 188.609 193.338 190.877 189.990 192.846 186.077 188.384 192.607 dd10m 1586671200 54 201.085 202.339 201.761 203.356 201.363 202.976 199.176 203.174 205.157 204.788 200.835 202.299 200.921 200.773 206.970 202.079 201.228 202.682 201.270 196.776 203.727 dd10m 1586692800 60 208.119 201.980 213.182 219.215 204.596 209.024 207.521 210.055 218.866 207.244 212.371 220.170 200.666 216.056 213.077 204.554 212.112 199.741 199.219 200.876 211.475 dd10m 1586714400 66 171.126 172.035 173.020 188.650 173.021 184.254 169.888 186.251 173.756 178.143 174.573 168.933 171.130 171.791 168.297 173.871 176.449 170.226 172.510 171.417 169.535 dd10m 1586736000 72 194.412 196.451 196.396 194.687 195.011 198.871 191.382 200.841 196.829 191.965 195.231 194.649 194.180 197.397 193.054 192.961 194.824 195.636 192.265 192.688 193.429 dd10m 1586757600 78 195.525 197.738 194.514 189.275 197.624 201.386 190.418 193.724 192.452 192.805 194.106 194.144 195.201 196.152 193.460 192.235 191.963 200.849 192.233 193.010 193.974 dd10m 1586779200 84 202.004 191.925 195.816 193.974 200.719 250.590 200.382 204.872 200.910 194.988 195.188 191.682 212.109 210.450 204.946 205.724 200.311 216.349 189.541 191.679 215.026 dd10m 1586800800 90 158.719 277.735 147.662 173.335 151.997 344.341 188.530 203.954 178.709 170.784 154.145 178.531 240.459 244.651 207.810 196.312 334.916 241.504 169.830 152.533 262.517 dd10m 1586822400 96 203.841 277.713 203.436 186.515 202.085 16.322 191.930 203.947 194.689 184.343 196.905 195.249 214.381 328.665 203.112 212.743 257.422 233.067 193.810 212.194 1.613 dd10m 1586844000 102 48.001 35.359 46.998 158.565 46.314 45.411 208.617 17.225 227.929 82.890 74.424 161.207 16.141 16.638 131.441 355.061 75.528 1.198 191.477 56.152 29.497 dd10m 1586865600 108 62.942 78.915 67.921 97.716 71.993 93.002 19.412 53.732 17.745 82.855 99.138 105.297 56.825 44.809 127.465 49.986 116.146 41.393 98.759 91.826 72.295 dd10m 1586887200 114 85.211 91.023 92.332 109.232 99.285 116.442 42.813 76.487 53.801 111.697 117.326 118.810 87.646 68.996 129.172 82.162 120.923 76.609 105.779 111.013 93.525 dd10m 1586908800 120 156.939 153.812 153.565 146.511 149.001 170.064 87.182 158.692 127.373 167.091 156.336 157.362 149.337 149.244 157.015 154.141 168.094 150.223 140.960 152.274 161.576 dd10m 1586930400 126 159.413 153.682 158.382 153.132 154.242 175.325 103.532 167.268 150.891 169.164 157.668 164.546 157.127 172.659 168.513 144.752 172.920 156.665 152.646 159.943 175.955 dd10m 1586952000 132 152.740 146.053 152.622 146.509 142.200 161.650 115.253 157.106 149.603 142.555 140.442 151.860 149.106 135.109 140.914 140.626 164.850 153.347 152.250 157.782 121.188 dd10m 1586973600 138 156.081 157.934 160.126 164.848 156.696 167.393 114.642 161.357 161.112 160.369 150.367 177.934 156.371 147.267 150.408 131.403 157.055 149.207 153.990 165.825 152.442 dd10m 1586995200 144 177.667 183.230 183.268 195.376 185.757 183.610 166.829 189.205 181.620 188.260 177.695 188.961 185.239 194.320 176.060 166.885 184.529 181.008 173.668 183.312 179.264 dd10m 1587016800 150 184.800 184.396 192.025 227.431 200.879 176.274 176.750 201.962 192.040 206.988 195.972 196.912 186.339 255.300 169.579 168.125 200.221 183.345 349.506 176.278 205.745 dd10m 1587038400 156 216.439 187.489 196.698 243.159 294.480 198.691 121.081 165.733 177.092 153.658 219.417 136.703 202.350 90.617 164.408 179.525 209.102 167.847 346.135 209.758 233.215 dd10m 1587060000 162 163.078 196.735 176.868 196.356 105.730 203.387 146.610 165.992 172.226 123.380 151.333 146.412 226.329 121.657 168.479 186.001 85.981 164.117 336.100 260.840 302.515 dd10m 1587081600 168 205.757 189.789 195.866 227.011 182.451 215.088 206.925 187.957 201.711 184.825 188.138 188.624 236.172 210.010 193.586 197.958 184.981 186.160 343.779 279.430 281.513 dd10m 1587103200 174 192.930 197.647 198.698 217.137 171.594 301.848 218.945 191.800 182.396 184.537 199.689 218.915 318.263 231.912 194.200 201.303 213.610 191.733 357.476 287.621 300.918 dd10m 1587124800 180 158.465 233.816 164.605 223.005 144.398 79.529 47.216 198.005 173.834 147.757 169.186 133.391 6.002 58.649 213.909 312.883 126.711 295.141 56.727 310.756 8.338 dd10m 1587146400 186 134.924 242.403 163.899 178.553 151.542 114.000 136.064 190.241 168.849 143.468 173.434 131.430 19.341 111.575 170.608 123.937 142.010 116.104 126.878 18.138 81.794 dd10m 1587168000 192 186.393 240.521 191.096 194.449 180.452 171.622 197.971 198.812 181.432 185.028 221.116 187.810 191.026 188.390 200.512 203.872 193.311 173.760 190.367 184.259 168.944 dd10m 1587189600 198 182.818 248.426 187.827 194.068 184.058 157.624 185.927 249.115 193.255 181.119 204.249 205.778 161.651 189.567 189.263 157.347 193.485 180.705 194.443 192.436 163.247 dd10m 1587211200 204 209.150 303.567 199.486 193.124 180.598 153.213 177.284 323.355 191.318 139.930 72.032 325.379 108.305 91.041 131.068 84.155 181.879 156.592 131.831 5.979 83.658 dd10m 1587232800 210 228.366 328.879 271.971 191.561 173.138 158.323 145.411 345.734 112.443 165.111 134.796 32.689 84.341 123.937 134.778 129.329 253.237 161.453 111.837 52.350 98.585 dd10m 1587254400 216 246.993 295.577 199.765 201.142 212.315 180.904 187.644 321.501 214.167 201.923 192.403 196.113 187.588 197.251 183.079 189.230 304.328 191.065 196.217 6.095 186.565 dd10m 1587276000 222 311.156 221.694 225.014 248.749 196.973 180.372 199.683 226.765 261.021 213.625 222.900 194.165 181.530 211.227 192.529 212.676 333.088 214.363 202.480 11.813 215.387 dd10m 1587297600 228 1.411 305.873 339.315 286.855 165.716 155.159 162.001 286.443 27.266 339.138 208.268 256.111 31.796 18.153 193.473 82.360 2.444 353.196 61.261 22.161 42.056 dd10m 1587319200 234 23.311 344.348 17.750 318.234 141.735 165.394 156.991 304.051 22.911 10.255 296.953 94.279 98.658 27.241 178.570 111.816 357.868 142.039 97.411 45.728 347.696 dd10m 1587340800 240 124.867 232.400 354.824 306.515 209.165 181.379 195.959 294.238 91.006 303.405 204.221 160.520 173.385 192.119 195.904 181.736 350.414 198.916 204.854 139.099 280.914 ff10m 1586498400 6 1.119 0.993 1.110 1.098 1.246 1.162 1.097 1.080 1.107 1.191 0.957 1.147 1.269 1.079 1.094 1.082 1.155 1.207 0.954 1.118 1.214 ff10m 1586520000 12 0.738 0.781 0.706 0.546 0.539 0.816 0.886 0.856 1.031 1.056 0.752 0.657 0.745 0.700 0.814 0.652 0.627 0.662 0.628 0.685 0.799 ff10m 1586541600 18 1.228 1.398 1.323 0.852 0.998 1.220 1.178 1.228 1.406 1.385 1.158 1.182 1.127 1.304 1.465 1.095 1.330 1.227 1.229 1.214 1.126 ff10m 1586563200 24 0.102 0.245 0.485 0.873 0.807 0.119 0.399 0.176 0.106 0.399 0.154 0.403 0.162 0.549 0.861 0.249 0.081 0.183 0.201 0.482 0.385 ff10m 1586584800 30 1.229 1.284 1.261 0.529 0.107 1.125 1.349 1.390 1.255 1.159 1.220 1.267 1.203 1.277 1.073 1.180 1.056 0.816 1.244 0.263 1.069 ff10m 1586606400 36 1.449 1.452 1.551 1.403 1.156 1.231 1.618 1.639 1.702 1.161 1.577 1.623 1.619 1.526 1.003 1.413 1.314 1.155 1.409 1.290 1.369 ff10m 1586628000 42 1.248 1.234 1.279 1.253 1.184 1.180 1.302 1.380 1.348 1.065 1.237 1.366 1.221 1.217 0.982 1.154 1.190 1.092 1.323 1.131 1.056 ff10m 1586649600 48 2.191 2.177 2.225 2.227 2.168 2.343 2.152 2.028 2.179 2.220 2.145 2.151 1.992 2.192 2.279 2.043 2.223 2.135 2.323 2.029 2.159 ff10m 1586671200 54 2.175 2.053 2.246 2.257 2.135 2.294 2.240 2.029 2.182 2.290 2.200 2.139 2.017 2.269 2.100 2.097 2.200 2.055 2.287 2.089 2.172 ff10m 1586692800 60 1.924 1.801 1.781 2.111 1.971 2.075 1.905 1.564 1.792 2.013 2.115 1.663 1.708 1.793 1.649 1.899 2.001 1.717 2.222 1.915 1.870 ff10m 1586714400 66 1.791 1.799 1.733 1.252 1.781 1.605 1.843 1.752 1.589 1.769 1.727 1.506 1.882 1.692 1.777 1.796 1.748 1.910 2.206 1.980 1.647 ff10m 1586736000 72 3.128 3.069 3.055 3.042 2.930 2.770 3.440 2.821 3.065 3.182 3.064 2.994 3.269 2.940 3.264 3.257 2.995 3.164 3.383 3.338 3.034 ff10m 1586757600 78 2.819 2.604 2.757 3.210 2.586 2.494 3.174 2.691 2.926 3.064 2.784 2.633 2.872 2.691 3.121 3.089 2.807 2.719 2.732 2.805 2.932 ff10m 1586779200 84 1.665 1.055 1.297 2.331 1.548 0.570 2.778 1.650 1.954 1.891 1.691 2.391 1.671 1.389 2.123 2.304 1.700 1.249 2.263 1.786 1.927 ff10m 1586800800 90 0.520 0.178 0.736 1.485 0.457 0.996 1.219 0.372 1.061 1.151 0.665 0.818 0.179 0.129 0.697 0.714 0.413 0.325 1.212 0.758 0.395 ff10m 1586822400 96 1.832 0.527 1.556 2.454 1.493 1.218 2.637 1.755 2.404 2.245 0.715 2.277 1.448 0.619 1.603 2.012 0.441 1.741 2.399 1.301 1.278 ff10m 1586844000 102 0.409 1.946 0.908 1.176 1.399 2.218 1.504 1.760 1.099 1.014 1.963 1.364 1.981 2.534 1.922 1.742 1.551 2.064 1.591 2.246 2.360 ff10m 1586865600 108 3.351 3.017 3.520 3.126 3.283 2.758 2.890 3.273 4.167 3.624 2.992 2.960 3.353 3.074 2.923 3.311 2.614 3.633 2.691 3.372 2.602 ff10m 1586887200 114 2.699 2.423 2.961 3.019 2.763 2.405 4.006 2.581 3.358 2.831 2.548 2.795 3.145 2.814 2.396 2.976 2.541 3.174 3.178 2.607 2.139 ff10m 1586908800 120 3.028 2.712 3.295 3.741 2.757 3.222 2.622 2.716 2.705 3.152 2.810 3.762 3.112 2.262 2.893 3.281 3.268 3.280 4.063 3.316 2.309 ff10m 1586930400 126 2.881 2.768 3.377 3.851 2.661 3.511 3.306 2.468 3.057 2.060 2.440 3.970 2.630 2.275 2.631 2.597 2.969 2.831 4.313 3.164 1.828 ff10m 1586952000 132 3.467 3.639 2.957 3.169 2.572 3.350 3.887 2.760 3.748 3.108 3.192 4.203 2.908 2.012 2.011 3.080 2.183 3.129 4.185 3.600 1.758 ff10m 1586973600 138 2.833 3.046 3.396 1.634 2.555 3.339 2.820 2.827 3.578 2.664 3.291 3.134 2.580 1.894 2.050 1.993 2.828 2.390 2.360 3.409 2.742 ff10m 1586995200 144 4.073 3.795 4.585 2.197 3.559 4.163 2.670 3.533 4.421 3.501 4.167 3.363 3.750 2.146 2.507 3.092 4.229 3.071 1.456 4.616 3.655 ff10m 1587016800 150 3.459 4.087 3.693 1.528 2.966 3.969 1.709 1.878 3.515 2.495 3.446 2.464 3.814 0.572 2.188 3.444 2.195 2.499 1.116 4.490 3.357 ff10m 1587038400 156 2.189 3.923 2.267 0.775 1.611 3.128 1.639 2.088 2.908 0.660 0.725 1.303 3.335 0.999 2.541 2.588 1.233 1.799 1.349 3.765 1.546 ff10m 1587060000 162 1.059 2.679 1.572 0.741 1.205 1.117 1.467 1.584 3.554 0.893 1.431 1.768 1.269 1.350 2.523 2.005 0.570 1.014 1.821 1.995 0.745 ff10m 1587081600 168 2.041 3.194 2.714 2.059 2.194 2.126 2.017 3.002 3.588 2.293 2.585 2.228 1.729 1.748 3.429 2.504 2.213 2.006 1.618 1.983 1.652 ff10m 1587103200 174 1.565 2.774 2.138 1.991 2.182 0.607 1.219 2.584 2.817 2.339 2.492 1.367 0.957 0.933 2.689 2.038 1.678 1.845 1.224 1.568 0.966 ff10m 1587124800 180 0.837 2.242 1.869 1.543 2.220 1.772 0.879 2.560 4.391 1.354 1.490 1.099 1.907 1.936 1.835 0.292 1.414 0.540 1.812 2.072 2.619 ff10m 1587146400 186 1.371 1.053 1.334 1.247 2.373 1.764 1.459 2.005 3.719 0.824 1.288 0.995 1.277 1.510 1.399 1.062 1.414 1.539 1.465 1.870 1.865 ff10m 1587168000 192 2.629 2.449 3.380 2.807 3.435 2.409 2.212 2.612 3.699 2.080 1.982 2.490 1.009 2.223 2.678 0.935 2.793 2.314 2.083 1.491 2.128 ff10m 1587189600 198 2.648 1.585 2.603 2.396 3.299 2.413 1.908 1.666 2.628 1.680 1.507 2.079 1.137 1.706 2.019 1.391 2.435 2.238 1.711 1.349 1.987 ff10m 1587211200 204 1.960 2.926 1.595 1.814 2.895 3.766 1.248 1.575 1.241 1.938 1.204 0.330 0.892 1.403 1.672 1.387 1.328 2.487 0.917 0.637 1.805 ff10m 1587232800 210 0.778 2.868 0.535 1.088 2.437 2.832 1.443 1.908 0.480 1.243 1.272 0.906 1.244 1.017 1.906 1.715 1.469 2.439 0.903 0.826 1.739 ff10m 1587254400 216 1.705 1.362 1.650 2.408 2.267 3.071 2.706 1.629 1.728 2.358 2.562 0.872 1.569 1.888 3.212 2.818 0.905 2.974 1.709 0.530 2.109 ff10m 1587276000 222 1.302 1.352 2.069 1.345 2.359 2.571 2.121 1.520 1.094 2.124 1.967 0.838 1.334 1.615 2.992 1.120 0.963 1.975 1.047 2.213 1.158 ff10m 1587297600 228 2.564 1.101 2.547 0.722 0.756 2.548 1.201 1.877 1.286 1.143 1.283 0.530 0.936 0.902 1.941 1.296 1.278 1.306 1.037 3.874 1.192 ff10m 1587319200 234 1.916 1.644 1.777 1.083 1.070 2.683 1.268 1.372 1.831 0.403 0.856 0.558 1.149 1.405 1.224 0.372 1.257 1.490 0.964 2.841 2.568 ff10m 1587340800 240 0.946 2.283 2.830 1.313 1.212 2.920 2.546 2.237 0.983 0.954 1.660 1.886 2.429 1.314 2.832 2.076 1.598 1.660 1.200 1.339 1.859 apcpsfc 1586498400 6 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 apcpsfc 1586520000 12 0.048 0.048 0.048 0.048 0.000 0.048 0.037 0.048 0.048 0.048 0.074 0.000 0.048 0.000 0.000 0.048 0.048 0.000 0.048 0.000 0.074 apcpsfc 1586541600 18 0.170 0.170 0.184 0.217 0.170 0.217 0.170 0.170 0.170 0.170 0.318 0.170 0.170 0.124 0.112 0.217 0.160 0.256 0.217 0.170 0.509 apcpsfc 1586563200 24 0.015 0.048 0.020 0.027 0.012 0.020 0.000 0.027 0.012 0.012 0.048 0.017 0.020 0.010 0.003 0.015 0.015 0.000 0.012 0.015 0.056 apcpsfc 1586584800 30 0.000 0.000 0.000 0.000 0.000 0.010 0.000 0.010 0.000 0.000 0.014 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.014 apcpsfc 1586606400 36 0.125 0.196 0.110 0.161 0.093 0.126 0.148 0.135 0.122 0.149 0.196 0.135 0.196 0.142 0.091 0.152 0.126 0.088 0.068 0.158 0.183 apcpsfc 1586628000 42 1.129 1.273 0.805 1.257 1.154 0.916 0.864 0.801 0.535 1.357 1.239 0.636 1.092 1.112 1.060 1.138 1.124 0.994 0.479 0.861 1.462 apcpsfc 1586649600 48 1.391 1.608 0.964 1.104 1.633 0.821 0.512 0.545 0.466 1.531 1.274 0.495 0.738 1.006 1.527 1.162 1.358 0.769 0.636 0.339 1.926 apcpsfc 1586671200 54 0.987 1.038 0.949 0.366 0.801 0.496 0.817 1.438 0.812 0.394 1.183 1.164 0.921 0.524 0.848 1.128 0.626 0.889 0.812 1.278 0.629 apcpsfc 1586692800 60 0.100 0.271 0.148 0.052 0.124 0.043 0.075 0.789 0.249 0.023 0.170 0.397 0.295 0.049 0.137 0.170 0.034 0.167 0.070 0.461 0.053 apcpsfc 1586714400 66 0.447 0.509 0.597 0.721 0.567 0.922 0.385 1.335 0.673 0.353 0.756 0.803 0.400 0.591 0.663 0.512 0.373 0.265 0.557 0.611 0.470 apcpsfc 1586736000 72 0.086 0.237 0.211 0.259 0.411 0.205 0.059 0.947 0.245 0.341 0.300 0.216 0.067 0.165 0.234 0.143 0.177 0.093 0.047 0.016 0.660 apcpsfc 1586757600 78 0.034 0.072 0.083 0.050 0.129 0.099 0.026 0.081 0.114 0.006 0.135 0.465 0.015 0.194 0.055 0.010 0.089 0.097 0.001 0.035 0.061 apcpsfc 1586779200 84 0.065 0.023 0.057 0.000 0.133 0.174 0.000 0.000 0.009 0.000 0.026 0.035 0.023 0.009 0.010 0.000 0.191 0.235 0.051 0.083 0.160 apcpsfc 1586800800 90 0.703 0.885 0.428 0.320 0.401 1.227 0.332 0.245 0.218 0.037 0.132 0.707 0.290 0.605 0.413 0.223 1.516 1.618 0.772 0.888 1.031 apcpsfc 1586822400 96 0.433 1.532 0.386 0.209 0.511 1.679 0.404 0.383 0.263 0.043 0.089 0.377 0.393 0.726 0.287 0.567 0.435 0.470 0.352 1.136 0.581 apcpsfc 1586844000 102 0.000 0.136 0.009 0.000 0.438 0.184 0.112 0.357 0.021 0.692 0.287 0.020 0.053 0.259 0.009 0.016 0.009 0.070 0.000 0.232 0.480 apcpsfc 1586865600 108 0.196 0.511 0.409 0.236 0.898 0.143 1.247 1.164 1.255 0.314 0.854 0.079 0.594 0.517 0.000 0.637 0.053 0.626 0.057 1.034 0.356 apcpsfc 1586887200 114 0.572 2.045 0.577 1.280 1.162 0.232 2.883 1.846 0.476 0.587 1.156 0.390 0.069 0.053 0.710 0.184 0.158 0.509 0.428 2.122 1.298 apcpsfc 1586908800 120 0.680 0.680 0.285 0.201 0.833 0.053 1.485 0.596 0.048 0.545 0.237 0.000 0.359 0.127 0.048 1.187 0.000 0.782 0.354 0.838 0.746 apcpsfc 1586930400 126 0.053 0.000 0.053 0.074 0.371 0.000 0.519 0.100 0.122 0.382 0.000 0.000 0.074 0.280 0.048 0.074 0.000 0.053 0.079 0.413 0.127 apcpsfc 1586952000 132 0.000 0.000 0.000 0.719 0.980 0.000 0.143 0.033 0.000 0.048 0.026 0.000 0.000 0.052 0.175 0.000 0.000 0.000 0.466 0.000 0.046 apcpsfc 1586973600 138 0.012 0.000 0.000 1.957 0.557 0.000 0.184 0.011 0.000 0.000 0.000 0.727 0.000 0.114 0.354 0.010 0.000 0.022 0.276 0.037 0.124 apcpsfc 1586995200 144 0.010 0.010 0.000 2.630 0.000 0.048 0.490 0.014 0.000 0.000 0.000 0.055 0.000 0.000 0.000 0.000 0.000 0.000 0.100 0.072 0.000 apcpsfc 1587016800 150 0.143 0.000 0.000 6.122 0.000 0.000 0.920 0.000 0.048 0.000 0.010 0.396 0.000 0.000 0.014 0.000 0.067 0.000 2.533 0.043 0.000 apcpsfc 1587038400 156 1.872 0.000 0.165 5.662 0.292 1.441 0.265 0.000 0.000 0.049 0.406 0.053 0.048 0.100 0.926 1.027 1.960 0.302 5.756 1.858 0.150 apcpsfc 1587060000 162 0.430 0.800 0.807 6.050 0.588 0.122 0.387 0.191 0.000 1.033 0.459 0.000 0.749 0.249 0.726 3.178 2.103 0.483 8.599 4.913 1.570 apcpsfc 1587081600 168 0.017 0.509 0.018 3.933 0.000 0.000 0.048 0.621 0.000 0.096 0.000 0.000 1.939 0.000 0.320 0.723 0.466 0.012 2.817 0.441 0.380 apcpsfc 1587103200 174 0.000 0.150 0.000 0.756 0.000 0.033 0.048 0.982 0.000 0.000 0.000 0.000 0.852 0.000 0.140 1.366 0.000 0.000 0.837 0.170 0.053 apcpsfc 1587124800 180 0.000 1.239 0.000 0.214 0.000 0.096 0.824 1.911 0.000 0.000 0.000 0.000 2.010 0.012 0.597 0.245 0.026 0.000 0.380 0.062 0.000 apcpsfc 1587146400 186 0.048 3.554 0.000 0.952 0.000 0.301 5.647 1.911 0.143 0.042 0.000 0.000 3.398 0.696 1.233 0.827 0.136 0.026 0.127 0.224 0.000 apcpsfc 1587168000 192 0.000 0.845 0.000 0.000 0.048 0.055 1.778 2.773 0.239 0.000 0.000 0.000 0.555 0.134 0.000 0.057 0.000 0.010 0.000 0.000 0.000 apcpsfc 1587189600 198 0.000 0.079 0.000 0.000 0.000 0.000 0.003 3.956 0.048 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 apcpsfc 1587211200 204 0.000 1.644 0.000 0.000 0.371 0.000 0.303 5.438 0.557 0.000 0.133 0.054 0.111 0.023 0.000 0.000 0.037 0.012 0.000 0.000 0.000 apcpsfc 1587232800 210 0.014 2.277 0.861 0.394 1.341 0.000 1.335 4.193 2.093 0.000 1.136 0.521 1.793 0.246 0.005 0.124 2.073 0.533 0.254 0.121 0.106 apcpsfc 1587254400 216 0.620 0.183 0.415 1.312 1.312 0.051 0.018 0.437 0.749 0.020 0.141 0.733 1.029 0.015 0.000 0.052 0.711 0.497 0.000 0.059 0.010 apcpsfc 1587276000 222 1.053 0.003 0.005 2.672 0.061 0.012 0.010 0.062 0.269 0.372 0.118 2.313 0.075 0.000 0.000 0.003 0.175 1.195 0.000 0.026 0.000 apcpsfc 1587297600 228 1.109 0.000 0.442 2.761 0.129 0.827 0.048 0.000 0.423 0.320 0.596 3.904 1.361 0.369 0.295 1.521 1.317 2.060 0.000 0.016 0.000 apcpsfc 1587319200 234 1.046 0.000 1.857 6.419 3.160 2.463 1.626 0.008 2.442 1.336 8.335 6.661 2.858 3.855 2.290 6.238 5.262 5.111 0.194 0.060 0.000 apcpsfc 1587340800 240 0.063 0.138 4.575 3.074 3.949 2.293 0.769 0.144 0.274 1.649 5.457 3.762 0.651 0.559 0.050 0.531 2.121 2.975 0.003 0.000 0.000 tmp2m 1586498400 6 275.411 275.502 275.437 275.450 275.314 275.494 275.550 275.511 275.411 275.511 275.729 275.254 275.433 275.198 275.115 275.403 275.367 275.324 275.433 275.411 275.659 tmp2m 1586520000 12 284.442 284.313 284.494 284.621 284.530 284.282 284.472 284.139 284.060 284.355 284.155 284.447 284.451 284.547 284.516 284.246 284.500 284.495 284.351 284.404 284.150 tmp2m 1586541600 18 277.312 277.671 277.157 277.543 277.112 277.326 277.306 277.566 277.305 277.296 277.556 276.732 277.520 277.298 276.946 277.417 277.338 277.228 277.326 277.509 277.879 tmp2m 1586563200 24 272.418 272.953 272.466 272.736 272.582 273.026 272.433 272.832 272.255 273.138 273.137 273.090 272.530 273.075 272.714 272.346 272.194 272.237 272.612 272.423 273.178 tmp2m 1586584800 30 276.594 276.901 276.371 276.670 276.584 276.738 276.454 276.581 276.344 276.556 277.129 276.729 276.603 276.612 276.165 276.438 276.508 276.565 276.476 276.809 277.064 tmp2m 1586606400 36 284.805 284.622 284.545 284.632 285.388 285.193 284.396 284.296 284.384 285.186 284.173 284.444 284.300 284.497 285.552 284.641 284.920 285.459 285.036 284.856 284.399 tmp2m 1586628000 42 278.082 278.068 277.959 278.202 278.228 278.298 277.836 278.091 277.938 278.208 278.208 277.913 277.948 278.013 278.169 277.987 278.191 278.115 278.029 278.046 278.251 tmp2m 1586649600 48 275.684 275.811 275.661 275.956 275.876 275.728 275.604 275.520 275.451 276.012 275.854 275.624 275.718 275.683 275.924 275.772 275.779 275.726 275.703 275.521 276.336 tmp2m 1586671200 54 276.654 276.537 276.532 276.361 276.636 276.357 276.590 276.555 276.620 276.290 276.606 276.697 276.638 276.250 276.403 276.628 276.381 276.614 276.461 276.492 276.524 tmp2m 1586692800 60 284.543 284.405 284.470 284.923 284.502 284.463 284.828 283.162 284.505 284.958 284.319 284.157 284.420 284.554 284.691 284.443 284.813 284.524 284.759 284.016 285.136 tmp2m 1586714400 66 277.405 277.328 277.473 276.470 277.470 276.829 277.774 276.973 277.218 277.239 277.475 277.554 277.516 276.989 277.490 277.427 277.396 277.619 278.017 277.545 277.441 tmp2m 1586736000 72 274.245 273.817 274.399 274.160 274.562 273.705 274.464 273.932 274.056 274.321 274.840 274.492 273.913 273.837 274.233 274.338 274.663 274.261 274.651 274.444 274.461 tmp2m 1586757600 78 275.207 274.890 275.113 274.917 275.458 274.876 275.240 274.603 274.877 274.893 275.418 275.328 275.016 274.733 275.104 275.073 275.376 275.240 275.497 275.509 275.203 tmp2m 1586779200 84 283.087 283.841 284.100 283.523 283.224 284.150 283.097 283.912 284.039 284.182 284.295 283.290 282.622 283.989 283.176 282.783 282.203 282.506 283.061 282.868 282.386 tmp2m 1586800800 90 276.763 276.904 277.304 276.621 276.988 276.791 276.800 276.764 276.853 277.538 277.044 276.249 276.568 276.512 277.520 277.051 276.406 276.179 276.414 277.142 276.859 tmp2m 1586822400 96 273.084 274.165 272.648 273.953 274.043 274.264 274.133 273.203 273.858 274.671 274.423 273.405 274.095 273.566 272.929 273.959 272.105 272.800 273.603 274.202 272.884 tmp2m 1586844000 102 275.597 275.454 275.609 275.692 275.482 274.913 275.243 275.487 275.155 275.483 275.611 275.604 275.766 275.169 275.554 275.396 275.476 274.751 275.553 275.388 274.866 tmp2m 1586865600 108 281.558 281.964 280.659 281.891 279.830 282.178 276.913 278.986 277.554 280.459 280.616 283.660 280.629 279.219 282.489 278.994 283.357 277.925 282.933 280.508 280.583 tmp2m 1586887200 114 276.156 276.376 276.264 276.768 276.093 277.031 269.788 275.957 272.844 277.206 276.655 277.459 274.943 274.647 277.045 274.875 277.002 274.522 276.453 276.547 275.374 tmp2m 1586908800 120 274.054 273.786 274.177 273.656 273.803 274.389 266.386 274.025 270.007 275.042 273.946 274.117 274.334 273.457 274.043 274.004 274.128 273.515 274.242 274.402 274.051 tmp2m 1586930400 126 274.515 273.991 274.477 274.083 274.109 275.045 268.919 274.124 273.831 275.534 274.791 275.338 274.508 274.605 275.072 273.956 275.155 273.714 274.393 274.118 274.821 tmp2m 1586952000 132 283.398 284.017 283.467 281.221 281.586 285.006 277.280 282.815 283.282 284.658 283.925 283.759 284.176 283.823 283.616 283.679 284.872 282.694 281.525 282.943 284.047 tmp2m 1586973600 138 278.153 278.353 278.287 276.625 277.004 278.798 272.832 278.116 276.699 278.940 278.262 277.099 277.882 277.848 278.367 277.102 279.553 277.017 277.165 277.681 278.506 tmp2m 1586995200 144 274.242 274.312 274.745 274.107 273.708 276.510 270.104 274.869 273.352 274.628 274.126 274.600 273.685 273.276 274.002 273.207 276.187 272.971 273.564 275.058 274.651 tmp2m 1587016800 150 275.959 276.152 276.185 274.081 275.748 277.797 272.059 276.346 275.851 276.904 276.192 275.687 275.904 276.979 276.249 274.862 276.870 275.521 275.249 275.692 276.632 tmp2m 1587038400 156 281.657 286.980 284.220 277.372 285.034 282.443 280.066 286.739 285.744 286.454 284.429 285.102 286.020 286.709 283.785 281.361 282.921 283.767 278.691 280.381 285.480 tmp2m 1587060000 162 278.088 279.793 279.084 276.011 278.435 278.533 275.086 280.239 279.298 280.347 279.564 279.387 278.204 280.067 279.479 275.939 278.802 278.398 276.872 276.494 279.943 tmp2m 1587081600 168 274.222 276.356 275.158 275.602 275.748 274.274 271.758 277.942 274.929 276.966 275.930 275.157 274.517 275.492 276.742 274.238 277.054 275.625 275.569 274.675 276.872 tmp2m 1587103200 174 277.310 277.162 277.220 275.139 277.854 277.293 274.722 278.911 277.111 278.604 277.861 277.712 277.195 279.198 277.105 275.230 277.854 277.006 276.129 275.251 277.665 tmp2m 1587124800 180 287.642 283.390 288.376 281.226 288.589 287.097 282.326 284.770 286.957 289.584 289.143 288.141 283.791 288.681 284.446 284.793 287.374 287.910 280.447 283.869 287.536 tmp2m 1587146400 186 280.512 278.047 281.366 277.961 282.137 280.518 276.855 280.171 280.849 282.411 281.636 280.235 277.615 281.005 279.643 278.386 281.815 279.975 277.930 277.434 279.567 tmp2m 1587168000 192 277.330 275.131 277.683 275.447 278.767 276.697 274.672 278.315 279.529 278.384 277.955 277.381 273.828 277.401 276.666 273.571 278.224 277.261 275.315 273.732 276.720 tmp2m 1587189600 198 279.547 277.360 279.829 277.129 280.832 279.308 277.183 279.420 280.735 281.323 280.579 279.620 278.317 280.364 278.934 278.884 280.463 279.719 278.306 278.126 279.933 tmp2m 1587211200 204 290.329 283.080 292.353 288.105 289.657 289.551 287.068 282.052 289.634 291.554 291.366 290.382 288.832 291.720 290.958 289.966 291.522 290.058 289.356 289.161 292.391 tmp2m 1587232800 210 283.053 278.828 284.188 281.973 283.714 284.029 281.178 279.699 282.465 284.550 284.154 282.377 281.389 284.309 284.327 282.383 283.495 284.047 282.264 280.289 282.953 tmp2m 1587254400 216 279.500 274.433 279.269 279.626 280.907 279.118 277.277 276.777 279.689 280.292 279.601 278.973 277.632 279.451 280.395 278.582 279.787 279.789 277.821 276.056 279.164 tmp2m 1587276000 222 280.406 275.951 281.424 280.166 280.991 279.925 279.099 276.427 280.719 281.515 280.362 280.243 278.957 281.570 280.936 280.206 280.991 280.540 280.753 278.729 281.124 tmp2m 1587297600 228 286.431 288.926 289.057 286.438 289.985 287.559 289.228 287.600 289.860 290.523 289.066 283.993 287.268 290.653 290.711 287.864 287.756 286.352 292.032 286.061 292.808 tmp2m 1587319200 234 282.355 281.594 282.655 281.485 283.402 282.764 282.947 280.622 283.459 282.998 282.590 280.217 280.767 283.161 284.355 282.577 282.469 282.403 283.981 279.363 284.678 tmp2m 1587340800 240 279.342 278.032 280.797 279.670 280.388 279.612 279.625 278.019 280.219 280.253 280.669 279.042 278.025 278.796 280.800 278.943 280.944 280.133 278.921 272.473 278.473 tcdcclm 1586498400 6 0.000 0.021 0.000 0.000 0.007 0.087 0.038 0.000 0.000 0.046 0.120 0.053 0.038 0.007 0.007 0.007 0.037 0.000 0.000 0.000 0.038 tcdcclm 1586520000 12 1.256 1.391 1.248 1.217 1.235 1.468 1.200 1.382 1.290 1.315 1.678 1.002 1.256 0.637 0.658 1.256 1.273 1.256 1.265 1.030 1.594 tcdcclm 1586541600 18 3.032 3.163 3.147 2.982 2.853 3.432 2.728 3.089 3.026 2.926 3.833 2.691 3.154 2.739 2.723 3.107 3.179 2.983 3.362 2.824 3.889 tcdcclm 1586563200 24 1.748 2.474 1.595 1.363 0.820 2.634 1.547 2.364 1.377 2.108 2.868 2.526 2.080 1.920 1.128 1.843 1.456 1.846 2.256 1.615 2.650 tcdcclm 1586584800 30 1.070 1.723 0.402 0.171 0.534 1.561 0.455 1.935 0.290 1.083 2.568 1.485 1.592 1.177 0.203 0.605 0.296 0.597 0.679 1.283 2.782 tcdcclm 1586606400 36 1.321 1.448 1.223 1.443 1.230 1.356 1.322 1.924 1.154 1.770 2.730 1.566 1.273 1.317 1.087 1.425 1.415 0.974 1.246 1.246 1.421 tcdcclm 1586628000 42 5.173 4.804 4.424 5.254 5.388 4.978 5.255 4.690 4.247 5.392 5.583 4.710 5.129 4.987 5.197 5.171 4.692 5.087 4.614 4.891 5.382 tcdcclm 1586649600 48 4.519 4.897 4.358 4.736 4.778 4.421 4.917 4.691 4.032 5.422 4.681 4.648 4.907 4.699 5.172 5.279 4.639 5.113 4.460 5.115 5.453 tcdcclm 1586671200 54 5.283 5.536 4.925 4.101 5.257 5.062 5.453 5.468 4.767 4.109 5.540 5.450 5.661 5.219 5.261 5.727 4.754 5.286 4.849 5.752 4.753 tcdcclm 1586692800 60 1.290 2.413 2.569 0.429 1.221 1.049 1.696 4.936 2.526 0.653 1.370 3.093 2.946 0.708 1.112 1.970 0.775 2.547 1.810 4.009 0.536 tcdcclm 1586714400 66 2.224 0.936 3.231 2.362 3.898 0.595 2.355 3.015 1.491 2.372 3.282 5.515 0.748 2.235 2.606 2.451 1.856 2.910 1.511 2.747 3.570 tcdcclm 1586736000 72 4.397 2.551 5.562 4.947 6.115 0.862 5.100 5.455 3.320 6.358 6.279 6.519 3.467 4.280 4.187 5.124 5.618 4.941 6.167 5.623 5.928 tcdcclm 1586757600 78 5.871 4.964 5.957 5.789 6.771 1.715 6.101 5.925 5.524 5.543 6.747 6.989 5.997 5.667 4.802 5.812 7.024 5.959 6.858 7.037 6.452 tcdcclm 1586779200 84 6.187 6.222 4.261 5.375 6.300 4.648 7.072 4.612 4.403 5.614 3.529 6.724 7.315 4.630 6.654 6.724 6.827 6.354 6.822 7.306 6.554 tcdcclm 1586800800 90 6.322 6.172 5.326 5.005 5.369 6.743 5.801 4.135 4.422 6.340 3.352 5.854 5.789 5.255 6.694 5.411 6.229 6.922 5.292 5.914 6.140 tcdcclm 1586822400 96 4.971 6.423 1.987 6.539 7.659 6.487 6.768 4.283 7.098 7.857 7.466 3.895 5.747 4.424 5.715 6.439 2.147 2.995 6.766 7.572 4.339 tcdcclm 1586844000 102 6.567 3.185 2.813 7.819 7.852 4.935 7.878 7.558 7.907 7.701 7.758 5.821 6.468 4.468 6.221 6.428 0.236 5.218 7.672 6.751 6.603 tcdcclm 1586865600 108 6.798 2.893 6.041 7.531 7.593 4.441 7.869 7.757 7.361 6.878 7.298 4.603 5.952 6.983 6.281 6.710 1.735 7.416 6.678 7.199 6.686 tcdcclm 1586887200 114 6.290 6.142 6.014 7.297 6.995 2.506 7.793 6.795 5.808 5.767 6.058 4.613 3.318 2.800 6.542 3.832 3.516 5.805 6.813 6.428 5.256 tcdcclm 1586908800 120 5.507 4.605 5.614 5.934 6.727 2.577 6.263 4.698 3.966 5.826 5.214 2.353 3.919 4.827 4.549 5.639 2.278 5.711 6.789 6.222 5.245 tcdcclm 1586930400 126 3.912 2.468 5.306 5.895 7.504 2.003 4.700 4.177 5.701 5.667 5.509 2.988 3.862 4.702 3.956 3.464 1.758 4.451 6.584 7.291 4.655 tcdcclm 1586952000 132 1.820 0.380 2.925 6.508 6.402 0.457 3.169 1.009 0.954 1.699 3.440 4.458 0.254 2.942 3.743 0.776 0.598 1.263 6.481 2.161 1.921 tcdcclm 1586973600 138 2.032 0.504 1.899 7.294 4.879 0.585 3.548 1.375 0.187 1.088 2.117 5.373 0.195 2.249 2.792 0.869 3.005 2.271 7.383 4.971 2.593 tcdcclm 1586995200 144 2.368 0.866 2.286 7.035 3.219 4.112 3.703 1.976 0.636 0.394 1.728 4.135 0.857 0.314 1.764 0.187 5.983 0.751 6.114 6.155 0.537 tcdcclm 1587016800 150 3.733 3.668 4.796 7.867 4.175 4.293 5.348 0.897 2.431 0.445 2.934 5.017 1.862 0.250 5.498 0.971 4.640 1.206 7.322 4.924 1.863 tcdcclm 1587038400 156 5.579 4.954 4.544 7.722 1.599 5.402 4.264 1.044 0.401 2.216 3.065 2.289 2.919 1.685 5.245 3.016 6.905 4.487 7.775 5.134 2.524 tcdcclm 1587060000 162 4.803 4.553 5.960 7.510 4.862 5.232 3.850 5.902 3.040 6.655 4.413 1.856 3.584 5.776 4.043 6.848 6.323 5.374 7.811 7.872 5.721 tcdcclm 1587081600 168 3.166 3.113 1.230 7.832 3.417 1.441 2.797 7.730 4.840 3.645 3.239 3.179 2.519 1.842 4.669 5.689 5.504 7.759 7.331 6.249 4.266 tcdcclm 1587103200 174 4.501 5.458 4.317 6.350 2.149 2.791 1.720 6.750 7.043 1.815 4.679 5.301 3.206 0.139 5.941 5.988 5.391 7.372 6.520 4.872 2.385 tcdcclm 1587124800 180 5.269 4.124 5.394 4.406 4.787 4.925 3.917 6.760 6.945 2.700 4.985 4.494 4.558 0.707 5.111 2.634 4.782 2.492 6.456 1.901 2.622 tcdcclm 1587146400 186 2.608 4.630 5.422 5.158 4.192 5.099 6.450 6.718 7.052 4.657 4.973 3.533 3.293 5.037 4.007 5.642 5.497 3.394 4.973 0.910 2.428 tcdcclm 1587168000 192 4.905 4.481 4.647 4.499 5.780 4.123 5.382 7.026 7.400 4.183 5.833 6.511 1.298 3.251 4.043 2.155 4.066 5.346 2.280 1.473 0.098 tcdcclm 1587189600 198 3.747 1.754 3.046 3.929 5.245 1.050 0.648 7.198 4.587 5.721 5.252 6.211 0.331 1.528 2.085 1.777 5.097 2.235 1.073 1.348 0.059 tcdcclm 1587211200 204 4.079 3.587 1.172 5.156 5.539 3.692 2.790 7.552 2.643 3.791 5.135 5.459 2.011 4.106 3.895 2.982 5.128 3.682 0.181 3.643 0.059 tcdcclm 1587232800 210 5.014 6.239 4.980 6.199 6.606 5.856 5.323 7.020 5.108 3.592 5.085 5.711 5.202 5.665 5.294 5.960 6.470 5.238 1.726 6.754 0.248 tcdcclm 1587254400 216 5.827 4.232 4.295 6.525 6.667 5.749 4.935 5.311 4.321 6.511 5.396 6.619 5.956 3.141 6.759 5.044 7.636 6.730 0.289 7.580 0.570 tcdcclm 1587276000 222 6.168 3.800 6.266 6.643 4.722 4.559 6.056 3.269 4.933 6.374 5.730 7.315 2.117 4.059 5.399 4.138 6.702 6.868 2.477 3.365 0.841 tcdcclm 1587297600 228 4.488 3.311 6.473 6.160 5.327 6.831 4.946 0.643 3.813 6.274 4.355 7.399 1.811 5.160 5.363 4.603 7.155 6.547 4.390 0.280 1.367 tcdcclm 1587319200 234 3.295 3.403 7.057 6.311 5.586 7.533 6.193 4.924 2.013 5.221 6.111 7.085 1.503 5.071 5.410 5.394 5.833 6.462 6.254 0.266 1.801 tcdcclm 1587340800 240 4.302 2.789 6.932 5.741 7.155 7.471 6.285 4.908 6.408 5.663 5.751 7.101 2.163 1.389 3.174 3.793 4.423 6.416 2.716 0.118 0.923 partykit/inst/ULGcourse-2020/Data/GENS_00_innsbruck-flughafen.txt0000644000176200001440000016115614172227777024041 0ustar liggesusers# ASCII output from GENSvis.py # Contains interpolated values from the # GFS ensemble on 1.000000 x 1.000000 degrees # The data in here are for station # 11120: INNSBRUCK-FLUGHAFEN # Station position: 11.3553 47.2589 # Used grid point 1: 12.0000 48.0000 # Used grid point 2: 12.0000 47.0000 # Used grid point 3: 11.0000 47.0000 # Used grid point 4: 11.0000 48.0000 varname timestamp step mem0 mem1 mem2 mem3 mem4 mem5 mem6 mem7 mem8 mem9 mem10 mem11 mem12 mem13 mem14 mem15 mem16 mem17 mem18 mem19 mem20 tmax2m 1520920800 6 -2.996 -2.210 -2.945 -3.348 -2.930 -3.836 -2.478 -3.191 -2.966 -3.307 -3.746 -2.532 -2.507 -2.817 -4.753 -2.387 -3.917 -3.683 -3.149 -3.485 -2.983 tmax2m 1520942400 12 1.124 1.509 1.090 1.278 0.584 1.353 0.488 1.199 0.960 1.202 1.168 1.447 0.719 0.869 1.435 1.743 1.085 0.977 1.447 1.364 0.998 tmax2m 1520964000 18 1.342 1.602 1.256 1.544 0.924 1.413 0.687 1.514 1.200 1.328 1.377 1.482 1.002 1.280 1.453 1.770 1.334 1.104 1.530 1.566 1.299 tmax2m 1520985600 24 -2.741 -3.259 -2.764 -3.112 -2.748 -2.219 -2.686 -2.838 -2.403 -2.595 -2.572 -2.559 -2.708 -2.891 -2.828 -2.734 -2.637 -2.680 -2.188 -3.070 -2.694 tmax2m 1521007200 30 -5.489 -8.782 -5.415 -6.627 -5.155 -8.470 -4.776 -6.570 -6.689 -5.006 -7.354 -5.983 -4.814 -6.675 -4.145 -4.686 -4.420 -4.286 -4.151 -4.643 -6.681 tmax2m 1521028800 36 0.988 0.770 0.798 1.004 1.246 1.086 1.129 1.257 0.950 1.181 1.012 0.929 1.169 1.052 0.771 1.133 0.850 0.879 1.280 0.965 0.982 tmax2m 1521050400 42 1.336 1.203 1.121 1.370 1.370 1.487 1.618 1.405 1.381 1.443 1.407 1.314 1.462 1.556 1.147 1.446 1.146 1.249 1.537 1.344 1.489 tmax2m 1521072000 48 -3.042 -3.087 -2.733 -3.141 -2.871 -2.656 -2.315 -3.265 -2.983 -2.638 -2.986 -2.755 -2.558 -2.964 -2.484 -2.690 -2.578 -2.789 -2.239 -2.993 -2.866 tmax2m 1521093600 54 -3.844 -5.125 -4.033 -3.901 -3.631 -3.875 -3.485 -3.944 -4.384 -3.710 -3.566 -3.604 -3.654 -3.732 -4.462 -3.479 -4.035 -3.701 -3.343 -3.879 -3.665 tmax2m 1521115200 60 1.503 2.050 1.731 2.023 2.393 1.734 2.040 1.742 1.815 1.774 1.410 2.150 1.875 1.924 1.816 1.613 2.136 1.470 2.488 1.784 2.268 tmax2m 1521136800 66 1.971 2.212 2.041 2.167 2.413 1.988 2.393 2.183 1.857 2.317 1.823 2.180 2.276 2.249 1.680 2.160 2.160 1.831 2.566 2.052 2.500 tmax2m 1521158400 72 -0.654 -0.646 -0.729 -0.223 -0.325 -1.111 0.003 -1.018 -0.926 -0.644 -0.814 -0.170 -0.642 -0.681 -0.919 -0.446 -0.833 -0.731 -0.318 -0.853 -0.098 tmax2m 1521180000 78 -1.411 -1.044 -2.312 -0.962 -0.724 -2.092 -0.772 -2.345 -1.848 -2.173 -1.566 -0.847 -1.821 -1.917 -1.539 -0.193 -1.480 -1.588 -1.240 -2.102 -0.632 tmax2m 1521201600 84 1.466 1.259 1.507 1.992 2.459 1.669 1.650 0.866 2.082 2.434 1.027 0.346 1.858 1.428 0.913 2.267 1.471 2.293 1.209 2.361 1.898 tmax2m 1521223200 90 1.836 1.912 1.706 2.150 2.669 1.745 1.641 1.172 2.245 2.501 1.732 0.449 2.220 1.524 1.119 1.657 1.805 2.480 1.603 2.575 1.980 tmax2m 1521244800 96 -0.910 -1.480 -0.695 -1.109 -0.263 -1.228 -1.349 -2.081 -0.454 -0.147 -1.340 -1.866 -1.023 -1.370 -1.056 -1.271 -0.074 -1.087 -3.014 -0.860 -0.453 tmax2m 1521266400 102 -2.484 -2.726 -1.921 -2.750 -1.662 -2.815 -2.232 -3.411 -1.811 -1.803 -2.390 -3.805 -2.522 -2.412 -2.340 -3.998 -1.267 -2.071 -4.041 -2.442 -1.601 tmax2m 1521288000 108 -1.623 -2.472 -2.300 -0.321 -0.130 -0.961 1.074 0.104 -2.043 -1.619 -2.292 -1.585 -0.619 -2.034 -1.180 -0.845 0.412 0.107 0.036 -1.156 -1.250 tmax2m 1521309600 114 -1.784 -2.335 -3.332 -0.203 -0.203 -0.908 0.679 0.457 -3.018 -2.117 -2.174 -1.584 -0.659 -2.077 -1.198 -1.340 0.321 0.023 0.087 -1.222 -0.893 tmax2m 1521331200 120 -4.474 -4.033 -9.186 -2.714 -3.240 -3.164 -3.178 -3.931 -8.424 -5.216 -4.462 -4.203 -2.974 -4.783 -4.453 -4.303 -2.331 -2.577 -2.454 -3.326 -2.790 tmax2m 1521352800 126 -6.722 -4.539 -12.887 -4.831 -5.664 -5.168 -5.671 -5.703 -11.009 -6.977 -6.400 -6.284 -4.411 -7.133 -7.435 -6.209 -5.993 -4.440 -4.273 -5.033 -5.771 tmax2m 1521374400 132 -1.752 -2.176 -10.340 -1.917 -0.741 -2.891 0.501 -1.461 -5.011 -4.019 -4.709 -1.864 0.483 -2.613 -3.029 -0.417 -5.119 -0.683 -1.983 -3.058 -0.774 tmax2m 1521396000 138 -1.662 -2.080 -9.858 -2.083 -0.682 -2.806 0.834 -1.532 -4.364 -3.955 -5.064 -1.512 0.592 -2.455 -2.681 -0.086 -5.045 -0.021 -1.745 -3.038 -0.692 tmax2m 1521417600 144 -5.175 -5.540 -14.227 -5.385 -4.374 -5.139 -3.174 -4.094 -6.763 -7.049 -8.547 -6.344 -2.772 -5.206 -5.279 -3.134 -9.074 -3.993 -4.175 -6.356 -3.521 tmax2m 1521439200 150 -6.718 -6.595 -15.154 -6.253 -14.554 -5.930 -4.176 -6.379 -8.318 -14.936 -11.012 -7.788 -4.563 -7.100 -6.649 -4.836 -13.886 -4.813 -4.936 -8.700 -6.548 tmax2m 1521460800 156 -1.976 0.205 -7.522 -0.944 0.024 -0.234 -3.082 -4.532 -1.821 -4.197 -1.784 -2.939 0.183 0.014 0.166 0.917 -5.655 -0.215 -0.487 -3.437 -1.379 tmax2m 1521482400 162 -1.923 0.552 -6.887 -0.478 0.551 -0.636 -3.220 -4.297 -1.923 -4.019 -1.676 -2.904 0.201 0.555 0.641 1.393 -5.363 -0.259 1.444 -3.412 -1.154 tmax2m 1521504000 168 -4.706 -2.441 -10.614 -4.290 -4.705 -5.155 -7.024 -9.303 -5.065 -9.564 -4.558 -6.747 -2.870 -2.641 -3.184 -2.776 -10.494 -2.991 -1.307 -6.183 -3.730 tmax2m 1521525600 174 -7.362 -5.236 -14.634 -4.050 -5.125 -12.398 -9.326 -10.406 -7.523 -12.339 -7.639 -10.069 -5.458 -4.775 -5.066 -3.630 -17.744 -4.234 -4.000 -9.544 -9.101 tmax2m 1521547200 180 -4.846 -1.187 -3.214 0.707 -0.770 0.265 -6.901 -8.096 -2.416 -8.405 -0.058 -7.039 1.054 0.829 -1.989 2.724 -4.343 0.535 1.803 -3.422 -0.212 tmax2m 1521568800 186 -4.884 -1.285 -2.598 1.016 -1.031 0.608 -6.850 -7.880 -2.617 -7.857 0.076 -6.983 1.066 0.961 -1.954 3.190 -3.813 0.609 1.931 -3.509 -0.198 tmax2m 1521590400 192 -8.370 -3.322 -7.041 -1.802 -3.662 -2.670 -10.453 -10.034 -7.365 -12.544 -3.736 -9.332 -2.565 -3.621 -9.146 1.024 -8.199 -2.431 -0.779 -6.154 -4.466 tmax2m 1521612000 198 -10.714 -3.778 -19.649 -3.804 -6.600 -1.400 -15.868 -11.642 -10.160 -15.689 -7.015 -10.217 -3.531 -6.822 -19.072 1.676 -11.849 -7.382 -1.650 -7.462 -8.683 tmax2m 1521633600 204 -6.139 -0.753 -0.644 -2.285 -7.405 1.347 -6.055 -8.455 -8.454 0.582 -7.944 -5.518 0.371 -3.704 -2.700 4.691 -0.322 2.495 1.287 -1.620 -4.350 tmax2m 1521655200 210 -5.932 -0.700 -0.112 -2.166 -7.625 1.140 -6.099 -7.609 -8.084 0.924 -8.042 -5.404 0.350 -3.688 -2.444 4.874 -0.315 3.031 1.413 -1.567 -4.246 tmax2m 1521676800 216 -10.617 -3.911 -3.622 -5.495 -11.835 -0.959 -10.400 -15.081 -11.873 -2.642 -12.486 -8.945 -2.742 -10.823 -10.455 1.959 -4.473 -0.238 -1.619 -5.583 -11.188 tmax2m 1521698400 222 -17.233 -6.092 -11.664 -8.469 -15.354 -3.269 -12.761 -16.871 -13.229 -4.115 -16.722 -9.884 -5.239 -22.184 -15.440 0.432 -5.633 -1.938 -4.241 -6.627 -19.935 tmax2m 1521720000 228 -7.211 -4.095 -0.536 -5.908 -7.813 -5.953 -7.867 -2.676 -8.378 1.201 -8.829 -6.033 -3.658 -3.697 -3.119 2.313 -1.673 3.178 -1.800 -0.192 -3.619 tmax2m 1521741600 234 -6.833 -3.642 -0.238 -5.489 -7.508 -7.026 -7.837 -1.943 -8.132 1.041 -8.568 -5.889 -3.439 -3.270 -3.084 2.651 -1.059 3.076 -1.504 0.034 -2.315 tmax2m 1521763200 240 -12.328 -6.635 -6.141 -10.812 -10.989 -9.434 -13.044 -4.921 -11.679 -2.733 -14.420 -9.333 -6.130 -13.520 -7.465 0.371 -4.136 -0.473 -5.786 -4.472 -10.702 dd10m 1520920800 6 292.263 275.547 273.523 280.913 310.628 291.603 307.343 265.279 286.688 289.693 277.434 280.640 308.079 299.734 275.461 279.258 291.207 294.851 279.295 279.466 302.878 dd10m 1520942400 12 293.026 287.216 290.139 282.562 304.419 288.697 313.111 291.623 295.605 286.579 290.038 290.641 307.077 295.387 282.544 286.968 286.598 294.494 292.120 285.126 288.142 dd10m 1520964000 18 295.564 290.622 294.684 290.080 300.960 300.163 306.249 299.181 295.444 300.756 297.220 294.579 299.964 297.139 292.091 289.732 297.175 293.987 302.375 291.620 300.666 dd10m 1520985600 24 275.670 262.057 278.981 271.627 276.225 262.824 270.502 275.363 270.486 279.752 266.383 276.002 279.422 270.395 283.478 282.451 283.634 282.821 282.642 278.388 271.083 dd10m 1521007200 30 287.831 282.194 288.722 280.760 287.839 266.216 284.572 270.029 276.619 272.451 283.744 292.888 287.103 281.992 305.508 294.692 300.711 298.310 298.530 294.441 269.924 dd10m 1521028800 36 272.156 318.516 178.587 309.755 209.977 307.171 207.542 228.472 278.030 217.892 266.772 295.556 216.732 237.663 343.128 260.105 322.806 257.962 100.461 304.019 260.259 dd10m 1521050400 42 151.523 141.485 156.185 141.461 152.206 146.025 160.648 150.782 150.734 153.826 153.934 151.957 157.948 154.673 137.119 154.701 148.342 155.007 156.451 144.098 157.160 dd10m 1521072000 48 176.546 175.259 176.242 177.323 177.664 177.492 178.223 175.798 177.611 177.712 175.409 177.219 175.834 175.521 176.858 177.879 178.193 174.474 178.955 175.713 178.095 dd10m 1521093600 54 173.891 175.198 172.058 175.838 176.106 174.965 173.811 172.637 173.882 172.283 172.158 174.883 172.772 172.248 173.101 174.569 177.625 173.124 180.166 174.302 176.203 dd10m 1521115200 60 169.170 169.362 164.789 169.509 167.415 165.956 168.469 160.606 164.096 164.588 166.493 170.440 167.107 165.522 168.436 170.608 171.520 169.487 170.644 168.972 171.469 dd10m 1521136800 66 161.897 160.824 169.022 162.290 170.573 161.974 161.454 176.041 161.762 171.030 176.371 166.512 165.097 166.128 164.482 169.218 170.371 162.139 157.659 167.578 166.412 dd10m 1521158400 72 176.754 167.119 201.690 166.456 184.008 183.253 176.279 222.745 185.674 192.884 195.051 174.126 188.818 198.108 166.042 170.692 180.936 175.150 179.682 200.246 177.465 dd10m 1521180000 78 213.139 250.197 288.001 201.892 207.311 254.199 271.043 285.623 276.941 171.267 313.452 249.948 231.920 233.376 195.925 160.382 224.810 237.878 286.147 201.246 206.787 dd10m 1521201600 84 290.541 301.347 14.328 270.467 196.744 307.256 288.839 322.289 296.681 144.760 321.580 302.528 234.628 262.759 249.492 224.281 189.115 299.952 306.394 156.697 204.808 dd10m 1521223200 90 13.697 42.786 96.487 343.993 160.605 17.549 71.855 123.868 122.345 162.020 123.873 349.418 133.732 61.681 299.888 289.109 159.607 39.348 26.160 151.200 157.073 dd10m 1521244800 96 108.414 57.685 133.214 177.774 172.878 127.262 176.721 244.106 138.093 224.524 157.562 8.240 171.422 25.784 359.941 279.028 164.094 148.955 174.378 159.654 313.525 dd10m 1521266400 102 35.747 352.671 99.689 116.392 220.426 101.034 152.344 323.337 100.573 321.323 126.798 20.724 205.923 14.087 357.276 291.618 116.836 41.981 143.640 14.790 350.552 dd10m 1521288000 108 1.637 355.402 51.217 47.285 299.634 22.867 34.930 359.548 44.270 349.247 354.650 21.088 349.150 23.577 348.866 327.188 350.263 13.253 54.945 336.217 354.755 dd10m 1521309600 114 355.347 352.339 15.752 13.842 335.969 14.997 24.311 39.743 11.739 0.783 8.095 22.362 352.997 30.342 359.345 352.491 327.738 359.158 18.134 318.055 0.678 dd10m 1521331200 120 354.280 359.197 1.629 16.018 292.950 16.226 20.164 100.697 357.059 5.067 8.248 10.200 333.992 40.872 6.475 332.907 331.129 10.639 23.935 308.235 6.289 dd10m 1521352800 126 0.855 1.619 7.813 24.279 282.530 9.939 45.907 43.176 0.585 6.306 359.642 0.830 318.618 53.875 16.504 21.068 330.196 29.956 7.780 320.102 115.717 dd10m 1521374400 132 62.972 21.640 21.625 65.818 289.604 34.388 133.825 38.968 23.197 14.057 352.922 1.949 321.280 90.247 47.869 152.619 332.659 60.990 349.651 331.292 79.224 dd10m 1521396000 138 101.737 82.533 30.672 60.187 325.109 57.625 132.495 16.593 100.053 41.141 348.347 63.608 17.166 107.925 87.146 141.030 349.583 92.877 13.408 351.055 119.099 dd10m 1521417600 144 157.158 163.282 16.364 165.390 252.629 169.958 143.984 14.305 168.398 267.078 288.979 154.632 134.949 148.423 154.337 177.948 356.807 250.541 174.984 280.897 161.077 dd10m 1521439200 150 138.888 153.895 35.415 159.262 256.625 173.083 30.281 348.859 170.477 5.826 188.511 70.858 113.015 146.732 159.027 159.206 12.835 335.189 159.391 286.699 183.726 dd10m 1521460800 156 84.334 134.348 77.226 159.379 226.569 6.860 353.084 329.932 101.687 1.186 170.293 56.381 141.824 126.440 142.955 160.771 27.915 116.099 169.193 27.492 30.818 dd10m 1521482400 162 45.134 24.531 49.094 151.705 49.014 3.131 350.720 327.136 110.346 347.487 155.089 23.963 145.253 104.831 107.899 165.420 21.233 167.379 157.742 25.453 29.138 dd10m 1521504000 168 58.877 333.834 54.465 157.866 173.934 266.965 341.699 320.402 151.539 326.704 174.301 14.479 165.308 126.810 19.015 181.228 21.748 182.727 181.121 44.743 64.471 dd10m 1521525600 174 54.724 357.952 48.920 98.638 158.333 207.936 341.111 316.140 131.878 324.428 178.581 13.506 165.128 82.389 14.352 167.836 13.208 197.950 140.578 56.161 17.416 dd10m 1521547200 180 44.338 125.483 59.830 100.019 134.900 184.919 340.774 310.028 70.851 344.003 323.444 28.039 142.190 45.993 10.983 171.484 55.170 147.747 83.951 49.407 24.033 dd10m 1521568800 186 37.590 132.696 72.939 28.575 9.020 167.906 348.429 327.584 50.904 345.398 357.228 14.529 128.272 18.490 3.660 163.970 29.353 39.967 98.299 42.373 7.975 dd10m 1521590400 192 54.211 145.786 109.746 14.243 322.264 177.563 4.304 331.391 358.864 258.148 349.807 4.675 168.170 9.854 328.485 166.293 180.401 297.035 125.242 61.779 5.650 dd10m 1521612000 198 27.464 355.063 112.410 350.741 334.844 180.728 18.940 326.761 327.382 209.876 349.747 359.944 20.424 357.966 313.184 168.457 205.443 246.264 76.154 65.142 27.143 dd10m 1521633600 204 24.071 18.990 82.428 15.312 343.673 210.753 18.630 324.436 340.029 209.608 353.964 14.436 27.404 8.215 357.349 158.545 207.048 202.033 30.318 69.912 42.380 dd10m 1521655200 210 5.676 7.375 86.335 18.406 350.655 264.158 10.683 357.826 321.731 179.777 347.051 0.659 17.230 14.715 0.956 159.879 266.546 173.590 11.195 66.487 36.272 dd10m 1521676800 216 333.661 338.562 7.105 6.934 320.880 329.614 7.567 204.722 256.430 200.168 306.216 3.295 10.267 23.250 262.639 225.226 275.926 191.694 7.289 165.004 57.953 dd10m 1521698400 222 332.428 319.663 24.509 355.012 305.413 350.674 358.263 203.192 314.397 195.072 296.843 2.635 6.457 47.515 302.173 329.837 341.399 190.198 5.841 171.368 51.028 dd10m 1521720000 228 0.259 351.798 31.747 6.944 5.471 353.578 11.240 234.133 324.032 217.343 322.548 4.658 9.343 32.926 352.674 328.642 21.001 224.440 10.393 112.530 57.253 dd10m 1521741600 234 354.069 356.361 43.680 4.459 45.195 350.960 3.059 156.316 331.457 188.758 294.622 351.486 3.665 45.438 356.940 338.176 105.369 263.710 7.368 15.891 47.740 dd10m 1521763200 240 301.310 317.950 61.050 19.008 200.872 338.646 17.278 184.074 264.188 171.338 212.583 329.534 357.432 198.632 248.407 338.675 180.458 337.356 7.617 275.606 158.778 ff10m 1520920800 6 1.203 0.927 1.242 1.150 1.259 1.555 1.430 0.959 0.892 1.357 1.041 1.337 0.994 1.090 1.341 1.459 1.375 1.474 1.111 1.448 1.290 ff10m 1520942400 12 1.515 1.638 1.705 1.804 1.504 1.528 1.652 1.656 1.327 1.431 1.603 1.603 1.416 1.195 2.016 1.677 1.801 2.091 1.550 1.989 1.461 ff10m 1520964000 18 1.785 1.874 1.846 1.790 1.651 1.604 1.555 1.876 1.759 1.739 1.660 1.856 1.801 1.755 1.917 1.914 1.814 1.843 1.847 1.901 1.735 ff10m 1520985600 24 2.218 2.409 2.232 2.426 1.943 2.204 2.080 2.009 2.171 1.920 2.431 2.318 2.029 2.365 2.243 2.287 2.116 2.130 1.998 2.300 2.051 ff10m 1521007200 30 1.546 1.855 1.503 1.650 1.329 1.660 1.322 1.340 1.606 1.431 1.881 1.756 1.497 1.587 1.801 1.780 1.473 1.665 1.413 1.748 1.629 ff10m 1521028800 36 0.337 0.750 0.634 0.573 0.668 0.661 0.952 0.363 0.373 0.304 0.602 0.559 0.850 0.139 0.806 0.385 0.421 0.429 0.224 0.578 0.574 ff10m 1521050400 42 1.542 1.154 1.738 1.535 1.649 1.363 1.987 1.629 1.324 1.774 1.669 1.615 1.821 1.663 1.339 1.855 1.671 1.796 1.970 1.567 1.601 ff10m 1521072000 48 3.242 2.584 3.252 3.087 3.422 3.358 3.309 3.286 3.059 3.318 3.468 3.264 3.506 3.341 3.050 3.468 3.212 3.348 3.514 2.949 3.509 ff10m 1521093600 54 4.040 3.777 4.076 4.057 3.981 3.902 4.290 3.988 3.921 3.973 4.291 4.132 4.234 4.064 3.833 4.231 3.926 4.175 4.088 4.106 4.107 ff10m 1521115200 60 4.851 4.617 4.852 4.606 4.738 4.456 4.920 5.042 4.644 4.841 5.041 4.884 5.103 4.720 4.786 5.138 4.816 5.210 4.629 4.823 4.820 ff10m 1521136800 66 4.280 4.708 3.683 4.903 4.044 3.835 4.660 4.091 3.948 3.625 3.711 4.596 4.252 3.774 4.425 3.942 4.539 4.684 4.473 4.078 3.965 ff10m 1521158400 72 3.281 4.600 1.823 4.463 2.649 2.466 3.448 1.607 2.382 2.194 1.652 3.090 3.091 2.257 3.799 2.953 3.058 3.949 3.226 2.382 2.964 ff10m 1521180000 78 2.159 2.433 0.879 3.076 1.973 1.879 2.687 1.089 2.098 2.046 1.024 1.473 1.904 1.484 1.967 3.292 1.098 2.129 2.726 1.540 1.994 ff10m 1521201600 84 1.836 1.855 0.530 2.420 1.987 2.018 1.580 0.720 0.748 1.923 1.175 2.726 1.062 0.403 2.196 3.267 0.712 1.608 2.314 1.521 2.044 ff10m 1521223200 90 1.178 1.204 1.142 0.310 2.601 1.549 0.453 0.731 1.639 1.245 1.288 1.763 1.115 0.922 0.462 2.699 2.545 1.083 0.651 1.960 1.353 ff10m 1521244800 96 0.613 0.150 1.597 1.513 3.168 1.495 2.157 0.207 2.163 1.135 2.022 0.951 2.094 1.874 0.802 1.645 2.199 1.316 2.223 2.133 1.774 ff10m 1521266400 102 0.978 1.870 1.319 0.798 1.515 0.709 0.328 1.031 1.533 1.656 0.268 2.021 0.571 3.197 1.397 1.772 0.686 1.738 1.457 1.841 2.420 ff10m 1521288000 108 3.135 3.081 1.430 0.782 2.075 2.124 3.137 1.859 2.487 2.982 2.951 3.295 2.685 2.943 2.657 1.986 0.541 3.994 1.606 2.284 1.866 ff10m 1521309600 114 3.600 3.032 3.330 1.732 2.792 3.539 3.683 1.422 3.545 3.037 2.630 3.089 3.303 2.402 3.260 2.417 2.722 4.073 2.594 2.525 2.024 ff10m 1521331200 120 2.581 2.672 2.336 1.125 1.834 3.020 2.043 0.805 2.696 2.299 2.159 2.192 1.876 1.396 2.044 1.385 3.962 2.857 1.960 2.017 0.139 ff10m 1521352800 126 1.642 2.429 2.659 1.394 2.099 2.804 1.510 1.691 2.326 2.082 2.551 2.242 0.794 2.148 1.923 0.448 3.707 1.768 1.178 2.778 0.412 ff10m 1521374400 132 1.066 2.375 3.335 1.372 2.345 2.291 2.279 2.504 2.050 2.712 3.063 1.961 1.255 2.510 1.854 1.650 3.678 0.763 1.296 2.605 0.797 ff10m 1521396000 138 1.743 2.021 2.595 1.488 1.620 1.583 2.647 2.981 1.706 2.095 1.781 1.646 1.179 2.361 1.755 1.124 2.596 1.503 1.337 1.667 1.499 ff10m 1521417600 144 1.813 2.495 2.104 1.784 1.584 1.463 2.416 2.227 2.144 0.120 1.082 1.361 0.395 2.589 1.892 0.889 1.590 0.579 2.611 0.971 1.795 ff10m 1521439200 150 1.211 2.645 2.612 2.843 1.272 0.897 0.880 2.699 1.608 1.374 1.914 1.879 1.071 2.477 2.257 2.264 1.793 1.138 3.480 1.066 0.950 ff10m 1521460800 156 2.242 3.112 2.766 3.319 1.060 1.762 2.699 4.055 1.275 3.079 1.800 3.310 1.649 2.545 2.089 3.135 3.024 0.789 3.003 1.605 2.125 ff10m 1521482400 162 2.150 0.797 2.492 2.690 1.275 1.828 3.111 3.471 1.741 3.330 2.205 3.626 1.930 2.352 1.310 3.032 2.514 1.973 1.636 2.350 2.162 ff10m 1521504000 168 1.884 2.109 1.732 2.926 2.048 1.249 2.042 3.427 1.672 2.974 2.641 2.859 2.941 2.044 1.398 2.515 1.310 3.853 1.683 1.318 1.186 ff10m 1521525600 174 1.951 1.098 1.983 1.759 2.905 2.038 2.308 3.768 1.454 3.342 2.056 2.433 2.923 1.922 2.761 2.973 1.196 2.580 1.102 1.376 1.316 ff10m 1521547200 180 3.100 1.331 2.934 2.517 3.116 3.091 4.130 5.499 2.544 4.459 0.355 3.151 2.371 3.380 3.608 4.185 1.774 0.286 1.852 2.325 2.097 ff10m 1521568800 186 2.621 1.605 2.146 3.632 3.632 3.552 2.208 6.106 2.262 2.528 2.427 2.753 1.984 4.088 2.451 4.125 1.612 0.760 1.765 2.297 2.925 ff10m 1521590400 192 1.945 1.392 1.322 2.405 5.485 4.832 1.700 4.825 2.634 0.936 3.782 1.887 0.857 3.674 1.881 4.967 1.156 1.551 1.676 1.461 2.046 ff10m 1521612000 198 2.191 1.423 1.105 2.301 2.937 3.239 1.561 2.417 2.878 1.555 4.259 2.420 1.972 2.903 1.482 4.459 1.734 1.272 1.099 1.153 2.132 ff10m 1521633600 204 3.794 2.445 1.433 2.757 3.757 1.670 3.907 2.538 4.299 1.349 5.481 4.237 2.550 4.295 2.597 3.128 1.714 1.582 2.702 1.470 4.349 ff10m 1521655200 210 3.003 2.022 1.020 2.812 2.916 0.744 3.278 1.558 2.067 1.844 4.244 3.544 2.686 3.048 1.883 1.898 0.313 1.817 3.134 1.004 3.351 ff10m 1521676800 216 1.382 1.924 0.208 2.298 1.598 1.824 3.091 1.636 2.013 2.693 1.817 3.226 2.470 1.660 0.765 0.858 0.873 2.979 3.003 1.196 2.185 ff10m 1521698400 222 1.432 2.001 0.510 2.077 1.186 2.530 2.930 2.072 2.395 2.963 2.589 3.287 2.473 0.824 1.252 2.207 2.042 2.323 2.950 1.373 1.874 ff10m 1521720000 228 3.648 3.069 2.307 3.191 1.672 4.159 4.040 0.407 3.632 1.865 3.985 3.530 3.144 2.400 2.642 2.639 1.277 1.767 3.697 0.882 3.088 ff10m 1521741600 234 1.669 2.853 1.547 2.602 0.877 5.370 2.991 1.415 2.242 1.010 1.722 2.399 3.193 1.169 2.258 2.615 1.038 0.599 2.493 0.792 2.231 ff10m 1521763200 240 1.147 2.481 0.706 0.997 0.714 3.910 2.146 2.415 1.667 1.824 3.146 1.760 2.495 2.139 0.519 2.252 2.245 2.789 0.698 1.031 1.728 apcpsfc 1520920800 6 1.087 1.937 0.721 0.674 1.656 0.497 1.478 0.951 1.348 0.879 0.738 2.124 3.012 1.666 0.293 1.180 0.634 0.674 1.092 0.646 1.549 apcpsfc 1520942400 12 2.310 1.928 2.193 1.982 3.025 1.502 2.587 2.595 3.326 1.846 2.284 1.827 3.659 3.109 1.110 1.256 1.825 1.978 2.009 1.459 2.178 apcpsfc 1520964000 18 1.311 1.182 1.266 1.089 1.554 1.826 2.032 1.208 1.790 1.689 1.564 1.528 1.584 1.226 1.216 1.071 1.350 1.245 1.804 0.943 1.314 apcpsfc 1520985600 24 0.430 0.316 0.411 0.512 0.331 0.335 0.339 0.291 0.305 0.414 0.354 0.441 0.373 0.380 0.721 0.669 0.608 0.495 0.604 0.726 0.339 apcpsfc 1521007200 30 0.409 0.403 0.260 0.451 0.443 0.175 0.452 0.183 0.150 0.248 0.488 0.607 0.443 0.313 0.844 0.661 0.577 0.696 0.518 0.588 0.309 apcpsfc 1521028800 36 0.597 0.587 0.454 0.445 0.423 0.572 0.573 0.336 0.489 0.338 0.367 0.608 0.428 0.571 0.876 0.547 0.735 0.676 0.616 0.456 0.589 apcpsfc 1521050400 42 0.555 0.556 0.500 0.523 0.571 0.710 0.632 0.447 0.543 0.726 0.506 0.448 0.440 0.514 0.845 0.497 0.768 0.575 0.458 0.409 0.561 apcpsfc 1521072000 48 0.048 0.015 0.045 0.000 0.051 0.074 0.023 0.012 0.074 0.042 0.037 0.035 0.048 0.000 0.096 0.037 0.122 0.033 0.026 0.000 0.048 apcpsfc 1521093600 54 0.048 0.000 0.029 0.000 0.074 0.122 0.057 0.000 0.048 0.048 0.066 0.048 0.096 0.048 0.000 0.048 0.067 0.048 0.074 0.074 0.074 apcpsfc 1521115200 60 0.722 0.143 0.730 0.674 0.578 0.456 0.965 0.557 0.504 0.896 0.947 0.504 0.711 0.774 0.361 1.018 0.224 0.578 0.361 0.409 0.796 apcpsfc 1521136800 66 0.705 0.918 1.342 1.028 1.420 0.891 0.630 1.101 0.951 1.134 1.645 0.853 0.690 0.879 0.954 1.125 1.357 0.609 1.384 0.695 1.443 apcpsfc 1521158400 72 1.362 0.483 2.578 1.428 2.344 1.440 2.083 3.674 1.984 1.475 2.621 2.212 1.371 1.749 1.056 2.661 1.790 1.330 2.609 1.732 2.520 apcpsfc 1521180000 78 3.937 3.643 3.752 2.149 4.322 5.428 5.406 4.888 4.893 1.091 5.715 8.005 4.121 4.753 3.153 3.289 5.514 3.462 6.095 2.345 4.612 apcpsfc 1521201600 84 5.010 5.011 3.008 5.211 1.923 4.583 3.284 4.116 1.106 2.483 4.919 6.277 4.117 3.859 5.428 1.997 4.987 2.780 2.786 1.077 4.160 apcpsfc 1521223200 90 4.323 3.014 5.021 4.208 0.552 3.577 2.431 3.259 3.446 5.408 2.812 3.406 3.873 5.592 5.511 6.077 2.612 3.059 0.841 1.263 4.323 apcpsfc 1521244800 96 4.044 4.235 2.587 2.161 0.394 2.937 1.196 2.282 2.379 6.344 1.787 2.984 1.744 5.341 5.674 3.142 1.927 3.072 0.170 0.306 9.847 apcpsfc 1521266400 102 4.234 6.090 3.908 3.372 2.020 3.685 0.250 1.380 2.756 5.789 2.424 3.706 1.034 4.209 5.584 1.824 3.946 1.838 1.199 3.845 5.350 apcpsfc 1521288000 108 4.629 5.753 5.728 4.533 2.670 3.925 0.922 1.050 3.643 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5.256 5.518 5.360 5.493 4.831 5.009 5.242 5.428 5.163 5.202 5.046 4.711 6.002 5.128 5.870 5.050 5.232 5.155 4.628 tcdcclm 1521072000 48 3.923 2.347 4.208 3.426 4.097 4.259 3.583 3.183 4.075 4.030 3.460 4.044 3.971 3.745 4.226 3.950 4.111 4.067 4.155 2.671 4.028 tcdcclm 1521093600 54 4.979 2.715 4.513 4.819 5.919 5.451 4.690 4.730 4.563 4.770 5.543 4.722 4.995 5.695 4.040 5.464 5.098 5.399 5.283 3.775 6.026 tcdcclm 1521115200 60 6.834 6.479 7.364 7.321 7.260 7.088 7.464 6.900 6.773 7.229 7.311 6.867 6.998 7.214 5.890 7.203 6.472 7.324 6.635 6.508 6.958 tcdcclm 1521136800 66 7.629 7.259 7.862 7.615 7.825 7.389 7.591 7.823 7.797 7.777 7.862 7.776 7.823 7.664 7.874 7.615 7.729 7.690 7.639 7.755 7.825 tcdcclm 1521158400 72 7.333 7.766 7.323 7.938 7.367 7.487 7.826 7.631 7.573 7.117 7.829 7.305 7.208 7.487 7.549 7.238 7.795 7.067 7.853 7.512 6.811 tcdcclm 1521180000 78 7.193 7.391 7.112 6.553 7.434 7.774 7.299 7.848 7.717 6.689 7.905 7.944 7.134 7.443 7.815 7.840 7.807 6.784 7.635 6.884 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mem15 mem16 mem17 mem18 mem19 mem20 tmax2m 1586844000 6 273.273 273.141 273.196 273.094 272.980 273.326 273.318 273.136 273.335 272.944 273.389 273.461 273.508 272.992 273.133 273.395 273.455 273.576 273.381 273.609 273.441 tmax2m 1586865600 12 273.300 273.389 273.198 273.092 273.444 272.758 272.570 273.619 273.787 272.935 273.414 273.206 273.626 274.144 272.608 273.545 273.205 273.273 273.109 273.161 273.787 tmax2m 1586887200 18 273.633 273.637 273.594 273.459 273.858 273.153 272.927 273.876 273.989 273.310 273.672 273.520 273.993 274.432 273.114 273.950 273.507 273.740 273.375 273.554 274.089 tmax2m 1586908800 24 267.711 267.994 267.913 267.585 268.116 267.564 267.589 267.904 268.018 267.263 268.113 268.262 268.052 268.329 267.757 268.097 268.170 267.816 267.748 267.935 268.169 tmax2m 1586930400 30 270.247 270.046 270.264 270.349 270.377 270.085 269.502 270.118 270.629 270.129 270.159 270.005 270.587 270.941 270.081 270.386 270.071 270.587 269.943 270.075 270.725 tmax2m 1586952000 36 283.536 282.595 280.881 282.802 283.440 283.205 281.532 282.371 283.747 284.037 282.390 282.183 281.154 282.724 282.080 282.794 282.421 284.124 282.557 283.302 283.049 tmax2m 1586973600 42 284.433 283.495 284.696 283.195 284.618 284.101 282.360 282.747 284.634 284.830 283.502 282.867 285.055 285.773 283.034 283.454 283.143 284.987 283.741 283.637 284.993 tmax2m 1586995200 48 274.371 274.529 274.338 274.628 274.487 274.398 273.387 274.192 274.525 274.044 274.068 274.312 274.621 274.795 274.006 274.372 274.303 274.587 274.110 274.441 274.652 tmax2m 1587016800 54 275.898 275.915 275.916 275.771 275.917 275.645 275.448 275.821 276.082 275.921 275.767 275.780 275.960 276.132 275.791 275.916 275.693 276.030 275.847 275.980 275.936 tmax2m 1587038400 60 286.242 286.636 285.841 286.513 285.972 286.375 285.872 285.879 286.525 286.369 286.343 286.241 286.181 286.718 285.812 286.072 286.208 286.447 286.331 286.744 286.376 tmax2m 1587060000 66 286.096 286.514 285.422 286.693 286.500 286.750 285.351 284.951 286.497 286.417 286.190 285.748 286.084 286.798 284.786 286.266 285.386 286.383 285.492 286.627 286.526 tmax2m 1587081600 72 277.289 276.929 277.011 276.976 277.486 276.616 276.807 276.781 277.164 276.884 276.585 277.414 276.927 277.593 277.717 277.609 277.460 277.379 277.270 277.599 276.344 tmax2m 1587103200 78 278.144 278.280 277.853 278.242 277.909 278.268 277.696 277.806 278.367 278.363 278.428 277.894 278.026 278.265 277.649 278.328 278.128 278.057 278.152 278.194 278.334 tmax2m 1587124800 84 288.522 289.047 286.259 288.597 286.135 288.292 285.631 287.987 288.684 288.895 288.336 288.139 288.417 288.098 288.517 288.457 288.683 287.316 287.956 288.744 288.954 tmax2m 1587146400 90 288.056 289.118 286.219 287.897 286.139 287.719 285.364 287.775 288.362 288.412 288.031 288.075 287.662 287.608 288.426 288.044 288.249 287.279 287.292 288.679 288.813 tmax2m 1587168000 96 278.658 278.527 278.189 278.275 277.177 279.375 277.076 279.290 279.866 278.467 280.231 280.116 279.341 279.804 279.574 278.372 278.678 278.098 278.641 278.739 279.639 tmax2m 1587189600 102 279.659 279.567 279.279 279.418 278.789 278.648 278.880 278.872 278.925 279.206 278.686 278.672 279.145 279.028 279.315 279.675 279.449 279.540 278.752 279.715 278.753 tmax2m 1587211200 108 286.500 288.360 285.963 287.605 288.185 283.917 286.865 285.134 286.371 287.975 287.074 283.097 285.155 285.468 287.592 288.250 287.688 289.120 285.930 287.117 284.544 tmax2m 1587232800 114 286.047 287.502 285.828 287.382 287.855 283.679 285.186 284.298 285.293 287.016 285.702 282.809 284.824 284.716 286.214 287.925 286.327 287.760 285.916 286.019 284.186 tmax2m 1587254400 120 280.561 280.126 280.759 280.983 281.574 279.532 280.352 279.020 280.195 280.466 280.489 278.963 279.678 280.047 280.357 282.104 280.229 281.375 279.046 280.551 280.044 tmax2m 1587276000 126 279.142 279.326 279.439 279.446 279.926 278.427 278.528 279.281 278.838 279.822 279.016 278.732 279.114 279.184 279.686 279.732 279.406 279.971 279.555 279.680 278.675 tmax2m 1587297600 132 282.932 283.332 284.718 284.999 282.428 282.605 284.777 284.876 284.142 284.429 285.611 284.384 284.581 283.669 285.248 287.331 284.341 281.400 285.305 282.949 282.108 tmax2m 1587319200 138 283.391 283.901 283.911 284.956 283.302 282.777 284.784 284.323 283.866 284.732 284.393 284.285 284.228 284.215 284.582 285.825 284.236 282.090 284.322 283.265 282.151 tmax2m 1587340800 144 280.930 280.297 280.455 281.400 280.359 279.633 281.088 281.304 280.414 281.206 280.130 279.935 280.817 281.238 281.049 282.475 281.455 280.418 280.340 280.441 280.016 tmax2m 1587362400 150 279.295 278.571 278.989 279.805 279.599 277.546 279.304 279.817 278.753 279.703 278.433 279.026 279.321 279.663 279.398 280.719 279.390 278.989 279.089 278.493 278.506 tmax2m 1587384000 156 285.314 280.542 281.192 281.200 287.213 280.008 281.754 282.623 287.911 282.030 281.473 285.175 286.215 285.248 287.222 287.183 283.482 281.849 287.211 282.505 285.187 tmax2m 1587405600 162 285.191 280.997 281.372 281.039 287.036 279.807 281.114 282.088 287.581 282.867 281.792 284.773 285.918 285.196 286.699 286.092 284.010 281.473 287.432 283.390 284.963 tmax2m 1587427200 168 280.137 278.848 278.862 279.327 281.651 277.808 277.936 278.572 281.622 279.597 278.793 279.582 279.947 280.848 281.278 281.737 280.773 278.684 281.048 279.566 279.860 tmax2m 1587448800 174 278.207 277.680 276.509 276.776 278.916 275.869 275.182 276.248 278.201 277.723 276.860 276.646 278.008 277.876 278.424 277.854 278.891 276.890 279.312 277.905 277.713 tmax2m 1587470400 180 279.936 278.415 279.261 276.937 286.707 278.860 275.906 279.942 284.397 278.352 280.286 278.904 283.542 283.265 282.282 284.671 285.643 282.906 286.066 281.645 281.573 tmax2m 1587492000 186 280.095 278.860 279.034 277.285 285.865 278.605 276.592 280.345 284.565 277.556 281.015 279.140 283.122 281.556 282.350 282.073 285.704 282.196 286.534 281.327 280.726 tmax2m 1587513600 192 278.841 276.110 276.742 273.982 281.010 276.485 275.615 277.636 280.831 275.358 277.766 276.437 279.352 277.864 279.217 276.952 281.336 278.290 281.705 278.735 278.248 tmax2m 1587535200 198 278.351 276.953 275.797 272.793 279.321 276.574 276.272 276.348 278.476 274.398 276.173 275.868 278.039 276.218 278.000 276.822 280.262 277.068 279.596 277.058 276.898 tmax2m 1587556800 204 281.556 283.906 279.255 280.183 285.697 280.925 280.954 279.761 287.883 275.648 281.176 280.794 277.168 275.631 280.459 280.551 286.576 278.396 286.972 279.329 281.879 tmax2m 1587578400 210 281.707 284.243 278.394 280.161 286.170 280.957 280.230 279.862 287.816 275.474 281.422 281.047 276.594 275.385 280.906 280.368 286.318 278.132 286.551 279.036 282.008 tmax2m 1587600000 216 277.344 280.049 274.423 275.767 282.515 278.473 277.721 276.358 281.629 273.821 277.114 277.569 274.482 272.969 277.664 277.092 280.718 275.324 281.389 275.221 277.649 tmax2m 1587621600 222 275.660 277.905 271.518 273.405 280.731 277.682 275.735 273.129 279.141 272.427 274.032 276.034 272.505 270.627 273.761 276.443 278.860 272.491 279.993 271.096 272.530 tmax2m 1587643200 228 281.262 282.130 272.391 278.355 287.371 285.036 278.557 279.066 282.484 275.092 281.740 280.702 275.960 272.600 278.548 279.560 279.055 272.675 286.577 274.907 282.445 tmax2m 1587664800 234 280.534 281.812 272.694 279.121 286.041 284.060 278.110 279.042 283.063 275.382 281.815 280.545 276.107 272.590 278.625 279.672 278.953 272.790 286.259 275.370 283.070 tmax2m 1587686400 240 276.065 277.906 267.418 276.229 280.049 280.224 274.980 274.552 280.359 272.958 276.619 277.685 273.506 269.778 272.081 276.438 276.697 268.768 281.503 272.722 275.647 dd10m 1586844000 6 341.513 341.768 339.977 339.296 338.712 339.978 343.593 343.961 341.857 341.564 338.846 344.699 340.985 343.998 339.656 340.886 341.043 338.721 343.686 338.942 345.688 dd10m 1586865600 12 352.351 352.681 351.885 352.884 351.327 355.012 356.357 351.715 352.328 354.285 348.788 354.494 351.990 349.750 355.895 352.283 351.859 354.518 352.643 353.293 351.467 dd10m 1586887200 18 20.608 20.742 18.299 22.781 16.734 28.157 23.625 16.460 17.850 24.576 16.250 24.239 15.797 16.190 22.750 22.238 18.142 21.825 22.287 24.216 20.571 dd10m 1586908800 24 186.484 185.449 178.676 192.697 175.264 180.806 214.862 188.590 177.465 183.396 182.744 180.710 180.771 183.367 203.099 178.471 177.829 182.824 204.049 184.527 175.994 dd10m 1586930400 30 195.517 190.191 193.794 195.673 202.481 177.656 163.759 223.987 214.944 203.477 198.424 209.938 196.585 194.813 165.430 190.760 211.722 201.484 190.410 162.259 193.546 dd10m 1586952000 36 35.652 38.966 43.684 31.611 54.321 57.088 33.119 18.487 33.087 33.384 34.526 32.949 32.024 36.858 28.087 38.834 40.634 33.512 38.839 38.625 52.640 dd10m 1586973600 42 80.387 84.372 99.479 86.288 90.022 101.004 62.321 67.096 87.401 68.843 76.737 77.275 80.248 90.004 69.611 84.316 83.127 70.602 78.496 82.453 88.684 dd10m 1586995200 48 185.541 184.695 192.972 180.806 190.328 184.257 184.424 185.723 187.897 186.607 183.376 183.751 187.591 190.517 184.715 185.464 182.926 185.897 187.742 185.286 184.103 dd10m 1587016800 54 205.548 204.114 217.224 198.707 209.525 204.503 207.133 208.118 207.658 201.278 201.568 201.249 203.968 206.284 206.383 208.031 206.671 208.857 208.175 204.634 203.406 dd10m 1587038400 60 273.993 276.944 302.471 246.527 254.768 293.352 272.181 308.278 285.220 259.541 274.767 274.560 279.163 290.952 287.450 251.135 293.998 275.069 300.240 279.352 266.882 dd10m 1587060000 66 4.901 10.273 3.836 341.424 9.366 6.611 26.356 7.246 18.535 356.017 19.194 348.269 23.655 35.028 347.429 6.141 359.765 27.160 11.642 3.223 17.722 dd10m 1587081600 72 230.278 237.619 235.634 227.341 214.724 227.723 242.009 208.420 225.051 231.009 228.468 235.389 218.817 221.136 231.548 229.098 218.164 224.214 226.470 256.748 217.617 dd10m 1587103200 78 234.629 239.653 248.272 221.075 258.989 206.473 252.235 212.047 226.220 244.724 207.360 219.487 216.841 218.679 246.755 221.285 225.907 258.368 220.296 243.790 224.377 dd10m 1587124800 84 297.629 324.236 321.866 304.607 326.544 222.483 317.577 321.112 276.299 282.767 251.763 264.148 306.987 240.078 295.997 296.850 310.224 325.339 281.177 332.230 272.227 dd10m 1587146400 90 80.105 73.444 22.990 61.159 21.515 139.921 11.758 111.365 111.913 21.413 150.388 148.619 94.906 176.364 144.819 51.243 88.481 21.838 37.186 101.808 105.656 dd10m 1587168000 96 201.765 203.114 198.165 200.182 206.412 207.141 210.521 209.237 232.376 222.725 208.157 216.916 200.834 220.044 203.180 204.347 213.087 204.774 210.526 210.310 192.419 dd10m 1587189600 102 212.117 241.534 205.319 200.588 193.623 235.055 203.821 265.542 243.708 263.970 264.687 256.881 215.427 277.348 241.340 206.643 222.787 207.040 268.194 252.821 212.046 dd10m 1587211200 108 237.893 232.385 226.578 197.518 249.671 286.870 193.188 303.531 278.751 288.702 273.716 270.058 244.337 287.783 241.961 192.353 227.677 158.848 308.276 285.819 258.311 dd10m 1587232800 114 209.039 20.407 198.152 186.014 139.107 310.393 206.849 36.945 336.804 17.003 331.895 308.471 338.977 18.709 273.795 178.859 194.503 154.360 15.438 354.310 262.679 dd10m 1587254400 120 197.680 183.323 226.080 198.593 183.134 210.216 213.509 176.994 355.974 184.877 207.506 245.753 157.459 169.875 222.736 201.592 197.818 199.352 184.848 192.610 197.598 dd10m 1587276000 126 175.233 189.259 262.823 220.855 176.724 248.899 217.550 172.462 163.855 181.848 235.573 199.925 160.511 175.152 267.568 229.607 199.712 182.610 187.013 184.153 163.157 dd10m 1587297600 132 168.243 176.189 222.975 237.993 191.222 267.729 247.709 171.800 153.973 179.985 301.852 201.717 170.746 155.174 67.662 229.099 293.541 243.122 150.293 145.767 162.081 dd10m 1587319200 138 150.606 189.200 163.709 157.566 196.192 16.456 162.494 163.346 153.825 161.665 30.717 115.539 159.505 151.169 122.588 162.600 150.449 27.048 155.796 85.174 151.248 dd10m 1587340800 144 163.566 188.979 250.045 165.962 186.022 72.372 173.692 182.166 174.458 177.187 132.208 187.709 172.009 170.308 170.087 173.704 164.882 109.304 178.456 162.971 168.395 dd10m 1587362400 150 174.499 177.404 354.542 171.859 165.665 79.455 163.924 228.594 182.766 174.825 97.498 167.883 175.663 164.191 175.180 185.494 162.487 92.268 180.851 148.489 159.042 dd10m 1587384000 156 177.583 172.701 44.739 152.675 156.587 87.774 133.515 331.043 126.943 158.112 93.696 144.423 173.445 153.163 143.587 167.687 143.286 94.393 162.494 146.504 109.943 dd10m 1587405600 162 144.465 221.804 70.517 158.458 162.580 100.051 22.131 26.752 143.594 139.623 98.714 120.450 173.043 138.178 147.703 148.175 125.486 96.218 165.775 104.875 110.798 dd10m 1587427200 168 152.235 303.714 99.363 285.028 180.347 127.745 31.131 47.414 161.600 150.505 105.663 127.223 182.955 160.611 165.572 167.783 149.555 134.029 179.257 144.970 143.119 dd10m 1587448800 174 137.332 331.491 107.215 314.241 188.303 126.527 46.600 78.049 142.871 114.419 114.164 86.461 197.261 126.454 92.372 187.576 158.019 156.118 171.616 155.562 144.872 dd10m 1587470400 180 148.712 352.170 108.967 334.164 164.265 118.126 84.885 90.726 115.687 36.635 112.672 66.157 143.814 35.711 94.801 40.768 157.857 91.672 154.584 88.399 78.240 dd10m 1587492000 186 158.470 34.842 173.243 8.237 176.753 35.838 113.696 95.586 126.664 19.827 95.597 60.167 186.392 14.128 91.911 33.131 171.838 129.098 142.685 51.996 41.541 dd10m 1587513600 192 178.083 163.535 193.733 53.385 182.479 163.045 142.124 145.170 150.488 57.178 115.358 67.321 198.358 36.577 127.722 113.370 203.636 220.478 173.657 32.001 46.698 dd10m 1587535200 198 201.633 162.382 234.637 53.053 200.137 67.710 133.362 26.494 161.732 12.036 93.450 60.350 269.873 25.578 50.192 132.711 248.909 259.414 186.161 26.384 43.320 dd10m 1587556800 204 216.560 166.771 312.236 44.361 232.254 85.144 79.289 22.630 130.998 41.708 49.927 49.991 323.700 22.279 43.727 157.137 296.590 1.187 185.415 43.911 52.051 dd10m 1587578400 210 225.158 163.368 340.613 32.638 171.767 86.711 68.288 11.746 165.455 37.374 43.808 48.829 345.607 30.231 32.722 131.923 313.842 16.907 244.574 44.937 43.976 dd10m 1587600000 216 208.341 181.064 349.810 30.972 178.131 142.554 93.621 16.331 195.154 32.928 92.988 101.494 340.791 30.346 24.390 174.835 9.303 27.975 177.797 56.565 49.651 dd10m 1587621600 222 294.676 188.274 11.208 41.204 170.656 146.376 18.049 19.402 214.235 15.757 108.353 71.012 355.185 25.817 0.733 188.457 44.068 27.318 178.165 54.317 49.505 dd10m 1587643200 228 356.272 222.736 10.049 58.873 176.980 81.621 19.004 24.091 223.478 29.371 80.948 62.245 8.931 24.854 357.339 46.739 53.631 32.904 151.464 55.747 48.956 dd10m 1587664800 234 359.393 289.897 5.356 53.430 225.473 62.571 5.528 14.797 226.100 23.979 65.301 68.576 9.252 17.141 1.268 16.872 46.372 29.877 173.443 44.262 62.832 dd10m 1587686400 240 6.776 297.258 293.154 56.988 213.145 17.123 337.941 6.645 216.902 19.458 143.159 139.251 3.272 13.635 7.361 348.658 97.075 33.255 212.133 81.063 169.340 ff10m 1586844000 6 3.644 3.497 3.500 3.597 3.523 3.790 3.818 3.475 3.572 3.663 3.696 3.820 3.703 3.402 3.883 3.651 3.717 3.728 3.737 3.659 3.665 ff10m 1586865600 12 3.832 3.959 3.822 3.891 3.779 3.837 3.915 3.920 3.899 3.823 3.915 3.972 3.738 3.924 3.715 3.768 3.877 3.690 3.850 3.748 3.794 ff10m 1586887200 18 2.265 2.448 2.383 2.227 2.330 2.247 2.249 2.328 2.251 2.157 2.366 2.446 2.259 2.310 2.284 2.309 2.336 2.228 2.254 2.337 2.308 ff10m 1586908800 24 0.772 0.790 0.799 0.813 0.895 0.881 0.252 0.727 0.586 0.816 0.565 0.522 0.901 1.063 0.717 0.969 0.511 1.074 0.758 0.718 0.932 ff10m 1586930400 30 0.593 0.351 0.854 0.471 0.781 0.883 0.319 0.550 0.733 0.853 0.833 0.329 0.853 0.781 0.226 0.664 0.318 0.747 0.416 0.440 0.694 ff10m 1586952000 36 1.941 2.275 1.598 2.344 1.729 1.892 2.206 2.140 1.937 1.742 2.157 2.237 1.515 1.631 2.075 2.127 2.133 1.772 2.054 2.162 1.778 ff10m 1586973600 42 1.481 1.541 1.231 1.665 1.111 1.527 1.740 1.582 1.362 1.381 1.641 1.561 1.301 1.349 1.463 1.541 1.559 1.285 1.380 1.560 1.449 ff10m 1586995200 48 2.389 2.459 2.389 2.580 2.354 2.426 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1.232 0.785 1.151 0.956 1.115 0.619 0.564 0.344 1.322 1.027 0.633 0.466 0.740 0.757 0.685 1.226 0.448 0.416 0.675 ff10m 1587168000 96 2.269 2.344 2.360 2.205 1.400 2.571 2.149 2.506 1.712 2.048 2.171 2.394 2.582 2.466 2.181 2.250 2.243 2.004 2.324 2.233 2.170 ff10m 1587189600 102 1.969 1.627 2.373 2.234 1.648 2.023 2.085 1.558 1.609 1.385 1.783 1.220 2.206 1.802 1.488 2.005 1.828 1.547 1.871 1.541 1.839 ff10m 1587211200 108 1.109 1.304 1.835 1.999 0.535 1.735 1.094 2.144 2.232 1.255 1.972 1.341 2.177 2.174 0.331 1.452 0.789 0.393 2.401 1.392 0.950 ff10m 1587232800 114 0.814 0.375 1.550 2.422 1.640 0.493 1.701 1.037 1.559 0.763 1.797 0.647 0.818 1.338 0.067 1.278 0.746 1.034 1.519 0.785 0.660 ff10m 1587254400 120 1.840 2.567 1.660 2.703 3.502 1.167 2.295 1.888 0.325 2.521 0.820 1.583 0.458 2.304 1.490 2.101 1.793 2.577 2.381 1.702 1.773 ff10m 1587276000 126 1.424 2.467 1.242 2.413 3.068 0.662 1.940 1.832 1.678 2.726 1.278 1.472 1.092 1.644 1.010 1.693 1.649 2.210 2.331 1.016 2.105 ff10m 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0.296 apcpsfc 1587600000 216 2.269 0.190 1.416 1.489 0.135 0.877 2.221 1.958 7.589 4.270 0.074 3.044 1.294 6.746 0.256 4.261 5.560 6.120 5.381 6.592 0.100 apcpsfc 1587621600 222 0.380 0.894 1.698 1.391 0.025 0.057 1.972 0.344 6.518 3.357 0.096 1.430 1.206 3.724 0.083 2.192 7.108 5.938 0.552 8.394 0.000 apcpsfc 1587643200 228 1.771 2.179 0.797 2.915 0.459 1.122 2.161 0.074 6.214 2.619 0.430 3.216 2.367 1.984 0.048 5.285 7.120 3.581 0.619 6.161 0.000 apcpsfc 1587664800 234 7.619 6.978 0.200 2.284 3.014 5.944 4.143 0.218 7.073 5.542 1.568 4.751 2.884 1.439 0.552 6.888 8.178 2.529 3.428 3.569 0.000 apcpsfc 1587686400 240 6.163 7.591 0.000 1.478 1.804 2.025 2.888 0.822 6.090 6.527 0.249 0.922 1.329 1.023 0.476 3.075 4.570 2.384 4.903 0.792 0.005 tmp2m 1586844000 6 268.607 268.923 268.292 268.556 268.238 268.348 267.995 268.499 268.938 267.741 268.899 268.970 268.971 269.001 268.372 268.623 269.055 268.635 268.387 268.821 268.985 tmp2m 1586865600 12 273.300 273.389 273.198 273.101 273.444 272.758 272.570 273.619 273.787 272.935 273.414 273.206 273.626 274.144 272.608 273.545 273.205 273.300 273.109 273.161 273.787 tmp2m 1586887200 18 268.073 268.326 268.230 267.960 268.443 268.030 267.972 268.197 268.390 267.778 268.453 268.672 268.397 268.679 268.084 268.424 268.549 268.157 268.101 268.283 268.448 tmp2m 1586908800 24 259.523 259.464 259.573 259.921 260.301 259.225 257.768 259.834 259.905 259.173 259.515 258.337 260.257 261.653 258.789 260.180 258.706 260.291 259.071 259.030 260.524 tmp2m 1586930400 30 270.247 270.046 270.217 270.297 270.302 270.085 269.449 269.970 270.555 270.082 270.028 270.005 270.539 270.819 270.007 270.291 270.018 270.465 269.864 270.013 270.668 tmp2m 1586952000 36 280.242 280.116 280.539 280.407 280.908 280.577 280.672 280.083 280.739 280.533 280.029 279.927 280.852 281.179 279.818 280.279 280.012 280.598 280.021 280.187 280.842 tmp2m 1586973600 42 273.383 273.580 273.202 273.870 273.399 273.656 273.434 273.505 273.362 273.136 273.524 273.595 273.311 273.585 273.197 273.440 273.449 273.263 273.065 273.566 273.619 tmp2m 1586995200 48 272.973 272.951 272.999 273.072 273.112 272.858 272.034 272.720 273.196 272.693 272.682 272.792 273.221 273.364 272.651 272.897 272.818 273.173 272.747 272.930 273.252 tmp2m 1587016800 54 275.898 275.915 275.916 275.762 275.917 275.645 275.448 275.821 276.073 275.904 275.767 275.780 275.960 276.132 275.791 275.906 275.677 276.030 275.847 275.980 275.936 tmp2m 1587038400 60 286.242 286.504 285.814 286.174 285.972 286.375 285.759 285.614 286.525 286.211 286.211 285.929 286.181 286.718 285.525 286.072 286.208 286.399 286.283 286.691 286.139 tmp2m 1587060000 66 277.590 277.739 277.387 277.351 277.821 277.521 276.954 277.309 277.919 276.957 277.275 277.769 277.317 277.758 277.752 277.772 277.773 277.693 277.764 277.793 277.572 tmp2m 1587081600 72 274.241 274.205 274.613 274.592 274.559 273.770 274.507 274.458 274.549 274.350 274.100 273.718 275.027 274.714 274.151 274.451 274.069 274.475 273.814 274.280 274.397 tmp2m 1587103200 78 278.144 278.254 277.853 278.215 277.909 278.268 277.696 277.806 278.367 278.363 278.402 277.894 278.026 278.265 277.623 278.302 278.102 278.057 278.152 278.194 278.298 tmp2m 1587124800 84 288.395 289.047 286.037 288.401 286.056 287.826 285.255 288.013 288.657 288.895 288.283 287.800 287.308 287.907 288.517 288.430 288.683 287.290 287.956 288.744 288.674 tmp2m 1587146400 90 278.521 278.810 277.995 278.497 278.205 279.411 277.483 279.048 279.949 279.451 280.361 280.272 279.105 280.013 279.782 278.531 279.197 278.498 278.983 279.171 279.864 tmp2m 1587168000 96 277.352 277.286 277.040 277.206 275.343 277.035 276.111 277.814 278.210 276.843 277.140 278.106 277.724 277.696 277.576 277.267 276.826 276.946 277.511 277.858 277.738 tmp2m 1587189600 102 279.659 279.567 279.279 279.418 278.789 278.648 278.880 278.872 278.875 279.206 278.686 278.624 279.145 279.019 279.306 279.675 279.449 279.540 278.752 279.715 278.657 tmp2m 1587211200 108 286.165 287.210 285.963 287.509 287.872 283.658 285.613 284.695 285.354 287.593 286.310 282.892 284.859 285.236 286.428 287.884 286.739 288.346 285.842 286.417 284.342 tmp2m 1587232800 114 280.794 280.548 280.918 281.169 281.721 279.650 280.311 279.390 280.279 280.806 280.710 279.323 279.807 280.356 280.594 282.094 280.371 281.491 279.475 280.713 280.262 tmp2m 1587254400 120 278.397 278.378 278.808 278.873 279.657 277.679 278.219 277.850 278.303 278.855 277.661 277.613 278.381 278.205 279.404 279.235 278.620 279.487 276.821 278.705 277.228 tmp2m 1587276000 126 278.877 279.221 279.389 279.446 279.609 278.262 278.441 279.281 278.707 279.679 278.894 278.732 279.114 279.053 279.686 279.732 279.111 279.594 279.555 279.454 278.675 tmp2m 1587297600 132 282.856 283.306 284.252 284.803 282.360 282.552 284.734 284.293 283.872 284.403 284.700 284.215 284.354 283.669 285.045 286.167 283.842 281.248 284.653 282.923 282.099 tmp2m 1587319200 138 281.008 280.533 280.490 281.517 280.511 279.754 281.131 281.435 280.564 281.405 280.326 279.975 280.861 281.316 281.184 282.527 281.428 280.406 280.536 280.528 280.099 tmp2m 1587340800 144 279.005 278.212 278.963 279.740 277.528 277.433 279.212 279.257 278.375 279.382 278.370 278.193 278.796 279.154 279.228 280.342 279.343 278.950 278.176 278.389 277.937 tmp2m 1587362400 150 279.269 278.354 278.632 279.011 279.599 277.226 278.909 279.626 278.727 279.703 277.931 278.665 279.103 279.615 279.042 280.654 278.924 277.834 279.115 277.889 278.147 tmp2m 1587384000 156 285.012 280.542 281.135 281.056 287.160 279.955 281.440 281.968 287.806 281.609 281.378 285.127 286.093 285.095 287.222 286.605 283.464 281.605 287.211 282.488 284.982 tmp2m 1587405600 162 280.327 278.934 279.091 279.401 281.857 277.754 278.101 278.707 281.844 279.987 278.904 279.691 280.234 280.938 281.355 281.800 280.934 278.719 281.265 279.675 280.085 tmp2m 1587427200 168 278.210 277.676 276.447 276.924 278.430 275.823 275.300 276.226 277.614 277.750 276.938 276.627 278.004 277.636 278.147 277.441 278.920 276.566 278.809 276.950 277.179 tmp2m 1587448800 174 277.734 276.476 275.513 274.875 278.724 275.513 273.396 275.002 278.154 277.014 275.797 275.710 277.960 277.707 277.640 277.321 278.492 276.752 279.321 277.750 277.661 tmp2m 1587470400 180 279.831 278.388 278.262 276.744 285.686 278.511 275.906 279.915 284.291 277.718 280.238 278.856 282.980 281.964 282.208 283.000 285.643 282.196 286.066 280.991 280.783 tmp2m 1587492000 186 278.935 276.160 276.677 274.520 281.393 276.629 275.625 277.831 281.027 275.311 278.023 276.577 279.278 278.030 279.343 277.119 281.626 278.512 281.935 278.883 278.374 tmp2m 1587513600 192 277.324 275.263 273.864 271.441 277.291 275.267 274.356 275.006 276.049 273.875 274.998 275.002 277.226 275.717 277.335 275.068 278.524 276.041 277.273 276.912 276.612 tmp2m 1587535200 198 277.271 276.953 275.274 272.793 279.262 276.548 276.193 275.924 278.380 273.589 275.982 275.851 276.312 274.470 277.134 276.688 279.652 276.326 279.548 275.969 276.411 tmp2m 1587556800 204 281.420 283.784 278.737 280.120 285.331 280.490 280.897 279.470 287.613 275.556 281.128 280.715 277.028 275.100 280.459 280.047 286.421 278.195 286.671 279.301 281.832 tmp2m 1587578400 210 277.901 280.100 274.677 275.990 282.667 278.714 277.911 276.756 281.935 273.987 277.481 277.795 274.418 273.301 277.750 277.306 280.936 275.518 281.646 275.476 278.117 tmp2m 1587600000 216 274.256 277.525 271.425 273.276 279.711 276.521 275.400 271.807 278.708 272.334 271.243 275.279 272.154 270.736 273.250 276.253 278.874 272.665 279.703 271.253 272.415 tmp2m 1587621600 222 275.581 277.730 269.734 273.020 280.727 277.630 275.294 272.426 278.744 272.132 273.999 276.017 272.368 269.449 271.807 276.390 277.521 270.591 279.776 270.983 272.038 tmp2m 1587643200 228 280.957 281.819 272.386 278.328 286.628 284.166 278.383 279.063 282.484 275.092 281.740 280.303 275.960 272.600 278.548 279.417 278.814 272.675 286.329 274.859 282.445 tmp2m 1587664800 234 276.267 278.092 267.708 276.520 280.075 280.476 275.600 274.897 280.588 273.284 277.212 278.028 273.895 269.882 272.546 277.067 277.015 269.094 281.630 273.031 276.274 tmp2m 1587686400 240 274.072 276.602 262.793 272.196 276.996 277.029 272.578 271.699 278.809 270.703 271.558 274.912 270.501 267.779 267.507 274.641 274.731 265.405 278.632 266.969 272.437 tcdcclm 1586844000 6 5.958 5.952 5.762 5.856 5.479 5.908 6.474 5.905 6.277 5.665 6.226 6.216 6.071 5.670 5.759 6.129 6.033 6.292 6.286 5.698 6.216 tcdcclm 1586865600 12 3.756 3.054 3.328 3.702 3.449 4.385 4.190 3.376 3.707 3.999 4.442 4.475 3.005 2.909 4.691 3.200 4.734 3.486 4.120 4.101 3.852 tcdcclm 1586887200 18 1.047 1.882 0.986 1.189 0.500 2.681 3.422 0.566 0.710 1.950 2.053 2.381 0.635 0.346 2.772 0.745 1.984 0.815 2.521 1.224 0.863 tcdcclm 1586908800 24 0.308 0.329 0.294 0.308 0.186 0.482 0.813 0.350 0.316 0.206 0.791 1.097 0.291 0.245 0.648 0.346 0.753 0.224 0.639 0.350 0.388 tcdcclm 1586930400 30 0.098 0.052 0.105 0.143 0.098 0.084 0.038 0.105 0.098 0.105 0.112 0.046 0.105 0.143 0.136 0.241 0.105 0.098 0.076 0.084 0.156 tcdcclm 1586952000 36 0.028 0.271 0.103 0.897 1.073 0.374 0.387 0.126 0.305 0.245 0.780 0.021 0.169 0.094 0.541 0.118 0.216 0.013 0.296 0.063 0.063 tcdcclm 1586973600 42 0.788 1.474 1.494 0.968 3.637 0.468 0.890 1.216 1.176 1.067 0.704 1.016 2.279 1.153 0.959 0.911 0.771 0.940 0.803 0.442 1.658 tcdcclm 1586995200 48 3.331 2.443 2.629 3.594 3.284 1.849 2.279 3.025 2.367 2.794 2.804 4.512 4.948 4.135 3.079 2.912 3.052 4.144 2.839 3.162 5.285 tcdcclm 1587016800 54 4.162 3.521 3.111 4.655 3.902 3.778 3.568 3.761 3.743 3.719 3.931 5.249 4.342 4.263 3.621 3.958 3.816 4.186 3.462 3.844 4.507 tcdcclm 1587038400 60 2.065 1.923 1.566 2.967 1.329 2.694 3.733 2.385 1.732 3.519 1.760 2.939 2.106 1.735 3.594 2.861 1.441 1.474 3.286 2.316 1.582 tcdcclm 1587060000 66 6.938 6.822 6.960 6.674 5.276 4.405 6.203 6.188 6.680 6.286 6.673 6.752 7.165 6.259 7.097 6.540 6.889 6.992 6.788 5.952 6.924 tcdcclm 1587081600 72 2.464 2.621 1.822 2.766 2.839 2.275 6.455 1.615 1.483 3.162 1.917 3.399 2.369 2.573 4.487 2.671 2.220 2.904 2.353 5.981 2.458 tcdcclm 1587103200 78 2.314 2.657 3.813 3.821 2.013 2.988 3.440 3.930 3.470 0.881 0.937 2.611 4.297 3.139 3.683 2.996 2.766 4.575 4.334 2.066 3.094 tcdcclm 1587124800 84 1.182 0.348 2.012 2.723 0.999 3.431 2.005 6.127 4.434 1.516 3.743 1.994 3.200 3.561 1.722 3.886 4.360 2.126 5.816 2.402 3.016 tcdcclm 1587146400 90 3.612 4.063 2.796 5.533 3.406 4.954 2.891 5.899 6.748 5.765 7.811 5.606 5.823 5.184 5.786 5.380 6.132 3.598 6.070 4.513 4.862 tcdcclm 1587168000 96 4.836 5.498 5.391 5.334 3.286 5.111 3.104 6.561 7.474 6.319 6.945 7.230 6.158 6.326 6.877 4.907 2.003 5.321 6.064 6.723 7.719 tcdcclm 1587189600 102 5.958 5.803 6.450 5.664 6.548 6.487 4.439 6.697 4.430 3.938 4.508 7.521 6.673 6.882 6.454 6.189 3.929 6.824 7.129 7.003 7.787 tcdcclm 1587211200 108 6.507 4.207 6.690 6.977 4.660 6.406 6.180 6.406 5.587 5.642 5.388 7.422 6.646 6.662 5.743 6.206 5.607 6.344 4.372 6.651 7.070 tcdcclm 1587232800 114 6.800 7.186 7.839 7.720 6.279 7.287 7.436 6.991 7.406 7.386 6.254 7.076 7.281 6.706 7.030 6.630 7.072 6.306 5.481 6.965 6.925 tcdcclm 1587254400 120 7.127 6.540 7.913 7.497 7.642 7.088 7.406 6.322 7.625 6.721 5.905 7.202 7.423 6.579 7.716 7.748 7.866 7.560 5.123 7.528 6.740 tcdcclm 1587276000 126 7.730 6.850 7.313 7.249 7.499 6.441 7.417 7.322 5.263 7.806 5.920 7.656 7.515 7.542 7.295 7.866 7.469 7.805 6.642 7.210 7.214 tcdcclm 1587297600 132 7.684 7.923 7.708 7.679 7.958 7.069 6.755 5.468 7.337 7.216 6.466 6.000 7.116 7.437 6.986 7.028 6.773 7.937 7.110 7.800 7.890 tcdcclm 1587319200 138 7.209 7.622 7.958 7.767 6.666 7.408 6.606 7.915 7.958 7.137 7.613 7.056 7.574 7.637 7.248 7.684 7.760 7.343 7.804 7.313 7.898 tcdcclm 1587340800 144 7.734 7.358 7.958 7.734 6.166 7.862 7.741 7.951 7.632 7.909 7.568 7.357 7.853 7.917 7.653 7.589 7.452 7.835 7.479 7.796 7.887 tcdcclm 1587362400 150 7.714 7.839 7.883 7.930 6.668 7.808 7.393 7.834 5.534 7.827 7.669 6.632 7.423 7.713 6.492 7.004 7.655 7.625 6.169 7.283 6.765 tcdcclm 1587384000 156 7.131 7.979 7.742 7.979 6.828 7.958 7.722 7.644 4.652 7.979 7.551 7.631 6.959 7.265 3.569 7.108 7.267 6.936 6.821 7.930 6.756 tcdcclm 1587405600 162 7.663 7.741 7.738 7.979 6.814 7.945 7.791 7.972 6.597 7.074 6.429 7.892 7.485 7.581 5.627 7.487 7.718 6.806 7.739 6.854 7.905 tcdcclm 1587427200 168 7.829 7.972 7.944 7.867 5.223 7.667 7.865 7.993 7.498 6.721 7.105 7.714 6.614 5.575 6.815 5.804 7.706 6.247 7.868 5.098 7.905 tcdcclm 1587448800 174 7.853 7.401 7.927 7.356 4.172 7.046 7.906 7.822 7.285 6.976 7.692 7.833 5.173 4.521 7.787 2.345 7.583 5.990 7.667 4.127 7.411 tcdcclm 1587470400 180 7.805 7.666 7.731 7.522 4.809 7.852 7.623 7.091 7.616 7.837 7.430 7.432 5.452 4.876 7.921 3.541 7.276 6.997 7.103 7.056 7.668 tcdcclm 1587492000 186 7.923 6.788 7.564 6.845 6.297 7.771 7.777 7.135 7.287 7.913 7.300 7.640 7.247 7.572 7.729 7.807 7.257 6.272 6.416 7.471 7.822 tcdcclm 1587513600 192 7.635 6.709 7.907 6.040 7.230 7.307 7.225 7.379 3.205 7.822 6.353 6.818 7.954 7.945 7.549 7.633 6.744 5.945 6.015 7.626 7.597 tcdcclm 1587535200 198 3.480 3.764 7.902 6.096 2.262 6.719 6.820 7.322 1.871 7.525 5.310 5.512 7.868 7.951 6.225 7.252 3.087 6.466 5.339 6.887 5.706 tcdcclm 1587556800 204 6.262 5.144 7.009 6.530 3.600 6.972 6.447 6.889 2.134 7.517 5.178 5.747 7.707 7.657 5.814 6.844 4.951 7.371 6.165 5.906 5.060 tcdcclm 1587578400 210 6.497 5.940 7.452 7.610 5.302 7.604 7.521 7.062 5.030 7.875 4.590 5.826 7.802 7.681 5.088 7.485 6.577 7.134 6.977 6.346 4.771 tcdcclm 1587600000 216 4.553 6.682 7.252 7.352 5.366 6.071 6.835 6.712 5.826 7.500 2.432 6.421 7.556 7.794 4.868 7.437 6.879 7.718 7.786 7.280 4.352 tcdcclm 1587621600 222 2.817 5.786 7.277 6.679 5.691 4.693 7.111 6.549 6.582 7.700 1.091 6.084 7.134 7.888 4.696 7.039 7.595 7.972 7.784 7.567 1.489 tcdcclm 1587643200 228 3.682 7.286 5.967 6.278 5.505 4.654 6.880 4.806 7.145 7.707 2.674 5.784 7.431 7.864 1.613 7.706 7.716 7.805 7.534 6.043 0.267 tcdcclm 1587664800 234 6.703 7.667 3.436 6.916 7.496 5.608 7.623 6.461 7.083 7.421 4.454 6.044 7.218 7.673 3.863 7.758 7.587 7.506 6.568 5.966 1.026 tcdcclm 1587686400 240 6.964 7.822 0.922 6.597 5.840 5.605 6.807 6.770 7.442 7.670 3.186 4.913 6.204 7.423 6.016 7.455 7.315 7.401 7.027 4.840 1.961 partykit/inst/ULGcourse-2020/Data/GENS_00_innsbruck_20200415.dat0000644000176200001440000016114414172227777023007 0ustar liggesusers# ASCII output from GENSvis.py # Contains interpolated values from the # GFS ensemble on 1.000000 x 1.000000 degrees # The data in here are for station # 11120: INNSBRUCK # Station position: 11.3553 47.2589 # Used grid point 1: 12.0000 48.0000 # Used grid point 2: 12.0000 47.0000 # Used grid point 3: 11.0000 47.0000 # Used grid point 4: 11.0000 48.0000 varname timestamp step mem0 mem1 mem2 mem3 mem4 mem5 mem6 mem7 mem8 mem9 mem10 mem11 mem12 mem13 mem14 mem15 mem16 mem17 mem18 mem19 mem20 tmax2m 1586930400 6 269.370 269.341 269.418 269.606 269.358 269.170 269.300 269.344 269.369 269.358 269.120 269.550 269.413 269.583 269.459 269.365 269.492 269.229 269.253 269.275 269.191 tmax2m 1586952000 12 280.043 280.220 280.297 280.275 279.811 279.483 279.858 280.113 279.801 279.795 279.969 280.140 279.891 279.808 279.539 279.462 279.870 280.365 279.663 280.184 280.131 tmax2m 1586973600 18 280.791 281.073 280.853 281.059 280.880 280.736 280.401 280.861 280.911 280.795 280.634 280.617 280.997 280.979 280.691 280.516 280.770 281.053 280.727 280.879 280.905 tmax2m 1586995200 24 274.564 274.704 274.638 274.781 274.495 274.625 274.272 274.546 274.598 274.607 274.459 274.528 274.577 274.733 274.507 274.612 274.572 274.607 274.538 274.611 274.585 tmax2m 1587016800 30 275.281 275.484 275.176 275.202 275.303 274.945 275.561 275.491 275.450 275.307 275.425 275.398 275.429 275.241 275.425 275.411 275.272 275.346 275.298 274.997 275.286 tmax2m 1587038400 36 283.587 283.950 283.602 283.491 283.788 283.488 283.331 283.662 283.678 284.033 283.425 283.330 283.705 283.670 283.575 283.731 283.327 283.721 283.447 283.645 283.592 tmax2m 1587060000 42 284.553 284.837 284.883 284.335 285.635 285.201 284.210 285.027 284.774 284.691 284.448 284.436 285.495 285.470 285.087 285.322 284.244 284.814 284.847 285.392 285.296 tmax2m 1587081600 48 273.631 274.126 273.826 273.670 274.232 273.374 276.430 274.408 274.113 274.477 273.623 274.618 274.903 273.565 273.778 273.620 273.735 275.420 274.498 274.218 274.253 tmax2m 1587103200 54 277.156 277.316 277.152 277.113 277.051 277.112 276.900 277.090 277.173 277.294 277.273 277.102 277.237 277.294 277.230 277.278 277.278 277.206 277.216 277.056 277.185 tmax2m 1587124800 60 286.686 287.073 286.694 286.288 286.348 286.027 286.747 286.543 287.839 287.500 286.157 286.911 286.342 286.217 287.040 286.953 286.075 285.782 285.621 286.249 286.434 tmax2m 1587146400 66 286.987 287.019 287.006 287.309 286.174 286.370 286.955 286.669 287.662 286.852 287.096 286.790 286.705 286.605 287.006 286.958 286.311 286.586 286.047 286.721 286.855 tmax2m 1587168000 72 277.268 277.607 277.887 277.624 277.070 277.255 276.826 277.092 277.435 277.803 277.556 276.464 277.049 276.960 278.070 277.061 277.029 277.157 277.056 277.228 277.083 tmax2m 1587189600 78 278.596 278.054 277.817 278.171 278.263 278.736 278.481 278.391 278.990 278.693 278.632 278.292 278.634 278.676 278.880 278.428 278.613 278.714 278.437 278.320 278.700 tmax2m 1587211200 84 288.408 286.629 285.772 286.467 287.761 287.923 288.757 288.123 288.411 288.438 287.487 286.935 288.814 287.960 288.940 286.256 286.730 289.213 289.011 286.903 288.803 tmax2m 1587232800 90 287.889 286.617 285.834 286.316 287.274 287.562 288.706 287.884 287.355 288.373 287.424 286.693 288.567 287.213 288.517 286.083 286.746 289.081 288.595 287.019 288.412 tmax2m 1587254400 96 279.288 278.677 278.135 279.466 278.809 280.074 279.801 279.102 280.180 279.555 278.833 278.704 280.500 279.223 279.518 279.422 278.793 279.606 280.226 278.452 279.231 tmax2m 1587276000 102 279.235 278.854 277.309 278.967 278.997 279.107 279.508 279.776 279.596 279.248 279.346 277.511 279.726 278.822 279.126 278.106 278.958 279.792 279.333 278.031 279.667 tmax2m 1587297600 108 285.543 286.626 282.716 283.780 287.168 282.006 285.867 283.623 284.525 282.033 287.540 282.658 286.783 283.979 284.592 283.697 285.467 283.890 285.000 283.319 286.710 tmax2m 1587319200 114 285.294 285.596 283.181 283.826 287.234 281.686 285.660 283.638 284.832 282.169 286.405 283.310 285.127 284.279 284.782 283.944 285.245 283.567 284.476 283.556 285.058 tmax2m 1587340800 120 279.715 279.562 276.677 279.836 280.146 278.443 280.386 279.890 280.419 279.545 280.526 277.697 281.325 279.820 279.133 278.876 280.210 279.417 279.545 278.336 280.432 tmax2m 1587362400 126 277.835 277.804 274.685 278.084 279.269 276.623 278.434 278.402 277.898 277.374 277.394 276.158 279.323 278.384 277.477 276.452 277.508 277.020 277.878 277.840 277.578 tmax2m 1587384000 132 282.142 279.280 282.718 280.664 288.392 279.738 283.680 279.996 281.179 281.885 282.472 283.401 282.391 282.859 282.596 280.445 282.492 282.731 281.601 285.951 278.384 tmax2m 1587405600 138 282.294 278.313 282.870 280.739 288.541 280.386 283.022 280.123 280.968 282.088 282.997 283.441 283.285 282.140 282.053 280.444 282.174 283.481 281.173 286.455 277.834 tmax2m 1587427200 144 277.117 275.299 275.150 278.060 280.097 275.476 278.958 278.275 278.457 279.003 276.914 275.666 280.327 278.466 277.132 276.712 278.543 278.807 278.173 277.911 275.220 tmax2m 1587448800 150 274.596 272.044 274.281 275.643 276.073 272.618 276.354 276.120 275.711 276.147 273.297 271.735 278.199 275.533 274.725 274.267 275.293 276.464 275.282 274.750 272.753 tmax2m 1587470400 156 284.548 279.085 286.052 284.524 287.279 283.163 284.068 277.686 281.076 285.473 281.614 281.079 282.521 282.376 284.502 283.348 279.947 287.285 281.133 283.460 281.445 tmax2m 1587492000 162 284.752 280.081 286.309 284.731 287.373 283.829 284.049 277.060 281.201 286.177 281.975 281.383 281.843 282.928 284.980 283.756 280.029 287.688 281.370 283.707 282.041 tmax2m 1587513600 168 276.479 274.473 275.761 278.969 277.274 275.115 278.063 273.865 274.638 278.099 274.509 274.459 278.290 276.242 276.693 276.553 273.292 277.072 274.646 276.308 275.859 tmax2m 1587535200 174 275.989 271.822 277.207 277.068 276.318 274.329 275.727 271.908 272.250 278.242 272.846 271.719 276.878 274.789 275.995 274.040 271.296 276.505 274.370 274.664 272.267 tmax2m 1587556800 180 285.925 282.580 287.031 285.951 286.008 282.040 283.712 276.818 278.863 288.399 281.189 279.812 280.043 282.570 286.077 283.867 280.594 284.348 283.377 283.857 281.440 tmax2m 1587578400 186 286.145 283.277 287.231 285.795 286.196 282.056 283.925 277.735 279.044 288.345 281.172 280.069 280.628 282.468 286.608 284.148 280.724 284.434 283.170 284.120 281.883 tmax2m 1587600000 192 276.683 275.725 279.331 279.912 277.685 275.898 275.542 276.010 275.230 278.921 274.680 273.114 277.894 275.678 277.866 277.430 273.634 277.183 274.294 276.695 274.480 tmax2m 1587621600 198 276.960 276.027 278.570 279.378 278.736 275.801 274.781 275.048 273.865 279.457 272.218 269.896 276.166 273.823 275.360 275.320 273.441 275.851 274.174 276.606 274.875 tmax2m 1587643200 204 285.572 287.031 283.277 284.506 291.147 285.616 284.765 280.683 282.134 288.943 281.598 278.697 282.494 279.331 283.697 282.587 282.463 283.587 281.988 287.992 283.017 tmax2m 1587664800 210 285.602 287.311 283.594 285.161 291.202 285.855 284.826 280.744 282.418 287.681 281.966 278.712 282.653 279.177 284.145 281.814 282.561 283.077 282.002 287.934 283.008 tmax2m 1587686400 216 277.807 278.275 278.169 280.724 281.693 276.840 276.133 277.565 276.661 280.486 275.089 272.974 277.846 271.698 277.585 277.210 276.150 277.810 275.477 279.735 273.997 tmax2m 1587708000 222 275.182 277.346 275.441 279.724 280.538 275.025 275.568 275.575 275.108 278.811 273.630 271.579 276.038 266.721 275.843 275.622 273.300 276.656 274.299 278.006 273.695 tmax2m 1587729600 228 287.573 282.672 282.681 285.859 289.376 284.771 285.104 278.714 283.590 285.312 283.120 280.968 284.481 274.285 287.425 280.536 275.700 284.633 279.307 280.729 281.604 tmax2m 1587751200 234 287.530 281.970 282.693 285.692 288.233 285.586 285.624 278.648 283.731 284.024 283.338 281.028 284.589 274.833 287.335 280.555 275.689 284.443 277.245 280.518 281.926 tmax2m 1587772800 240 277.347 277.586 276.436 281.014 282.394 276.825 277.221 276.666 275.318 279.597 275.023 273.770 276.678 269.077 277.693 276.418 273.100 279.054 273.584 278.316 275.563 dd10m 1586930400 6 192.590 187.489 184.965 190.897 195.838 187.661 193.768 200.182 199.450 192.338 195.378 193.789 188.681 191.483 192.597 192.428 202.482 193.491 190.712 185.549 192.368 dd10m 1586952000 12 40.522 43.430 41.964 39.360 42.910 44.529 37.809 36.862 34.981 43.406 40.288 35.754 33.044 41.800 40.352 48.819 46.209 31.118 46.717 49.343 42.014 dd10m 1586973600 18 99.757 102.769 110.339 103.127 111.183 111.937 84.770 90.278 96.976 100.846 89.808 85.219 100.134 109.971 87.512 108.386 96.621 97.139 107.875 110.669 99.133 dd10m 1586995200 24 190.399 191.198 191.649 189.047 192.892 189.803 190.243 191.080 189.151 188.863 187.928 183.808 191.712 192.437 191.649 193.266 188.105 188.510 190.106 190.837 191.036 dd10m 1587016800 30 210.077 210.184 212.970 208.259 210.747 209.536 206.672 210.592 206.094 207.990 207.957 208.285 210.661 209.860 210.184 212.287 209.912 211.061 208.622 211.655 208.954 dd10m 1587038400 36 274.328 293.290 298.990 260.213 290.677 275.000 283.880 288.887 262.724 253.466 269.278 271.471 268.232 278.180 277.964 275.863 271.532 269.150 258.744 278.883 276.332 dd10m 1587060000 42 0.294 13.952 3.470 2.007 2.362 353.743 348.367 1.515 355.986 329.672 359.932 354.711 1.717 359.383 1.390 19.896 359.357 345.656 349.445 356.855 348.363 dd10m 1587081600 48 264.176 254.576 233.303 236.116 268.889 253.901 304.020 264.102 243.118 236.165 284.179 308.886 265.912 245.788 218.741 226.566 248.477 281.422 243.329 282.698 316.183 dd10m 1587103200 54 241.019 248.230 219.913 232.933 261.923 252.532 264.818 232.785 228.342 231.999 252.574 239.252 244.263 227.906 230.921 241.339 237.557 257.291 254.520 245.299 244.677 dd10m 1587124800 60 336.135 338.559 347.614 328.692 335.986 331.546 334.753 335.956 333.021 339.922 341.968 357.735 334.929 336.519 343.353 337.594 341.805 332.909 338.714 340.458 350.521 dd10m 1587146400 66 7.159 357.464 14.799 7.736 12.604 16.163 14.704 16.137 26.551 7.036 16.376 32.604 5.067 20.856 17.833 26.816 28.661 13.604 5.727 5.899 19.575 dd10m 1587168000 72 247.841 269.269 288.403 276.648 239.559 224.116 240.259 233.883 224.556 241.090 245.321 252.108 234.990 233.053 233.723 236.055 243.203 229.417 225.636 283.292 234.684 dd10m 1587189600 78 256.115 276.690 291.408 265.680 270.538 238.995 231.460 261.167 257.980 256.314 287.819 249.245 230.949 247.614 231.696 270.612 285.969 255.905 240.612 270.091 234.160 dd10m 1587211200 84 310.317 327.995 334.575 323.734 321.913 295.269 322.854 311.960 347.833 321.318 349.341 322.569 303.367 306.268 312.012 322.687 358.118 358.326 265.238 332.830 289.605 dd10m 1587232800 90 57.411 24.069 12.820 79.559 18.528 18.421 65.392 36.224 96.420 37.578 42.824 352.768 127.773 36.029 56.257 341.649 74.731 65.341 128.302 8.654 21.156 dd10m 1587254400 96 205.782 215.203 234.596 184.329 237.727 233.016 203.869 200.260 201.688 193.562 211.741 305.873 192.882 199.588 207.571 239.868 190.428 191.952 198.577 248.666 210.152 dd10m 1587276000 102 308.660 18.223 0.335 210.379 357.390 325.162 335.459 196.729 243.846 260.236 261.468 8.399 216.855 343.700 338.346 345.676 178.982 209.782 221.374 353.923 221.886 dd10m 1587297600 108 33.602 40.118 37.482 34.772 39.081 12.352 31.275 142.479 5.977 8.880 21.118 44.359 331.658 31.769 28.478 46.099 48.646 341.026 281.418 34.394 52.947 dd10m 1587319200 114 65.047 71.273 63.391 77.453 62.755 65.352 70.371 78.559 32.840 54.879 48.087 48.607 129.576 72.284 58.445 48.727 51.799 40.653 26.099 77.785 70.861 dd10m 1587340800 120 131.078 140.104 106.122 131.147 146.849 95.491 139.920 129.171 93.067 105.771 94.975 103.250 160.560 137.167 124.618 101.940 107.010 81.647 94.281 134.424 88.473 dd10m 1587362400 126 90.950 101.670 76.041 122.799 164.610 70.433 135.612 103.302 109.867 104.206 89.051 72.404 150.531 149.435 90.306 106.645 115.173 116.466 111.528 93.934 69.820 dd10m 1587384000 132 69.440 74.020 71.744 126.312 44.585 51.142 96.008 102.673 103.907 95.196 73.346 47.465 159.155 109.969 75.322 72.610 100.837 115.665 89.062 76.363 62.342 dd10m 1587405600 138 72.509 102.031 79.659 129.340 45.044 59.065 106.542 90.662 96.335 105.766 71.207 48.094 148.239 48.415 71.935 79.419 96.641 136.417 71.059 78.644 71.269 dd10m 1587427200 144 108.584 131.150 139.359 146.630 86.467 92.481 120.788 100.401 98.389 146.964 79.657 66.079 161.756 75.582 108.232 123.277 102.600 175.891 73.630 112.890 120.714 dd10m 1587448800 150 105.241 129.802 144.851 152.957 107.293 94.169 97.781 68.165 68.929 143.292 65.781 54.785 151.355 71.044 105.157 129.100 56.825 170.595 59.195 51.018 121.713 dd10m 1587470400 156 74.709 113.803 84.586 139.887 85.134 81.067 67.840 46.890 64.120 112.896 58.244 51.366 86.064 81.530 67.677 112.856 59.265 88.624 62.534 49.816 91.505 dd10m 1587492000 162 74.772 113.592 96.569 148.842 102.944 84.069 80.143 33.361 68.634 109.693 67.128 50.773 82.823 85.226 63.489 110.432 67.602 71.495 69.884 56.044 64.284 dd10m 1587513600 168 145.017 155.333 190.232 173.744 182.920 158.276 120.253 72.250 107.159 183.154 121.820 49.211 119.427 147.235 99.327 164.204 102.046 158.022 137.352 108.449 78.663 dd10m 1587535200 174 98.567 147.031 238.143 173.299 234.263 44.986 43.601 103.930 118.368 181.747 60.095 12.102 123.973 86.665 46.236 155.940 75.721 26.014 115.702 19.912 54.220 dd10m 1587556800 180 65.496 117.745 331.992 183.705 350.314 62.376 42.411 106.427 111.588 69.852 47.444 17.718 103.842 53.294 41.024 106.650 62.789 47.930 60.755 29.212 49.838 dd10m 1587578400 186 63.344 131.411 326.197 175.345 26.649 82.429 54.697 100.465 115.629 94.946 45.383 32.608 80.671 58.140 22.738 129.321 69.501 48.892 44.413 41.927 57.655 dd10m 1587600000 192 256.052 186.413 278.302 211.263 203.745 164.134 143.541 146.500 154.086 180.905 47.145 41.803 98.249 68.377 2.891 169.238 146.164 112.343 190.506 164.235 157.074 dd10m 1587621600 198 307.932 198.177 313.882 237.849 203.910 192.390 156.436 134.403 148.722 203.868 36.799 58.199 86.236 14.660 16.104 174.345 122.974 140.138 342.353 197.092 30.905 dd10m 1587643200 204 344.786 26.046 321.796 81.712 227.845 34.352 50.211 98.728 78.253 111.230 37.706 53.852 69.199 11.617 32.243 136.714 62.104 56.831 23.640 205.188 24.077 dd10m 1587664800 210 11.409 93.414 356.321 92.548 197.533 25.923 59.735 103.547 64.505 189.628 44.246 56.911 66.114 14.795 51.021 169.957 55.182 41.127 19.364 210.286 20.627 dd10m 1587686400 216 125.785 200.254 27.100 173.827 213.128 308.660 188.590 186.226 206.304 209.983 158.273 130.827 143.933 23.949 149.339 206.229 166.417 199.270 9.614 219.030 17.739 dd10m 1587708000 222 165.508 337.482 40.126 193.713 211.272 344.969 256.596 191.271 327.953 220.806 170.156 118.490 36.799 25.903 168.199 229.683 27.389 218.413 22.572 263.935 11.633 dd10m 1587729600 228 69.829 36.328 42.702 172.760 234.775 21.328 359.769 116.460 344.324 204.807 23.968 39.912 35.558 26.350 56.824 312.442 39.738 49.680 39.443 277.321 11.214 dd10m 1587751200 234 81.534 36.042 38.220 230.562 281.029 19.187 0.535 294.771 333.043 195.739 17.376 30.897 29.700 24.889 91.592 323.253 27.057 96.598 32.955 307.392 18.527 dd10m 1587772800 240 204.355 86.229 68.202 228.056 199.698 248.567 281.178 335.000 247.058 189.149 265.880 119.123 200.611 15.855 214.512 275.835 28.468 179.640 54.265 215.159 59.556 ff10m 1586930400 6 1.137 1.189 1.120 1.086 1.040 1.308 1.099 1.141 1.220 1.167 1.330 0.924 1.239 1.076 1.001 1.223 0.786 1.236 1.124 1.182 1.277 ff10m 1586952000 12 1.807 1.999 1.734 1.912 1.715 1.724 2.096 1.926 1.846 1.616 1.866 2.082 1.189 1.430 1.836 1.771 1.806 1.717 1.791 1.811 1.912 ff10m 1586973600 18 1.355 1.348 1.339 1.414 1.227 1.395 1.359 1.332 1.405 1.266 1.432 1.524 1.329 1.398 1.337 1.250 1.358 1.383 1.418 1.391 1.407 ff10m 1586995200 24 2.559 2.586 2.600 2.674 2.499 2.648 2.489 2.500 2.563 2.549 2.520 2.581 2.575 2.638 2.498 2.504 2.520 2.624 2.560 2.655 2.549 ff10m 1587016800 30 2.299 2.356 2.293 2.387 2.300 2.397 2.223 2.286 2.362 2.345 2.282 2.275 2.214 2.331 2.350 2.251 2.269 2.278 2.329 2.331 2.314 ff10m 1587038400 36 1.220 1.115 1.383 1.271 1.311 1.185 1.210 1.247 1.227 1.137 1.237 1.235 1.098 1.256 1.407 1.065 1.377 1.052 1.003 1.147 1.137 ff10m 1587060000 42 0.856 0.752 1.156 0.930 1.007 0.910 1.016 0.993 0.731 0.510 0.912 0.886 0.867 0.830 0.993 0.900 0.930 0.717 0.582 1.069 0.719 ff10m 1587081600 48 0.491 0.723 0.448 0.969 0.722 0.533 0.828 0.439 0.739 0.589 0.492 0.398 0.383 0.636 0.341 1.103 0.797 0.478 0.535 0.629 0.546 ff10m 1587103200 54 1.000 1.085 1.262 1.206 1.343 1.080 1.095 1.165 1.266 0.909 0.746 0.709 1.107 1.230 1.201 1.126 1.191 0.862 0.919 1.130 0.823 ff10m 1587124800 60 1.493 1.800 1.397 1.453 2.065 1.504 1.793 1.364 1.281 1.179 1.360 1.645 1.755 1.548 1.279 1.391 1.390 1.692 1.388 1.548 1.279 ff10m 1587146400 66 1.343 1.489 1.404 1.195 1.537 1.219 1.423 0.996 1.027 1.383 1.416 1.247 1.493 1.098 1.382 1.150 1.160 1.477 1.344 1.510 1.186 ff10m 1587168000 72 1.138 1.261 1.217 1.098 1.201 1.863 1.225 1.701 1.477 1.147 1.201 1.380 1.128 1.489 1.200 1.666 1.181 1.368 1.387 0.759 1.586 ff10m 1587189600 78 0.799 1.049 1.125 1.008 0.700 1.406 1.119 0.991 0.844 1.071 0.871 0.918 0.844 1.061 0.819 1.201 0.791 0.754 0.981 0.994 1.164 ff10m 1587211200 84 1.239 2.210 2.099 1.542 1.448 1.667 0.975 1.494 0.562 1.473 1.659 1.742 0.904 1.589 0.827 2.306 1.527 0.668 0.639 2.078 1.364 ff10m 1587232800 90 1.202 1.636 1.476 1.327 1.534 0.580 1.089 0.884 0.604 1.008 1.531 1.755 0.881 1.242 1.095 1.629 1.347 1.164 0.603 1.651 1.111 ff10m 1587254400 96 1.892 1.243 1.177 2.361 1.141 1.615 1.820 2.449 2.078 1.494 1.702 1.436 3.013 1.506 1.834 1.177 1.974 2.304 2.271 1.595 1.709 ff10m 1587276000 102 0.319 0.859 1.666 0.849 0.880 1.316 1.037 1.853 0.834 0.537 0.378 2.452 1.940 0.825 0.819 1.694 1.222 1.554 1.371 2.275 0.152 ff10m 1587297600 108 3.594 2.623 3.577 2.837 2.388 3.165 3.201 0.791 2.398 2.420 1.681 3.054 0.835 2.912 3.369 2.539 1.533 2.122 1.679 3.460 2.270 ff10m 1587319200 114 2.689 2.642 2.919 2.495 2.778 2.426 2.243 1.380 2.767 2.646 3.269 3.034 1.265 2.742 2.500 3.190 2.864 3.119 3.007 2.783 2.201 ff10m 1587340800 120 1.938 1.962 2.068 2.477 1.938 1.821 1.953 1.296 1.873 2.124 2.031 1.609 2.756 2.384 1.607 2.109 2.112 2.442 2.019 2.054 1.643 ff10m 1587362400 126 1.991 1.897 2.443 2.927 1.603 2.400 1.831 1.670 2.252 2.281 2.429 1.118 2.791 2.071 1.742 2.227 2.009 2.666 1.935 1.684 2.465 ff10m 1587384000 132 4.021 3.912 3.814 3.480 3.788 4.245 3.010 2.592 2.976 3.186 3.691 3.607 3.077 1.702 3.792 3.842 2.843 3.135 2.766 3.374 4.413 ff10m 1587405600 138 3.520 3.920 3.060 3.260 2.728 3.954 2.448 2.542 2.723 2.534 3.039 3.350 2.243 2.202 3.537 3.450 2.176 2.680 2.757 2.834 4.131 ff10m 1587427200 144 2.495 3.382 2.121 3.231 1.644 2.460 1.786 2.119 2.379 2.137 2.296 1.840 2.095 2.219 2.601 2.844 1.925 2.274 2.526 1.569 3.441 ff10m 1587448800 150 1.984 3.161 1.767 3.503 1.531 2.513 1.651 2.127 3.072 1.882 2.834 2.722 1.572 3.264 1.857 2.774 3.701 1.274 3.546 2.425 2.898 ff10m 1587470400 156 3.294 3.501 2.655 3.806 2.609 3.261 3.428 3.969 4.391 2.333 4.600 4.259 1.899 3.983 3.591 3.220 4.860 1.434 4.302 4.192 3.244 ff10m 1587492000 162 2.588 2.888 1.793 3.605 1.480 2.504 2.451 3.712 3.990 1.602 3.168 3.019 2.141 2.759 2.687 2.505 3.757 1.560 3.412 2.733 3.139 ff10m 1587513600 168 1.581 2.374 1.852 4.106 2.031 1.418 0.946 2.735 3.163 1.561 1.805 1.128 2.131 1.638 1.358 2.516 2.050 0.460 2.227 0.685 1.728 ff10m 1587535200 174 1.079 2.014 1.109 3.902 1.073 1.494 1.462 3.145 3.150 0.396 1.970 2.563 2.127 1.109 0.970 2.551 2.278 1.866 1.293 1.657 2.451 ff10m 1587556800 180 2.900 2.655 2.122 3.440 2.487 3.516 4.344 3.659 3.573 2.079 4.760 4.699 2.296 3.278 3.132 2.801 4.088 3.737 3.106 3.471 4.214 ff10m 1587578400 186 1.876 1.939 1.465 1.986 1.805 2.533 3.417 2.339 3.012 1.402 3.493 3.981 2.092 2.245 2.691 2.749 2.687 2.974 2.103 2.265 2.883 ff10m 1587600000 192 1.094 2.308 1.808 2.476 1.434 1.964 1.942 2.020 2.502 1.863 1.327 2.149 2.100 1.122 1.746 2.869 1.629 1.327 0.983 1.334 1.315 ff10m 1587621600 198 1.622 1.957 1.855 0.894 1.772 0.632 1.626 1.479 1.723 1.772 1.420 2.111 1.749 2.005 1.949 2.435 0.889 0.538 0.986 1.834 1.124 ff10m 1587643200 204 4.025 0.490 3.147 0.459 0.834 3.035 2.239 1.455 2.061 0.404 3.546 3.657 2.909 3.999 3.381 1.173 2.498 0.980 2.659 0.681 3.712 ff10m 1587664800 210 3.074 0.837 3.029 0.994 0.277 2.302 1.662 0.811 1.542 0.554 2.362 3.034 2.181 4.273 2.412 1.028 1.606 0.840 1.561 1.473 2.331 ff10m 1587686400 216 0.814 1.363 1.589 1.365 2.222 0.276 1.942 1.370 1.025 2.154 1.298 1.079 0.918 2.803 1.511 1.958 1.023 1.868 1.288 3.090 0.922 ff10m 1587708000 222 1.376 0.513 1.439 1.111 1.856 0.972 0.982 1.052 0.745 1.793 0.271 0.221 0.825 2.908 1.456 1.269 0.574 0.849 1.578 1.955 1.958 ff10m 1587729600 228 1.224 2.166 2.827 0.533 1.068 3.261 2.901 0.472 1.949 1.673 2.200 2.208 2.554 4.436 1.373 0.755 2.541 0.372 2.371 1.342 4.099 ff10m 1587751200 234 0.708 2.574 2.958 0.676 0.795 1.793 1.932 0.673 1.075 1.955 1.467 1.846 1.697 3.637 0.489 1.008 2.377 0.760 2.994 0.651 3.176 ff10m 1587772800 240 1.837 1.365 1.465 1.473 1.333 0.907 0.953 1.335 2.167 3.324 1.575 0.588 1.771 0.361 2.110 0.764 1.787 1.850 2.015 1.590 0.488 apcpsfc 1586930400 6 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 apcpsfc 1586952000 12 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 apcpsfc 1586973600 18 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 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0.123 0.137 0.067 0.000 0.026 0.282 0.164 0.195 0.024 0.032 apcpsfc 1587146400 66 1.278 1.701 1.631 1.451 1.834 1.382 1.339 1.061 0.509 1.037 1.341 1.525 1.551 1.347 1.161 1.149 1.752 1.218 1.578 1.389 1.309 apcpsfc 1587168000 72 0.515 0.690 1.313 1.133 0.328 0.201 0.251 0.412 0.070 0.126 0.226 0.160 0.403 0.272 0.153 0.132 0.258 0.180 0.298 0.458 0.079 apcpsfc 1587189600 78 0.028 0.088 0.234 0.253 0.037 0.114 0.010 0.009 0.030 0.013 0.039 0.068 0.020 0.098 0.018 0.088 0.098 0.030 0.000 0.009 0.002 apcpsfc 1587211200 84 0.344 0.754 0.827 0.837 0.225 0.241 0.070 0.283 0.417 0.191 0.378 0.281 0.145 0.459 0.176 0.792 0.580 0.125 0.142 0.413 0.224 apcpsfc 1587232800 90 1.243 1.938 2.365 1.579 1.639 1.838 0.944 1.878 4.272 0.639 1.814 1.928 1.459 1.492 1.427 2.905 1.747 0.815 1.676 1.457 1.084 apcpsfc 1587254400 96 0.009 0.232 0.115 0.963 0.063 2.295 0.274 0.059 1.006 0.086 0.083 0.686 0.506 0.578 0.091 0.809 0.058 0.007 0.610 0.117 0.111 apcpsfc 1587276000 102 0.043 0.000 0.045 2.017 0.009 2.239 0.217 0.849 1.441 2.151 0.001 0.229 1.018 0.509 0.210 0.457 0.048 0.332 1.951 0.267 0.075 apcpsfc 1587297600 108 0.397 0.371 0.140 1.889 0.127 3.417 0.800 3.868 2.628 6.388 0.472 0.201 0.492 0.912 0.555 0.595 1.015 2.838 1.903 0.341 0.528 apcpsfc 1587319200 114 0.291 0.572 0.000 2.211 1.174 0.540 1.824 8.084 5.066 2.697 2.173 0.170 3.136 0.657 0.390 1.656 1.389 5.861 6.161 0.000 2.538 apcpsfc 1587340800 120 0.121 0.203 0.000 2.558 0.023 0.524 0.413 8.987 0.305 0.122 0.169 0.092 1.385 0.196 0.100 0.439 0.170 1.684 0.678 0.099 3.477 apcpsfc 1587362400 126 0.583 1.474 0.000 1.469 0.076 1.995 0.492 7.830 0.249 0.992 0.100 0.074 2.659 1.034 0.275 0.423 0.140 0.034 0.222 0.100 5.955 apcpsfc 1587384000 132 0.618 6.075 0.000 4.201 0.008 0.492 1.319 9.652 6.899 1.336 0.264 0.000 3.589 2.668 0.332 0.760 0.617 0.416 4.445 0.000 6.974 apcpsfc 1587405600 138 0.418 6.804 0.000 2.412 0.000 0.201 2.810 6.832 8.795 1.591 0.129 0.000 0.862 15.093 0.368 0.675 1.317 0.189 12.806 0.014 5.960 apcpsfc 1587427200 144 0.131 2.105 0.000 0.425 0.000 0.081 1.039 3.778 2.318 0.143 0.019 0.000 0.308 3.548 0.106 0.344 0.871 0.000 2.275 0.010 1.921 apcpsfc 1587448800 150 0.048 0.937 0.000 0.274 0.000 0.010 0.254 5.373 0.261 0.048 0.014 0.000 0.222 0.128 0.000 0.142 0.218 0.000 0.315 0.024 0.153 apcpsfc 1587470400 156 0.000 0.239 0.000 0.217 0.000 0.000 0.122 3.052 0.153 0.143 0.000 0.000 1.738 0.048 0.000 0.048 0.025 0.000 0.000 0.000 0.048 apcpsfc 1587492000 162 0.000 0.048 0.000 0.148 0.000 0.000 0.224 2.974 0.452 0.048 0.000 0.000 6.002 0.010 0.000 0.000 0.000 0.000 0.000 0.000 0.143 apcpsfc 1587513600 168 0.000 0.000 0.000 0.005 0.000 0.000 0.000 6.522 0.858 0.000 0.000 0.000 2.372 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 apcpsfc 1587535200 174 0.000 0.000 0.000 0.041 0.000 0.000 0.010 4.097 0.908 0.000 0.000 0.000 1.071 0.010 0.000 0.000 0.000 0.000 0.000 0.000 0.000 apcpsfc 1587556800 180 0.000 0.000 0.000 0.217 0.000 0.026 0.000 1.933 0.675 0.000 0.000 0.045 3.068 0.015 0.000 0.000 0.000 0.026 0.000 0.000 0.000 apcpsfc 1587578400 186 0.000 0.000 1.272 0.426 0.000 0.364 0.000 1.745 1.361 0.000 0.000 0.004 7.424 0.148 0.000 0.201 0.003 1.327 0.048 0.000 0.000 apcpsfc 1587600000 192 0.000 0.000 1.121 0.114 0.000 0.000 0.000 0.366 0.282 0.000 0.005 0.000 6.093 0.201 0.000 0.170 0.024 1.502 0.000 0.000 0.000 apcpsfc 1587621600 198 0.000 0.000 0.795 0.540 0.000 0.000 0.007 0.678 0.010 0.000 0.003 0.003 0.312 0.129 0.000 0.441 0.003 0.438 0.011 0.000 0.000 apcpsfc 1587643200 204 0.000 0.000 1.595 2.045 0.000 0.000 0.000 1.159 0.179 1.351 0.000 0.006 0.206 0.117 0.000 1.639 0.056 1.658 0.129 0.000 0.000 apcpsfc 1587664800 210 0.013 0.259 1.620 5.848 0.303 0.040 0.046 5.057 0.681 4.266 0.000 0.129 0.240 0.530 0.000 4.327 1.224 4.371 0.512 2.199 0.000 apcpsfc 1587686400 216 0.000 0.005 0.447 4.018 0.156 0.003 0.005 3.443 0.079 0.254 0.005 0.068 0.005 0.218 0.000 2.277 1.494 1.519 0.100 3.545 0.000 apcpsfc 1587708000 222 0.000 0.215 0.023 0.706 0.026 0.000 0.000 3.004 0.003 0.357 0.003 0.000 0.000 0.014 0.000 1.792 2.540 0.631 0.141 4.994 0.000 apcpsfc 1587729600 228 0.000 1.985 0.100 2.264 0.577 0.000 0.000 4.284 0.003 2.682 0.003 0.022 0.000 0.005 0.000 3.347 4.599 0.965 1.781 5.681 0.004 apcpsfc 1587751200 234 0.032 6.835 3.377 9.964 4.562 0.000 0.000 7.548 0.027 3.954 0.021 0.353 0.007 0.005 0.065 6.366 8.500 4.691 8.561 9.314 0.128 apcpsfc 1587772800 240 0.000 3.325 3.721 6.382 1.804 0.000 0.000 8.499 0.003 1.013 0.000 0.284 0.000 0.000 0.000 2.033 6.003 3.792 4.295 5.665 0.000 tmp2m 1586930400 6 269.344 269.341 269.392 269.532 269.284 269.144 269.274 269.391 269.369 269.358 269.111 269.524 269.413 269.583 269.385 269.365 269.418 269.229 269.227 269.249 269.191 tmp2m 1586952000 12 279.285 279.435 279.411 279.358 279.547 279.378 279.173 279.455 279.490 279.532 279.084 279.508 279.843 279.760 279.202 279.409 279.133 279.496 279.399 279.394 279.320 tmp2m 1586973600 18 271.477 271.669 271.912 271.994 271.482 272.147 270.890 271.208 271.606 271.255 271.329 271.721 271.391 272.142 271.112 271.486 271.484 271.529 271.917 272.185 271.594 tmp2m 1586995200 24 273.035 273.130 273.087 273.230 272.978 272.992 272.761 273.026 273.018 273.074 272.961 272.974 273.035 273.161 272.978 273.004 273.009 273.070 273.061 273.018 272.887 tmp2m 1587016800 30 275.281 275.484 275.167 275.154 275.303 274.897 275.561 275.491 275.450 275.298 275.408 275.398 275.429 275.241 275.415 275.411 275.272 275.346 275.298 274.949 275.276 tmp2m 1587038400 36 283.396 283.876 283.506 282.918 283.597 283.423 283.236 283.614 283.343 283.269 283.043 283.043 283.561 283.623 283.479 283.683 283.040 283.408 283.256 283.597 283.518 tmp2m 1587060000 42 275.193 275.509 275.266 275.509 275.167 274.944 277.030 275.568 275.830 275.899 275.335 275.773 276.503 274.996 275.207 275.148 275.011 276.236 275.567 275.351 275.572 tmp2m 1587081600 48 272.607 272.724 272.314 272.111 273.399 272.145 274.048 272.610 272.407 272.231 272.502 272.521 272.910 272.497 272.442 272.414 272.808 274.142 273.293 273.204 273.366 tmp2m 1587103200 54 277.156 277.289 277.152 277.113 277.051 277.112 276.900 277.063 277.147 277.247 277.273 277.102 277.237 277.294 277.230 277.278 277.278 277.206 277.190 277.056 277.185 tmp2m 1587124800 60 285.991 285.565 285.951 286.118 285.106 285.883 285.170 286.065 286.666 286.375 286.130 285.403 285.551 286.000 286.467 286.544 285.879 285.804 285.595 285.841 286.100 tmp2m 1587146400 66 277.840 278.178 278.762 278.348 277.617 277.979 277.620 277.608 278.337 278.590 278.381 278.002 277.848 278.110 278.455 277.967 278.063 277.900 277.911 277.854 277.914 tmp2m 1587168000 72 274.938 275.317 275.624 275.237 274.623 275.967 274.925 275.644 275.169 275.059 275.203 274.652 275.339 275.252 275.003 275.530 274.762 275.180 274.928 275.032 275.380 tmp2m 1587189600 78 278.569 278.054 277.783 278.171 278.263 278.736 278.455 278.374 278.990 278.693 278.632 278.292 278.629 278.649 278.841 278.428 278.613 278.688 278.437 278.320 278.700 tmp2m 1587211200 84 287.985 286.639 285.698 286.359 287.362 287.844 288.678 287.997 288.066 288.386 287.413 286.756 288.608 287.575 288.684 286.109 286.630 289.048 288.650 286.903 288.423 tmp2m 1587232800 90 279.020 279.144 278.666 278.779 279.445 279.849 279.208 279.492 280.288 279.372 279.378 279.137 280.147 279.122 279.453 279.544 278.801 279.727 280.299 279.148 279.152 tmp2m 1587254400 96 277.588 276.400 274.623 278.229 275.423 278.403 278.081 278.097 278.167 277.897 276.520 275.469 279.136 277.476 277.860 276.153 277.109 277.900 278.523 276.065 277.562 tmp2m 1587276000 102 279.235 278.724 277.154 278.733 278.988 278.942 279.499 279.776 279.586 279.222 279.310 277.131 279.365 278.702 279.126 277.772 278.949 279.783 279.141 277.960 279.640 tmp2m 1587297600 108 285.264 285.830 282.716 283.667 287.097 281.248 285.772 283.485 284.259 281.962 286.883 282.658 285.904 283.883 284.502 283.575 285.367 283.358 284.681 283.218 285.358 tmp2m 1587319200 114 279.819 279.591 277.020 280.005 280.236 278.505 280.572 279.913 280.480 279.679 280.626 277.965 281.424 279.745 279.337 279.137 280.356 279.655 279.541 277.637 280.493 tmp2m 1587340800 120 277.628 277.794 273.519 277.928 277.743 276.547 278.143 278.406 277.810 275.958 276.470 274.196 279.288 277.904 276.854 276.100 276.114 276.697 276.323 276.658 277.723 tmp2m 1587362400 126 277.543 276.961 274.611 277.401 279.209 275.652 278.011 277.348 277.370 277.035 277.157 276.141 278.898 278.351 277.401 276.245 277.238 276.424 277.451 277.840 276.139 tmp2m 1587384000 132 282.142 278.212 282.718 280.587 288.345 279.712 282.585 279.948 280.770 281.885 282.424 283.354 282.391 282.223 282.044 280.291 282.418 282.588 281.066 285.951 277.743 tmp2m 1587405600 138 277.465 275.482 275.716 278.282 280.152 275.889 279.344 278.492 278.609 279.146 277.172 276.045 280.465 278.692 277.506 276.816 278.694 279.098 278.224 278.359 275.341 tmp2m 1587427200 144 273.658 272.060 271.511 275.222 273.892 272.207 276.431 276.167 275.595 275.192 273.106 270.703 277.584 275.494 273.445 274.211 275.323 273.527 275.535 273.667 272.838 tmp2m 1587448800 150 274.553 271.362 274.248 275.626 275.922 272.575 276.121 274.786 274.579 276.122 272.276 271.735 277.991 274.813 274.606 273.701 273.503 276.464 273.883 274.654 272.357 tmp2m 1587470400 156 284.548 279.085 286.052 284.524 287.279 283.163 284.068 277.202 281.076 285.473 281.614 281.079 282.067 282.376 284.502 283.348 279.894 287.285 281.072 283.434 281.323 tmp2m 1587492000 162 276.963 274.720 276.278 279.372 277.930 275.546 278.467 274.039 274.977 278.594 274.931 274.851 278.325 276.791 277.133 276.813 273.662 277.952 275.014 276.777 276.307 tmp2m 1587513600 168 272.158 269.606 273.112 275.070 273.289 271.613 272.662 271.448 271.856 273.776 270.293 269.257 276.850 272.709 271.521 271.850 269.226 273.307 271.204 270.787 270.843 tmp2m 1587535200 174 275.989 271.788 277.207 277.068 276.318 274.329 275.784 271.908 272.059 278.194 272.829 271.719 276.476 274.772 275.995 274.014 271.263 276.502 274.335 274.664 272.225 tmp2m 1587556800 180 285.925 282.580 287.031 285.409 285.907 282.040 283.712 276.818 278.863 288.351 281.036 279.812 280.008 282.443 286.077 283.884 280.603 284.322 283.250 283.725 281.440 tmp2m 1587578400 186 277.462 276.038 279.657 280.203 278.274 276.387 276.086 276.145 275.464 279.473 275.072 273.623 277.955 275.804 278.277 277.681 274.156 277.379 275.157 277.087 274.844 tmp2m 1587600000 192 272.094 271.208 276.973 275.770 273.528 271.671 271.268 272.521 270.799 275.148 269.419 268.281 275.424 272.349 273.533 272.331 269.842 273.892 270.122 271.060 270.122 tmp2m 1587621600 198 276.960 276.027 278.523 279.226 278.736 275.801 274.765 275.048 273.822 279.412 272.218 269.896 275.816 273.823 275.313 275.320 273.441 275.825 274.158 276.540 274.875 tmp2m 1587643200 204 285.572 286.983 283.202 284.522 290.943 285.568 284.717 280.599 282.134 287.590 281.550 278.697 282.434 279.322 283.697 282.491 282.320 283.130 281.723 287.774 283.017 tmp2m 1587664800 210 278.499 279.551 278.523 280.784 282.653 277.556 277.199 277.807 277.262 281.227 275.709 273.439 278.303 272.238 278.142 277.595 276.891 278.362 275.971 279.806 275.432 tmp2m 1587686400 216 270.868 273.131 274.281 278.608 278.803 269.626 271.723 274.822 270.821 276.950 269.240 267.527 272.078 266.426 271.993 273.484 272.121 274.405 271.119 277.840 268.929 tmp2m 1587708000 222 275.182 277.329 275.336 279.724 280.495 275.025 275.568 275.405 275.073 278.785 273.677 271.579 276.030 266.487 275.843 275.622 273.173 276.612 274.299 277.656 273.686 tmp2m 1587729600 228 287.526 282.101 282.606 285.508 288.458 284.771 285.056 278.614 283.590 284.299 283.120 280.894 284.385 274.285 287.378 280.372 275.621 284.477 278.306 280.580 281.604 tmp2m 1587751200 234 278.245 277.882 276.626 281.015 282.800 277.827 278.261 276.792 276.232 279.965 276.169 274.444 277.362 269.837 278.909 276.936 273.184 279.241 273.930 278.427 276.233 tmp2m 1587772800 240 273.469 274.180 272.493 279.142 280.011 271.339 271.609 274.617 272.427 276.115 270.619 268.898 271.221 264.778 274.755 274.428 270.140 276.870 271.370 276.616 268.907 tcdcclm 1586930400 6 0.000 0.059 0.052 0.052 0.000 0.000 0.059 0.078 0.059 0.000 0.073 0.052 0.073 0.013 0.013 0.073 0.052 0.142 0.059 0.000 0.038 tcdcclm 1586952000 12 0.105 0.235 0.263 0.651 0.392 0.273 0.403 0.078 0.084 0.000 0.144 0.046 0.088 0.038 0.154 0.325 0.084 0.063 0.105 0.038 0.113 tcdcclm 1586973600 18 0.251 0.556 0.506 0.152 0.333 0.642 0.712 0.197 0.231 0.080 0.073 0.704 0.639 0.543 0.235 0.200 0.111 0.324 0.220 0.210 0.259 tcdcclm 1586995200 24 2.554 2.469 2.628 2.626 2.118 2.686 1.086 2.106 2.573 1.595 1.451 2.070 3.042 2.997 2.185 2.734 1.695 2.725 2.287 2.546 2.578 tcdcclm 1587016800 30 3.094 2.461 1.667 2.336 3.000 3.350 4.254 2.632 3.202 2.944 3.203 2.143 3.480 2.275 3.591 3.733 2.710 2.580 2.251 2.523 3.205 tcdcclm 1587038400 36 2.515 3.417 3.225 3.550 2.586 2.564 3.234 3.154 2.100 2.342 2.419 2.301 2.443 2.351 2.861 1.898 2.373 3.001 3.116 2.277 2.366 tcdcclm 1587060000 42 4.734 5.820 3.794 6.359 4.091 3.485 5.774 4.913 6.014 6.625 4.733 4.749 4.195 4.097 4.249 5.149 5.569 6.746 5.777 3.539 4.989 tcdcclm 1587081600 48 4.389 5.762 2.465 3.198 5.586 1.819 6.745 5.057 4.568 4.216 3.696 4.903 4.877 0.996 3.514 0.381 4.589 6.707 5.986 4.659 6.224 tcdcclm 1587103200 54 3.399 3.018 2.331 4.717 3.872 3.618 4.909 2.232 2.558 3.244 3.640 5.680 3.031 3.572 3.132 2.507 4.450 4.853 3.099 3.228 3.641 tcdcclm 1587124800 60 2.438 2.865 3.835 2.675 2.058 2.121 1.901 4.192 2.600 3.207 2.574 3.655 1.971 3.219 3.626 3.769 2.861 0.951 1.402 2.722 2.290 tcdcclm 1587146400 66 1.516 3.013 5.397 2.108 1.651 2.311 1.922 4.033 3.121 3.458 3.504 3.671 2.242 3.343 3.326 4.343 3.964 1.166 1.997 2.135 2.424 tcdcclm 1587168000 72 1.665 2.576 3.865 4.532 1.166 4.975 2.100 3.330 3.073 3.611 5.249 1.954 4.430 2.701 3.835 4.265 2.537 2.367 1.480 4.284 1.801 tcdcclm 1587189600 78 2.458 3.136 2.549 5.269 3.573 6.063 3.906 4.006 4.038 4.141 2.950 2.932 4.098 3.787 4.366 5.109 3.652 3.893 2.358 4.032 4.079 tcdcclm 1587211200 84 3.524 4.209 4.130 5.493 3.903 4.635 3.968 3.501 4.896 4.541 3.096 4.334 3.532 5.159 4.345 5.312 6.347 3.598 3.411 2.654 3.997 tcdcclm 1587232800 90 5.178 4.508 4.725 5.170 4.904 6.372 5.051 5.642 6.750 6.225 4.996 5.161 5.421 6.208 5.420 5.676 4.845 5.251 6.352 3.135 5.312 tcdcclm 1587254400 96 7.037 7.218 4.170 7.673 1.684 7.781 7.579 6.904 7.156 7.635 4.341 4.478 7.312 7.315 6.659 4.663 4.343 5.576 7.533 4.307 7.119 tcdcclm 1587276000 102 6.324 5.142 4.716 7.966 3.512 7.400 7.600 6.905 6.626 7.238 1.693 5.920 7.392 7.690 6.681 6.009 7.368 7.333 7.791 4.846 5.178 tcdcclm 1587297600 108 6.204 6.262 3.771 7.267 5.336 6.611 5.447 7.488 6.290 7.293 5.304 5.281 5.935 5.885 6.715 5.596 7.058 7.825 6.741 4.474 6.580 tcdcclm 1587319200 114 6.493 6.305 3.572 7.176 6.017 6.943 7.141 7.689 6.321 6.323 6.367 5.127 7.750 5.102 4.502 5.696 5.732 7.429 7.629 5.635 7.459 tcdcclm 1587340800 120 6.446 7.758 2.882 7.049 7.386 6.366 6.701 7.923 6.099 5.325 6.086 4.417 7.094 6.990 5.504 5.696 5.589 6.951 7.657 5.570 7.186 tcdcclm 1587362400 126 6.453 7.230 3.407 7.513 7.479 6.210 6.703 7.944 7.125 4.808 4.149 5.138 7.909 7.596 5.584 6.125 4.559 6.874 7.796 6.702 6.099 tcdcclm 1587384000 132 6.270 7.582 0.688 7.631 6.065 5.499 6.577 7.728 7.657 5.986 4.880 0.812 7.691 6.961 5.995 6.100 5.631 5.964 7.240 6.354 6.153 tcdcclm 1587405600 138 4.451 6.134 0.487 7.278 4.476 4.862 6.451 7.438 7.274 5.289 2.644 0.456 7.406 7.687 5.566 5.683 5.805 3.754 7.675 4.450 6.351 tcdcclm 1587427200 144 4.386 5.777 0.390 7.179 6.761 4.349 5.959 7.537 7.248 3.923 3.435 0.393 7.724 7.180 4.070 5.293 5.620 0.654 6.793 5.985 5.964 tcdcclm 1587448800 150 3.232 4.420 0.292 7.577 4.342 3.387 5.404 7.741 5.881 3.219 2.433 1.010 7.555 4.736 2.475 4.877 4.767 0.178 5.725 2.725 4.877 tcdcclm 1587470400 156 0.570 2.395 0.118 7.070 3.640 0.309 2.444 7.262 4.529 2.982 0.046 0.118 7.344 2.405 0.136 1.525 1.191 0.181 0.681 0.059 2.634 tcdcclm 1587492000 162 0.098 0.653 0.223 6.211 0.932 0.216 3.196 7.570 4.818 0.378 0.059 0.080 7.793 1.693 0.098 0.271 0.164 0.171 0.105 0.067 3.176 tcdcclm 1587513600 168 0.098 0.178 0.672 2.721 1.878 0.424 1.529 7.800 5.250 0.038 0.143 0.080 7.673 1.070 0.059 0.098 0.317 0.568 0.195 1.215 1.464 tcdcclm 1587535200 174 0.135 0.098 3.022 4.006 5.150 2.658 0.653 7.761 4.295 0.000 0.195 0.140 7.530 1.623 0.059 0.059 0.424 1.412 0.455 0.156 1.911 tcdcclm 1587556800 180 0.038 0.059 5.542 4.229 6.691 1.113 0.105 7.320 4.468 1.326 0.105 0.846 7.837 0.707 0.052 0.038 0.118 1.314 0.136 0.095 0.073 tcdcclm 1587578400 186 0.059 0.786 7.146 5.223 4.808 4.641 0.176 6.854 5.785 3.644 0.401 0.558 7.479 2.615 2.609 3.197 0.447 3.065 3.054 0.341 0.067 tcdcclm 1587600000 192 1.475 1.550 6.432 4.179 3.185 1.355 0.204 5.729 3.321 4.328 0.575 3.878 6.131 4.400 5.920 3.660 0.874 5.683 4.417 0.073 0.156 tcdcclm 1587621600 198 4.107 0.616 7.121 6.714 2.078 0.170 0.736 5.551 0.852 0.878 1.006 3.958 4.246 4.248 4.385 4.488 0.675 4.098 2.826 1.554 0.612 tcdcclm 1587643200 204 3.224 0.102 5.847 6.974 2.333 0.059 0.296 5.983 1.612 1.739 0.216 1.228 3.709 4.094 0.376 4.193 0.795 3.388 4.322 4.652 4.681 tcdcclm 1587664800 210 0.543 3.558 5.783 6.343 4.906 0.266 0.697 7.212 2.939 4.786 0.286 1.058 2.718 3.933 0.088 5.551 4.534 4.863 7.486 6.754 5.165 tcdcclm 1587686400 216 0.095 1.646 6.324 6.018 3.469 0.059 0.915 6.727 2.117 4.950 0.294 0.818 1.065 4.527 0.067 5.463 5.657 4.026 6.531 7.530 0.392 tcdcclm 1587708000 222 0.073 3.591 6.415 5.380 1.995 0.059 0.968 6.751 0.788 6.559 0.237 0.317 0.382 1.036 0.319 5.572 6.149 4.605 3.467 7.488 0.067 tcdcclm 1587729600 228 0.109 4.578 5.673 3.794 2.668 0.114 0.080 7.499 0.181 6.764 0.252 0.649 0.139 1.147 0.288 5.922 7.395 3.815 7.087 7.624 0.217 tcdcclm 1587751200 234 0.956 5.542 7.167 6.799 5.309 1.285 0.309 7.797 1.241 7.132 0.735 5.070 0.227 1.092 2.925 5.778 7.775 5.811 7.899 7.708 1.146 tcdcclm 1587772800 240 0.920 5.897 7.448 7.468 5.795 0.733 0.695 7.528 1.668 6.279 0.741 5.725 0.447 0.255 1.357 4.910 7.723 5.685 7.579 7.581 0.290 partykit/inst/ULGcourse-2020/Data/GENS_00_innsbruck_20200411.dat0000644000176200001440000016114414172227777023003 0ustar liggesusers# ASCII output from GENSvis.py # Contains interpolated values from the # GFS ensemble on 1.000000 x 1.000000 degrees # The data in here are for station # 11120: INNSBRUCK # Station position: 11.3553 47.2589 # Used grid point 1: 12.0000 48.0000 # Used grid point 2: 12.0000 47.0000 # Used grid point 3: 11.0000 47.0000 # Used grid point 4: 11.0000 48.0000 varname timestamp step mem0 mem1 mem2 mem3 mem4 mem5 mem6 mem7 mem8 mem9 mem10 mem11 mem12 mem13 mem14 mem15 mem16 mem17 mem18 mem19 mem20 tmax2m 1586584800 6 275.542 275.703 275.528 275.561 275.705 275.578 275.598 275.359 275.260 275.534 275.607 275.574 275.587 275.629 275.563 275.577 275.452 275.409 275.500 275.594 275.653 tmax2m 1586606400 12 284.190 283.383 284.074 284.644 284.203 284.273 283.919 283.722 283.923 284.557 283.641 283.899 283.673 283.314 284.096 284.161 284.057 284.695 283.901 284.032 284.274 tmax2m 1586628000 18 284.059 283.532 284.217 284.378 283.167 284.139 283.993 283.877 284.115 284.657 283.531 283.851 283.615 283.312 284.043 284.195 284.160 284.588 284.451 284.470 283.450 tmax2m 1586649600 24 277.687 277.855 277.691 277.887 277.924 277.457 277.735 277.319 277.457 277.762 277.794 277.638 277.733 277.803 277.741 277.724 277.809 277.592 277.618 277.689 277.818 tmax2m 1586671200 30 276.835 276.880 276.956 276.825 276.872 276.868 276.925 276.764 276.903 276.790 276.921 276.760 276.794 276.824 276.886 276.830 276.982 276.912 276.947 276.947 276.899 tmax2m 1586692800 36 284.098 284.101 284.220 284.093 283.777 283.880 284.312 283.620 283.667 283.954 283.866 283.903 284.298 284.016 284.187 284.095 284.320 283.645 284.272 283.846 283.884 tmax2m 1586714400 42 284.260 284.363 284.461 284.434 283.920 283.923 284.479 283.880 283.793 284.180 284.050 284.227 284.566 284.182 284.433 284.406 284.616 283.867 284.480 284.147 284.123 tmax2m 1586736000 48 277.436 276.914 277.547 277.168 277.373 277.569 277.685 276.968 277.321 277.360 277.574 277.119 277.167 277.546 277.556 277.578 277.613 277.470 277.700 277.389 277.282 tmax2m 1586757600 54 275.733 275.977 275.771 275.714 275.598 275.597 275.570 275.722 275.806 275.495 275.768 275.759 275.558 275.584 275.585 275.728 275.726 275.671 275.850 275.963 275.589 tmax2m 1586779200 60 284.794 284.647 284.280 284.620 284.968 284.268 282.300 284.580 284.501 284.347 284.047 285.632 284.358 283.904 284.115 283.859 284.478 285.085 283.255 284.957 283.754 tmax2m 1586800800 66 284.597 284.231 284.013 284.122 284.768 283.889 282.392 284.236 284.315 284.422 284.132 285.502 284.155 283.887 284.172 283.728 284.552 284.983 282.912 284.896 283.722 tmax2m 1586822400 72 277.410 276.778 277.371 277.342 277.301 276.937 276.401 276.839 277.271 276.698 277.224 277.663 277.005 277.027 276.876 276.989 276.436 277.251 276.964 277.397 277.158 tmax2m 1586844000 78 275.176 273.079 275.265 274.138 275.626 273.970 274.995 274.031 274.729 275.256 275.035 275.447 275.207 275.035 275.163 274.555 275.067 274.442 274.823 274.463 274.953 tmax2m 1586865600 84 278.819 277.514 280.218 278.633 280.340 277.777 274.796 277.433 281.718 276.653 277.912 280.184 278.580 278.326 279.702 277.639 280.084 278.651 278.082 279.949 278.174 tmax2m 1586887200 90 279.368 278.310 280.971 280.407 280.696 278.460 274.811 278.025 282.262 277.010 278.416 280.768 279.361 279.456 280.086 278.245 280.859 279.121 278.717 280.834 278.688 tmax2m 1586908800 96 272.627 271.812 274.166 274.832 273.621 271.777 268.727 271.724 276.106 270.960 271.970 274.586 274.005 272.902 273.248 271.486 274.757 272.477 272.527 275.400 272.055 tmax2m 1586930400 102 275.045 273.821 275.223 274.640 275.032 274.573 270.192 273.709 275.205 273.330 273.470 275.506 275.598 274.533 274.668 274.157 274.860 275.441 273.543 275.290 273.494 tmax2m 1586952000 108 286.159 284.111 284.992 283.475 287.001 286.038 282.129 285.561 283.282 285.697 285.655 283.891 287.081 286.230 283.134 285.847 285.591 283.258 285.124 284.025 284.911 tmax2m 1586973600 114 285.024 284.430 283.842 283.380 287.498 286.465 283.363 285.931 282.911 285.943 285.817 283.661 287.141 286.613 282.695 284.985 284.913 282.817 285.344 284.241 285.394 tmax2m 1586995200 120 277.516 275.573 277.262 277.734 277.887 276.753 275.394 275.250 278.260 277.178 276.941 278.545 278.644 276.388 277.407 276.968 277.783 278.079 276.033 278.094 276.849 tmax2m 1587016800 126 276.979 276.972 277.579 275.738 277.916 277.631 274.471 276.625 276.062 276.724 276.493 277.131 278.282 277.725 276.297 275.889 276.493 276.500 276.609 276.468 276.339 tmax2m 1587038400 132 288.258 288.129 288.400 286.783 287.717 287.008 285.896 288.654 286.637 289.711 289.078 288.693 288.064 288.104 287.685 287.092 287.135 287.701 287.410 286.124 287.610 tmax2m 1587060000 138 288.115 287.895 288.154 286.422 287.564 286.506 285.623 288.762 286.599 290.074 289.564 288.001 288.686 288.140 287.702 287.479 287.738 288.271 287.501 285.715 287.627 tmax2m 1587081600 144 278.833 278.001 279.445 278.677 279.927 278.221 275.451 279.276 279.856 278.534 278.047 280.167 280.206 280.639 278.426 278.715 278.696 279.603 279.247 280.314 278.510 tmax2m 1587103200 150 279.037 278.652 279.026 279.256 280.220 279.412 278.247 278.864 279.424 280.273 279.908 279.764 279.161 278.450 278.667 278.602 279.033 280.016 278.749 278.968 278.972 tmax2m 1587124800 156 290.996 287.077 290.078 290.811 288.470 290.685 289.113 288.219 287.421 291.126 290.762 289.900 289.455 291.760 289.042 288.039 287.206 289.175 288.903 288.741 289.616 tmax2m 1587146400 162 291.047 287.100 289.930 291.180 288.669 290.345 289.361 287.879 287.011 291.304 290.765 290.126 290.315 291.555 287.471 288.193 286.767 288.939 287.700 288.789 290.076 tmax2m 1587168000 168 281.797 279.394 281.794 280.813 280.868 280.787 279.168 281.048 281.653 280.939 281.043 282.618 281.936 282.858 281.072 280.193 279.160 282.108 281.459 281.919 281.838 tmax2m 1587189600 174 280.601 278.613 280.820 280.014 280.636 279.893 280.313 279.204 279.598 281.353 280.063 280.325 281.493 280.900 279.637 279.153 279.346 280.463 279.592 279.958 280.810 tmax2m 1587211200 180 290.983 289.448 290.169 288.325 291.705 290.405 289.977 284.811 289.944 290.937 291.307 290.403 290.404 289.709 286.952 284.844 288.425 288.188 288.254 290.059 291.097 tmax2m 1587232800 186 289.936 289.829 290.237 288.450 291.779 290.671 288.255 284.238 289.524 291.041 291.142 290.570 290.495 288.379 285.546 284.360 287.675 286.703 287.759 289.720 290.874 tmax2m 1587254400 192 282.768 279.671 283.399 281.079 281.777 283.107 281.082 278.588 282.403 281.957 282.010 283.635 283.691 282.382 280.837 280.317 279.945 282.046 281.203 282.674 282.639 tmax2m 1587276000 198 282.312 280.204 281.546 278.971 281.720 281.162 280.292 277.193 280.584 281.572 281.000 281.745 281.951 281.110 280.185 279.775 278.799 281.585 280.841 282.125 282.002 tmax2m 1587297600 204 289.657 289.448 291.746 287.464 289.682 289.040 288.487 281.039 289.460 292.672 289.410 291.695 292.818 283.353 286.435 287.689 289.050 288.097 287.262 289.492 292.771 tmax2m 1587319200 210 289.513 289.665 291.280 287.429 289.365 289.284 288.551 281.760 289.333 292.929 289.442 291.470 291.475 284.134 285.829 287.594 288.637 287.959 286.938 289.573 292.000 tmax2m 1587340800 216 281.858 280.432 283.430 281.091 282.059 281.572 280.864 277.121 282.598 282.693 281.747 285.415 284.609 278.447 282.261 281.292 282.438 282.720 282.150 283.160 283.485 tmax2m 1587362400 222 280.159 279.579 282.212 278.048 281.845 277.511 277.788 275.112 280.298 280.818 277.373 282.744 282.640 275.812 279.887 279.894 279.687 281.865 279.879 280.486 282.950 tmax2m 1587384000 228 286.402 287.396 292.377 287.781 288.508 284.067 284.249 282.448 288.421 285.626 284.225 290.853 290.179 282.581 287.092 283.593 287.707 287.732 286.830 291.498 287.731 tmax2m 1587405600 234 286.363 287.391 291.704 288.737 288.565 284.098 283.392 282.025 288.043 284.963 283.458 289.839 289.829 282.521 287.095 283.650 287.144 287.718 286.749 291.868 286.958 tmax2m 1587427200 240 280.246 279.756 282.661 282.129 282.830 278.637 280.201 275.727 283.238 279.205 277.658 284.953 282.573 276.881 282.324 279.225 283.072 282.144 282.504 285.730 283.335 dd10m 1586584800 6 299.846 311.041 316.112 292.726 297.302 285.701 309.436 296.989 302.683 304.860 303.103 289.348 298.754 306.660 305.545 299.263 295.391 289.351 315.158 296.773 282.533 dd10m 1586606400 12 27.436 30.794 32.544 28.917 27.893 30.586 25.065 21.068 30.560 22.672 27.638 23.718 23.411 26.941 29.901 29.285 30.750 26.641 28.586 28.844 26.192 dd10m 1586628000 18 75.469 81.577 78.768 74.002 78.612 76.165 79.354 71.705 70.440 68.618 79.755 73.353 74.984 79.477 83.715 75.573 85.021 69.358 79.220 73.952 69.970 dd10m 1586649600 24 196.819 196.081 195.291 197.918 194.713 196.407 197.125 196.001 197.512 198.086 197.492 196.784 196.879 194.982 195.807 196.484 197.617 196.181 192.296 193.674 198.611 dd10m 1586671200 30 206.906 203.835 203.512 206.175 206.155 203.655 202.342 206.025 206.401 206.267 206.654 204.833 203.568 205.030 206.445 204.459 205.012 202.889 204.866 203.138 206.518 dd10m 1586692800 36 210.413 213.586 209.952 212.530 211.937 213.299 205.566 218.323 218.333 208.344 213.901 212.693 205.560 213.449 208.195 205.970 212.183 211.459 209.199 208.278 213.286 dd10m 1586714400 42 182.377 195.704 181.198 185.912 189.648 179.186 176.510 186.628 181.358 175.629 179.858 195.450 180.707 182.259 180.325 176.473 176.890 181.407 179.583 182.693 190.546 dd10m 1586736000 48 199.452 210.202 197.224 198.452 199.958 205.322 195.549 205.589 200.161 198.195 200.192 202.314 196.360 196.355 195.516 202.262 199.556 203.814 196.557 199.661 198.492 dd10m 1586757600 54 208.318 227.962 205.879 204.853 205.353 222.595 198.803 220.771 208.087 201.873 210.716 210.678 201.521 202.157 198.808 224.913 205.748 215.859 203.935 208.369 200.474 dd10m 1586779200 60 281.961 307.924 264.835 263.308 274.012 316.091 225.324 317.086 260.956 236.976 276.580 303.546 248.004 250.455 237.113 328.137 266.662 315.421 246.908 291.134 246.737 dd10m 1586800800 66 348.252 349.322 340.168 338.546 338.265 349.353 253.092 353.603 341.370 308.592 350.030 351.792 345.263 332.995 350.980 346.819 17.776 348.093 335.082 352.196 336.282 dd10m 1586822400 72 1.932 348.618 2.041 357.308 3.011 356.012 306.833 354.975 11.187 336.609 354.934 17.928 5.324 323.911 12.179 2.896 135.829 353.492 355.093 11.997 3.265 dd10m 1586844000 78 4.742 0.002 14.247 16.246 11.374 2.096 3.584 355.160 23.004 353.385 358.761 15.689 19.313 0.850 20.642 7.360 25.305 351.457 0.233 28.954 5.386 dd10m 1586865600 84 18.031 15.411 24.685 54.291 17.301 17.782 355.702 11.919 52.834 3.909 358.884 28.702 33.802 11.580 34.279 7.615 45.352 18.262 9.913 45.364 6.029 dd10m 1586887200 90 46.816 41.087 58.353 82.715 43.804 48.007 24.445 34.314 75.833 46.565 17.482 61.441 79.859 43.760 58.180 35.560 64.353 54.796 33.457 87.344 28.548 dd10m 1586908800 96 157.214 139.596 163.090 168.179 168.329 171.474 145.858 165.011 164.625 149.312 149.885 158.188 174.665 177.894 138.265 157.894 150.443 162.289 151.104 162.218 143.136 dd10m 1586930400 102 177.507 177.599 181.000 164.713 179.338 198.084 124.879 146.834 170.929 171.892 121.719 185.364 201.834 185.810 138.020 174.979 179.497 186.515 137.996 179.320 167.726 dd10m 1586952000 108 79.184 60.821 64.781 107.763 104.277 67.790 117.717 51.275 119.052 105.266 105.167 86.376 78.300 62.632 111.784 89.972 105.017 86.327 98.522 159.873 133.265 dd10m 1586973600 114 112.021 103.121 83.750 134.801 121.218 110.929 135.088 63.197 118.789 137.318 127.338 128.405 133.553 66.456 127.705 132.173 120.499 123.614 91.657 145.115 139.731 dd10m 1586995200 120 180.832 184.868 201.999 172.399 186.411 188.312 172.019 177.752 174.549 178.937 178.138 178.426 193.463 188.345 177.955 177.785 179.712 182.094 175.480 180.298 181.974 dd10m 1587016800 126 192.506 195.558 272.102 174.872 225.886 205.367 191.779 330.462 179.483 205.168 192.592 199.555 214.200 194.770 195.921 183.656 188.172 187.319 188.924 184.847 194.459 dd10m 1587038400 132 80.788 149.584 52.275 228.622 17.727 19.844 210.756 101.572 164.799 342.556 239.485 104.374 46.461 151.492 115.888 171.237 199.542 221.854 146.277 184.995 231.163 dd10m 1587060000 138 107.219 84.665 106.179 104.837 57.314 75.564 148.753 126.964 349.117 65.958 65.735 64.402 119.979 162.379 111.916 346.448 98.711 114.005 161.381 180.022 141.864 dd10m 1587081600 144 189.021 234.122 190.214 193.325 202.687 208.661 211.788 198.552 210.086 221.020 202.829 190.096 190.177 193.171 188.749 237.510 235.083 224.537 195.746 206.066 196.654 dd10m 1587103200 150 189.020 289.424 194.290 160.620 183.234 161.013 245.720 241.170 168.467 136.030 158.952 172.948 189.593 213.961 204.493 323.049 294.901 182.899 202.916 200.731 189.872 dd10m 1587124800 156 90.174 345.031 173.374 73.112 139.720 56.065 85.863 55.269 132.457 101.150 106.575 132.215 169.838 74.016 62.848 31.765 12.606 116.380 36.322 151.012 146.769 dd10m 1587146400 162 114.670 358.896 62.796 53.704 128.625 93.430 115.666 258.156 142.132 108.348 110.118 144.812 132.744 138.200 104.773 82.570 26.924 153.958 122.950 156.682 132.936 dd10m 1587168000 168 185.272 47.321 200.575 27.749 209.581 177.335 204.253 310.730 197.006 204.463 187.987 191.721 210.067 228.601 192.428 179.080 333.034 198.614 184.932 202.797 197.603 dd10m 1587189600 174 199.935 121.523 209.164 13.477 222.220 175.757 203.430 302.100 209.519 200.844 190.773 190.172 83.520 224.097 217.685 181.982 31.454 194.518 185.680 209.933 200.621 dd10m 1587211200 180 106.801 122.229 139.596 43.896 143.015 117.513 12.695 323.755 61.497 48.856 78.201 176.482 118.791 337.981 131.272 141.667 22.338 141.900 160.257 194.500 103.061 dd10m 1587232800 186 92.463 55.079 147.339 50.108 67.777 129.857 29.733 338.331 111.594 79.031 98.879 164.279 137.124 348.893 164.793 152.377 55.917 153.245 163.027 252.563 128.598 dd10m 1587254400 192 221.695 298.228 200.560 140.061 220.581 183.972 354.650 351.137 184.846 189.524 253.255 204.963 188.012 335.286 193.910 200.024 132.424 201.936 196.509 310.216 190.747 dd10m 1587276000 198 270.290 15.946 212.247 147.811 242.903 242.467 33.001 12.905 186.893 228.899 330.042 215.365 202.763 347.837 186.043 221.297 143.212 226.893 258.896 333.908 210.986 dd10m 1587297600 204 39.275 38.907 273.976 79.756 350.657 47.911 40.763 43.565 28.636 17.520 18.502 57.817 354.933 337.045 164.172 3.315 104.415 30.551 38.235 3.737 333.703 dd10m 1587319200 210 62.512 82.834 130.500 98.779 33.233 52.573 62.097 47.288 71.499 17.759 43.449 129.450 50.924 352.841 173.027 332.848 137.624 344.582 72.211 28.888 59.112 dd10m 1587340800 216 145.022 169.955 220.241 160.631 190.089 133.247 119.216 59.116 185.151 246.132 108.217 175.844 206.518 351.143 181.682 335.855 168.781 249.302 139.177 101.563 213.984 dd10m 1587362400 222 111.121 165.245 221.694 163.040 241.368 91.118 146.445 87.328 170.035 266.630 116.370 184.378 3.981 12.494 174.399 12.158 167.299 332.667 149.412 126.088 265.852 dd10m 1587384000 228 64.879 40.538 183.308 112.538 46.691 57.535 131.399 60.102 148.412 313.237 94.730 125.780 34.694 28.057 169.477 30.742 150.018 8.967 108.114 116.757 1.664 dd10m 1587405600 234 70.012 55.011 39.397 84.478 45.797 37.139 146.883 82.224 153.570 359.312 97.940 130.323 43.571 47.633 172.006 70.055 150.359 11.319 144.016 136.110 3.298 dd10m 1587427200 240 84.677 145.804 200.424 153.847 55.558 34.147 161.457 146.511 177.481 3.226 127.623 157.083 78.564 93.915 180.365 139.276 168.587 342.122 175.066 184.734 358.291 ff10m 1586584800 6 0.686 0.736 0.651 0.733 0.583 0.711 0.712 0.822 0.650 0.716 0.798 0.750 0.690 0.745 0.626 0.665 0.692 0.658 0.648 0.618 0.672 ff10m 1586606400 12 1.666 1.725 1.724 1.569 1.455 1.680 1.668 1.729 1.794 1.486 1.594 1.669 1.794 1.629 1.624 1.642 1.498 1.521 1.794 1.646 1.440 ff10m 1586628000 18 1.257 1.412 1.349 1.203 1.174 1.230 1.232 1.324 1.338 1.199 1.201 1.278 1.253 1.246 1.186 1.238 1.155 1.238 1.338 1.271 1.128 ff10m 1586649600 24 2.138 2.219 2.171 2.116 2.161 2.105 2.166 2.142 2.192 2.139 2.091 2.194 2.085 2.117 2.176 2.073 2.115 2.054 2.164 2.089 2.049 ff10m 1586671200 30 2.151 2.207 2.211 2.064 2.115 2.223 2.181 2.094 2.080 2.113 2.116 2.168 2.142 2.235 2.212 2.172 2.217 2.077 2.193 2.072 2.179 ff10m 1586692800 36 1.867 1.879 2.022 1.793 1.942 1.885 1.972 1.777 1.799 1.798 1.953 1.918 2.010 2.125 2.076 1.845 1.893 1.907 1.975 1.898 1.867 ff10m 1586714400 42 1.711 1.506 1.699 1.588 1.618 1.742 1.816 1.343 1.605 1.772 1.591 1.417 1.758 1.787 1.907 1.780 1.789 1.735 1.736 1.722 1.624 ff10m 1586736000 48 2.855 2.724 2.816 2.892 2.754 2.743 3.139 2.634 2.812 2.955 2.808 2.675 3.054 2.852 3.050 2.651 2.825 2.886 2.894 2.930 2.823 ff10m 1586757600 54 2.310 1.951 2.404 2.389 2.407 2.129 2.712 2.113 2.343 2.595 2.289 2.253 2.516 2.502 2.582 2.195 2.276 2.273 2.451 2.346 2.485 ff10m 1586779200 60 1.145 1.801 1.171 1.394 0.819 1.752 1.399 1.641 1.231 1.382 1.193 1.143 0.978 1.449 1.129 1.960 0.778 1.316 1.338 1.315 1.549 ff10m 1586800800 66 1.772 3.075 1.885 1.995 1.349 2.696 0.741 2.432 1.773 0.787 1.544 1.994 1.382 1.322 0.634 2.608 0.930 1.987 1.433 2.314 1.587 ff10m 1586822400 72 2.532 2.598 2.438 3.304 2.468 2.977 1.271 2.461 2.104 1.824 1.987 1.815 2.956 1.173 1.699 2.505 0.471 2.589 2.429 2.540 2.617 ff10m 1586844000 78 3.004 3.161 2.866 2.134 2.897 2.998 3.641 2.863 2.251 3.811 3.256 2.265 2.797 2.978 2.888 3.085 1.817 2.960 3.138 1.585 2.814 ff10m 1586865600 84 3.135 3.104 2.721 2.490 2.895 2.924 4.067 3.323 1.992 3.914 3.388 2.749 3.210 2.969 3.117 3.311 2.950 3.359 3.224 2.860 3.283 ff10m 1586887200 90 2.185 2.381 1.954 2.145 2.125 2.232 2.598 2.278 1.860 2.333 2.732 1.976 2.159 1.980 2.244 2.462 2.462 2.255 2.568 2.024 2.393 ff10m 1586908800 96 1.784 1.434 1.672 1.886 1.645 2.172 1.250 0.779 1.974 1.756 0.930 1.645 2.056 1.501 1.554 1.801 2.074 1.873 1.297 2.237 1.207 ff10m 1586930400 102 1.640 1.295 1.356 1.430 1.513 1.554 1.610 0.833 1.676 1.690 0.882 1.761 1.689 0.801 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9.931 2.564 10.332 2.925 1.926 0.492 apcpsfc 1587254400 192 1.010 0.509 0.000 0.000 0.106 0.010 0.096 3.398 0.406 0.000 0.897 0.057 0.012 16.592 8.437 1.690 0.822 4.041 2.447 1.229 0.000 apcpsfc 1587276000 198 0.041 0.003 0.000 0.047 0.000 0.026 0.000 0.636 0.000 0.000 0.000 0.000 0.000 6.755 3.009 0.000 0.007 2.350 0.909 0.041 0.026 apcpsfc 1587297600 204 0.370 0.000 0.434 0.238 0.966 0.183 0.025 0.385 1.043 0.000 0.017 0.252 0.420 0.758 1.968 1.487 0.412 3.324 2.213 0.735 0.158 apcpsfc 1587319200 210 1.528 0.121 2.619 1.884 1.316 0.632 1.301 0.271 1.756 0.338 0.122 2.205 3.058 0.805 3.627 6.617 2.064 7.808 4.876 0.945 1.571 apcpsfc 1587340800 216 0.166 0.081 0.337 0.445 0.061 0.119 0.669 0.173 0.868 0.273 0.026 0.122 0.318 0.950 0.150 9.734 0.199 2.406 1.110 0.055 0.331 apcpsfc 1587362400 222 0.071 0.039 0.000 0.016 0.000 0.292 0.812 0.034 0.008 0.568 0.010 0.024 0.000 0.198 0.086 1.284 0.007 0.062 0.100 0.000 0.024 apcpsfc 1587384000 228 0.627 0.054 0.669 0.020 0.897 0.298 4.810 0.345 0.557 3.958 0.538 0.510 0.884 0.264 0.228 1.192 0.404 1.531 3.184 0.000 3.602 apcpsfc 1587405600 234 0.923 0.186 3.830 0.061 4.898 0.358 12.349 1.573 1.384 6.564 1.722 1.685 3.548 1.131 0.447 3.266 0.730 3.558 4.814 0.282 13.702 apcpsfc 1587427200 240 0.145 0.361 1.027 0.282 3.881 0.179 3.898 3.225 0.191 0.984 2.517 0.954 0.598 0.032 0.502 1.285 0.041 0.431 0.158 0.012 6.466 tmp2m 1586584800 6 275.542 275.703 275.528 275.561 275.696 275.578 275.598 275.359 275.260 275.534 275.607 275.565 275.577 275.620 275.554 275.577 275.452 275.409 275.500 275.594 275.653 tmp2m 1586606400 12 282.874 282.282 282.820 283.064 282.939 282.878 282.787 282.757 282.696 283.236 282.564 282.679 282.431 282.292 282.810 282.749 282.882 283.020 282.770 282.878 283.099 tmp2m 1586628000 18 277.768 277.792 277.758 277.880 277.865 277.749 277.786 277.650 277.513 277.851 277.778 277.789 277.702 277.737 277.761 277.810 277.759 277.668 277.733 277.840 277.943 tmp2m 1586649600 24 275.946 275.719 276.047 275.922 276.203 275.784 275.806 275.680 275.210 275.824 275.980 275.756 275.841 276.084 275.900 275.957 276.150 275.747 275.966 275.873 276.295 tmp2m 1586671200 30 276.787 276.832 276.956 276.825 276.824 276.868 276.925 276.764 276.903 276.790 276.873 276.760 276.746 276.729 276.838 276.735 276.887 276.912 276.899 276.947 276.899 tmp2m 1586692800 36 284.079 284.067 284.203 284.084 283.767 283.797 284.312 283.610 283.667 283.954 283.857 283.877 284.272 283.950 284.135 284.095 284.311 283.636 284.246 283.846 283.884 tmp2m 1586714400 42 277.394 276.787 277.480 277.076 277.275 277.630 277.664 276.804 277.388 277.458 277.611 277.066 277.267 277.411 277.545 277.521 277.597 277.502 277.601 277.556 277.272 tmp2m 1586736000 48 274.677 274.349 274.924 274.788 274.690 274.646 274.411 274.648 274.906 274.353 274.812 274.585 274.515 274.908 274.691 274.838 274.675 274.414 274.746 274.803 274.786 tmp2m 1586757600 54 275.472 275.722 275.415 275.539 275.319 275.233 275.324 275.396 275.570 275.140 275.524 275.437 275.286 275.310 275.372 275.422 275.369 275.375 275.563 275.735 275.345 tmp2m 1586779200 60 284.737 284.460 284.280 284.563 284.920 284.098 282.205 284.410 284.501 284.347 284.047 285.632 284.262 283.809 284.115 283.811 284.461 284.976 283.159 284.862 283.754 tmp2m 1586800800 66 277.592 276.920 277.497 277.260 277.417 276.989 276.873 276.955 277.497 276.407 277.431 277.788 277.004 277.140 276.690 277.107 276.883 277.328 277.164 277.471 277.384 tmp2m 1586822400 72 275.202 273.121 275.213 274.264 275.535 274.062 274.920 274.157 274.773 275.273 275.071 275.555 275.168 274.107 275.067 274.629 273.746 274.584 274.863 274.542 275.069 tmp2m 1586844000 78 273.322 270.537 273.436 271.360 273.759 271.777 272.858 272.328 273.562 273.454 273.708 274.089 272.188 274.432 273.950 272.280 274.964 272.605 273.071 272.280 272.779 tmp2m 1586865600 84 278.819 277.514 280.218 278.633 280.356 277.777 274.796 277.433 281.691 276.653 277.912 280.137 278.580 278.326 279.702 277.639 279.988 278.651 278.082 279.902 278.157 tmp2m 1586887200 90 272.941 272.112 274.082 273.044 273.886 271.986 269.149 272.019 275.798 271.213 272.339 274.656 272.819 273.210 273.617 271.816 275.088 272.698 272.783 274.002 272.365 tmp2m 1586908800 96 270.897 268.990 272.856 273.606 272.141 270.103 263.988 269.011 274.658 269.186 268.282 272.893 272.691 271.267 271.283 268.523 271.700 271.097 268.981 274.140 268.614 tmp2m 1586930400 102 275.045 273.795 275.223 274.640 275.032 274.573 270.139 273.630 275.205 273.330 273.417 275.506 275.598 274.533 274.668 274.157 274.860 275.441 273.543 275.290 273.494 tmp2m 1586952000 108 285.633 284.111 284.674 283.227 287.001 286.011 281.976 285.561 283.112 285.697 285.628 283.243 287.034 286.060 282.515 285.773 284.950 282.658 285.088 284.025 284.884 tmp2m 1586973600 114 277.318 275.207 277.671 277.977 278.067 276.449 275.453 275.712 278.651 277.267 276.892 278.460 278.877 276.486 277.400 277.289 277.331 278.204 276.475 278.473 276.943 tmp2m 1586995200 120 274.618 273.853 274.528 274.536 275.150 274.606 272.224 273.213 274.934 273.841 274.216 275.206 275.258 274.274 274.248 273.864 275.034 275.439 273.653 274.348 273.977 tmp2m 1587016800 126 277.027 276.972 277.552 275.747 277.898 277.614 274.471 276.625 276.062 276.724 276.493 277.105 278.273 277.699 276.297 275.889 276.493 276.325 276.609 276.495 276.339 tmp2m 1587038400 132 288.157 288.033 288.374 286.639 287.717 286.654 285.896 288.575 286.589 289.711 288.982 288.640 287.932 288.104 287.646 287.044 287.061 287.701 287.362 285.932 287.658 tmp2m 1587060000 138 279.455 278.755 279.681 279.097 280.294 278.847 275.784 279.286 280.011 279.216 278.878 280.635 280.511 280.685 278.953 278.664 279.597 280.227 279.482 280.336 279.091 tmp2m 1587081600 144 276.338 276.139 277.038 275.380 277.204 275.689 274.053 276.518 275.023 276.118 275.475 276.169 276.761 276.589 276.195 276.545 275.974 276.454 276.315 276.553 276.434 tmp2m 1587103200 150 279.037 278.652 279.026 279.256 280.220 279.386 278.247 278.864 279.367 280.225 279.882 279.764 279.161 278.450 278.667 278.602 279.033 279.942 278.749 278.968 278.972 tmp2m 1587124800 156 290.996 287.051 290.078 290.811 288.231 290.320 289.113 288.028 287.104 291.126 290.709 289.900 289.455 291.591 288.253 288.039 286.989 289.122 288.307 288.646 289.616 tmp2m 1587146400 162 282.276 279.936 282.001 281.491 281.394 281.009 279.799 281.126 281.699 281.559 281.323 282.708 282.510 282.904 281.139 280.531 280.037 282.117 281.701 282.227 282.176 tmp2m 1587168000 168 279.043 275.651 279.554 276.369 278.125 278.251 276.486 279.108 278.565 277.171 277.515 278.570 279.143 278.885 278.867 277.565 274.708 279.390 277.333 278.402 278.016 tmp2m 1587189600 174 280.566 278.577 280.820 280.014 280.636 279.893 280.287 278.190 279.553 281.327 280.063 280.325 281.493 280.900 279.637 279.118 279.310 280.463 279.592 279.958 280.793 tmp2m 1587211200 180 290.643 289.369 290.143 288.277 291.577 290.452 288.098 284.479 289.531 290.889 291.202 290.403 290.378 288.934 285.778 284.268 287.980 287.129 288.245 289.738 291.071 tmp2m 1587232800 186 282.962 280.351 283.582 281.435 282.413 283.275 281.409 278.720 282.633 282.338 282.429 283.824 283.890 282.482 280.825 280.454 280.030 282.268 281.283 282.843 283.013 tmp2m 1587254400 192 279.517 275.554 280.213 275.981 278.282 278.419 275.901 276.036 278.284 278.512 277.726 279.659 279.850 280.488 278.878 277.469 275.297 280.139 278.722 278.812 279.811 tmp2m 1587276000 198 282.217 280.177 281.546 278.955 281.598 281.153 280.218 275.922 280.584 281.572 280.991 281.695 281.951 279.990 279.975 279.766 278.799 281.532 280.841 282.125 282.002 tmp2m 1587297600 204 289.535 289.400 291.576 287.416 289.268 289.040 288.452 281.039 289.216 292.608 289.410 291.478 291.595 283.353 285.820 287.615 288.902 287.519 287.080 289.459 292.331 tmp2m 1587319200 210 282.585 281.027 283.899 281.297 282.942 282.001 281.222 277.625 282.924 283.479 282.359 285.593 284.926 278.794 282.448 281.503 282.649 282.980 282.418 283.633 284.115 tmp2m 1587340800 216 277.850 277.800 279.987 277.650 277.832 276.133 275.939 274.827 278.807 278.853 275.371 282.260 279.112 274.417 279.414 278.994 278.882 278.259 278.016 278.283 280.421 tmp2m 1587362400 222 280.159 279.579 282.212 277.826 281.845 277.485 277.755 274.956 280.298 280.679 277.356 282.505 282.592 275.594 279.751 279.198 279.630 281.806 279.863 280.381 282.859 tmp2m 1587384000 228 286.328 287.300 291.772 287.733 288.387 283.972 283.613 282.109 288.050 285.230 283.786 290.265 289.813 282.520 286.822 283.550 287.162 287.508 286.713 291.450 287.047 tmp2m 1587405600 234 280.720 280.289 283.732 282.527 283.016 278.967 280.469 276.026 283.450 279.323 277.974 285.203 283.186 277.168 282.594 279.486 283.298 282.556 282.580 285.881 283.487 tmp2m 1587427200 240 275.321 275.472 278.997 277.624 278.567 274.362 278.326 274.445 279.038 275.127 274.539 280.856 276.097 273.403 279.454 276.761 278.386 280.017 277.669 281.435 281.480 tcdcclm 1586584800 6 0.239 0.239 0.261 0.156 0.437 0.152 0.220 0.419 0.170 0.114 1.006 0.622 0.506 0.500 0.647 0.477 0.448 0.312 0.114 0.717 0.356 tcdcclm 1586606400 12 1.538 3.134 1.511 1.405 2.304 1.355 2.184 1.363 1.227 1.364 3.122 1.792 2.557 3.128 1.883 1.847 1.823 1.572 1.494 2.123 1.564 tcdcclm 1586628000 18 4.755 4.506 4.379 4.632 5.594 4.491 4.130 4.643 4.605 4.242 5.495 5.156 4.491 4.190 4.612 4.242 4.293 4.588 4.573 5.009 4.503 tcdcclm 1586649600 24 4.217 3.653 4.515 4.341 5.358 3.865 4.205 3.926 3.358 4.406 4.841 4.262 4.586 4.910 4.373 4.763 4.968 5.052 4.651 5.184 4.773 tcdcclm 1586671200 30 5.514 5.425 5.462 5.012 5.569 5.437 5.504 5.425 5.290 5.196 5.391 5.381 5.064 5.161 5.360 5.620 5.110 5.670 5.548 5.447 5.289 tcdcclm 1586692800 36 2.636 2.049 1.730 3.067 3.819 3.374 1.632 3.768 3.773 2.672 2.898 3.121 1.798 1.561 1.223 2.339 0.855 3.955 1.747 3.899 2.889 tcdcclm 1586714400 42 2.476 1.266 2.032 2.704 4.377 2.419 1.584 2.525 3.685 1.648 3.919 3.342 1.229 3.354 1.780 2.360 1.867 3.147 3.014 3.977 4.290 tcdcclm 1586736000 48 5.526 4.593 6.106 6.172 6.215 5.049 3.145 5.567 5.598 4.168 5.706 5.577 4.476 6.591 4.971 6.301 5.792 5.811 5.845 5.453 6.025 tcdcclm 1586757600 54 6.699 6.319 6.090 6.911 6.177 5.883 4.733 6.105 6.818 4.982 6.830 6.449 5.748 5.944 6.321 6.922 5.748 6.502 6.557 6.547 6.713 tcdcclm 1586779200 60 5.649 3.897 4.222 4.668 3.557 4.328 7.410 3.160 5.073 4.455 6.629 4.417 4.816 4.233 5.004 4.027 4.970 2.716 6.893 5.746 5.711 tcdcclm 1586800800 66 6.015 5.669 5.987 6.112 6.609 6.176 7.418 5.292 5.427 5.716 5.974 4.828 6.357 5.330 6.140 4.966 5.101 3.954 6.987 6.586 5.915 tcdcclm 1586822400 72 6.957 6.289 6.490 7.130 7.195 6.756 7.927 6.862 5.853 7.475 6.594 6.944 7.024 3.826 7.241 7.052 6.938 6.368 7.352 6.999 6.768 tcdcclm 1586844000 78 6.162 5.497 6.826 6.380 6.385 5.803 7.815 5.963 5.011 7.737 6.650 7.347 6.823 5.010 7.345 7.303 6.364 5.823 6.377 5.405 7.257 tcdcclm 1586865600 84 3.047 2.476 3.144 1.575 3.036 3.036 5.246 3.513 3.521 4.313 5.178 2.978 2.642 6.241 3.364 3.458 6.529 3.493 3.971 1.910 2.757 tcdcclm 1586887200 90 0.119 0.220 0.334 0.334 0.494 0.059 1.135 0.237 1.864 0.292 0.534 0.762 0.160 1.711 0.290 0.080 3.243 0.178 0.139 1.523 0.157 tcdcclm 1586908800 96 0.216 0.178 0.743 2.927 0.300 0.199 1.835 0.321 5.293 0.223 2.372 1.540 0.541 0.560 0.881 0.373 0.380 0.185 0.199 3.111 0.160 tcdcclm 1586930400 102 2.377 1.608 4.995 4.654 3.013 2.952 0.160 0.581 4.777 1.095 0.518 4.907 5.004 3.186 3.315 2.981 0.547 3.204 0.515 5.222 0.233 tcdcclm 1586952000 108 3.011 2.888 3.094 3.512 1.484 2.351 0.038 2.918 2.695 0.543 1.616 3.666 1.834 1.917 4.317 1.554 2.756 4.920 0.794 1.345 0.084 tcdcclm 1586973600 114 5.011 3.124 6.038 5.124 3.882 3.399 0.021 1.745 5.242 0.868 0.735 5.260 3.097 2.540 4.892 5.064 5.119 5.236 3.271 3.582 1.629 tcdcclm 1586995200 120 3.055 1.088 3.186 1.852 1.426 1.200 0.118 0.124 1.886 0.142 0.696 1.855 0.342 1.972 2.341 0.763 2.607 4.418 1.950 0.822 0.196 tcdcclm 1587016800 126 1.146 3.365 1.463 4.725 1.295 0.917 0.160 0.153 1.125 0.067 1.719 3.601 3.221 2.858 1.422 0.439 2.541 2.790 2.839 0.059 2.312 tcdcclm 1587038400 132 4.241 1.589 4.536 5.037 5.385 5.061 4.641 0.116 0.797 3.490 4.881 5.881 6.782 1.881 4.322 5.325 4.144 3.792 5.280 2.518 5.077 tcdcclm 1587060000 138 4.907 5.094 4.029 4.770 5.660 4.389 6.672 2.833 3.887 3.224 5.578 6.227 2.332 1.861 5.967 5.779 3.957 5.588 7.511 5.311 7.098 tcdcclm 1587081600 144 1.733 6.348 1.583 1.512 6.398 1.780 1.816 5.743 3.207 3.026 1.084 1.657 1.447 2.240 5.201 4.918 2.070 2.918 7.438 3.614 7.270 tcdcclm 1587103200 150 2.757 1.470 5.294 3.718 6.722 4.247 0.059 4.369 1.923 1.205 3.714 0.217 3.883 1.166 6.598 3.130 0.921 3.559 5.100 4.922 6.587 tcdcclm 1587124800 156 3.526 1.495 4.794 5.158 4.872 5.956 0.153 5.512 5.666 0.093 5.490 2.370 5.897 3.945 5.857 3.190 4.372 6.367 3.348 6.099 5.382 tcdcclm 1587146400 162 5.048 2.327 6.520 3.477 3.836 4.630 2.420 6.751 6.718 1.053 6.179 3.441 3.369 5.081 6.349 6.627 5.818 6.767 5.910 6.142 1.613 tcdcclm 1587168000 168 5.862 4.506 6.946 3.849 4.594 5.919 0.799 7.427 6.606 3.778 5.124 4.218 5.336 5.934 5.913 5.635 2.429 6.791 4.280 3.518 3.116 tcdcclm 1587189600 174 6.839 4.789 5.190 5.926 6.450 6.178 2.699 5.293 5.624 5.943 3.207 4.740 7.063 4.666 5.749 4.859 4.454 5.573 6.174 4.612 3.774 tcdcclm 1587211200 180 5.982 3.705 5.594 2.118 4.976 3.392 4.875 4.274 3.475 3.483 5.559 6.920 7.126 4.896 5.621 6.516 3.663 6.402 7.396 6.451 3.911 tcdcclm 1587232800 186 6.405 2.465 6.532 3.936 4.845 2.883 4.396 6.200 5.532 2.744 7.052 6.539 6.385 6.685 7.282 7.365 3.520 7.334 7.676 7.638 5.278 tcdcclm 1587254400 192 6.757 0.527 6.736 2.729 3.697 3.284 0.422 7.752 4.389 4.341 6.054 5.552 5.850 7.915 7.668 6.942 0.457 7.083 7.098 7.135 5.449 tcdcclm 1587276000 198 4.257 3.362 6.765 2.169 5.049 2.328 0.067 6.676 3.438 5.734 4.551 6.731 4.772 7.699 6.969 5.539 0.191 6.646 5.115 5.953 6.610 tcdcclm 1587297600 204 2.807 3.228 5.903 0.823 2.352 3.249 0.108 5.807 2.221 5.887 0.600 4.955 2.012 5.755 6.186 5.593 0.839 5.431 5.616 5.244 4.784 tcdcclm 1587319200 210 2.778 0.178 5.045 1.988 3.509 1.186 1.005 3.644 4.192 1.569 0.636 5.119 2.716 1.619 5.909 6.282 2.805 5.943 6.077 3.313 5.467 tcdcclm 1587340800 216 0.896 0.596 1.320 2.965 2.094 1.521 0.457 3.700 3.020 4.606 0.282 6.738 0.872 4.665 5.521 7.220 1.448 6.847 4.193 1.804 4.927 tcdcclm 1587362400 222 1.275 2.026 2.208 1.934 4.652 1.155 2.153 2.129 4.691 2.589 0.562 5.422 0.168 5.730 5.438 6.295 3.473 3.232 1.312 1.172 6.350 tcdcclm 1587384000 228 1.687 1.753 1.206 1.355 5.671 1.841 3.603 2.893 2.856 5.368 1.836 4.887 0.151 5.632 6.320 5.074 3.908 3.333 1.680 0.218 6.882 tcdcclm 1587405600 234 0.944 1.202 3.018 3.777 6.027 1.748 6.585 5.449 3.897 6.522 2.331 6.325 0.502 3.601 7.125 4.573 4.471 3.652 5.000 1.763 7.278 tcdcclm 1587427200 240 1.204 2.207 1.228 2.296 6.342 3.564 5.975 7.040 3.382 6.561 4.058 6.242 0.433 3.655 6.819 5.406 2.771 4.528 1.293 1.963 7.654 partykit/inst/ULGcourse-2020/Data/GENS_00_innsbruck_20200412.dat0000644000176200001440000016114414172227777023004 0ustar liggesusers# ASCII output from GENSvis.py # Contains interpolated values from the # GFS ensemble on 1.000000 x 1.000000 degrees # The data in here are for station # 11120: INNSBRUCK # Station position: 11.3553 47.2589 # Used grid point 1: 12.0000 48.0000 # Used grid point 2: 12.0000 47.0000 # Used grid point 3: 11.0000 47.0000 # Used grid point 4: 11.0000 48.0000 varname timestamp step mem0 mem1 mem2 mem3 mem4 mem5 mem6 mem7 mem8 mem9 mem10 mem11 mem12 mem13 mem14 mem15 mem16 mem17 mem18 mem19 mem20 tmax2m 1586671200 6 276.296 276.370 276.175 276.296 276.618 276.139 276.330 276.222 276.113 276.248 276.401 276.184 276.544 276.361 275.896 276.118 276.010 276.049 276.351 276.596 276.348 tmax2m 1586692800 12 283.980 284.146 283.790 284.150 283.722 283.823 284.023 284.076 284.043 284.006 283.614 284.068 283.893 283.526 284.162 283.896 284.208 284.006 284.097 283.729 284.095 tmax2m 1586714400 18 283.667 283.893 283.596 283.961 283.367 283.633 283.949 283.734 283.665 283.624 283.384 283.840 283.471 283.105 283.908 283.712 284.057 283.649 283.836 283.548 283.732 tmax2m 1586736000 24 276.881 276.772 277.022 277.125 277.053 277.181 277.226 277.048 277.035 277.109 277.290 277.029 276.943 276.902 277.079 276.967 277.055 277.351 277.084 277.178 277.389 tmax2m 1586757600 30 275.269 275.232 275.122 275.214 275.275 275.345 275.170 275.356 275.100 275.022 275.288 275.269 275.031 275.028 274.986 275.400 275.262 275.179 275.360 275.446 275.272 tmax2m 1586779200 36 284.028 283.583 283.851 284.186 283.201 283.220 283.785 283.350 284.312 284.377 283.775 283.742 284.666 284.356 284.217 283.167 283.793 283.759 283.477 284.227 283.391 tmax2m 1586800800 42 283.791 283.184 283.728 283.940 282.909 282.507 283.665 283.274 284.248 284.153 283.509 283.286 284.558 284.153 284.074 282.681 283.489 283.338 283.077 283.913 282.921 tmax2m 1586822400 48 276.967 276.626 276.916 276.986 276.818 276.311 277.172 276.967 277.131 277.021 277.257 276.992 277.103 276.861 277.150 276.382 277.066 276.625 276.641 277.145 276.794 tmax2m 1586844000 54 273.644 272.465 273.674 273.143 274.081 272.377 274.126 273.948 274.690 272.221 274.488 273.946 273.341 273.250 273.982 272.331 274.248 272.844 273.026 273.870 273.006 tmax2m 1586865600 60 276.966 276.790 276.693 276.828 277.175 276.581 276.248 276.615 278.313 276.396 276.065 276.992 278.309 277.083 277.841 275.695 277.950 276.678 276.012 278.303 274.815 tmax2m 1586887200 66 277.606 277.350 277.211 277.503 277.859 277.134 276.984 277.317 279.435 277.023 276.511 277.626 279.198 278.072 278.581 276.157 279.172 277.317 276.601 279.413 275.226 tmax2m 1586908800 72 271.002 270.864 270.887 270.906 271.362 270.789 271.008 271.208 273.002 270.662 270.436 270.947 273.524 271.726 272.093 269.926 272.675 271.287 270.514 273.201 269.193 tmax2m 1586930400 78 273.708 273.734 273.371 273.413 274.196 273.373 273.361 273.395 275.176 273.311 272.717 273.651 275.149 273.895 274.283 272.650 274.256 273.274 273.019 274.883 271.656 tmax2m 1586952000 84 284.189 284.915 284.597 283.599 285.753 284.886 283.188 283.889 284.894 284.497 284.397 284.245 284.173 284.122 284.092 283.812 283.350 283.378 282.995 284.327 283.592 tmax2m 1586973600 90 284.580 285.494 285.155 283.845 285.648 285.678 283.693 284.425 285.730 284.715 285.474 284.884 284.114 284.936 284.380 284.433 283.851 283.849 283.614 284.690 284.645 tmax2m 1586995200 96 275.559 276.606 275.868 275.071 277.850 277.185 275.290 275.133 277.140 275.917 275.192 276.105 276.942 275.787 275.619 275.116 275.896 274.975 274.953 277.451 274.592 tmax2m 1587016800 102 276.924 276.575 276.580 276.597 276.318 276.160 276.275 276.716 277.642 276.263 276.888 276.759 277.231 276.962 276.812 276.332 276.899 277.005 276.641 276.986 276.274 tmax2m 1587038400 108 287.750 287.236 286.634 286.588 287.200 288.110 286.729 288.029 288.022 286.938 287.841 287.946 287.893 287.205 287.185 287.209 286.760 287.273 288.091 288.117 287.755 tmax2m 1587060000 114 288.032 287.189 286.533 286.803 286.699 288.218 287.094 286.701 288.049 287.240 288.080 288.244 288.016 286.764 287.468 287.799 286.951 285.776 287.261 288.363 287.951 tmax2m 1587081600 120 278.165 278.892 278.636 279.764 279.378 279.118 277.859 278.777 279.452 278.891 278.023 278.427 278.580 279.487 278.712 277.261 278.876 278.856 278.016 279.789 277.401 tmax2m 1587103200 126 278.564 277.945 277.248 277.862 277.515 277.758 277.746 278.559 278.431 277.690 278.319 278.310 279.438 277.501 278.205 279.356 277.580 278.162 278.493 278.699 278.861 tmax2m 1587124800 132 287.719 286.070 279.460 284.777 281.593 286.525 285.072 284.730 286.503 283.688 285.599 287.197 289.580 281.709 286.836 290.065 285.922 283.783 285.728 287.205 286.095 tmax2m 1587146400 138 287.640 286.387 279.669 284.697 281.232 287.171 284.903 283.505 286.361 283.343 285.526 287.613 289.150 281.770 286.643 290.617 285.794 283.809 285.592 287.278 285.404 tmax2m 1587168000 144 279.367 278.954 277.309 279.085 276.459 280.249 278.141 278.449 279.438 279.142 278.659 279.800 280.474 276.852 279.670 282.307 279.147 278.088 279.458 280.233 278.757 tmax2m 1587189600 150 279.307 275.835 276.675 278.972 274.320 279.419 276.861 276.987 277.652 278.627 278.191 279.230 280.890 275.169 278.731 280.306 276.732 275.518 277.035 278.730 279.092 tmax2m 1587211200 156 290.596 285.039 279.619 289.413 281.053 289.714 288.351 281.494 287.503 285.590 287.652 287.412 291.914 276.710 288.306 290.217 278.163 283.877 287.432 286.302 287.885 tmax2m 1587232800 162 290.765 285.456 278.965 288.902 281.413 288.656 288.411 282.565 287.863 285.310 286.687 287.351 291.802 277.008 288.196 289.230 278.945 283.995 287.676 286.170 287.151 tmax2m 1587254400 168 281.247 276.955 275.608 281.190 274.146 282.132 278.652 278.881 279.758 280.868 279.798 281.790 283.437 271.298 280.746 283.089 272.724 275.667 280.609 279.800 279.913 tmax2m 1587276000 174 280.307 277.352 273.456 279.635 273.073 281.080 277.470 275.962 278.959 279.022 278.760 279.405 280.797 269.595 279.322 281.775 270.213 275.424 278.722 277.220 279.542 tmax2m 1587297600 180 290.249 288.527 278.178 289.869 279.181 289.167 286.918 286.055 291.118 288.440 287.444 289.605 291.714 280.771 284.951 289.623 281.420 286.287 286.016 286.692 284.511 tmax2m 1587319200 186 289.363 288.547 278.054 290.042 279.521 288.275 287.032 286.487 290.232 288.386 287.440 289.663 291.790 281.526 284.153 289.613 281.585 286.780 286.050 286.977 283.943 tmax2m 1587340800 192 282.908 278.459 275.272 283.437 273.947 283.296 277.601 279.005 281.095 282.530 281.340 281.182 284.653 273.343 280.333 284.303 273.866 276.543 278.096 278.750 280.067 tmax2m 1587362400 198 281.140 278.882 274.492 281.227 272.484 282.219 274.939 279.921 280.301 280.942 280.318 280.187 282.576 271.494 279.743 283.728 275.293 276.965 277.725 278.386 279.069 tmax2m 1587384000 204 292.733 289.954 278.880 284.943 282.401 292.673 283.129 292.352 291.050 289.355 288.541 289.327 293.680 276.442 283.737 290.850 289.559 286.798 286.229 291.879 283.579 tmax2m 1587405600 210 291.840 290.270 279.818 284.630 283.020 291.544 282.992 292.822 290.939 288.685 287.818 289.192 293.807 276.363 283.666 290.625 289.410 286.932 285.924 292.223 284.255 tmax2m 1587427200 216 283.023 278.689 277.231 281.387 275.683 284.958 275.254 282.478 283.442 282.763 281.565 280.323 285.777 272.149 280.411 284.035 278.594 278.170 278.472 280.761 281.347 tmax2m 1587448800 222 281.760 278.059 274.486 279.421 274.998 282.570 270.840 282.115 280.010 281.322 279.444 276.599 284.276 269.000 277.204 282.065 276.377 273.364 275.996 279.601 278.955 tmax2m 1587470400 228 287.544 286.281 282.658 283.065 285.327 283.336 280.630 291.004 285.785 287.460 287.576 284.738 289.697 276.144 280.288 288.167 284.550 281.316 285.098 288.934 285.533 tmax2m 1587492000 234 286.848 286.164 283.639 283.137 285.666 282.663 281.091 291.544 285.601 287.517 287.889 284.959 289.584 276.575 280.125 288.785 284.740 281.332 284.446 289.326 285.190 tmax2m 1587513600 240 281.100 278.645 279.014 279.719 278.006 278.889 274.658 282.441 279.611 282.358 279.460 277.672 284.205 272.151 277.294 281.337 276.746 274.859 277.801 279.775 281.287 dd10m 1586671200 6 204.682 203.394 203.457 204.302 203.994 205.118 203.028 205.600 206.087 203.997 204.907 205.667 203.039 201.380 204.162 203.102 205.091 207.326 205.560 204.832 205.970 dd10m 1586692800 12 211.735 209.896 208.883 211.265 211.010 219.193 210.246 212.332 217.978 207.792 217.120 212.875 208.842 211.087 207.849 209.841 209.875 216.513 212.086 209.140 216.469 dd10m 1586714400 18 194.320 199.107 187.283 192.164 196.589 191.201 186.800 190.547 194.715 188.569 188.265 193.170 203.158 194.320 189.237 190.369 193.537 184.968 194.061 188.951 193.450 dd10m 1586736000 24 202.579 206.985 201.850 204.840 203.835 207.114 201.508 203.953 202.664 199.691 201.944 202.319 203.721 201.451 201.043 203.705 202.252 202.429 204.443 204.322 203.488 dd10m 1586757600 30 217.208 221.998 214.463 216.780 217.900 225.428 213.144 218.526 216.027 215.694 218.855 214.753 215.605 214.738 211.558 223.575 213.837 221.044 217.448 216.883 212.651 dd10m 1586779200 36 298.772 311.065 301.954 297.594 282.608 314.342 273.820 311.196 294.965 285.310 293.799 278.562 304.256 280.282 284.889 308.265 284.746 300.747 293.847 312.246 266.222 dd10m 1586800800 42 347.991 351.976 339.687 345.586 346.055 352.532 331.349 354.104 357.009 333.041 346.398 348.594 347.382 346.479 341.265 347.225 344.643 346.692 344.232 355.840 342.792 dd10m 1586822400 48 358.429 356.757 354.182 358.583 358.813 345.786 352.024 358.129 4.139 1.973 355.253 0.603 2.590 359.887 359.527 352.618 357.035 353.353 353.990 2.729 356.588 dd10m 1586844000 54 354.574 354.851 348.880 349.625 357.047 347.907 357.128 353.186 5.934 347.001 348.378 355.935 6.429 351.685 2.900 346.283 0.833 351.021 341.059 9.716 341.994 dd10m 1586865600 60 10.241 3.908 1.886 8.660 9.416 357.642 16.758 8.023 13.740 5.036 351.197 6.982 32.125 9.463 26.890 358.151 25.914 7.979 2.230 29.243 347.414 dd10m 1586887200 66 34.390 34.426 22.322 33.194 33.222 24.692 44.694 24.446 43.927 38.374 10.329 26.365 71.614 31.047 57.861 29.514 59.424 24.842 30.302 66.148 14.194 dd10m 1586908800 72 176.682 179.655 171.991 170.392 170.162 172.802 163.762 185.171 179.680 168.754 187.693 167.845 167.438 183.547 173.843 174.095 199.978 180.036 184.037 176.286 182.402 dd10m 1586930400 78 218.885 203.139 196.247 202.158 193.352 188.196 197.821 306.611 221.195 184.449 288.999 203.299 196.634 216.301 207.879 193.101 301.443 292.448 284.566 198.737 234.438 dd10m 1586952000 84 26.938 43.993 55.492 20.852 113.223 82.380 47.354 24.675 27.438 75.844 9.099 52.064 43.500 31.489 31.398 43.152 22.861 21.239 28.148 34.259 22.927 dd10m 1586973600 90 79.031 119.448 113.947 70.282 155.694 138.853 97.973 73.719 93.365 113.566 64.825 113.518 85.341 111.340 76.069 77.753 62.296 62.926 76.870 118.711 65.481 dd10m 1586995200 96 179.125 189.686 192.215 174.777 203.863 189.159 176.958 178.376 183.206 181.867 180.375 182.975 178.805 201.346 181.038 175.391 167.386 183.791 179.250 185.179 177.104 dd10m 1587016800 102 193.184 206.884 199.117 176.027 220.914 205.270 193.325 194.877 196.048 192.579 192.391 202.312 191.120 213.277 188.694 184.833 181.176 204.469 196.268 205.175 184.914 dd10m 1587038400 108 241.964 263.375 236.905 159.720 264.267 278.549 233.358 292.461 217.795 209.865 237.645 259.696 220.501 255.440 245.101 222.039 215.811 274.675 277.312 234.409 205.875 dd10m 1587060000 114 207.625 216.781 182.973 175.831 248.436 263.839 203.173 36.466 152.844 190.800 150.136 303.007 63.774 233.435 155.175 120.173 243.901 300.190 24.923 194.282 102.165 dd10m 1587081600 120 238.125 226.748 275.775 207.916 281.389 256.120 221.665 238.703 227.245 226.842 246.017 246.885 220.009 241.256 243.043 208.373 242.039 246.681 233.044 224.234 219.037 dd10m 1587103200 126 280.243 261.872 319.481 265.013 294.718 276.630 264.328 287.433 268.531 303.365 271.595 288.418 227.176 305.715 279.607 194.749 269.350 282.379 284.468 263.507 279.915 dd10m 1587124800 132 330.536 297.140 312.531 359.128 318.596 323.073 313.647 339.837 334.562 44.225 339.319 336.685 91.069 302.107 339.287 166.668 295.849 317.700 320.400 329.371 10.463 dd10m 1587146400 138 23.689 350.738 328.970 13.233 338.119 53.273 344.250 8.936 2.100 19.351 5.820 37.048 77.376 323.384 323.302 138.654 324.215 344.911 335.079 15.706 88.020 dd10m 1587168000 144 157.166 4.514 333.456 193.829 341.461 195.028 7.666 355.954 20.636 186.996 137.241 154.513 205.427 323.685 250.313 194.631 305.969 10.411 10.145 37.801 197.119 dd10m 1587189600 150 70.184 15.622 5.927 186.268 353.154 226.708 65.768 0.624 50.873 158.092 160.543 136.049 199.446 349.296 289.607 196.551 352.686 21.075 116.547 4.240 196.549 dd10m 1587211200 156 88.132 17.148 2.158 92.091 357.631 326.913 43.941 31.833 75.322 147.517 82.770 126.927 93.591 344.888 3.845 128.857 4.589 19.746 166.053 353.976 139.972 dd10m 1587232800 162 110.503 43.078 24.298 127.843 19.214 72.858 46.855 31.473 117.814 163.206 64.454 124.479 133.392 4.459 40.832 128.522 27.733 30.981 168.633 10.827 102.741 dd10m 1587254400 168 174.501 144.205 56.366 187.986 357.761 172.813 172.924 36.556 182.841 187.254 170.061 172.047 183.128 38.102 186.316 184.908 45.867 90.204 262.367 23.896 206.126 dd10m 1587276000 174 185.791 117.529 82.739 188.543 16.056 178.683 32.523 58.901 205.181 189.822 168.904 172.769 184.554 71.836 165.492 183.749 52.955 95.047 344.076 53.508 188.012 dd10m 1587297600 180 110.517 78.657 83.912 128.819 17.798 176.209 30.020 53.311 34.915 167.187 140.721 78.220 163.424 85.444 118.967 184.281 56.193 53.871 17.324 54.399 90.068 dd10m 1587319200 186 129.716 105.104 97.960 136.975 24.990 160.522 31.552 86.673 73.792 149.972 141.921 110.150 140.065 57.010 135.237 168.528 72.714 66.904 57.708 77.406 37.276 dd10m 1587340800 192 179.562 203.100 131.989 165.734 39.952 190.995 25.645 152.833 163.910 191.208 178.712 152.755 183.258 57.929 161.007 215.792 138.488 80.643 135.877 165.275 156.093 dd10m 1587362400 198 198.497 233.345 135.286 161.770 32.775 201.571 27.085 163.825 177.499 206.410 185.220 153.265 202.880 50.368 164.785 255.364 179.569 88.822 125.499 180.661 172.055 dd10m 1587384000 204 56.469 1.234 140.774 142.766 35.281 72.642 32.885 79.618 83.695 6.744 74.375 55.222 135.130 49.027 95.007 6.379 17.069 33.341 50.922 220.093 157.582 dd10m 1587405600 210 86.844 354.459 141.601 158.260 40.110 165.147 43.404 111.815 101.690 94.909 93.062 60.367 45.176 43.976 53.037 12.760 21.726 33.306 44.428 28.591 157.730 dd10m 1587427200 216 205.327 304.487 165.387 191.932 150.281 239.516 111.828 198.754 164.547 258.252 171.588 79.617 323.681 47.799 49.168 29.816 332.210 50.785 143.791 312.235 174.829 dd10m 1587448800 222 254.252 345.787 160.067 231.579 317.014 308.929 38.728 236.804 145.254 344.487 4.048 31.821 343.011 44.966 59.147 41.518 343.008 40.955 155.300 346.476 178.669 dd10m 1587470400 228 15.786 29.216 142.900 21.568 344.833 340.731 27.072 11.187 42.908 10.479 23.562 34.573 26.971 46.112 88.094 52.292 358.983 49.111 82.639 45.641 169.955 dd10m 1587492000 234 49.157 38.739 152.688 36.895 334.448 350.969 35.089 1.152 34.418 22.438 27.862 51.786 50.052 36.144 90.032 68.388 8.257 56.755 115.309 58.905 163.341 dd10m 1587513600 240 80.308 80.336 173.857 33.288 288.053 352.976 168.656 289.334 290.058 67.957 222.323 122.062 79.769 278.164 141.913 169.525 311.746 145.605 160.614 186.379 180.919 ff10m 1586671200 6 2.243 2.241 2.271 2.235 2.151 2.285 2.242 2.239 2.281 2.269 2.257 2.269 2.186 2.275 2.354 2.266 2.326 2.218 2.224 2.213 2.271 ff10m 1586692800 12 1.767 1.688 1.796 1.707 1.927 1.337 1.748 1.675 1.696 1.791 1.809 1.831 1.873 2.060 1.629 1.835 1.698 1.493 1.717 1.940 1.721 ff10m 1586714400 18 1.738 1.791 1.791 1.814 1.835 1.750 1.796 1.621 1.691 1.896 1.681 1.734 1.803 1.918 1.827 1.785 1.776 1.709 1.709 1.784 1.837 ff10m 1586736000 24 2.796 2.781 2.846 2.708 2.795 2.737 2.788 2.722 2.748 2.911 2.799 2.810 2.748 2.886 2.903 2.751 2.810 2.765 2.755 2.806 2.624 ff10m 1586757600 30 2.284 2.240 2.404 2.286 2.202 2.128 2.391 2.299 2.306 2.534 2.236 2.226 2.333 2.372 2.342 2.245 2.272 2.308 2.230 2.218 2.284 ff10m 1586779200 36 1.560 1.898 1.692 1.791 1.477 2.123 1.463 1.825 1.313 1.598 1.672 1.395 1.528 1.665 1.246 1.960 1.459 2.064 1.396 1.417 1.747 ff10m 1586800800 42 2.410 2.900 2.403 2.479 2.357 3.070 2.033 2.476 2.039 2.128 1.875 2.140 2.454 2.680 2.293 2.988 2.071 2.839 2.346 2.412 2.201 ff10m 1586822400 48 3.158 2.695 3.225 3.244 2.943 2.602 3.582 2.887 2.585 3.231 2.904 3.180 3.122 2.786 3.360 3.096 3.096 3.094 3.257 2.997 3.424 ff10m 1586844000 54 2.967 2.994 3.107 2.756 3.096 2.708 3.110 2.915 2.667 3.039 3.313 2.968 2.315 3.037 2.548 3.329 2.660 2.980 3.146 2.623 3.484 ff10m 1586865600 60 3.315 3.543 3.578 3.344 3.321 3.558 3.254 3.388 2.736 3.517 3.721 3.488 2.890 3.111 3.007 3.729 2.934 3.309 3.440 2.793 3.891 ff10m 1586887200 66 2.162 2.276 2.362 2.300 2.229 2.434 2.262 2.330 2.238 2.199 2.489 2.304 2.047 2.104 2.246 2.169 1.990 2.327 2.187 2.062 2.481 ff10m 1586908800 72 1.465 1.646 1.317 1.415 1.856 1.620 1.544 0.660 1.733 1.722 0.785 1.343 1.776 1.186 1.813 1.675 1.478 0.864 1.458 1.629 0.788 ff10m 1586930400 78 0.794 1.154 0.953 1.066 1.754 1.470 0.580 0.369 1.192 1.457 0.498 1.019 1.107 1.118 0.926 1.032 0.713 0.562 0.430 1.421 0.579 ff10m 1586952000 84 2.076 1.321 1.551 2.133 0.851 1.664 2.165 2.035 1.833 0.898 1.833 1.887 1.928 1.436 1.899 1.602 2.874 2.311 2.375 1.638 2.099 ff10m 1586973600 90 1.845 1.614 1.504 1.994 1.685 1.909 1.778 1.773 1.693 1.465 1.774 1.743 1.662 0.989 1.529 1.785 2.148 1.852 1.920 1.636 1.902 ff10m 1586995200 96 2.444 2.812 2.283 2.272 2.443 2.613 2.540 2.520 2.485 2.223 2.324 2.521 2.250 2.028 2.243 2.378 2.464 2.407 2.467 2.751 2.365 ff10m 1587016800 102 2.391 2.565 2.564 2.336 2.406 2.592 2.560 2.593 2.078 2.315 2.234 2.355 2.073 2.432 2.423 2.445 3.056 2.327 2.384 2.481 2.121 ff10m 1587038400 108 1.089 1.743 1.308 2.295 1.366 1.042 1.476 1.070 0.785 1.524 0.997 1.249 0.656 1.245 0.976 1.040 1.718 1.391 1.293 1.326 0.556 ff10m 1587060000 114 0.145 0.729 0.643 2.419 1.529 0.428 0.694 0.309 0.647 0.901 0.698 0.357 0.465 1.702 0.492 0.620 0.770 0.505 0.509 1.064 0.652 ff10m 1587081600 120 2.186 2.607 1.914 3.064 2.446 2.047 2.352 1.952 2.032 2.059 2.192 2.138 2.125 2.389 2.165 2.232 2.054 2.369 2.222 2.399 1.438 ff10m 1587103200 126 1.516 2.256 1.463 1.145 3.465 1.387 1.949 1.168 1.430 1.401 1.036 1.584 1.116 2.555 1.339 1.860 1.855 2.429 1.521 1.485 0.929 ff10m 1587124800 132 2.054 3.970 2.751 1.201 4.811 2.123 4.129 1.931 2.650 2.010 1.881 2.839 0.219 4.615 1.429 0.902 2.791 4.146 2.848 2.333 1.162 ff10m 1587146400 138 1.748 3.579 1.986 1.101 3.101 1.339 2.582 2.480 2.392 0.619 1.685 1.969 1.383 3.035 0.717 1.480 2.391 3.107 2.584 1.965 0.826 ff10m 1587168000 144 0.642 2.192 1.254 1.376 2.080 2.278 1.000 1.030 2.271 0.753 0.558 1.275 1.653 2.758 1.606 2.469 2.609 2.190 1.246 0.586 1.651 ff10m 1587189600 150 0.774 1.732 0.804 1.238 2.071 1.446 0.412 1.572 1.634 1.608 1.073 1.545 0.743 2.659 0.641 1.446 3.635 1.832 1.181 1.190 1.651 ff10m 1587211200 156 1.164 1.855 1.830 0.827 2.884 1.086 0.951 2.853 2.428 1.975 1.495 1.685 0.982 3.293 1.487 0.452 3.754 3.447 1.406 3.210 0.416 ff10m 1587232800 162 1.875 1.810 2.365 1.385 2.403 1.779 1.827 2.855 1.989 1.779 1.820 2.019 1.835 3.374 1.726 1.281 3.248 2.671 0.684 2.620 0.416 ff10m 1587254400 168 2.324 0.706 2.065 2.232 0.990 2.188 0.675 0.857 2.200 2.522 2.651 2.128 2.461 2.297 1.720 2.391 1.682 1.066 1.145 1.426 1.058 ff10m 1587276000 174 1.844 1.073 2.206 1.631 1.901 1.711 1.282 1.857 0.972 2.049 1.775 1.253 2.525 1.395 1.332 2.440 2.485 0.497 2.214 0.962 1.195 ff10m 1587297600 180 1.609 2.063 3.399 1.650 3.608 1.853 3.392 3.642 1.707 0.986 2.313 2.854 1.502 2.324 2.336 1.265 3.986 3.541 4.220 3.556 0.380 ff10m 1587319200 186 1.652 1.490 3.194 2.021 3.558 1.549 2.804 2.535 1.531 1.696 1.432 2.025 2.010 2.156 2.539 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0.138 0.944 0.000 0.000 0.003 1.143 0.136 2.506 0.825 0.137 0.012 0.000 0.010 apcpsfc 1587211200 156 0.000 0.011 3.416 0.143 0.049 0.302 0.000 0.856 0.000 0.683 0.834 0.571 0.219 0.413 0.073 0.339 0.538 0.000 0.000 0.920 1.415 apcpsfc 1587232800 162 0.026 0.000 2.007 2.775 0.000 1.604 0.091 0.764 0.000 5.178 4.730 1.339 1.598 0.201 0.849 2.772 0.026 0.000 0.096 2.586 4.740 apcpsfc 1587254400 168 0.008 0.000 0.427 1.904 0.000 0.387 0.000 0.175 0.356 3.684 3.255 0.038 0.676 0.196 0.013 1.030 0.000 0.000 0.860 0.170 0.347 apcpsfc 1587276000 174 0.043 0.000 0.265 0.000 0.003 0.815 0.000 0.003 0.010 0.025 0.678 0.008 0.000 0.000 0.000 0.191 0.000 0.000 0.026 0.000 0.287 apcpsfc 1587297600 180 0.971 0.000 2.196 0.079 0.138 0.460 0.000 0.000 0.000 0.453 0.634 0.003 0.096 0.000 1.501 0.439 0.000 0.000 0.000 0.000 3.085 apcpsfc 1587319200 186 3.782 0.000 4.264 0.385 0.254 2.431 0.000 0.000 1.862 1.580 1.996 0.153 1.726 0.361 8.455 2.347 0.000 0.000 0.000 0.000 13.456 apcpsfc 1587340800 192 0.143 0.000 0.483 0.191 0.076 0.038 0.000 0.000 0.000 0.000 0.293 0.003 0.000 1.217 3.176 0.203 0.000 0.000 0.143 0.000 5.060 apcpsfc 1587362400 198 0.000 0.000 0.944 2.285 0.000 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.121 3.423 0.394 0.000 0.000 0.098 0.000 4.050 apcpsfc 1587384000 204 0.271 0.000 2.832 4.306 0.000 0.619 0.000 0.000 0.037 1.853 2.022 0.000 0.086 1.465 4.923 2.255 0.000 0.000 0.284 0.000 4.113 apcpsfc 1587405600 210 2.770 0.000 1.425 5.896 0.000 3.790 0.000 0.000 1.158 5.353 3.796 0.033 3.078 3.133 6.149 6.959 0.000 0.000 0.753 0.014 1.704 apcpsfc 1587427200 216 2.038 0.000 1.475 3.394 0.000 7.226 0.000 0.014 0.740 3.027 0.065 0.024 0.460 1.244 2.299 0.737 0.000 0.000 0.026 0.000 0.808 apcpsfc 1587448800 222 0.168 0.000 0.706 1.907 0.000 10.610 0.000 0.000 0.102 0.191 0.000 0.000 0.516 0.278 1.518 0.134 0.000 0.000 0.043 0.000 2.173 apcpsfc 1587470400 228 1.783 0.000 0.137 3.580 0.000 6.166 0.000 0.010 0.569 0.753 0.000 0.000 1.086 0.219 3.215 0.015 0.000 0.036 0.255 0.000 1.047 apcpsfc 1587492000 234 9.200 0.065 0.233 11.254 0.000 1.731 0.000 0.126 0.820 1.418 0.000 0.003 5.926 0.575 6.334 0.030 0.000 0.311 2.315 0.014 1.085 apcpsfc 1587513600 240 8.119 0.000 0.025 2.357 0.000 0.653 0.000 0.000 0.161 0.069 0.000 0.018 7.034 0.130 3.609 0.046 0.000 0.027 0.321 0.037 0.448 tmp2m 1586671200 6 276.296 276.344 276.148 276.296 276.565 276.139 276.330 276.222 276.087 276.222 276.348 276.131 276.417 276.370 275.896 276.118 275.884 276.049 276.304 276.522 276.348 tmp2m 1586692800 12 283.836 284.008 283.755 284.091 283.568 283.754 283.838 283.787 283.766 283.870 283.562 283.964 283.627 283.267 284.061 283.777 284.125 283.863 283.954 283.596 283.838 tmp2m 1586714400 18 276.772 276.709 277.037 277.164 276.943 277.211 277.134 277.002 276.988 277.063 277.198 276.828 276.787 276.987 276.982 276.937 276.906 277.202 277.169 277.141 277.385 tmp2m 1586736000 24 274.409 274.089 274.345 274.502 274.240 274.241 274.097 274.496 274.300 274.384 274.601 274.327 274.328 274.141 274.152 274.539 274.363 274.459 274.269 274.462 274.595 tmp2m 1586757600 30 275.125 275.086 274.859 275.103 275.149 275.141 274.924 275.116 275.007 274.792 275.212 275.134 274.809 274.876 274.784 275.229 275.075 275.103 275.189 275.327 275.160 tmp2m 1586779200 36 283.885 283.440 283.755 284.057 283.141 282.781 283.785 283.180 284.303 284.140 283.670 283.613 284.618 284.156 284.190 283.023 283.767 283.616 283.412 284.122 282.980 tmp2m 1586800800 42 277.049 276.687 277.016 277.038 276.935 276.415 277.296 276.992 277.183 277.099 277.308 277.061 277.154 276.996 277.271 276.417 277.144 276.686 276.666 277.270 276.846 tmp2m 1586822400 48 273.805 272.695 273.827 273.311 274.306 272.473 274.187 274.009 274.732 272.510 274.549 274.072 273.586 273.423 274.170 272.457 274.352 273.029 273.152 274.005 273.151 tmp2m 1586844000 54 270.677 269.836 270.715 270.057 271.254 269.801 270.335 271.251 272.643 269.905 271.287 271.194 270.882 271.293 271.056 269.670 271.357 270.290 269.871 271.418 269.245 tmp2m 1586865600 60 276.966 276.790 276.693 276.828 277.175 276.581 276.248 276.615 278.313 276.396 276.065 276.992 278.309 277.083 277.841 275.695 277.950 276.678 276.012 278.303 274.815 tmp2m 1586887200 66 271.373 271.204 271.161 271.216 271.602 271.108 271.182 271.418 273.229 270.985 270.670 271.234 272.723 272.057 272.222 270.323 272.451 271.530 270.902 272.902 269.546 tmp2m 1586908800 72 268.274 268.599 267.919 268.053 269.298 268.354 268.594 267.657 271.238 268.671 265.906 267.619 272.223 269.012 270.547 266.801 270.687 267.528 267.636 271.760 264.049 tmp2m 1586930400 78 273.708 273.708 273.344 273.413 274.196 273.347 273.361 273.395 275.176 273.311 272.643 273.607 275.149 273.895 274.283 272.650 274.256 273.274 273.019 274.883 271.521 tmp2m 1586952000 84 283.794 284.941 284.597 283.467 285.521 284.886 283.135 283.705 284.894 284.497 284.060 284.113 284.078 284.095 284.092 283.764 283.350 283.378 282.995 284.136 282.440 tmp2m 1586973600 90 275.425 276.057 275.551 275.148 277.813 277.130 274.838 274.712 276.473 275.883 274.898 275.717 276.824 275.244 275.663 274.955 276.126 275.077 274.912 277.133 274.726 tmp2m 1586995200 96 274.203 275.007 274.121 273.602 274.710 274.370 273.988 273.770 275.609 273.911 273.719 274.642 275.062 274.194 274.311 273.588 273.741 273.540 273.473 275.483 273.005 tmp2m 1587016800 102 276.924 276.575 276.580 276.597 276.318 276.160 276.275 276.716 277.594 276.263 276.888 276.759 277.231 276.962 276.812 276.332 276.899 277.005 276.641 276.930 276.274 tmp2m 1587038400 108 287.703 287.236 286.634 286.588 287.009 288.110 286.729 287.924 287.927 286.938 287.745 287.946 287.893 287.052 287.185 287.209 286.760 286.186 288.091 288.069 287.755 tmp2m 1587060000 114 278.940 278.831 278.928 279.837 279.465 278.681 278.357 278.514 280.007 279.024 278.681 279.002 279.155 279.504 278.679 277.548 278.687 278.739 278.421 280.209 278.099 tmp2m 1587081600 120 276.004 276.547 277.087 277.217 277.455 276.533 276.283 276.685 277.345 276.593 275.695 276.033 276.382 277.173 276.877 275.918 276.415 276.861 276.213 276.401 275.873 tmp2m 1587103200 126 278.564 277.945 276.197 277.845 276.810 277.758 277.746 278.559 278.431 277.690 278.310 278.300 279.438 277.380 278.188 279.356 277.580 278.129 278.493 278.699 278.861 tmp2m 1587124800 132 287.645 286.070 279.434 284.633 281.218 286.525 284.846 284.262 286.469 283.580 285.562 287.197 289.141 281.709 286.686 290.017 285.896 283.526 285.495 287.105 285.842 tmp2m 1587146400 138 279.807 279.087 277.335 279.200 276.676 280.069 278.469 278.587 279.617 279.230 279.004 280.180 280.615 276.961 279.701 282.358 279.294 278.239 279.537 280.586 279.487 tmp2m 1587168000 144 275.321 275.846 276.223 276.039 273.950 277.809 275.329 276.732 277.709 277.870 275.583 276.016 278.030 275.173 276.858 279.228 276.505 275.476 275.770 276.892 276.569 tmp2m 1587189600 150 279.307 274.789 276.226 278.972 273.507 279.419 276.800 276.935 276.760 278.580 278.191 279.203 280.864 273.285 278.731 280.306 275.766 274.607 276.904 278.712 279.092 tmp2m 1587211200 156 290.448 285.039 279.095 289.269 281.053 289.353 288.207 281.494 287.503 285.446 286.861 287.285 291.866 276.710 288.306 289.378 278.057 283.877 287.406 286.159 287.488 tmp2m 1587232800 162 281.336 277.558 275.860 281.421 274.610 282.103 279.283 278.913 279.694 280.916 280.093 281.949 283.676 271.779 280.892 283.302 273.068 276.059 280.608 279.979 280.798 tmp2m 1587254400 168 278.969 272.517 273.262 278.316 269.694 280.160 273.509 275.994 277.545 278.338 277.819 278.589 279.739 268.231 277.529 280.860 267.265 270.507 277.155 276.545 276.355 tmp2m 1587276000 174 280.307 277.352 273.055 279.635 273.064 280.889 277.470 275.697 278.763 278.879 278.760 279.405 280.823 269.534 279.322 281.584 270.230 275.424 278.521 276.981 279.533 tmp2m 1587297600 180 289.408 288.527 278.152 289.869 279.155 288.976 286.871 286.002 290.444 288.261 287.418 289.579 291.714 280.771 284.208 289.391 281.325 286.240 286.016 286.692 284.088 tmp2m 1587319200 186 283.247 278.617 275.463 283.611 274.138 283.483 278.119 279.295 281.576 282.617 281.604 281.551 284.778 273.835 280.485 284.508 274.188 277.291 278.443 279.338 280.219 tmp2m 1587340800 192 279.031 275.372 273.071 280.301 269.730 280.201 272.175 275.345 278.055 278.762 277.635 277.640 280.770 270.424 278.444 280.825 270.953 271.818 274.979 274.405 277.874 tmp2m 1587362400 198 281.140 278.873 274.148 281.052 272.484 282.061 274.939 279.921 280.303 280.942 280.318 280.187 282.519 270.985 279.277 283.728 275.276 276.965 277.682 278.386 278.952 tmp2m 1587384000 204 292.001 289.954 278.880 284.763 282.353 292.102 283.050 292.352 290.901 288.932 288.005 289.231 293.654 276.442 283.711 290.624 289.320 286.798 285.581 291.783 283.579 tmp2m 1587405600 210 283.963 280.432 277.222 281.506 276.223 285.152 275.806 283.263 283.699 283.219 281.971 281.093 286.004 272.432 280.676 284.521 279.305 278.688 279.024 282.339 281.592 tmp2m 1587427200 216 279.241 273.421 273.962 279.243 269.542 282.339 267.506 279.080 279.522 279.447 276.969 273.508 281.489 268.388 277.273 282.076 273.223 271.437 273.956 276.847 278.558 tmp2m 1587448800 222 281.760 278.059 274.469 279.327 275.020 282.108 270.823 282.115 279.591 281.322 279.397 276.566 284.276 268.957 275.902 280.975 276.361 273.364 275.953 279.601 278.823 tmp2m 1587470400 228 287.109 286.255 282.610 282.497 285.253 283.116 280.582 290.982 285.663 287.284 287.576 284.643 289.654 276.144 280.288 288.188 284.476 281.316 284.775 288.934 285.457 tmp2m 1587492000 234 281.295 279.245 279.078 279.888 278.523 279.316 275.133 283.022 280.137 282.560 280.205 278.229 284.356 272.661 277.489 282.305 277.285 275.392 278.238 280.922 281.664 tmp2m 1587513600 240 278.750 271.614 275.272 276.701 271.568 276.400 267.395 277.576 274.687 275.649 274.810 272.570 281.239 266.367 274.668 277.988 269.491 269.164 275.487 276.908 277.632 tcdcclm 1586671200 6 1.930 2.274 1.940 2.311 3.128 1.655 2.051 2.409 1.952 1.416 2.954 2.059 2.102 2.351 0.690 2.030 1.652 1.923 2.315 3.093 2.167 tcdcclm 1586692800 12 3.197 2.895 2.878 3.099 3.427 3.648 3.407 3.537 3.579 3.073 3.469 2.754 2.871 3.232 2.062 3.105 1.368 3.146 3.528 3.305 3.183 tcdcclm 1586714400 18 3.864 3.046 3.519 4.067 4.449 4.028 3.196 3.668 3.976 3.195 5.034 3.638 2.873 3.217 4.025 4.466 3.690 4.349 3.522 3.633 4.851 tcdcclm 1586736000 24 5.622 5.295 5.444 6.226 5.196 4.960 5.041 6.080 5.375 5.375 5.515 5.359 5.636 4.300 4.678 6.111 5.726 5.873 5.528 5.500 6.468 tcdcclm 1586757600 30 6.598 5.466 6.286 6.658 6.713 6.974 6.373 6.702 6.513 6.416 6.646 6.910 5.234 5.845 6.386 7.308 6.503 7.024 6.350 6.249 6.428 tcdcclm 1586779200 36 5.795 5.519 5.908 4.899 6.896 6.153 6.044 6.184 5.648 4.183 5.683 6.675 4.054 4.532 5.971 6.177 6.080 5.786 6.314 5.837 6.129 tcdcclm 1586800800 42 6.789 6.905 6.363 6.596 7.297 7.511 6.954 6.797 6.916 6.518 6.713 7.038 6.791 5.004 6.781 6.985 6.895 7.125 7.277 6.956 6.935 tcdcclm 1586822400 48 7.479 6.598 7.218 7.484 7.604 6.621 7.655 7.337 7.503 7.350 7.621 7.383 7.146 7.014 7.617 7.319 7.599 7.265 7.399 7.002 7.617 tcdcclm 1586844000 54 5.602 5.595 5.926 5.669 5.874 5.589 5.670 5.781 6.518 5.306 5.926 5.525 5.568 5.529 5.681 5.466 5.816 5.298 5.509 5.526 5.686 tcdcclm 1586865600 60 2.613 1.529 2.617 0.824 3.176 2.655 3.130 3.840 4.426 1.756 3.588 2.587 0.669 3.554 1.147 3.232 1.560 1.157 1.852 2.252 3.451 tcdcclm 1586887200 66 0.000 0.098 0.098 0.119 0.098 0.111 0.157 0.118 0.757 0.098 0.046 0.059 0.223 0.139 0.098 0.007 0.195 0.080 0.000 0.428 0.146 tcdcclm 1586908800 72 0.139 0.105 0.105 0.139 0.105 0.156 0.254 0.139 0.389 0.105 0.073 0.067 0.767 0.734 0.254 0.073 0.202 0.369 0.135 0.422 0.073 tcdcclm 1586930400 78 0.983 0.451 0.686 0.513 1.801 1.775 0.449 2.087 4.279 1.157 0.482 0.620 4.966 2.970 3.077 0.348 2.602 2.124 2.261 4.770 0.665 tcdcclm 1586952000 84 1.558 1.881 2.488 1.221 2.202 2.920 0.111 3.074 3.487 1.929 0.674 1.157 2.741 4.122 2.158 1.177 3.872 1.925 2.497 4.412 0.769 tcdcclm 1586973600 90 0.986 1.171 1.984 0.578 3.836 0.845 0.140 1.113 1.066 4.528 2.275 1.219 3.013 2.868 2.048 0.621 0.944 1.832 2.022 2.818 0.904 tcdcclm 1586995200 96 0.474 0.319 0.806 1.165 1.843 0.496 1.010 0.410 1.837 0.949 0.365 1.392 2.126 3.392 0.253 1.526 0.933 1.441 0.721 0.783 0.930 tcdcclm 1587016800 102 3.896 0.784 0.441 4.758 1.343 0.895 5.021 3.315 6.082 0.817 1.397 1.339 2.068 1.651 0.520 0.533 4.637 1.782 2.143 1.653 2.402 tcdcclm 1587038400 108 1.776 2.455 3.337 3.886 2.642 3.326 1.344 3.248 2.025 0.482 0.887 0.684 2.059 1.044 2.862 3.310 1.950 2.552 1.764 5.067 5.449 tcdcclm 1587060000 114 5.358 6.874 5.958 6.379 6.343 6.058 2.274 6.796 5.024 2.407 6.321 6.259 6.362 6.578 6.861 1.591 4.013 6.177 5.430 5.732 5.875 tcdcclm 1587081600 120 1.883 5.249 7.044 5.241 7.855 7.262 6.154 6.737 5.696 4.301 3.463 1.633 1.191 7.201 7.344 3.299 6.418 6.027 5.765 0.857 6.450 tcdcclm 1587103200 126 0.311 3.055 7.979 6.397 7.209 3.690 6.268 6.750 3.373 4.506 3.390 0.716 3.814 6.902 7.095 4.976 3.778 4.306 5.341 3.475 4.291 tcdcclm 1587124800 132 1.619 2.398 7.667 3.775 3.913 2.026 5.360 4.949 1.011 5.713 5.137 1.948 5.650 4.930 1.883 3.106 3.428 3.082 4.686 2.865 1.616 tcdcclm 1587146400 138 3.194 1.918 7.084 5.556 4.798 5.078 2.362 6.309 5.507 7.061 4.588 3.531 5.499 5.598 5.767 4.968 6.264 2.069 2.463 5.099 6.169 tcdcclm 1587168000 144 1.719 6.541 7.697 4.159 6.850 5.556 4.518 7.802 6.691 7.979 2.656 3.914 5.678 7.681 4.679 6.815 4.920 5.659 4.451 6.726 3.432 tcdcclm 1587189600 150 2.233 5.932 7.189 2.539 6.576 5.678 1.420 6.788 5.675 6.915 1.879 0.987 4.816 7.241 4.677 7.627 7.633 5.124 2.175 5.682 7.064 tcdcclm 1587211200 156 0.143 1.521 6.896 2.717 3.341 4.700 0.692 6.278 1.032 2.925 3.273 1.741 4.208 6.988 2.748 4.756 7.187 0.525 1.328 2.076 6.777 tcdcclm 1587232800 162 1.990 0.199 6.456 5.956 0.294 7.720 1.418 3.282 0.164 6.675 4.167 4.300 5.207 5.400 2.207 7.773 1.834 0.063 4.720 4.885 6.545 tcdcclm 1587254400 168 5.205 0.143 6.451 4.753 0.435 7.496 3.292 5.761 1.975 6.129 3.280 5.063 3.455 5.981 4.102 7.190 0.709 0.059 7.180 4.724 5.525 tcdcclm 1587276000 174 6.521 0.156 4.861 4.566 5.543 7.599 3.940 3.948 3.865 1.325 4.576 4.791 4.591 0.388 6.710 5.611 0.080 0.178 4.434 2.552 6.339 tcdcclm 1587297600 180 5.143 0.038 5.288 2.160 5.945 2.787 4.044 2.950 1.712 0.836 1.497 4.093 3.929 1.245 6.952 7.058 0.132 0.059 2.517 0.073 7.225 tcdcclm 1587319200 186 5.541 0.327 6.304 6.041 5.817 6.021 2.341 2.708 5.575 3.788 2.604 2.077 6.657 5.080 7.277 7.575 0.059 0.038 1.432 0.139 7.143 tcdcclm 1587340800 192 3.226 0.524 7.055 7.328 3.887 6.274 0.128 1.672 7.197 3.065 0.296 2.139 7.344 6.188 7.415 5.677 0.073 0.119 0.864 0.229 6.933 tcdcclm 1587362400 198 0.763 0.602 7.263 6.804 0.220 3.369 0.178 1.452 4.449 2.799 0.300 2.202 5.374 5.595 7.144 5.743 0.101 0.080 1.908 1.107 6.683 tcdcclm 1587384000 204 1.470 0.451 7.549 7.608 0.166 5.029 0.080 2.697 2.112 3.227 0.210 0.709 5.519 5.444 7.018 4.694 0.021 2.858 2.202 1.878 7.303 tcdcclm 1587405600 210 5.042 0.690 7.418 7.908 0.133 5.917 0.262 2.457 2.713 5.134 3.148 0.149 5.526 5.913 7.129 5.385 0.028 2.804 1.783 0.720 5.936 tcdcclm 1587427200 216 4.580 0.678 7.575 7.684 0.118 7.512 0.101 4.523 3.919 5.560 0.819 0.080 5.952 5.688 6.966 5.225 1.928 0.910 2.640 1.540 6.860 tcdcclm 1587448800 222 5.871 0.958 6.907 7.214 0.541 7.735 0.168 7.040 2.818 2.633 0.080 0.153 6.151 4.788 5.989 5.551 2.412 0.847 3.971 2.217 7.267 tcdcclm 1587470400 228 6.898 0.502 5.836 5.448 1.577 7.514 0.168 3.585 4.695 2.486 0.101 0.080 4.251 3.211 7.165 2.248 0.139 0.443 2.628 0.355 5.322 tcdcclm 1587492000 234 7.241 0.447 5.500 6.791 2.191 7.464 0.136 2.688 5.361 4.259 0.059 0.202 5.683 3.715 6.914 1.662 2.926 0.772 4.805 0.369 5.095 tcdcclm 1587513600 240 7.905 0.523 6.596 5.773 2.149 6.792 0.095 0.157 6.518 2.878 0.038 0.772 7.434 1.889 7.130 3.869 0.451 0.582 6.271 0.516 4.258 partykit/inst/ULGcourse-2020/Data/GENS_00_innsbruck_20200413.dat0000644000176200001440000016114414172227777023005 0ustar liggesusers# ASCII output from GENSvis.py # Contains interpolated values from the # GFS ensemble on 1.000000 x 1.000000 degrees # The data in here are for station # 11120: INNSBRUCK # Station position: 11.3553 47.2589 # Used grid point 1: 12.0000 48.0000 # Used grid point 2: 12.0000 47.0000 # Used grid point 3: 11.0000 47.0000 # Used grid point 4: 11.0000 48.0000 varname timestamp step mem0 mem1 mem2 mem3 mem4 mem5 mem6 mem7 mem8 mem9 mem10 mem11 mem12 mem13 mem14 mem15 mem16 mem17 mem18 mem19 mem20 tmax2m 1586757600 6 275.163 275.128 275.032 275.117 275.177 275.421 275.077 275.180 275.046 275.051 275.408 275.179 275.132 275.120 274.955 275.385 275.311 275.085 275.290 275.447 275.287 tmax2m 1586779200 12 283.018 282.116 283.579 283.214 282.569 282.523 283.520 281.955 283.450 283.341 282.680 283.270 283.559 283.223 283.710 282.914 283.431 283.042 282.479 282.894 283.060 tmax2m 1586800800 18 282.555 281.691 282.661 282.480 282.411 281.978 282.683 282.466 283.031 282.995 282.669 282.535 283.079 282.755 283.410 282.215 282.835 282.822 282.072 282.791 282.300 tmax2m 1586822400 24 276.475 276.365 276.484 276.224 276.566 276.225 276.514 276.631 276.460 276.566 276.518 276.518 276.523 276.375 276.613 276.277 276.699 276.250 276.270 276.796 276.303 tmax2m 1586844000 30 271.153 271.383 271.072 271.035 271.492 270.438 271.052 272.043 271.517 271.348 271.362 271.300 271.395 271.095 271.367 270.610 272.273 270.991 271.078 271.951 270.530 tmax2m 1586865600 36 273.883 274.648 273.374 273.763 273.777 273.162 272.279 275.173 275.389 273.300 274.041 273.391 275.079 274.426 274.558 273.500 274.149 273.261 272.805 274.969 273.431 tmax2m 1586887200 42 274.428 275.118 273.967 274.368 274.254 273.895 272.974 275.578 275.794 273.914 274.491 273.804 275.725 274.815 275.098 274.009 274.694 273.907 273.344 275.400 273.997 tmax2m 1586908800 48 268.809 269.159 268.471 268.561 268.639 268.349 267.542 269.668 269.910 268.472 268.887 268.687 269.814 268.992 269.264 268.577 269.030 268.329 267.805 269.211 268.499 tmax2m 1586930400 54 271.321 271.819 270.605 271.451 271.211 270.933 270.329 272.153 272.117 270.863 271.216 270.691 272.115 271.166 271.941 270.636 271.553 270.779 270.430 271.817 270.660 tmax2m 1586952000 60 282.150 283.309 281.575 282.526 283.034 282.894 282.329 283.276 283.631 281.840 282.352 284.178 282.839 282.583 283.817 281.909 282.331 282.585 282.153 283.088 281.812 tmax2m 1586973600 66 283.764 284.767 283.198 284.924 284.809 284.907 283.400 284.577 285.660 283.467 283.968 285.006 284.191 284.663 284.910 285.209 284.480 283.288 283.516 284.439 283.812 tmax2m 1586995200 72 275.210 275.120 274.943 275.437 275.383 275.503 274.295 275.191 275.873 275.069 275.232 275.181 275.212 275.218 275.320 275.305 275.608 274.752 275.034 275.546 275.369 tmax2m 1587016800 78 275.770 276.444 275.579 275.596 275.544 275.606 275.598 276.262 276.173 275.833 275.392 275.779 276.232 275.910 276.053 275.408 275.598 276.108 275.754 275.333 275.344 tmax2m 1587038400 84 285.579 285.262 284.138 286.336 286.017 286.009 285.716 285.139 286.685 285.948 286.311 285.681 286.392 286.174 285.710 286.249 286.249 285.897 285.596 286.575 286.499 tmax2m 1587060000 90 285.274 284.851 284.197 286.301 286.078 285.687 285.297 284.443 286.262 285.852 286.364 285.446 285.864 286.161 285.204 286.021 286.140 285.152 285.652 286.707 285.852 tmax2m 1587081600 96 276.769 278.021 277.585 277.648 278.102 277.499 277.353 277.957 278.262 276.644 277.971 277.423 277.889 277.644 277.610 276.874 277.272 277.337 277.327 277.037 277.021 tmax2m 1587103200 102 277.017 277.088 276.742 276.908 276.683 276.834 276.866 276.859 277.441 277.309 277.164 276.724 277.668 277.169 277.429 277.776 277.509 277.125 277.077 277.703 277.868 tmax2m 1587124800 108 284.695 283.191 282.414 283.842 279.563 282.911 285.614 282.620 284.066 283.919 284.897 283.573 283.902 282.659 285.135 288.532 284.949 285.425 282.948 284.552 285.518 tmax2m 1587146400 114 284.734 283.001 282.705 283.214 278.880 282.916 285.921 282.133 284.172 283.796 284.997 283.984 283.999 281.996 285.093 287.866 284.956 285.380 282.447 284.439 285.369 tmax2m 1587168000 120 277.650 277.406 277.563 277.210 274.317 277.732 277.946 276.952 277.914 277.630 277.832 277.517 277.948 276.408 278.105 278.419 278.113 278.130 277.082 277.512 278.973 tmax2m 1587189600 126 276.804 274.204 275.635 275.498 271.305 275.151 277.369 275.397 276.258 276.358 277.649 277.010 276.734 273.922 277.477 279.059 277.041 276.993 275.399 276.928 277.771 tmax2m 1587211200 132 286.456 282.010 283.781 283.449 277.712 285.830 284.215 285.755 284.873 284.544 284.886 286.329 281.281 283.443 286.539 288.276 286.310 286.123 284.803 286.218 287.674 tmax2m 1587232800 138 286.543 281.986 283.847 283.852 278.326 285.682 283.130 285.847 283.656 284.664 284.039 286.335 281.358 283.946 286.317 287.620 286.813 286.279 284.990 286.239 287.603 tmax2m 1587254400 144 277.661 273.822 277.025 276.572 272.586 276.858 278.794 277.985 276.464 277.299 278.989 278.486 277.593 275.709 278.060 280.721 279.253 278.151 277.420 278.696 279.327 tmax2m 1587276000 150 276.671 273.145 274.331 274.732 272.160 275.457 277.114 275.929 271.632 275.097 278.221 276.845 274.769 273.304 276.608 279.762 277.966 277.302 275.918 276.696 278.743 tmax2m 1587297600 156 283.461 281.590 281.430 281.200 278.027 284.212 283.054 280.679 281.133 283.079 282.490 282.072 278.838 284.465 284.629 289.163 285.075 286.485 282.243 279.175 283.806 tmax2m 1587319200 162 282.506 281.567 280.644 281.465 277.356 283.347 282.624 280.324 281.429 283.269 281.993 280.921 279.063 284.945 284.736 288.223 284.685 286.655 281.520 279.958 283.382 tmax2m 1587340800 168 277.320 272.708 274.429 274.172 273.755 276.582 277.936 275.780 273.435 275.066 278.308 276.631 272.720 275.324 275.865 281.872 280.838 277.501 277.054 272.946 279.991 tmax2m 1587362400 174 273.507 271.599 270.424 270.679 270.399 275.004 275.848 273.084 270.648 272.876 276.778 271.504 270.608 273.953 272.289 278.765 278.394 276.610 274.990 270.478 278.620 tmax2m 1587384000 180 276.963 280.475 277.407 279.932 274.772 284.474 281.060 275.782 279.029 279.652 276.772 277.626 278.961 283.468 281.391 281.456 283.207 286.000 277.132 275.265 286.224 tmax2m 1587405600 186 277.028 280.770 277.476 280.200 274.554 284.781 281.015 276.016 279.343 279.889 275.934 277.369 279.213 283.685 281.517 281.399 282.526 286.056 277.097 275.566 286.421 tmax2m 1587427200 192 271.025 273.066 271.007 274.186 269.898 276.515 278.115 272.871 272.903 272.785 273.763 269.944 273.003 274.999 274.494 273.787 278.018 277.697 274.766 269.905 281.027 tmax2m 1587448800 198 269.150 272.009 269.771 271.329 268.806 273.698 277.432 273.057 271.747 269.181 273.438 269.622 271.491 272.284 271.138 271.518 276.348 277.089 273.072 268.148 278.727 tmax2m 1587470400 204 278.787 279.305 279.787 280.562 278.452 283.858 285.249 279.431 281.645 276.040 277.141 278.843 281.396 282.217 278.981 280.342 274.074 287.669 279.879 275.291 287.360 tmax2m 1587492000 210 279.106 279.366 280.735 280.600 279.879 284.575 284.040 280.082 281.925 276.213 277.285 279.025 281.718 282.688 279.189 280.622 273.771 286.640 280.127 275.431 287.263 tmax2m 1587513600 216 273.458 274.743 273.168 274.469 272.608 276.559 280.589 276.173 275.352 270.598 275.337 273.734 274.655 275.521 272.114 274.163 271.417 280.406 277.295 270.088 281.029 tmax2m 1587535200 222 271.154 272.561 273.393 271.384 274.345 275.454 277.960 273.119 273.899 269.561 274.253 272.230 272.331 273.312 269.094 269.778 270.758 277.712 275.882 269.434 277.422 tmax2m 1587556800 228 277.355 280.602 279.673 280.534 280.397 285.446 287.552 278.011 285.314 279.413 279.079 280.371 277.985 283.824 274.655 278.390 273.595 284.520 281.205 277.198 286.557 tmax2m 1587578400 234 277.679 281.158 279.796 280.577 280.826 285.724 287.909 277.815 284.325 279.992 279.549 280.729 278.166 284.257 275.324 278.558 273.953 283.041 281.969 277.714 286.870 tmax2m 1587600000 240 274.799 276.948 275.302 273.845 276.808 276.967 280.274 273.177 275.353 273.397 276.200 273.704 272.563 275.880 272.351 272.330 271.372 278.966 276.279 271.563 278.869 dd10m 1586757600 6 225.527 226.846 225.219 226.973 228.030 228.382 224.132 228.951 224.589 225.372 225.828 220.058 225.344 222.555 222.957 226.344 223.769 229.379 222.765 227.052 224.452 dd10m 1586779200 12 298.064 306.195 288.183 295.375 300.587 299.015 295.774 311.511 297.574 297.466 301.803 287.894 293.888 290.588 293.587 292.042 290.241 294.387 288.792 305.298 283.542 dd10m 1586800800 18 340.591 346.747 332.975 342.772 340.975 336.533 338.045 349.139 345.356 332.712 346.349 342.512 342.602 343.551 340.793 337.357 341.048 340.204 341.104 344.128 336.123 dd10m 1586822400 24 351.972 352.458 353.117 345.163 351.760 343.446 347.623 352.088 359.287 349.471 353.001 357.956 353.135 352.474 352.528 351.671 350.956 348.812 352.056 353.276 348.276 dd10m 1586844000 30 339.833 344.596 338.441 341.827 338.490 336.196 336.620 342.702 344.962 339.104 341.030 345.565 344.980 344.024 341.985 337.381 339.751 340.173 339.014 348.012 339.802 dd10m 1586865600 36 350.476 352.669 348.677 351.699 348.772 354.210 358.676 348.213 355.192 354.154 349.535 358.075 354.737 351.322 356.184 349.408 355.195 352.473 349.258 358.228 352.082 dd10m 1586887200 42 18.740 20.305 15.582 24.893 15.259 30.083 24.619 12.001 15.579 18.301 18.793 20.672 23.707 17.359 24.559 19.615 27.150 17.173 15.790 25.920 20.099 dd10m 1586908800 48 170.096 169.071 175.132 169.486 170.045 177.214 165.446 178.193 162.326 177.711 181.508 159.203 179.364 169.649 176.498 158.324 164.188 168.199 185.583 155.469 170.217 dd10m 1586930400 54 186.518 187.070 184.870 183.944 188.270 174.084 162.456 201.234 197.728 178.036 191.251 176.006 190.400 180.139 190.650 186.689 186.786 199.061 184.461 175.288 180.438 dd10m 1586952000 60 78.886 79.878 93.697 71.183 93.398 101.724 68.232 66.256 82.752 97.223 74.331 94.946 54.184 102.786 66.290 61.520 79.215 52.015 78.488 75.103 88.407 dd10m 1586973600 66 123.873 115.508 133.364 123.069 136.338 134.855 111.196 124.512 131.889 127.780 127.060 134.186 110.062 129.798 116.496 120.520 127.909 120.404 133.509 124.782 132.135 dd10m 1586995200 72 194.617 203.390 199.398 191.213 193.306 193.528 187.401 199.707 196.793 195.875 190.424 196.183 193.048 199.322 194.713 190.624 188.219 195.447 198.699 187.731 188.948 dd10m 1587016800 78 218.669 230.322 232.666 207.807 210.248 212.008 215.352 215.015 220.137 217.071 213.159 213.563 213.218 214.541 217.108 213.720 211.629 222.613 220.734 207.572 208.552 dd10m 1587038400 84 317.807 331.017 323.172 308.995 267.163 314.818 219.741 329.595 319.121 307.716 279.405 315.221 309.190 288.735 321.999 304.662 314.142 315.319 311.486 293.922 288.162 dd10m 1587060000 90 333.681 313.598 314.569 319.430 219.466 2.076 331.680 306.059 290.928 320.602 270.463 345.448 303.748 303.598 329.820 327.961 351.961 331.054 317.436 356.418 196.232 dd10m 1587081600 96 253.141 264.955 252.672 255.594 248.673 283.015 279.526 261.694 260.657 258.853 248.423 264.972 245.764 246.449 245.262 236.690 249.416 255.758 256.059 259.307 244.872 dd10m 1587103200 102 280.477 276.526 282.661 282.538 280.479 276.322 280.418 280.852 282.689 279.748 282.138 295.953 272.793 275.970 274.054 259.624 271.946 280.244 274.840 292.948 262.766 dd10m 1587124800 108 318.824 314.772 323.460 321.968 309.800 330.754 320.081 319.895 324.292 323.208 304.890 333.328 311.299 312.869 319.437 299.419 315.140 327.968 316.754 321.320 312.888 dd10m 1587146400 114 358.284 341.045 350.602 356.461 339.673 353.053 351.846 346.100 0.489 351.651 357.575 17.573 348.724 343.103 5.608 37.132 342.907 357.990 345.949 352.473 334.273 dd10m 1587168000 120 24.564 9.649 10.976 27.818 339.323 34.205 159.952 351.197 31.460 7.740 236.891 198.643 5.168 349.232 79.101 200.361 327.990 312.345 353.705 316.806 348.353 dd10m 1587189600 126 56.126 10.564 326.801 310.088 339.990 126.575 185.159 350.416 90.060 13.942 186.946 242.907 23.465 340.246 115.314 184.680 90.509 350.406 197.913 259.568 88.915 dd10m 1587211200 132 15.206 12.617 342.523 16.726 349.691 29.963 159.338 352.903 9.250 25.154 239.546 355.302 9.468 336.341 16.603 170.396 130.029 11.909 337.288 334.620 186.664 dd10m 1587232800 138 59.583 33.348 7.909 43.717 27.820 56.259 196.780 56.561 29.764 48.279 229.703 51.427 23.279 355.983 45.302 172.540 82.804 46.236 50.528 347.692 83.854 dd10m 1587254400 144 206.690 107.892 345.272 220.908 63.161 37.295 249.104 245.824 37.563 71.010 232.649 112.721 13.499 319.756 202.349 212.364 177.905 253.662 256.870 327.647 176.129 dd10m 1587276000 150 168.262 106.196 13.649 16.767 95.140 113.761 8.569 13.872 20.133 45.648 249.930 52.994 28.954 337.656 17.968 282.114 183.522 4.794 26.002 347.747 183.895 dd10m 1587297600 156 21.119 8.109 32.885 24.130 68.501 60.584 62.291 45.293 22.107 44.830 52.608 51.282 35.549 331.182 32.009 34.373 119.105 20.601 40.925 12.592 350.582 dd10m 1587319200 162 34.918 32.993 37.972 41.726 66.372 76.359 72.792 56.086 29.327 59.529 68.341 33.550 47.078 359.825 46.270 71.094 133.364 45.939 52.539 20.949 59.389 dd10m 1587340800 168 35.038 108.678 49.190 60.824 79.389 141.344 104.488 85.632 81.870 103.520 96.031 42.096 68.623 337.139 70.544 46.215 163.750 170.067 90.222 20.006 136.828 dd10m 1587362400 174 38.278 43.304 41.054 67.787 32.424 64.670 116.642 77.271 68.019 44.436 77.968 44.251 39.455 354.226 72.403 57.541 140.520 62.407 66.795 17.760 151.953 dd10m 1587384000 180 42.391 30.252 38.930 62.269 29.233 55.041 112.582 79.828 61.290 39.862 79.023 36.541 46.038 12.167 66.928 47.892 106.670 51.377 59.119 24.602 128.890 dd10m 1587405600 186 44.117 42.311 35.601 52.524 21.933 39.382 125.191 104.572 59.067 29.938 80.153 49.855 41.766 28.227 58.742 54.963 95.132 80.191 56.334 35.413 118.366 dd10m 1587427200 192 50.570 126.121 26.899 35.744 2.679 20.970 154.187 115.115 89.140 22.187 94.111 81.142 22.015 53.823 48.358 49.197 81.740 163.084 79.799 32.909 141.183 dd10m 1587448800 198 55.536 92.516 23.842 27.300 327.997 32.641 148.186 104.182 76.046 23.484 93.374 79.492 358.841 47.045 32.463 33.837 16.297 176.029 95.436 33.918 122.878 dd10m 1587470400 204 52.952 74.562 29.526 34.410 3.159 21.271 63.823 77.178 72.257 23.830 91.383 65.733 4.820 54.783 37.832 33.474 22.627 83.147 98.359 38.353 79.326 dd10m 1587492000 210 49.968 87.905 50.581 41.935 44.303 30.729 66.594 55.992 81.443 24.363 86.139 52.027 4.158 40.796 38.429 37.222 28.930 135.454 98.604 36.792 69.806 dd10m 1587513600 216 66.782 148.031 180.336 77.147 186.052 235.205 96.898 73.090 162.459 20.206 134.200 50.673 22.270 317.523 46.671 60.392 39.615 177.908 186.631 358.420 102.537 dd10m 1587535200 222 74.547 152.080 167.793 66.470 179.242 287.775 75.502 30.529 192.454 13.064 142.694 356.560 44.773 291.475 56.868 61.174 30.102 175.888 342.845 348.877 63.029 dd10m 1587556800 228 74.120 100.602 147.275 51.172 127.540 336.893 68.030 38.273 46.290 22.194 80.155 18.618 55.430 346.415 62.178 49.734 37.836 165.787 7.412 7.026 47.283 dd10m 1587578400 234 74.522 83.012 107.412 57.127 134.769 11.128 62.934 37.048 69.881 21.879 40.626 8.376 53.857 354.849 50.058 54.476 30.226 189.481 6.234 16.538 84.748 dd10m 1587600000 240 139.352 112.700 164.229 173.214 189.170 300.026 182.589 51.618 205.382 274.720 226.308 329.248 102.007 347.864 99.947 76.064 37.903 196.790 13.597 347.607 180.472 ff10m 1586757600 6 2.389 2.405 2.405 2.382 2.337 2.261 2.438 2.335 2.364 2.480 2.417 2.400 2.364 2.385 2.441 2.381 2.280 2.430 2.402 2.290 2.446 ff10m 1586779200 12 2.039 2.237 1.796 2.228 1.813 2.107 1.968 1.979 1.937 1.905 2.164 1.923 1.815 2.140 1.979 2.008 1.710 2.242 2.096 1.852 1.883 ff10m 1586800800 18 2.422 2.734 1.952 2.835 2.278 2.682 2.405 2.557 2.360 2.180 2.566 2.331 2.534 2.717 2.397 2.509 1.954 2.618 2.347 2.393 2.512 ff10m 1586822400 24 3.373 3.153 3.518 3.364 3.650 3.350 3.481 3.295 3.029 3.635 3.326 3.425 3.543 3.115 3.633 3.450 3.365 3.509 3.398 3.473 3.277 ff10m 1586844000 30 3.461 3.539 3.484 3.586 3.479 3.794 3.904 3.348 3.221 3.784 3.370 3.604 3.442 3.516 3.521 3.365 3.533 3.761 3.816 3.345 3.530 ff10m 1586865600 36 3.821 3.954 3.775 3.709 3.638 3.694 3.740 4.000 3.836 3.705 3.776 3.766 3.714 3.934 3.742 3.837 3.681 3.625 3.811 3.802 3.767 ff10m 1586887200 42 2.451 2.517 2.639 2.303 2.331 2.347 2.328 2.582 2.510 2.646 2.431 2.621 2.485 2.465 2.491 2.558 2.249 2.543 2.346 2.246 2.647 ff10m 1586908800 48 1.189 1.292 1.235 1.348 1.095 1.852 0.713 0.984 1.117 1.187 1.470 0.688 1.600 1.220 1.500 1.191 1.579 1.006 0.968 1.267 1.449 ff10m 1586930400 54 1.101 1.252 1.160 0.958 1.251 1.359 0.644 0.821 1.276 1.268 1.041 0.963 0.943 1.233 0.661 0.988 1.434 1.038 1.105 1.375 1.100 ff10m 1586952000 60 1.561 1.273 1.371 1.729 1.290 1.813 2.030 1.444 1.205 1.493 1.521 1.683 1.558 1.306 1.705 1.756 1.759 1.382 1.509 1.560 1.598 ff10m 1586973600 66 1.529 1.336 1.488 1.708 1.355 1.687 1.613 1.353 1.562 1.539 1.543 1.410 1.571 1.336 1.634 1.783 1.746 1.293 1.499 1.805 1.700 ff10m 1586995200 72 2.582 2.481 2.495 2.691 2.619 2.571 2.518 2.526 2.599 2.560 2.640 2.412 2.592 2.349 2.594 2.819 2.632 2.454 2.508 2.750 2.640 ff10m 1587016800 78 2.256 2.020 2.056 2.507 2.397 2.142 1.986 2.206 2.251 2.180 2.174 2.184 2.246 2.155 2.276 2.192 2.317 2.014 2.235 2.413 2.270 ff10m 1587038400 84 1.803 1.850 2.373 1.614 1.095 1.476 0.219 2.198 1.330 1.777 1.238 1.789 1.564 1.403 2.014 1.432 1.595 1.583 1.681 1.653 1.259 ff10m 1587060000 90 1.149 1.481 1.173 1.072 0.872 1.054 0.898 1.036 0.918 1.043 0.726 1.342 0.801 1.129 0.920 0.696 0.539 1.233 1.056 0.600 0.043 ff10m 1587081600 96 2.213 2.390 2.415 2.351 2.436 1.692 1.359 2.159 2.280 2.035 2.096 2.043 2.231 2.608 2.269 1.978 2.129 1.858 2.242 1.935 2.018 ff10m 1587103200 102 1.979 2.275 2.367 2.366 2.931 2.308 1.596 2.169 2.623 1.914 1.759 2.202 1.854 2.835 1.542 1.109 1.572 1.539 2.229 2.016 1.304 ff10m 1587124800 108 4.109 4.198 4.003 4.605 4.424 3.894 2.492 3.964 4.052 4.055 3.438 3.148 3.918 4.466 3.510 1.253 3.217 3.659 3.981 3.912 2.624 ff10m 1587146400 114 2.419 3.506 2.513 2.769 3.535 2.803 1.780 2.552 2.642 2.360 2.000 1.724 2.686 2.944 2.205 1.427 2.005 2.086 2.797 2.209 2.084 ff10m 1587168000 120 1.162 1.388 0.497 1.359 2.794 1.388 0.145 1.109 1.398 1.327 0.804 0.241 1.200 1.713 0.562 1.691 0.967 0.544 1.121 0.804 1.161 ff10m 1587189600 126 0.308 1.368 0.641 0.210 2.119 0.414 1.426 0.747 0.725 1.212 1.455 0.551 0.864 1.487 0.637 1.543 0.837 1.070 0.279 0.236 0.270 ff10m 1587211200 132 1.064 3.132 2.315 2.304 2.832 1.491 1.202 0.823 1.784 2.017 0.566 1.911 2.025 2.358 0.828 1.384 0.439 2.710 1.037 1.446 0.248 ff10m 1587232800 138 1.629 3.109 2.166 2.011 2.218 1.863 0.949 1.499 3.016 2.344 0.594 1.503 2.215 2.757 1.763 0.868 1.714 2.004 0.769 1.697 0.847 ff10m 1587254400 144 0.765 1.066 0.978 0.266 1.413 1.258 1.025 0.438 1.396 0.321 1.156 0.194 1.539 1.512 0.769 1.594 2.101 0.329 0.929 1.911 1.339 ff10m 1587276000 150 0.450 0.457 1.318 1.547 1.871 1.317 0.387 1.577 2.070 1.678 0.668 1.378 2.765 1.991 1.111 0.163 1.653 1.342 0.878 2.586 1.979 ff10m 1587297600 156 2.150 3.682 3.169 3.540 3.078 2.939 2.524 3.246 4.332 3.326 0.828 2.667 4.750 2.979 3.292 1.148 0.925 3.248 1.836 3.716 1.096 ff10m 1587319200 162 3.218 3.314 3.871 3.223 2.550 2.652 3.010 3.402 3.249 2.837 1.435 3.500 3.589 2.628 3.929 1.756 1.632 2.426 2.537 4.329 2.041 ff10m 1587340800 168 2.757 1.064 2.427 1.731 1.338 1.862 2.993 2.387 0.525 1.559 2.093 2.453 1.397 1.717 2.252 1.906 2.539 1.249 1.440 3.442 1.877 ff10m 1587362400 174 3.602 1.385 3.158 2.697 2.561 1.941 2.925 3.243 2.513 2.702 2.618 3.474 2.498 1.742 2.407 3.236 1.945 0.591 2.160 3.928 2.442 ff10m 1587384000 180 5.356 2.819 5.358 4.566 5.055 3.774 3.393 4.996 4.353 4.926 3.693 5.617 5.019 3.315 4.001 5.764 2.976 3.204 4.132 4.912 2.053 ff10m 1587405600 186 4.423 3.100 3.681 3.251 3.745 3.462 2.451 4.436 3.115 4.077 3.582 5.075 3.358 2.996 3.121 3.793 2.666 2.326 4.063 3.817 2.167 ff10m 1587427200 192 2.817 1.212 1.662 1.911 2.389 1.645 2.167 3.734 1.436 3.201 3.254 2.797 1.647 1.441 2.162 1.816 0.818 2.017 3.026 2.738 1.994 ff10m 1587448800 198 2.307 1.215 1.594 1.748 1.170 1.059 1.293 2.241 1.196 3.653 2.320 2.445 1.988 1.688 2.380 2.284 2.595 1.648 2.519 3.103 1.715 ff10m 1587470400 204 3.900 2.393 2.739 3.692 2.444 3.345 2.547 2.574 2.477 5.528 2.654 3.396 3.769 2.954 4.021 4.199 3.102 1.435 2.782 4.951 3.104 ff10m 1587492000 210 3.491 2.186 1.481 2.976 1.131 1.806 2.230 2.245 2.117 4.159 2.256 2.482 3.076 2.034 3.684 3.578 2.787 1.914 1.630 3.594 2.833 ff10m 1587513600 216 1.950 2.003 2.234 1.086 2.250 1.209 1.436 0.997 2.183 1.708 1.742 0.148 1.823 0.302 2.527 1.337 1.416 2.741 0.648 0.830 1.305 ff10m 1587535200 222 2.030 1.800 1.931 1.165 1.544 1.021 1.546 2.353 1.515 2.161 1.201 1.648 2.520 1.041 2.475 1.596 1.573 2.554 1.404 2.120 1.255 ff10m 1587556800 228 3.088 2.199 1.667 2.144 1.754 2.603 2.755 3.312 1.467 3.814 0.946 2.807 3.661 2.304 2.754 3.114 2.318 2.215 2.551 4.160 2.971 ff10m 1587578400 234 2.319 2.117 1.177 1.789 1.332 1.835 2.371 3.660 0.748 2.706 1.217 2.595 2.922 2.191 2.222 3.254 2.324 1.672 2.387 2.869 1.669 ff10m 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274.823 274.611 274.750 275.204 275.194 275.418 273.833 274.852 275.639 274.761 274.993 274.957 274.763 274.967 274.879 275.009 275.391 274.212 274.752 275.477 275.240 tmp2m 1586995200 72 273.349 273.572 272.982 273.419 273.504 273.078 272.576 273.761 274.042 273.213 273.341 273.343 273.497 273.454 273.488 273.144 273.571 273.244 273.234 273.371 273.092 tmp2m 1587016800 78 275.770 276.444 275.579 275.587 275.544 275.606 275.598 276.262 276.173 275.833 275.392 275.779 276.232 275.910 276.053 275.408 275.598 276.108 275.754 275.333 275.344 tmp2m 1587038400 84 285.335 284.664 283.928 286.284 285.921 286.009 285.594 284.695 286.685 285.948 286.311 285.576 286.096 286.174 285.466 286.043 286.249 285.775 285.596 286.575 285.841 tmp2m 1587060000 90 277.339 278.515 277.717 277.966 278.299 277.545 277.601 277.931 278.421 276.982 278.224 277.517 277.632 277.699 277.892 277.368 277.651 277.989 277.984 277.156 276.206 tmp2m 1587081600 96 275.121 275.483 275.302 275.749 275.866 276.234 275.085 276.351 276.363 275.231 276.401 276.025 275.812 276.657 275.111 274.728 275.168 274.920 275.059 276.098 274.553 tmp2m 1587103200 102 277.000 276.996 276.742 276.844 276.650 276.397 276.866 276.754 277.375 277.309 277.062 276.503 277.651 277.100 277.429 277.767 277.509 277.125 277.077 277.652 277.868 tmp2m 1587124800 108 284.695 283.034 282.386 283.330 278.646 282.801 285.614 282.194 283.883 283.725 284.844 283.547 283.850 282.158 284.986 288.283 284.901 285.340 282.354 284.488 285.461 tmp2m 1587146400 114 277.901 277.514 277.546 277.286 274.543 277.938 278.296 277.080 278.107 277.695 278.257 277.733 277.969 276.553 278.384 279.406 278.293 278.476 277.182 277.869 279.072 tmp2m 1587168000 120 274.435 274.236 274.940 275.032 271.222 274.610 274.194 275.070 275.333 275.433 273.979 273.845 276.040 273.605 275.676 276.267 276.272 274.808 275.105 274.779 276.828 tmp2m 1587189600 126 276.379 273.741 275.626 275.328 270.262 275.125 277.291 275.127 275.922 276.153 277.630 277.001 276.377 273.635 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267.019 270.380 275.205 270.083 268.626 268.525 272.376 267.445 269.169 269.006 269.730 269.164 276.099 274.221 271.772 267.218 277.415 tmp2m 1587448800 198 269.081 271.992 269.819 271.329 268.806 273.698 277.432 272.973 271.599 269.050 273.438 269.622 271.491 272.284 270.910 271.484 273.618 277.089 273.072 268.148 278.560 tmp2m 1587470400 204 278.787 279.305 279.797 280.543 278.431 283.858 284.374 279.383 281.648 276.040 277.067 278.796 281.396 282.217 278.981 280.342 273.799 286.742 279.306 275.291 287.360 tmp2m 1587492000 210 273.889 274.942 273.932 274.948 273.082 277.354 280.767 276.475 275.624 271.075 275.590 274.200 275.460 276.262 272.532 274.737 271.617 280.696 277.489 270.510 281.360 tmp2m 1587513600 216 270.632 271.621 269.908 268.670 271.257 271.370 277.362 269.483 270.894 266.525 273.576 268.191 272.405 269.524 268.698 268.199 270.160 276.862 273.599 266.210 275.206 tmp2m 1587535200 222 271.138 272.561 273.393 271.384 274.345 275.454 277.944 273.028 273.852 269.561 274.237 272.178 271.766 273.312 268.674 269.762 270.689 277.638 275.882 269.434 277.406 tmp2m 1587556800 228 277.259 280.602 279.673 280.486 280.350 285.371 287.543 277.985 285.186 279.413 279.031 280.323 277.985 283.777 274.655 278.342 273.595 283.408 281.157 277.198 286.557 tmp2m 1587578400 234 275.044 277.259 275.556 274.462 276.977 277.568 280.934 273.511 276.984 273.693 276.639 274.758 273.030 276.381 272.618 272.729 271.567 279.049 276.724 271.896 279.582 tmp2m 1587600000 240 272.351 273.415 271.617 269.860 272.291 271.898 275.406 269.593 271.431 267.757 273.267 269.033 267.076 271.466 267.704 268.742 267.717 277.379 272.315 267.700 274.903 tcdcclm 1586757600 6 6.846 7.098 6.829 6.957 6.658 7.017 6.873 7.178 7.217 7.003 7.029 7.098 7.091 6.997 6.860 6.741 6.827 7.127 7.045 6.984 6.894 tcdcclm 1586779200 12 6.907 7.216 5.718 3.417 7.469 7.144 6.154 7.083 4.899 5.931 6.181 7.111 6.326 5.680 5.402 7.113 6.096 5.964 7.641 6.826 7.238 tcdcclm 1586800800 18 5.940 6.269 6.257 5.712 7.096 6.377 5.483 6.477 4.704 5.634 6.339 5.545 5.630 5.227 5.118 5.629 5.264 5.570 5.916 5.704 6.183 tcdcclm 1586822400 24 6.766 6.731 7.148 6.773 7.285 6.844 6.968 6.634 6.528 7.094 7.049 6.842 6.951 6.684 6.839 7.123 7.064 7.299 7.092 6.872 6.854 tcdcclm 1586844000 30 5.214 5.230 5.441 5.333 5.227 5.226 5.756 5.348 5.014 5.970 5.205 5.253 5.304 5.298 4.960 5.445 5.403 5.812 5.371 5.390 5.316 tcdcclm 1586865600 36 3.809 3.066 4.810 4.232 4.572 4.347 5.546 3.206 2.811 4.983 3.912 5.051 2.964 3.787 3.049 4.155 4.543 4.691 5.373 2.166 4.217 tcdcclm 1586887200 42 0.123 0.117 0.894 0.330 0.561 0.628 1.782 0.117 0.067 1.633 0.274 2.955 0.067 0.198 0.108 0.807 0.295 1.942 2.054 0.036 0.806 tcdcclm 1586908800 48 0.038 0.046 0.392 0.067 0.256 0.067 0.478 0.038 0.021 0.532 0.067 1.120 0.046 0.067 0.067 0.358 0.105 0.642 0.639 0.046 0.294 tcdcclm 1586930400 54 0.139 0.084 0.214 0.447 0.193 0.156 0.650 0.208 0.328 0.186 0.317 0.052 0.165 0.145 0.153 0.167 0.241 0.072 0.363 0.131 0.090 tcdcclm 1586952000 60 1.463 1.053 1.542 2.460 1.793 1.337 2.366 1.355 1.963 0.252 1.634 0.614 0.532 1.368 0.471 1.441 1.220 1.237 2.064 0.804 0.386 tcdcclm 1586973600 66 1.767 1.756 1.189 2.337 2.649 2.312 2.274 1.683 1.984 1.043 1.435 1.844 1.730 2.260 0.486 1.479 1.233 1.652 1.985 0.499 2.106 tcdcclm 1586995200 72 1.467 0.841 1.195 2.304 2.705 2.556 2.287 1.521 0.773 1.602 2.024 3.483 2.210 1.488 2.413 1.884 1.290 2.225 1.781 0.841 1.933 tcdcclm 1587016800 78 0.906 0.244 0.306 1.929 0.707 2.555 3.650 1.019 0.504 2.476 1.443 3.371 2.310 0.781 2.797 1.306 1.147 1.423 2.091 0.275 0.457 tcdcclm 1587038400 84 0.969 1.386 2.067 0.368 0.409 0.453 2.066 1.424 1.327 0.511 0.896 1.317 1.648 0.438 1.733 1.719 1.564 2.089 0.842 0.115 4.132 tcdcclm 1587060000 90 5.646 6.593 5.786 5.726 5.582 5.295 5.770 6.695 6.696 5.814 6.290 6.064 5.674 6.491 6.691 7.099 6.819 6.968 5.939 4.497 5.804 tcdcclm 1587081600 96 3.706 4.684 6.171 5.196 7.595 6.715 6.161 6.715 6.409 3.403 7.127 5.883 5.744 6.652 3.174 3.155 3.527 3.029 3.435 6.532 5.759 tcdcclm 1587103200 102 2.787 5.173 4.908 5.924 7.709 7.260 2.857 4.731 5.268 4.909 4.071 4.311 6.208 6.815 3.220 0.955 6.280 4.475 3.809 6.322 4.583 tcdcclm 1587124800 108 0.491 3.640 3.703 2.128 7.729 5.107 1.545 3.296 2.117 2.654 2.420 3.722 5.138 4.696 4.797 3.117 5.397 2.022 5.121 3.824 2.261 tcdcclm 1587146400 114 0.754 3.749 2.668 3.098 7.531 4.786 3.112 3.887 1.757 2.103 3.078 1.809 3.379 5.247 4.601 6.088 1.915 3.822 4.912 3.283 5.827 tcdcclm 1587168000 120 4.193 5.579 5.686 6.201 6.867 6.331 2.331 6.139 5.187 5.038 0.656 1.384 6.857 5.744 4.174 4.468 3.949 4.718 6.521 4.798 6.114 tcdcclm 1587189600 126 3.463 3.689 2.055 5.619 6.059 3.798 3.440 4.203 3.043 2.231 2.558 0.599 6.847 4.980 2.941 6.499 3.426 3.817 2.424 4.019 5.702 tcdcclm 1587211200 132 3.387 1.756 1.268 2.975 2.741 0.164 7.598 2.469 1.019 2.330 5.812 0.957 7.024 0.799 2.399 6.231 2.597 1.198 1.478 2.542 3.595 tcdcclm 1587232800 138 3.146 1.201 1.945 2.638 1.488 1.034 7.410 3.584 3.295 3.807 7.701 4.877 5.685 0.482 2.555 7.868 5.421 1.317 3.508 3.663 5.569 tcdcclm 1587254400 144 2.155 0.325 3.213 1.838 3.729 1.750 6.892 7.189 3.640 5.488 7.614 6.210 5.412 1.643 1.453 6.862 5.779 0.640 4.822 4.220 7.188 tcdcclm 1587276000 150 3.908 0.261 1.678 2.616 4.650 4.547 7.389 6.013 0.271 3.220 7.024 5.782 5.628 0.269 1.301 5.766 5.267 2.477 6.761 6.224 7.175 tcdcclm 1587297600 156 3.159 0.202 2.689 1.850 5.096 1.159 6.908 5.214 0.067 0.514 7.391 5.388 3.242 0.435 0.901 4.515 5.717 3.553 6.793 4.941 7.528 tcdcclm 1587319200 162 5.535 0.250 4.453 0.510 5.939 1.211 7.255 5.484 0.087 0.300 7.862 5.830 0.248 0.303 0.940 5.793 7.416 3.273 5.848 2.333 7.648 tcdcclm 1587340800 168 5.757 0.139 5.229 0.341 5.834 2.972 7.959 6.153 0.263 0.720 7.813 5.309 0.254 0.137 0.891 7.598 7.787 5.775 5.903 5.545 5.936 tcdcclm 1587362400 174 5.772 0.139 3.926 0.491 4.964 1.667 7.710 5.796 0.316 3.343 7.643 3.443 0.178 0.660 1.017 6.752 7.631 5.210 6.767 6.339 6.282 tcdcclm 1587384000 180 3.011 0.265 1.138 0.307 4.284 0.021 6.485 5.851 1.721 0.588 7.573 0.993 0.139 0.403 0.313 2.517 7.254 2.967 6.487 3.356 6.913 tcdcclm 1587405600 186 3.345 1.710 0.503 0.164 5.104 0.059 7.637 6.293 2.851 0.597 7.621 3.244 0.327 0.229 1.621 0.334 7.731 0.481 6.539 1.500 7.077 tcdcclm 1587427200 192 4.435 4.087 1.145 0.241 5.558 0.392 7.566 7.490 0.889 3.060 7.881 4.003 2.462 0.682 0.623 0.105 7.934 0.833 6.995 4.245 6.688 tcdcclm 1587448800 198 1.642 3.370 0.122 0.227 1.488 0.224 5.710 7.694 2.560 0.695 7.508 2.123 0.361 0.271 3.206 0.147 7.907 4.314 7.296 1.553 4.456 tcdcclm 1587470400 204 0.532 4.175 0.227 0.333 0.919 0.174 5.389 6.756 0.325 2.574 7.368 2.121 0.157 0.101 0.666 0.196 7.809 5.667 6.991 2.277 3.001 tcdcclm 1587492000 210 4.506 5.399 0.638 0.694 0.922 1.621 5.548 5.612 3.137 4.204 7.593 3.769 0.937 0.178 3.880 0.378 7.877 3.811 7.577 1.915 5.180 tcdcclm 1587513600 216 5.949 5.774 1.712 0.872 1.174 2.198 5.475 3.979 1.859 3.103 6.625 2.454 4.033 0.139 6.591 0.370 7.879 3.381 7.734 1.266 5.068 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Originally, the method was implemented in the package \pkg{party} almost entirely in \proglang{C} while the new implementation is now almost entirely in \proglang{R}. In particular, this has the advantage that all the generic infrastructure from \pkg{partykit} can be reused, making many computations more modular and easily extensible. Hence, \code{partykit::ctree} is the new reference implementation that will be improved and developed further in the future. In almost all cases, the two implementations will produce identical trees. In exceptional cases, additional parameters have to be specified in order to ensure backward compatibility. These and novel features in \code{ctree:partykit} are introduced in Section~\ref{sec:novel}. \section{Introduction} The majority of recursive partitioning algorithms are special cases of a simple two-stage algorithm: First partition the observations by univariate splits in a recursive way and second fit a constant model in each cell of the resulting partition. The most popular implementations of such algorithms are `CART' \citep{Breiman+Friedman+Olshen:1984} and `C4.5' \citep{Quinlan:1993}. Not unlike AID, both perform an exhaustive search over all possible splits maximizing an information measure of node impurity selecting the covariate showing the best split. This approach has two fundamental problems: overfitting and a selection bias towards covariates with many possible splits. With respect to the overfitting problem \cite{Mingers:1987} notes that the algorithm \begin{quote} [\ldots] has no concept of statistical significance, and so cannot distinguish between a significant and an insignificant improvement in the information measure. \end{quote} With conditional inference trees \citep[see][for a full description of its methodological foundations]{Hothorn+Hornik+Zeileis:2006} we enter at the point where \cite{White+Liu:1994} demand for \begin{quote} [\ldots] a \textit{statistical} approach [to recursive partitioning] which takes into account the \textit{distributional} properties of the measures. \end{quote} We present a unified framework embedding recursive binary partitioning into the well defined theory of permutation tests developed by \cite{Strasser+Weber:1999}. The conditional distribution of statistics measuring the association between responses and covariates is the basis for an unbiased selection among covariates measured at different scales. Moreover, multiple test procedures are applied to determine whether no significant association between any of the covariates and the response can be stated and the recursion needs to stop. \section{Recursive binary partitioning} \label{algo} We focus on regression models describing the conditional distribution of a response variable $\Y$ given the status of $m$ covariates by means of tree-structured recursive partitioning. The response $\Y$ from some sample space $\sY$ may be multivariate as well. The $m$-dimensional covariate vector $\X = (X_1, \dots, X_m)$ is taken from a sample space $\sX = \sX_1 \times \cdots \times \sX_m$. Both response variable and covariates may be measured at arbitrary scales. We assume that the conditional distribution $D(\Y | \X)$ of the response $\Y$ given the covariates $\X$ depends on a function $f$ of the covariates \begin{eqnarray*} D(\Y | \X) = D(\Y | X_1, \dots, X_m) = D(\Y | f( X_1, \dots, X_m)), \end{eqnarray*} where we restrict ourselves to partition based regression relationships, i.e., $r$ disjoint cells $B_1, \dots, B_r$ partitioning the covariate space $\sX = \bigcup_{k = 1}^r B_k$. A model of the regression relationship is to be fitted based on a learning sample $\LS$, i.e., a random sample of $n$ independent and identically distributed observations, possibly with some covariates $X_{ji}$ missing, \begin{eqnarray*} \LS & = & \{ (\Y_i, X_{1i}, \dots, X_{mi}); i = 1, \dots, n \}. \end{eqnarray*} A generic algorithm for recursive binary partitioning for a given learning sample $\LS$ can be formulated using non-negative integer valued case weights $\w = (w_1, \dots, w_n)$. Each node of a tree is represented by a vector of case weights having non-zero elements when the corresponding observations are elements of the node and are zero otherwise. The following algorithm implements recursive binary partitioning: \begin{enumerate} \item For case weights $\w$ test the global null hypothesis of independence between any of the $m$ covariates and the response. Stop if this hypothesis cannot be rejected. Otherwise select the covariate $X_{j^*}$ with strongest association to $\Y$. \item Choose a set $A^* \subset \sX_{j^*}$ in order to split $\sX_{j^*}$ into two disjoint sets $A^*$ and $\sX_{j^*} \setminus A^*$. The case weights $\w_\text{left}$ and $\w_\text{right}$ determine the two subgroups with $w_{\text{left},i} = w_i I(X_{j^*i} \in A^*)$ and $w_{\text{right},i} = w_i I(X_{j^*i} \not\in A^*)$ for all $i = 1, \dots, n$ ($I(\cdot)$ denotes the indicator function). \item Recursively repeat steps 1 and 2 with modified case weights $\w_\text{left}$ and $\w_\text{right}$, respectively. \end{enumerate} The separation of variable selection and splitting procedure into steps 1 and 2 of the algorithm is the key for the construction of interpretable tree structures not suffering a systematic tendency towards covariates with many possible splits or many missing values. In addition, a statistically motivated and intuitive stopping criterion can be implemented: We stop when the global null hypothesis of independence between the response and any of the $m$ covariates cannot be rejected at a pre-specified nominal level~$\alpha$. The algorithm induces a partition $\{B_1, \dots, B_r\}$ of the covariate space $\sX$, where each cell $B \in \{B_1, \dots, B_r\}$ is associated with a vector of case weights. \section{Recursive partitioning by conditional inference} \label{framework} In the main part of this section we focus on step 1 of the generic algorithm. Unified tests for independence are constructed by means of the conditional distribution of linear statistics in the permutation test framework developed by \cite{Strasser+Weber:1999}. The determination of the best binary split in one selected covariate and the handling of missing values is performed based on standardized linear statistics within the same framework as well. \subsection{Variable selection and stopping criteria} At step 1 of the generic algorithm given in Section~\ref{algo} we face an independence problem. We need to decide whether there is any information about the response variable covered by any of the $m$ covariates. In each node identified by case weights $\w$, the global hypothesis of independence is formulated in terms of the $m$ partial hypotheses $H_0^j: D(\Y | X_j) = D(\Y)$ with global null hypothesis $H_0 = \bigcap_{j = 1}^m H_0^j$. When we are not able to reject $H_0$ at a pre-specified level $\alpha$, we stop the recursion. If the global hypothesis can be rejected, we measure the association between $\Y$ and each of the covariates $X_j, j = 1, \dots, m$, by test statistics or $P$-values indicating the deviation from the partial hypotheses $H_0^j$. For notational convenience and without loss of generality we assume that the case weights $w_i$ are either zero or one. The symmetric group of all permutations of the elements of $(1, \dots, n)$ with corresponding case weights $w_i = 1$ is denoted by $S(\LS, \w)$. A more general notation is given in the Appendix. We measure the association between $\Y$ and $X_j, j = 1, \dots, m$, by linear statistics of the form \begin{eqnarray} \label{linstat} \T_j(\LS, \w) = \vec \left( \sum_{i=1}^n w_i g_j(X_{ji}) h(\Y_i, (\Y_1, \dots, \Y_n))^\top \right) \in \R^{p_jq} \end{eqnarray} where $g_j: \sX_j \rightarrow \R^{p_j}$ is a non-random transformation of the covariate $X_j$. The transformation may be specified using the \code{xtrafo} argument (Note: this argument is currently not implemented in \code{partykit::ctree} but is available from \code{party::ctree}). %%If, for example, a ranking \textit{both} %%\code{x1} and \code{x2} is required, %%<>= %%party:::ctree(y ~ x1 + x2, data = ls, xtrafo = function(data) trafo(data, %%numeric_trafo = rank)) %%@ %%can be used. The \emph{influence function} $h: \sY \times \sY^n \rightarrow \R^q$ depends on the responses $(\Y_1, \dots, \Y_n)$ in a permutation symmetric way. %%, i.e., $h(\Y_i, (\Y_1, \dots, \Y_n)) = h(\Y_i, (\Y_{\sigma(1)}, \dots, %%\Y_{\sigma(n)}))$ for all permutations $\sigma \in S(\LS, \w)$. Section~\ref{examples} explains how to choose $g_j$ and $h$ in different practical settings. A $p_j \times q$ matrix is converted into a $p_jq$ column vector by column-wise combination using the `vec' operator. The influence function can be specified using the \code{ytrafo} argument. The distribution of $\T_j(\LS, \w)$ under $H_0^j$ depends on the joint distribution of $\Y$ and $X_j$, which is unknown under almost all practical circumstances. At least under the null hypothesis one can dispose of this dependency by fixing the covariates and conditioning on all possible permutations of the responses. This principle leads to test procedures known as \textit{permutation tests}. The conditional expectation $\mu_j \in \R^{p_jq}$ and covariance $\Sigma_j \in \R^{p_jq \times p_jq}$ of $\T_j(\LS, \w)$ under $H_0$ given all permutations $\sigma \in S(\LS, \w)$ of the responses are derived by \cite{Strasser+Weber:1999}: \begin{eqnarray} \mu_j & = & \E(\T_j(\LS, \w) | S(\LS, \w)) = \vec \left( \left( \sum_{i = 1}^n w_i g_j(X_{ji}) \right) \E(h | S(\LS, \w))^\top \right), \nonumber \\ \Sigma_j & = & \V(\T_j(\LS, \w) | S(\LS, \w)) \nonumber \\ & = & \frac{\ws}{\ws - 1} \V(h | S(\LS, \w)) \otimes \left(\sum_i w_i g_j(X_{ji}) \otimes w_i g_j(X_{ji})^\top \right) \label{expectcovar} \\ & - & \frac{1}{\ws - 1} \V(h | S(\LS, \w)) \otimes \left( \sum_i w_i g_j(X_{ji}) \right) \otimes \left( \sum_i w_i g_j(X_{ji})\right)^\top \nonumber \end{eqnarray} where $\ws = \sum_{i = 1}^n w_i$ denotes the sum of the case weights, $\otimes$ is the Kronecker product and the conditional expectation of the influence function is \begin{eqnarray*} \E(h | S(\LS, \w)) = \ws^{-1} \sum_i w_i h(\Y_i, (\Y_1, \dots, \Y_n)) \in \R^q \end{eqnarray*} with corresponding $q \times q$ covariance matrix \begin{eqnarray*} \V(h | S(\LS, \w)) = \ws^{-1} \sum_i w_i \left(h(\Y_i, (\Y_1, \dots, \Y_n)) - \E(h | S(\LS, \w)) \right) \\ \left(h(\Y_i, (\Y_1, \dots, \Y_n)) - \E(h | S(\LS, \w))\right)^\top. \end{eqnarray*} Having the conditional expectation and covariance at hand we are able to standardize a linear statistic $\T \in \R^{pq}$ of the form (\ref{linstat}) for some $p \in \{p_1, \dots, p_m\}$. Univariate test statistics~$c$ mapping an observed multivariate linear statistic $\bft \in \R^{pq}$ into the real line can be of arbitrary form. An obvious choice is the maximum of the absolute values of the standardized linear statistic \begin{eqnarray*} c_\text{max}(\bft, \mu, \Sigma) = \max_{k = 1, \dots, pq} \left| \frac{(\bft - \mu)_k}{\sqrt{(\Sigma)_{kk}}} \right| \end{eqnarray*} utilizing the conditional expectation $\mu$ and covariance matrix $\Sigma$. The application of a quadratic form $c_\text{quad}(\bft, \mu, \Sigma) = (\bft - \mu) \Sigma^+ (\bft - \mu)^\top$ is one alternative, although computationally more expensive because the Moore-Penrose inverse $\Sigma^+$ of $\Sigma$ is involved. The type of test statistic to be used can be specified by means of the \code{ctree\_control} function, for example <>= ctree_control(teststat = "max") @ uses $c_\text{max}$ and <>= ctree_control(teststat = "quad") @ takes $c_\text{quad}$ (the default). It is important to note that the test statistics $c(\bft_j, \mu_j, \Sigma_j), j = 1, \dots, m$, cannot be directly compared in an unbiased way unless all of the covariates are measured at the same scale, i.e., $p_1 = p_j, j = 2, \dots, m$. In order to allow for an unbiased variable selection we need to switch to the $P$-value scale because $P$-values for the conditional distribution of test statistics $c(\T_j(\LS, \w), \mu_j, \Sigma_j)$ can be directly compared among covariates measured at different scales. In step 1 of the generic algorithm we select the covariate with minimum $P$-value, i.e., the covariate $X_{j^*}$ with $j^* = \argmin_{j = 1, \dots, m} P_j$, where \begin{displaymath} P_j = \Prob_{H_0^j}(c(\T_j(\LS, \w), \mu_j, \Sigma_j) \ge c(\bft_j, \mu_j, \Sigma_j) | S(\LS, \w)) \end{displaymath} denotes the $P$-value of the conditional test for $H_0^j$. So far, we have only addressed testing each partial hypothesis $H_0^j$, which is sufficient for an unbiased variable selection. A global test for $H_0$ required in step 1 can be constructed via an aggregation of the transformations $g_j, j = 1, \dots, m$, i.e., using a linear statistic of the form \begin{eqnarray*} \T(\LS, \w) = \vec \left( \sum_{i=1}^n w_i \left(g_1(X_{1i})^\top, \dots, g_m(X_{mi})^\top\right)^\top h(\Y_i, (\Y_1, \dots, \Y_n))^\top \right). %%\in \R^{\sum_j p_jq} \end{eqnarray*} However, this approach is less attractive for learning samples with missing values. Universally applicable approaches are multiple test procedures based on $P_1, \dots, P_m$. Simple Bonferroni-adjusted $P$-values (the adjustment $1 - (1 - P_j)^m$ is used), available via <>= ctree_control(testtype = "Bonferroni") @ or a min-$P$-value resampling approach (Note: resampling is currently not implemented in \code{partykit::ctree}) %<>= %party:::ctree_control(testtype = "MonteCarlo") %@ are just examples and we refer to the multiple testing literature \citep[e.g.,][]{Westfall+Young:1993} for more advanced methods. We reject $H_0$ when the minimum of the adjusted $P$-values is less than a pre-specified nominal level $\alpha$ and otherwise stop the algorithm. In this sense, $\alpha$ may be seen as a unique parameter determining the size of the resulting trees. \subsection{Splitting criteria} Once we have selected a covariate in step 1 of the algorithm, the split itself can be established by any split criterion, including those established by \cite{Breiman+Friedman+Olshen:1984} or \cite{Shih:1999}. Instead of simple binary splits, multiway splits can be implemented as well, for example utilizing the work of \cite{OBrien:2004}. However, most splitting criteria are not applicable to response variables measured at arbitrary scales and we therefore utilize the permutation test framework described above to find the optimal binary split in one selected covariate $X_{j^*}$ in step~2 of the generic algorithm. The goodness of a split is evaluated by two-sample linear statistics which are special cases of the linear statistic (\ref{linstat}). For all possible subsets $A$ of the sample space $\sX_{j^*}$ the linear statistic \begin{eqnarray*} \T^A_{j^*}(\LS, \w) = \vec \left( \sum_{i=1}^n w_i I(X_{j^*i} \in A) h(\Y_i, (\Y_1, \dots, \Y_n))^\top \right) \in \R^{q} \end{eqnarray*} induces a two-sample statistic measuring the discrepancy between the samples $\{ \Y_i | w_i > 0 \text{ and } X_{ji} \in A; i = 1, \dots, n\}$ and $\{ \Y_i | w_i > 0 \text{ and } X_{ji} \not\in A; i = 1, \dots, n\}$. The conditional expectation $\mu_{j^*}^A$ and covariance $\Sigma_{j^*}^A$ can be computed by (\ref{expectcovar}). The split $A^*$ with a test statistic maximized over all possible subsets $A$ is established: \begin{eqnarray} \label{split} A^* = \argmax_A c(\bft_{j^*}^A, \mu_{j^*}^A, \Sigma_{j^*}^A). \end{eqnarray} The statistics $c(\bft_{j^*}^A, \mu_{j^*}^A, \Sigma_{j^*}^A)$ are available for each node with %<>= %party:::ctree_control(savesplitstats = TRUE) %@ and can be used to depict a scatter plot of the covariate $\sX_{j^*}$ against the statistics (Note: this feature is currently not implemented in \pkg{partykit}). Note that we do not need to compute the distribution of $c(\bft_{j^*}^A, \mu_{j^*}^A, \Sigma_{j^*}^A)$ in step~2. In order to anticipate pathological splits one can restrict the number of possible subsets that are evaluated, for example by introducing restrictions on the sample size or the sum of the case weights in each of the two groups of observations induced by a possible split. For example, <>= ctree_control(minsplit = 20) @ requires the sum of the weights in both the left and right daughter node to exceed the value of $20$. \subsection{Missing values and surrogate splits} If an observation $X_{ji}$ in covariate $X_j$ is missing, we set the corresponding case weight $w_i$ to zero for the computation of $\T_j(\LS, \w)$ and, if we would like to split in $X_j$, in $\T_{j}^A(\LS, \w)$ as well. Once a split $A^*$ in $X_j$ has been implemented, surrogate splits can be established by searching for a split leading to roughly the same division of the observations as the original split. One simply replaces the original response variable by a binary variable $I(X_{ji} \in A^*)$ coding the split and proceeds as described in the previous part. The number of surrogate splits can be controlled using <>= ctree_control(maxsurrogate = 3) @ \subsection{Fitting and inspecting a tree} For the sake of simplicity, we use a learning sample <>= ls <- data.frame(y = gl(3, 50, labels = c("A", "B", "C")), x1 = rnorm(150) + rep(c(1, 0, 0), c(50, 50, 50)), x2 = runif(150)) @ in the following illustrations. In \code{partykit::ctree}, the dependency structure and the variables may be specified in a traditional formula based way <>= library("partykit") ctree(y ~ x1 + x2, data = ls) @ Case counts $\w$ may be specified using the \code{weights} argument. Once we have fitted a conditional tree via <>= ct <- ctree(y ~ x1 + x2, data = ls) @ we can inspect the results via a \code{print} method <>= ct @ or by looking at a graphical representation as in Figure~\ref{party-plot1}. \begin{figure}[t!] \centering <>= plot(ct) @ \caption{A graphical representation of a classification tree. \label{party-plot1}} \end{figure} Each node can be extracted by its node number, i.e., the root node is <>= ct[1] @ This object is an object of class <>= class(ct[1]) @ and we refer to the manual pages for a description of those elements. The \code{predict} function computes predictions in the space of the response variable, in our case a factor <>= predict(ct, newdata = ls) @ When we are interested in properties of the conditional distribution of the response given the covariates, we use <>= predict(ct, newdata = ls[c(1, 51, 101),], type = "prob") @ which, in our case, is a data frame with conditional class probabilities. We can determine the node numbers of nodes some new observations are falling into by <>= predict(ct, newdata = ls[c(1,51,101),], type = "node") @ Finally, the \code{sctest} method can be used to extract the test statistics and $p$-values computed in each node. The function \code{sctest} is used because for the \code{mob} algorithm such a method (for \underline{s}tructural \underline{c}hange \underline{test}s) is also provided. To make the generic available, the \pkg{strucchange} package needs to be loaded (otherwise \code{sctest.constparty} would have to be called directly). <>= library("strucchange") sctest(ct) @ Here, we see that \code{x1} leads to a significant test result in the root node and is hence used for splitting. In the kid nodes, no more significant results are found and hence splitting stops. For other data sets, other stopping criteria might also be relevant (e.g., the sample size restrictions \code{minsplit}, \code{minbucket}, etc.). In case, splitting stops due to these, the test results may also be \code{NULL}. \section{Examples} \label{examples} \subsection{Univariate continuous or discrete regression} For a univariate numeric response $\Y \in \R$, the most natural influence function is the identity $h(\Y_i, (\Y_1, \dots, \Y_n)) = \Y_i$. In case some observations with extremely large or small values have been observed, a ranking of the observations may be appropriate: $h(\Y_i, (\Y_1, \dots, \Y_n)) = \sum_{k=1}^n w_k I(\Y_k \le \Y_i)$ for $i = 1, \dots, n$. Numeric covariates can be handled by the identity transformation $g_{ji}(x) = x$ (ranks are possible, too). Nominal covariates at levels $1, \dots, K$ are represented by $g_{ji}(k) = e_K(k)$, the unit vector of length $K$ with $k$th element being equal to one. Due to this flexibility, special test procedures like the Spearman test, the Wilcoxon-Mann-Whitney test or the Kruskal-Wallis test and permutation tests based on ANOVA statistics or correlation coefficients are covered by this framework. Splits obtained from (\ref{split}) maximize the absolute value of the standardized difference between two means of the values of the influence functions. For prediction, one is usually interested in an estimate of the expectation of the response $\E(\Y | \X = \x)$ in each cell, an estimate can be obtained by \begin{eqnarray*} \hat{\E}(\Y | \X = \x) = \left(\sum_{i=1}^n w_i(\x)\right)^{-1} \sum_{i=1}^n w_i(\x) \Y_i. \end{eqnarray*} \subsection{Censored regression} The influence function $h$ may be chosen as Logrank or Savage scores taking censoring into account and one can proceed as for univariate continuous regression. This is essentially the approach first published by \cite{Segal:1988}. An alternative is the weighting scheme suggested by \cite{Molinaro+Dudiot+VanDerLaan:2003}. A weighted Kaplan-Meier curve for the case weights $\w(\x)$ can serve as prediction. \subsection{$J$-class classification} The nominal response variable at levels $1, \dots, J$ is handled by influence functions\linebreak $h(\Y_i, (\Y_1, \dots, \Y_n)) = e_J(\Y_i)$. Note that for a nominal covariate $X_j$ at levels $1, \dots, K$ with $g_{ji}(k) = e_K(k)$ the corresponding linear statistic $\T_j$ is a vectorized contingency table. The conditional class probabilities can be estimated via \begin{eqnarray*} \hat{\Prob}(\Y = y | \X = \x) = \left(\sum_{i=1}^n w_i(\x)\right)^{-1} \sum_{i=1}^n w_i(\x) I(\Y_i = y), \quad y = 1, \dots, J. \end{eqnarray*} \subsection{Ordinal regression} Ordinal response variables measured at $J$ levels, and ordinal covariates measured at $K$ levels, are associated with score vectors $\xi \in \R^J$ and $\gamma \in \R^K$, respectively. Those scores reflect the `distances' between the levels: If the variable is derived from an underlying continuous variable, the scores can be chosen as the midpoints of the intervals defining the levels. The linear statistic is now a linear combination of the linear statistic $\T_j$ of the form \begin{eqnarray*} \M \T_j(\LS, \w) & = & \vec \left( \sum_{i=1}^n w_i \gamma^\top g_j(X_{ji}) \left(\xi^\top h(\Y_i, (\Y_1, \dots, \Y_n)\right)^\top \right) \end{eqnarray*} with $g_j(x) = e_K(x)$ and $h(\Y_i, (\Y_1, \dots, \Y_n)) = e_J(\Y_i)$. If both response and covariate are ordinal, the matrix of coefficients is given by the Kronecker product of both score vectors $\M = \xi \otimes \gamma \in \R^{1, KJ}$. In case the response is ordinal only, the matrix of coefficients $\M$ is a block matrix \begin{eqnarray*} \M = \left( \begin{array}{ccc} \xi_1 & & 0 \\ & \ddots & \\ 0 & & \xi_1 \end{array} \right| %%\left. %% \begin{array}{ccc} %% \xi_2 & & 0 \\ %% & \ddots & \\ %% 0 & & \xi_2 %% \end{array} \right| %%\left. \begin{array}{c} \\ \hdots \\ \\ \end{array} %%\right. \left| \begin{array}{ccc} \xi_q & & 0 \\ & \ddots & \\ 0 & & \xi_q \end{array} \right) %%\in \R^{K, KJ} %%\end{eqnarray*} \text{ or } %%and if one covariate is ordered %%\begin{eqnarray*} %%\M = \left( %% \begin{array}{cccc} %% \gamma & 0 & & 0 \\ %% 0 & \gamma & & \vdots \\ %% 0 & 0 & \hdots & 0 \\ %% \vdots & \vdots & & 0 \\ %% 0 & 0 & & \gamma %% \end{array} %% \right) \M = \text{diag}(\gamma) %%\in \R^{J, KJ} \end{eqnarray*} when one covariate is ordered but the response is not. For both $\Y$ and $X_j$ being ordinal, the corresponding test is known as linear-by-linear association test \citep{Agresti:2002}. Scores can be supplied to \code{ctree} using the \code{scores} argument, see Section~\ref{illustrations} for an example. \subsection{Multivariate regression} For multivariate responses, the influence function is a combination of influence functions appropriate for any of the univariate response variables discussed in the previous paragraphs, e.g., indicators for multiple binary responses \citep{Zhang:1998,Noh+Song+Park:2004}, Logrank or Savage scores for multiple failure times %%\citep[for example tooth loss times, ][]{SuFan2004} and the original observations or a rank transformation for multivariate regression \citep{Death:2002}. \section{Illustrations and applications} \label{illustrations} In this section, we present regression problems which illustrate the potential fields of application of the methodology. Conditional inference trees based on $c_\text{quad}$-type test statistics using the identity influence function for numeric responses and asymptotic $\chi^2$ distribution are applied. For the stopping criterion a simple Bonferroni correction is used and we follow the usual convention by choosing the nominal level of the conditional independence tests as $\alpha = 0.05$. \subsection{Tree pipit abundance} <>= data("treepipit", package = "coin") tptree <- ctree(counts ~ ., data = treepipit) @ \begin{figure}[t!] \centering <>= plot(tptree, terminal_panel = node_barplot) @ \caption{Conditional regression tree for the tree pipit data.} \end{figure} <>= p <- info_node(node_party(tptree))$p.value n <- table(predict(tptree, type = "node")) @ The impact of certain environmental factors on the population density of the tree pipit \textit{Anthus trivialis} %%in Frankonian oak forests is investigated by \cite{Mueller+Hothorn:2004}. The occurrence of tree pipits was recorded several times at $n = 86$ stands which were established on a long environmental gradient. Among nine environmental factors, the covariate showing the largest association to the number of tree pipits is the canopy overstorey $(P = \Sexpr{round(p, 3)})$. Two groups of stands can be distinguished: Sunny stands with less than $40\%$ canopy overstorey $(n = \Sexpr{n[1]})$ show a significantly higher density of tree pipits compared to darker stands with more than $40\%$ canopy overstorey $(n = \Sexpr{n[2]})$. This result is important for management decisions in forestry enterprises: Cutting the overstorey with release of old oaks creates a perfect habitat for this indicator species of near natural forest environments. \subsection{Glaucoma and laser scanning images} <>= data("GlaucomaM", package = "TH.data") gtree <- ctree(Class ~ ., data = GlaucomaM) @ <>= sp <- split_node(node_party(gtree))$varID @ Laser scanning images taken from the eye background are expected to serve as the basis of an automated system for glaucoma diagnosis. Although prediction is more important in this application \citep{Mardin+Hothorn+Peters:2003}, a simple visualization of the regression relationship is useful for comparing the structures inherent in the learning sample with subject matter knowledge. For $98$ patients and $98$ controls, matched by age and gender, $62$ covariates describing the eye morphology are available. The data is part of the \pkg{TH.data} package, \url{http://CRAN.R-project.org}). The first split in Figure~\ref{glaucoma} separates eyes with a volume above reference less than $\Sexpr{sp} \text{ mm}^3$ in the inferior part of the optic nerve head (\code{vari}). Observations with larger volume are mostly controls, a finding which corresponds to subject matter knowledge: The volume above reference measures the thickness of the nerve layer, expected to decrease with a glaucomatous damage of the optic nerve. Further separation is achieved by the volume above surface global (\code{vasg}) and the volume above reference in the temporal part of the optic nerve head (\code{vart}). \setkeys{Gin}{width=.9\textwidth} \begin{figure}[p!] \centering <>= plot(gtree) @ \caption{Conditional inference tree for the glaucoma data. For each inner node, the Bonferroni-adjusted $P$-values are given, the fraction of glaucomatous eyes is displayed for each terminal node. \label{glaucoma}} <>= plot(gtree, inner_panel = node_barplot, edge_panel = function(...) invisible(), tnex = 1) @ \caption{Conditional inference tree for the glaucoma data with the fraction of glaucomatous eyes displayed for both inner and terminal nodes. \label{glaucoma-inner}} \end{figure} The plot in Figure~\ref{glaucoma} is generated by <>= plot(gtree) @ \setkeys{Gin}{width=\textwidth} and shows the distribution of the classes in the terminal nodes. This distribution can be shown for the inner nodes as well, namely by specifying the appropriate panel generating function (\code{node\_barplot} in our case), see Figure~\ref{glaucoma-inner}. <>= plot(gtree, inner_panel = node_barplot, edge_panel = function(...) invisible(), tnex = 1) @ %% TH: split statistics are not saved in partykit %As mentioned in Section~\ref{framework}, it might be interesting to have a %look at the split statistics the split point estimate was derived from. %Those statistics can be extracted from the \code{splitstatistic} element %of a split and one can easily produce scatterplots against the selected %covariate. For all three inner nodes of \code{gtree}, we produce such a %plot in Figure~\ref{glaucoma-split}. For the root node, the estimated split point %seems very natural, since the process of split statistics seems to have a %clear maximum indicating that the simple split point model is something %reasonable to assume here. This is less obvious for nodes $2$ and, %especially, $3$. % %\begin{figure}[t!] %\centering %<>= %cex <- 1.6 %inner <- nodes(gtree, c(1, 2, 5)) %layout(matrix(1:length(inner), ncol = length(inner))) %out <- sapply(inner, function(i) { % splitstat <- i$psplit$splitstatistic % x <- GlaucomaM[[i$psplit$variableName]][splitstat > 0] % plot(x, splitstat[splitstat > 0], main = paste("Node", i$nodeID), % xlab = i$psplit$variableName, ylab = "Statistic", ylim = c(0, 10), % cex.axis = cex, cex.lab = cex, cex.main = cex) % abline(v = i$psplit$splitpoint, lty = 3) %}) %@ %\caption{Split point estimation in each inner node. The process of % the standardized two-sample test statistics for each possible % split point in the selected input variable is show. % The estimated split point is given as vertical dotted line. % \label{glaucoma-split}} %\end{figure} The class predictions of the tree for the learning sample (and for new observations as well) can be computed using the \code{predict} function. A comparison with the true class memberships is done by <>= table(predict(gtree), GlaucomaM$Class) @ When we are interested in conditional class probabilities, the \code{predict(, type = "prob")} method must be used. A graphical representation is shown in Figure~\ref{glaucoma-probplot}. \setkeys{Gin}{width=.5\textwidth} \begin{figure}[t!] \centering <>= prob <- predict(gtree, type = "prob")[,1] + runif(nrow(GlaucomaM), min = -0.01, max = 0.01) splitvar <- character_split(split_node(node_party(gtree)), data = data_party(gtree))$name plot(GlaucomaM[[splitvar]], prob, pch = as.numeric(GlaucomaM$Class), ylab = "Conditional Class Prob.", xlab = splitvar) abline(v = split_node(node_party(gtree))$breaks, lty = 2) legend(0.15, 0.7, pch = 1:2, legend = levels(GlaucomaM$Class), bty = "n") @ \caption{Estimated conditional class probabilities (slightly jittered) for the Glaucoma data depending on the first split variable. The vertical line denotes the first split point. \label{glaucoma-probplot}} \end{figure} \subsection{Node positive breast cancer} Recursive partitioning for censored responses has attracted a lot of interest \citep[e.g.,][]{Segal:1988,LeBlanc+Crowley:1992}. Survival trees using $P$-value adjusted Logrank statistics are used by \cite{Schumacher+Hollaender+Schwarzer:2001a} for the evaluation of prognostic factors for the German Breast Cancer Study Group (GBSG2) data, a prospective controlled clinical trial on the treatment of node positive breast cancer patients. Here, we use Logrank scores as well. Complete data of seven prognostic factors of $686$ women are used for prognostic modeling, the dataset is available within the \pkg{TH.data} package. The number of positive lymph nodes (\code{pnodes}) and the progesterone receptor (\code{progrec}) have been identified as prognostic factors in the survival tree analysis by \cite{Schumacher+Hollaender+Schwarzer:2001a}. Here, the binary variable coding whether a hormonal therapy was applied or not (\code{horTh}) additionally is part of the model depicted in Figure~\ref{gbsg2}, which was fitted using the following code: <>= data("GBSG2", package = "TH.data") library("survival") (stree <- ctree(Surv(time, cens) ~ ., data = GBSG2)) @ \setkeys{Gin}{width=\textwidth} \begin{figure}[t!] \centering <>= plot(stree) @ \caption{Tree-structured survival model for the GBSG2 data and the distribution of survival times in the terminal nodes. The median survival time is displayed in each terminal node of the tree. \label{gbsg2}} \end{figure} The estimated median survival time for new patients is less informative compared to the whole Kaplan-Meier curve estimated from the patients in the learning sample for each terminal node. We can compute those `predictions' by means of the \code{treeresponse} method <>= pn <- predict(stree, newdata = GBSG2[1:2,], type = "node") n <- predict(stree, type = "node") survfit(Surv(time, cens) ~ 1, data = GBSG2, subset = (n == pn[1])) survfit(Surv(time, cens) ~ 1, data = GBSG2, subset = (n == pn[2])) @ \subsection{Mammography experience} <>= data("mammoexp", package = "TH.data") mtree <- ctree(ME ~ ., data = mammoexp) @ \setkeys{Gin}{width=.9\textwidth, keepaspectratio=TRUE} \begin{figure}[t!] \centering <>= plot(mtree) @ \caption{Ordinal regression for the mammography experience data with the fractions of (never, within a year, over one year) given in the nodes. No admissible split was found for node 5 because only $5$ of $91$ women reported a family history of breast cancer and the sample size restrictions would require more than $5$ observations in each daughter node. \label{mammoexp}} \end{figure} Ordinal response variables are common in investigations where the response is a subjective human interpretation. We use an example given by \cite{Hosmer+Lemeshow:2000}, p.~264, studying the relationship between the mammography experience (never, within a year, over one year) and opinions about mammography expressed in questionnaires answered by $n = 412$ women. The resulting partition based on scores $\xi = (1,2,3)$ is given in Figure~\ref{mammoexp}. Women who (strongly) agree with the question `You do not need a mammogram unless you develop symptoms' seldomly have experienced a mammography. The variable \code{benefit} is a score with low values indicating a strong agreement with the benefits of the examination. For those women in (strong) disagreement with the first question above, low values of \code{benefit} identify persons being more likely to have experienced such an examination at all. \subsection{Hunting spiders} Finally, we take a closer look at a challenging dataset on animal abundance first reported by \cite{VanDerAart+SmeenkEnserink:1975} and re-analyzed by \cite{Death:2002} using regression trees dealing with multivariate responses. The abundance of $12$ hunting spider species is regressed on six environmental variables (\code{water}, \code{sand}, \code{moss}, \code{reft}, \code{twigs} and \code{herbs}) for $n = 28$ observations. Because of the small sample size we allow for a split if at least $5$ observations are element of a node The prognostic factor \code{water} found by \cite{Death:2002} is confirmed by the model shown in Figures~\ref{spider1} and~\ref{spider2} which additionally identifies \code{reft}. The data are available in package \pkg{mvpart} \citep{mvpart}. <>= data("HuntingSpiders", package = "partykit") sptree <- ctree(arct.lute + pard.lugu + zora.spin + pard.nigr + pard.pull + aulo.albi + troc.terr + alop.cune + pard.mont + alop.acce + alop.fabr + arct.peri ~ herbs + reft + moss + sand + twigs + water, data = HuntingSpiders, teststat = "max", minsplit = 5, pargs = GenzBretz(abseps = .1, releps = .1)) @ \setkeys{Gin}{width=\textwidth, keepaspectratio=TRUE} \begin{figure}[t!] \centering <>= plot(sptree, terminal_panel = node_barplot) @ \caption{Regression tree for hunting spider abundance with bars for the mean of each response. \label{spider1}} \end{figure} \setkeys{Gin}{height=.93\textheight, keepaspectratio=TRUE} \begin{figure}[p!] \centering <>= plot(sptree) @ \caption{Regression tree for hunting spider abundance with boxplots for each response. \label{spider2}} \end{figure} \section{Backward compatibility and novel functionality} \label{sec:novel} \code{partykit::ctree} is a complete reimplementation of \code{party::ctree}. The latter reference implementation is based on a monolithic \proglang{C} core and an \proglang{S4}-based \proglang{R} interface. The novel implementation of conditional inference trees in \pkg{partykit} is much more modular and was almost entirely written in \proglang{R} (package \pkg{partykit} does not contain any foreign language code as of version 1.2-0). Permutation tests are computed in the dedicated \proglang{R} add-on package \pkg{libcoin}. Nevertheless, both implementations will almost every time produce the same tree. There are, naturally, exceptions where ensuring backward-compatibility requires specific choices of hyper parameters in \code{partykit::ctree_control}. We will demonstrate how one can compute the same trees in \pkg{partykit} and \pkg{party} in this section. In addition, some novel features introduced in \pkg{partykit} 1.2-0 are described. \subsection{Regression} <>= library("party") set.seed(290875) @ We use the \code{airquality} data from package \pkg{party} and fit a regression tree after removal of missing response values. There are missing values in one of the explanatory variables, so we ask for three surrogate splits to be set-up: <>= data("airquality", package = "datasets") airq <- subset(airquality, !is.na(Ozone)) (airct_party <- party::ctree(Ozone ~ ., data = airq, controls = party::ctree_control(maxsurrogate = 3))) mean((airq$Ozone - predict(airct_party))^2) @ For this specific example, the same call produces the same tree under both \pkg{party} and \pkg{partykit}. To ensure this also for other patterns of missingness, the \code{numsurrogate} flag needs to be set in order to restrict the evaluation of surrogate splits to numeric variables only (this is a restriction hard-coded in \pkg{party}): <>= (airct_partykit <- partykit::ctree(Ozone ~ ., data = airq, control = partykit::ctree_control(maxsurrogate = 3, numsurrogate = TRUE))) mean((airq$Ozone - predict(airct_partykit))^2) table(predict(airct_party, type = "node"), predict(airct_partykit, type = "node")) max(abs(predict(airct_party) - predict(airct_partykit))) @ The results are identical as are the underlying test statistics: <>= airct_party@tree$criterion info_node(node_party(airct_partykit)) @ \code{partykit} has a nicer way or presenting the variable selection test statistics on the scale of the statistics and the $p$-values. In addition, the criterion to be maximised (here: $\log(1 - p-\text{value})$) is given. \subsection{Classification} For classification tasks with more than two classes, the default in \pkg{party} is a maximum-type test statistic on the multidimensional test statistic when computing splits. \pkg{partykit} employs a quadratic test statistic by default, because it was found to produce better splits empirically. One can switch-back to the old behaviour using the \code{splitstat} argument: <>= (irisct_party <- party::ctree(Species ~ .,data = iris)) (irisct_partykit <- partykit::ctree(Species ~ .,data = iris, control = partykit::ctree_control(splitstat = "maximum"))) table(predict(irisct_party, type = "node"), predict(irisct_partykit, type = "node")) @ The interface for computing conditional class probabilities changed from <>= tr_party <- treeresponse(irisct_party, newdata = iris) @ to <>= tr_partykit <- predict(irisct_partykit, type = "prob", newdata = iris) max(abs(do.call("rbind", tr_party) - tr_partykit)) @ leading to identical results. For ordinal regression, the conditional class probabilities can be computed in the very same way: <>= ### ordinal regression data("mammoexp", package = "TH.data") (mammoct_party <- party::ctree(ME ~ ., data = mammoexp)) ### estimated class probabilities tr_party <- treeresponse(mammoct_party, newdata = mammoexp) (mammoct_partykit <- partykit::ctree(ME ~ ., data = mammoexp)) ### estimated class probabilities tr_partykit <- predict(mammoct_partykit, newdata = mammoexp, type = "prob") max(abs(do.call("rbind", tr_party) - tr_partykit)) @ \subsection{Survival Analysis} Like in classification analysis, the \code{treeresponse} function from package \code{party} was replaced by the \code{predict} function with argument \code{type = "prob"} in \pkg{partykit}. The default survival trees are identical: <>= data("GBSG2", package = "TH.data") (GBSG2ct_party <- party::ctree(Surv(time, cens) ~ .,data = GBSG2)) (GBSG2ct_partykit <- partykit::ctree(Surv(time, cens) ~ .,data = GBSG2)) @ as are the conditional Kaplan-Meier estimators <>= tr_party <- treeresponse(GBSG2ct_party, newdata = GBSG2) tr_partykit <- predict(GBSG2ct_partykit, newdata = GBSG2, type = "prob") all.equal(lapply(tr_party, function(x) unclass(x)[!(names(x) %in% "call")]), lapply(tr_partykit, function(x) unclass(x)[!(names(x) %in% "call")]), check.names = FALSE) @ \subsection{New Features} \pkg{partykit} comes with additional arguments in \code{ctree_control} allowing a more detailed control over the tree growing. \begin{description} \item[\code{alpha}]: The user can optionally change the default nominal level of $\alpha = 0.05$; \code{mincriterion} is updated to $1 - \alpha$ and \code{logmincriterion} is then $\log(1 - \alpha)$. The latter allows variable selection on the scale of $\log(1 - p\text{-value})$: <>= (airct_partykit_1 <- partykit::ctree(Ozone ~ ., data = airq, control = partykit::ctree_control(maxsurrogate = 3, alpha = 0.001, numsurrogate = FALSE))) depth(airct_partykit_1) mean((airq$Ozone - predict(airct_partykit_1))^2) @ Lower values of $\alpha$ lead to smaller trees. \item[\code{splittest}]: This enables the computation of $p$-values for maximally selected statistics for variable selection. The default test statistic is not particularly powerful against cutpoint-alternatives but much faster to compute. Currently, $p$-value approximations are not available, so one has to rely on resampling for $p$-value estimation <>= (airct_partykit <- partykit::ctree(Ozone ~ ., data = airq, control = partykit::ctree_control(maxsurrogate = 3, splittest = TRUE, testtype = "MonteCarlo"))) @ \item[\code{saveinfo}]: Reduces the memory footprint by not storing test results as part of the tree. The core information about trees is then roughly half the size needed by \code{party}. \item[\code{nmax}]: Restricts the number of possible cutpoints to \code{nmax}, basically by treating all explanatory variables as ordered factors defined at quantiles of underlying numeric variables. This is mainly implemented in package \pkg{libcoin}. For the standard \code{ctree}, it is only appropriate to use in classification problems, where is can lead to substantial speed-ups: <>= (irisct_partykit_1 <- partykit::ctree(Species ~ .,data = iris, control = partykit::ctree_control(splitstat = "maximum", nmax = 25))) table(predict(irisct_partykit), predict(irisct_partykit_1)) @ \item[\code{multiway}]: Implements multiway splits in unordered factors, each level defines a corresponding daughter node: <>= GBSG2$tgrade <- factor(GBSG2$tgrade, ordered = FALSE) (GBSG2ct_partykit <- partykit::ctree(Surv(time, cens) ~ tgrade, data = GBSG2, control = partykit::ctree_control(multiway = TRUE, alpha = .5))) @ \item[\code{majority = FALSE}]: enables random assignment of non-splitable observations to daughter nodes preserving the node distribution. With \code{majority = TRUE}, these observations go with the majority (the only available behaviour of in \code{party::ctree}). \end{description} Two arguments of \code{ctree} are also interesting. The novel \code{cluster} argument allows conditional inference trees to be fitted to (simple forms of) correlated observations. For each cluster, the variance of the test statistics used for variable selection and also splitting is computed separately, leading to stratified permutation tests (in the sense that only observations within clusters are permuted). For example, we can cluster the data in the \code{airquality} dataset by month to be used as cluster variable: <>= airq$month <- factor(airq$Month) (airct_partykit_3 <- partykit::ctree(Ozone ~ Solar.R + Wind + Temp, data = airq, cluster = month, control = partykit::ctree_control(maxsurrogate = 3))) info_node(node_party(airct_partykit_3)) mean((airq$Ozone - predict(airct_partykit_3))^2) @ This reduces the number of partitioning variables and makes multiplicity adjustment less costly. The \code{ytrafo} argument has be made more general. \pkg{party} is not able to update influence functions $h$ within nodes. With the novel formula-based interface, users can create influence functions which are newly evaluated in each node. The following example illustrates how one can compute a survival tree with updated logrank scores: <>= ### with weight-dependent log-rank scores ### log-rank trafo for observations in this node only (= weights > 0) h <- function(y, x, start = NULL, weights, offset, estfun = TRUE, object = FALSE, ...) { if (is.null(weights)) weights <- rep(1, NROW(y)) s <- logrank_trafo(y[weights > 0,,drop = FALSE]) r <- rep(0, length(weights)) r[weights > 0] <- s list(estfun = matrix(as.double(r), ncol = 1), converged = TRUE, unweighted = TRUE) } partykit::ctree(Surv(time, cens) ~ ., data = GBSG2, ytrafo = h) @ The results are usually not very sensitive to (simple) updated influence functions. However, when one uses score functions of more complex models as influence functions (similar to the \code{mob} family of trees), it is necessary to refit models in each node. For example, we are interested in a normal linear model for ozone concentration given temperature; both the intercept and the regression coefficient for temperature shall vary across nodes of a tree. Such a ``permutation-based'' MOB, here taking clusters into account, can be set-up using <>= ### normal varying intercept / varying coefficient model (aka "mob") h <- function(y, x, start = NULL, weights = NULL, offset = NULL, cluster = NULL, ...) glm(y ~ 0 + x, family = gaussian(), start = start, weights = weights, ...) (airct_partykit_4 <- partykit::ctree(Ozone ~ Temp | Solar.R + Wind, data = airq, cluster = month, ytrafo = h, control = partykit::ctree_control(maxsurrogate = 3))) airq$node <- factor(predict(airct_partykit_4, type = "node")) summary(m <- glm(Ozone ~ node + node:Temp - 1, data = airq)) mean((predict(m) - airq$Ozone)^2) @ Both intercept and effect of temperature change considerably between nodes. The corresponding MOB can be fitted using <>= airq_lmtree <- partykit::lmtree(Ozone ~ Temp | Solar.R + Wind, data = airq, cluster = month) info_node(node_party(airq_lmtree)) mean((predict(airq_lmtree, newdata = airq) - airq$Ozone)^2) @ The $p$-values in the root node are similar but the two procedures find different splits. \code{mob} (and therefore \code{lmtree}) directly search for splits by optimising the objective function for all possible splits whereas \code{ctree} only works with the score functions. Argument \code{xtrafo} allowing the user to change the transformations $g_j$ of the covariates was removed from the user interface. <>= detach(package:party) @ \bibliography{party} \end{document} partykit/inst/doc/ctree.R0000644000176200001440000003625114723350637015111 0ustar liggesusers### R code from vignette source 'ctree.Rnw' ################################################### ### code chunk number 1: setup ################################################### suppressWarnings(RNGversion("3.5.2")) options(width = 70, SweaveHooks = list(leftpar = function() par(mai = par("mai") * c(1, 1.1, 1, 1)))) require("partykit") require("coin") require("strucchange") require("coin") require("Formula") require("survival") require("sandwich") set.seed(290875) ################################################### ### code chunk number 2: party-max ################################################### ctree_control(teststat = "max") ################################################### ### code chunk number 3: party-max ################################################### ctree_control(teststat = "quad") ################################################### ### code chunk number 4: party-Bonf ################################################### ctree_control(testtype = "Bonferroni") ################################################### ### code chunk number 5: party-minsplit ################################################### ctree_control(minsplit = 20) ################################################### ### code chunk number 6: party-maxsurr ################################################### ctree_control(maxsurrogate = 3) ################################################### ### code chunk number 7: party-data ################################################### ls <- data.frame(y = gl(3, 50, labels = c("A", "B", "C")), x1 = rnorm(150) + rep(c(1, 0, 0), c(50, 50, 50)), x2 = runif(150)) ################################################### ### code chunk number 8: party-formula ################################################### library("partykit") ctree(y ~ x1 + x2, data = ls) ################################################### ### code chunk number 9: party-fitted ################################################### ct <- ctree(y ~ x1 + x2, data = ls) ################################################### ### code chunk number 10: party-print ################################################### ct ################################################### ### code chunk number 11: party-plot ################################################### plot(ct) ################################################### ### code chunk number 12: party-nodes ################################################### ct[1] ################################################### ### code chunk number 13: party-nodelist ################################################### class(ct[1]) ################################################### ### code chunk number 14: party-predict ################################################### predict(ct, newdata = ls) ################################################### ### code chunk number 15: party-treeresponse ################################################### predict(ct, newdata = ls[c(1, 51, 101),], type = "prob") ################################################### ### code chunk number 16: party-where ################################################### predict(ct, newdata = ls[c(1,51,101),], type = "node") ################################################### ### code chunk number 17: party-sctest ################################################### library("strucchange") sctest(ct) ################################################### ### code chunk number 18: treepipit-ctree ################################################### data("treepipit", package = "coin") tptree <- ctree(counts ~ ., data = treepipit) ################################################### ### code chunk number 19: treepipit-plot ################################################### plot(tptree, terminal_panel = node_barplot) ################################################### ### code chunk number 20: treepipit-x ################################################### p <- info_node(node_party(tptree))$p.value n <- table(predict(tptree, type = "node")) ################################################### ### code chunk number 21: glaucoma-ctree ################################################### data("GlaucomaM", package = "TH.data") gtree <- ctree(Class ~ ., data = GlaucomaM) ################################################### ### code chunk number 22: glaucoma-x ################################################### sp <- split_node(node_party(gtree))$varID ################################################### ### code chunk number 23: glaucoma-plot ################################################### plot(gtree) ################################################### ### code chunk number 24: glaucoma-plot-inner ################################################### plot(gtree, inner_panel = node_barplot, edge_panel = function(...) invisible(), tnex = 1) ################################################### ### code chunk number 25: glaucoma-plot2 (eval = FALSE) ################################################### ## plot(gtree) ################################################### ### code chunk number 26: glaucoma-plot-inner (eval = FALSE) ################################################### ## plot(gtree, inner_panel = node_barplot, ## edge_panel = function(...) invisible(), tnex = 1) ################################################### ### code chunk number 27: glaucoma-prediction ################################################### table(predict(gtree), GlaucomaM$Class) ################################################### ### code chunk number 28: glaucoma-classprob ################################################### prob <- predict(gtree, type = "prob")[,1] + runif(nrow(GlaucomaM), min = -0.01, max = 0.01) splitvar <- character_split(split_node(node_party(gtree)), data = data_party(gtree))$name plot(GlaucomaM[[splitvar]], prob, pch = as.numeric(GlaucomaM$Class), ylab = "Conditional Class Prob.", xlab = splitvar) abline(v = split_node(node_party(gtree))$breaks, lty = 2) legend(0.15, 0.7, pch = 1:2, legend = levels(GlaucomaM$Class), bty = "n") ################################################### ### code chunk number 29: GBSGS-ctree ################################################### data("GBSG2", package = "TH.data") library("survival") (stree <- ctree(Surv(time, cens) ~ ., data = GBSG2)) ################################################### ### code chunk number 30: GBSG2-plot ################################################### plot(stree) ################################################### ### code chunk number 31: GBSG2-KM ################################################### pn <- predict(stree, newdata = GBSG2[1:2,], type = "node") n <- predict(stree, type = "node") survfit(Surv(time, cens) ~ 1, data = GBSG2, subset = (n == pn[1])) survfit(Surv(time, cens) ~ 1, data = GBSG2, subset = (n == pn[2])) ################################################### ### code chunk number 32: mammo-ctree ################################################### data("mammoexp", package = "TH.data") mtree <- ctree(ME ~ ., data = mammoexp) ################################################### ### code chunk number 33: mammo-plot ################################################### plot(mtree) ################################################### ### code chunk number 34: spider-ctree ################################################### data("HuntingSpiders", package = "partykit") sptree <- ctree(arct.lute + pard.lugu + zora.spin + pard.nigr + pard.pull + aulo.albi + troc.terr + alop.cune + pard.mont + alop.acce + alop.fabr + arct.peri ~ herbs + reft + moss + sand + twigs + water, data = HuntingSpiders, teststat = "max", minsplit = 5, pargs = GenzBretz(abseps = .1, releps = .1)) ################################################### ### code chunk number 35: spider-plot1 ################################################### plot(sptree, terminal_panel = node_barplot) ################################################### ### code chunk number 36: spider-plot2 ################################################### plot(sptree) ################################################### ### code chunk number 37: party-setup ################################################### library("party") set.seed(290875) ################################################### ### code chunk number 38: party-airq ################################################### data("airquality", package = "datasets") airq <- subset(airquality, !is.na(Ozone)) (airct_party <- party::ctree(Ozone ~ ., data = airq, controls = party::ctree_control(maxsurrogate = 3))) mean((airq$Ozone - predict(airct_party))^2) ################################################### ### code chunk number 39: partykit-airq ################################################### (airct_partykit <- partykit::ctree(Ozone ~ ., data = airq, control = partykit::ctree_control(maxsurrogate = 3, numsurrogate = TRUE))) mean((airq$Ozone - predict(airct_partykit))^2) table(predict(airct_party, type = "node"), predict(airct_partykit, type = "node")) max(abs(predict(airct_party) - predict(airct_partykit))) ################################################### ### code chunk number 40: party-partykit-airq ################################################### airct_party@tree$criterion info_node(node_party(airct_partykit)) ################################################### ### code chunk number 41: party-partykit-iris ################################################### (irisct_party <- party::ctree(Species ~ .,data = iris)) (irisct_partykit <- partykit::ctree(Species ~ .,data = iris, control = partykit::ctree_control(splitstat = "maximum"))) table(predict(irisct_party, type = "node"), predict(irisct_partykit, type = "node")) ################################################### ### code chunk number 42: party-iris ################################################### tr_party <- treeresponse(irisct_party, newdata = iris) ################################################### ### code chunk number 43: partykit-iris ################################################### tr_partykit <- predict(irisct_partykit, type = "prob", newdata = iris) max(abs(do.call("rbind", tr_party) - tr_partykit)) ################################################### ### code chunk number 44: party-partykit-mammoexp ################################################### ### ordinal regression data("mammoexp", package = "TH.data") (mammoct_party <- party::ctree(ME ~ ., data = mammoexp)) ### estimated class probabilities tr_party <- treeresponse(mammoct_party, newdata = mammoexp) (mammoct_partykit <- partykit::ctree(ME ~ ., data = mammoexp)) ### estimated class probabilities tr_partykit <- predict(mammoct_partykit, newdata = mammoexp, type = "prob") max(abs(do.call("rbind", tr_party) - tr_partykit)) ################################################### ### code chunk number 45: party-partykit-GBSG2 ################################################### data("GBSG2", package = "TH.data") (GBSG2ct_party <- party::ctree(Surv(time, cens) ~ .,data = GBSG2)) (GBSG2ct_partykit <- partykit::ctree(Surv(time, cens) ~ .,data = GBSG2)) ################################################### ### code chunk number 46: party-partykit-KM ################################################### tr_party <- treeresponse(GBSG2ct_party, newdata = GBSG2) tr_partykit <- predict(GBSG2ct_partykit, newdata = GBSG2, type = "prob") all.equal(lapply(tr_party, function(x) unclass(x)[!(names(x) %in% "call")]), lapply(tr_partykit, function(x) unclass(x)[!(names(x) %in% "call")]), check.names = FALSE) ################################################### ### code chunk number 47: nf-alpha ################################################### (airct_partykit_1 <- partykit::ctree(Ozone ~ ., data = airq, control = partykit::ctree_control(maxsurrogate = 3, alpha = 0.001, numsurrogate = FALSE))) depth(airct_partykit_1) mean((airq$Ozone - predict(airct_partykit_1))^2) ################################################### ### code chunk number 48: nf-maxstat ################################################### (airct_partykit <- partykit::ctree(Ozone ~ ., data = airq, control = partykit::ctree_control(maxsurrogate = 3, splittest = TRUE, testtype = "MonteCarlo"))) ################################################### ### code chunk number 49: nf-nmax ################################################### (irisct_partykit_1 <- partykit::ctree(Species ~ .,data = iris, control = partykit::ctree_control(splitstat = "maximum", nmax = 25))) table(predict(irisct_partykit), predict(irisct_partykit_1)) ################################################### ### code chunk number 50: nf-multiway ################################################### GBSG2$tgrade <- factor(GBSG2$tgrade, ordered = FALSE) (GBSG2ct_partykit <- partykit::ctree(Surv(time, cens) ~ tgrade, data = GBSG2, control = partykit::ctree_control(multiway = TRUE, alpha = .5))) ################################################### ### code chunk number 51: nf-cluster ################################################### airq$month <- factor(airq$Month) (airct_partykit_3 <- partykit::ctree(Ozone ~ Solar.R + Wind + Temp, data = airq, cluster = month, control = partykit::ctree_control(maxsurrogate = 3))) info_node(node_party(airct_partykit_3)) mean((airq$Ozone - predict(airct_partykit_3))^2) ################################################### ### code chunk number 52: nf-ytrafo-1 ################################################### ### with weight-dependent log-rank scores ### log-rank trafo for observations in this node only (= weights > 0) h <- function(y, x, start = NULL, weights, offset, estfun = TRUE, object = FALSE, ...) { if (is.null(weights)) weights <- rep(1, NROW(y)) s <- logrank_trafo(y[weights > 0,,drop = FALSE]) r <- rep(0, length(weights)) r[weights > 0] <- s list(estfun = matrix(as.double(r), ncol = 1), converged = TRUE, unweighted = TRUE) } partykit::ctree(Surv(time, cens) ~ ., data = GBSG2, ytrafo = h) ################################################### ### code chunk number 53: nf-ytrafo-2 ################################################### ### normal varying intercept / varying coefficient model (aka "mob") h <- function(y, x, start = NULL, weights = NULL, offset = NULL, cluster = NULL, ...) glm(y ~ 0 + x, family = gaussian(), start = start, weights = weights, ...) (airct_partykit_4 <- partykit::ctree(Ozone ~ Temp | Solar.R + Wind, data = airq, cluster = month, ytrafo = h, control = partykit::ctree_control(maxsurrogate = 3))) airq$node <- factor(predict(airct_partykit_4, type = "node")) summary(m <- glm(Ozone ~ node + node:Temp - 1, data = airq)) mean((predict(m) - airq$Ozone)^2) ################################################### ### code chunk number 54: airq-mob ################################################### airq_lmtree <- partykit::lmtree(Ozone ~ Temp | Solar.R + Wind, data = airq, cluster = month) info_node(node_party(airq_lmtree)) mean((predict(airq_lmtree, newdata = airq) - airq$Ozone)^2) ################################################### ### code chunk number 55: closing ################################################### detach(package:party) partykit/inst/doc/constparty.R0000644000176200001440000002655314723350631016213 0ustar liggesusers### R code from vignette source 'constparty.Rnw' ################################################### ### code chunk number 1: setup ################################################### suppressWarnings(RNGversion("3.5.2")) options(width = 70) library("partykit") set.seed(290875) ################################################### ### code chunk number 2: Titanic ################################################### data("Titanic", package = "datasets") ttnc <- as.data.frame(Titanic) ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] names(ttnc)[2] <- "Gender" ################################################### ### code chunk number 3: rpart ################################################### library("rpart") (rp <- rpart(Survived ~ ., data = ttnc, model = TRUE)) ################################################### ### code chunk number 4: rpart-party ################################################### (party_rp <- as.party(rp)) ################################################### ### code chunk number 5: rpart-plot-orig ################################################### plot(rp) text(rp) ################################################### ### code chunk number 6: rpart-plot ################################################### plot(party_rp) ################################################### ### code chunk number 7: rpart-pred ################################################### all.equal(predict(rp), predict(party_rp, type = "prob"), check.attributes = FALSE) ################################################### ### code chunk number 8: rpart-fitted ################################################### str(fitted(party_rp)) ################################################### ### code chunk number 9: rpart-prob ################################################### prop.table(do.call("table", fitted(party_rp)), 1) ################################################### ### code chunk number 10: J48 ################################################### if (require("RWeka")) { j48 <- J48(Survived ~ ., data = ttnc) } else { j48 <- rpart(Survived ~ ., data = ttnc) } print(j48) ################################################### ### code chunk number 11: J48-party ################################################### (party_j48 <- as.party(j48)) ################################################### ### code chunk number 12: J48-plot ################################################### plot(party_j48) ################################################### ### code chunk number 13: J48-pred ################################################### all.equal(predict(j48, type = "prob"), predict(party_j48, type = "prob"), check.attributes = FALSE) ################################################### ### code chunk number 14: PMML-Titantic ################################################### ttnc_pmml <- file.path(system.file("pmml", package = "partykit"), "ttnc.pmml") (ttnc_quest <- pmmlTreeModel(ttnc_pmml)) ################################################### ### code chunk number 15: PMML-Titanic-plot1 ################################################### plot(ttnc_quest) ################################################### ### code chunk number 16: ttnc2-reorder ################################################### ttnc2 <- ttnc[, names(ttnc_quest$data)] for(n in names(ttnc2)) { if(is.factor(ttnc2[[n]])) ttnc2[[n]] <- factor( ttnc2[[n]], levels = levels(ttnc_quest$data[[n]])) } ################################################### ### code chunk number 17: PMML-Titanic-augmentation ################################################### ttnc_quest2 <- party(ttnc_quest$node, data = ttnc2, fitted = data.frame( "(fitted)" = predict(ttnc_quest, ttnc2, type = "node"), "(response)" = ttnc2$Survived, check.names = FALSE), terms = terms(Survived ~ ., data = ttnc2) ) ttnc_quest2 <- as.constparty(ttnc_quest2) ################################################### ### code chunk number 18: PMML-Titanic-plot2 ################################################### plot(ttnc_quest2) ################################################### ### code chunk number 19: PMML-write ################################################### library("pmml") tfile <- tempfile() write(toString(pmml(rp)), file = tfile) ################################################### ### code chunk number 20: PMML-read ################################################### (party_pmml <- pmmlTreeModel(tfile)) all.equal(predict(party_rp, newdata = ttnc, type = "prob"), predict(party_pmml, newdata = ttnc, type = "prob"), check.attributes = FALSE) ################################################### ### code chunk number 21: mytree-1 ################################################### findsplit <- function(response, data, weights, alpha = 0.01) { ## extract response values from data y <- factor(rep(data[[response]], weights)) ## perform chi-squared test of y vs. x mychisqtest <- function(x) { x <- factor(x) if(length(levels(x)) < 2) return(NA) ct <- suppressWarnings(chisq.test(table(y, x), correct = FALSE)) pchisq(ct$statistic, ct$parameter, log = TRUE, lower.tail = FALSE) } xselect <- which(names(data) != response) logp <- sapply(xselect, function(i) mychisqtest(rep(data[[i]], weights))) names(logp) <- names(data)[xselect] ## Bonferroni-adjusted p-value small enough? if(all(is.na(logp))) return(NULL) minp <- exp(min(logp, na.rm = TRUE)) minp <- 1 - (1 - minp)^sum(!is.na(logp)) if(minp > alpha) return(NULL) ## for selected variable, search for split minimizing p-value xselect <- xselect[which.min(logp)] x <- rep(data[[xselect]], weights) ## set up all possible splits in two kid nodes lev <- levels(x[drop = TRUE]) if(length(lev) == 2) { splitpoint <- lev[1] } else { comb <- do.call("c", lapply(1:(length(lev) - 2), function(x) combn(lev, x, simplify = FALSE))) xlogp <- sapply(comb, function(q) mychisqtest(x %in% q)) splitpoint <- comb[[which.min(xlogp)]] } ## split into two groups (setting groups that do not occur to NA) splitindex <- !(levels(data[[xselect]]) %in% splitpoint) splitindex[!(levels(data[[xselect]]) %in% lev)] <- NA_integer_ splitindex <- splitindex - min(splitindex, na.rm = TRUE) + 1L ## return split as partysplit object return(partysplit(varid = as.integer(xselect), index = splitindex, info = list(p.value = 1 - (1 - exp(logp))^sum(!is.na(logp))))) } ################################################### ### code chunk number 22: mytree-2 ################################################### growtree <- function(id = 1L, response, data, weights, minbucket = 30) { ## for less than 30 observations stop here if (sum(weights) < minbucket) return(partynode(id = id)) ## find best split sp <- findsplit(response, data, weights) ## no split found, stop here if (is.null(sp)) return(partynode(id = id)) ## actually split the data kidids <- kidids_split(sp, data = data) ## set up all daugther nodes kids <- vector(mode = "list", length = max(kidids, na.rm = TRUE)) for (kidid in 1:length(kids)) { ## select observations for current node w <- weights w[kidids != kidid] <- 0 ## get next node id if (kidid > 1) { myid <- max(nodeids(kids[[kidid - 1]])) } else { myid <- id } ## start recursion on this daugther node kids[[kidid]] <- growtree(id = as.integer(myid + 1), response, data, w) } ## return nodes return(partynode(id = as.integer(id), split = sp, kids = kids, info = list(p.value = min(info_split(sp)$p.value, na.rm = TRUE)))) } ################################################### ### code chunk number 23: mytree-3 ################################################### mytree <- function(formula, data, weights = NULL) { ## name of the response variable response <- all.vars(formula)[1] ## data without missing values, response comes last data <- data[complete.cases(data), c(all.vars(formula)[-1], response)] ## data is factors only stopifnot(all(sapply(data, is.factor))) if (is.null(weights)) weights <- rep(1L, nrow(data)) ## weights are case weights, i.e., integers stopifnot(length(weights) == nrow(data) & max(abs(weights - floor(weights))) < .Machine$double.eps) ## grow tree nodes <- growtree(id = 1L, response, data, weights) ## compute terminal node number for each observation fitted <- fitted_node(nodes, data = data) ## return rich constparty object ret <- party(nodes, data = data, fitted = data.frame("(fitted)" = fitted, "(response)" = data[[response]], "(weights)" = weights, check.names = FALSE), terms = terms(formula)) as.constparty(ret) } ################################################### ### code chunk number 24: mytree-4 ################################################### (myttnc <- mytree(Survived ~ Class + Age + Gender, data = ttnc)) ################################################### ### code chunk number 25: mytree-5 ################################################### plot(myttnc) ################################################### ### code chunk number 26: mytree-pval ################################################### nid <- nodeids(myttnc) iid <- nid[!(nid %in% nodeids(myttnc, terminal = TRUE))] (pval <- unlist(nodeapply(myttnc, ids = iid, FUN = function(n) info_node(n)$p.value))) ################################################### ### code chunk number 27: mytree-nodeprune ################################################### myttnc2 <- nodeprune(myttnc, ids = iid[pval > 1e-5]) ################################################### ### code chunk number 28: mytree-nodeprune-plot ################################################### plot(myttnc2) ################################################### ### code chunk number 29: mytree-glm ################################################### logLik(glm(Survived ~ Class + Age + Gender, data = ttnc, family = binomial())) ################################################### ### code chunk number 30: mytree-bs ################################################### bs <- rmultinom(25, nrow(ttnc), rep(1, nrow(ttnc)) / nrow(ttnc)) ################################################### ### code chunk number 31: mytree-ll ################################################### bloglik <- function(prob, weights) sum(weights * dbinom(ttnc$Survived == "Yes", size = 1, prob[,"Yes"], log = TRUE)) ################################################### ### code chunk number 32: mytree-bsll ################################################### f <- function(w) { tr <- mytree(Survived ~ Class + Age + Gender, data = ttnc, weights = w) bloglik(predict(tr, newdata = ttnc, type = "prob"), as.numeric(w == 0)) } apply(bs, 2, f) ################################################### ### code chunk number 33: mytree-node ################################################### nttnc <- expand.grid(Class = levels(ttnc$Class), Gender = levels(ttnc$Gender), Age = levels(ttnc$Age)) nttnc ################################################### ### code chunk number 34: mytree-prob ################################################### predict(myttnc, newdata = nttnc, type = "node") predict(myttnc, newdata = nttnc, type = "response") predict(myttnc, newdata = nttnc, type = "prob") ################################################### ### code chunk number 35: mytree-FUN ################################################### predict(myttnc, newdata = nttnc, FUN = function(y, w) rank(table(rep(y, w)))) partykit/inst/doc/partykit.pdf0000644000176200001440000040026414723350653016223 0ustar liggesusers%PDF-1.5 %¿÷¢þ 1 0 obj << /Type /ObjStm /Length 4886 /Filter /FlateDecode /N 93 /First 788 >> stream xœÝ\isÛ8Òþþþ ~ÛLm…$npk6U¹ãÄN;çlÍF¢mîÈ’G¢ãdý> ‚”¢ìT½q$‚$Øhô…îFS<ˆhÈÀÚ$P‹ Î&•LÀc ˜æ6Hf9uXbñÅÎ$.ò€‹XL\*œË€«ýTÀ`x6qŒþ&\ãÜBôKs<Ò(¡pä²1Ìbhm5€\F$87A‡˜cÐ? 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ÂÝK€l¶PÊy^3šrFIbSŽº>(åˆm¥ÁB)T "yOƒHŽLÉÃ"@$û/É&Vy D*ü‘¢Í@’Q¬†iذ^V°,oˆdü"Åg€HIe°iOÁâ¯Á¤>= suppressWarnings(RNGversion("3.5.2")) options(width = 70) library("partykit") set.seed(290875) @ \section{Overview} \label{sec:overview} In the more than fifty years since \cite{Morgan+Sonquist:1963} published their seminal paper on ``automatic interaction detection'', a wide range of methods has been suggested that is usually termed ``recursive partitioning'' or ``decision trees'' or ``tree(-structured) models'' etc. Particularly influential were the algorithms CART \citep[classification and regression trees,][]{Breiman+Friedman+Olshen:1984}, C4.5 \citep{Quinlan:1993}, QUEST/GUIDE \citep{Loh+Shih:1997,Loh:2002}, and CTree \citep{Hothorn+Hornik+Zeileis:2006} among many others \citep[see][for a recent overview]{Loh:2014}. Reflecting the heterogeneity of conceptual algorithms, a wide range of computational implementations in various software systems emerged: Typically the original authors of an algorithm also provide accompanying software but many software systems, e.g., including \pkg{Weka} \citep{Witten+Frank:2005} or \proglang{R} \citep{R}, also provide collections of various types of trees. Within \proglang{R} the list of prominent packages includes \pkg{rpart} \citep[implementing the CART algorithm]{rpart}, \pkg{mvpart} \citep[for multivariate CART]{mvpart}, \pkg{RWeka} \citep[containing interfaces to J4.8, M5', LMT from \pkg{Weka}]{RWeka}, and \pkg{party} \citep[implementing CTree and MOB]{party} among many others. See the CRAN task view ``Machine Learning'' \citep{ctv} for an overview. All of these algorithms and software implementations have to deal with very similar challenges. However, due to the fragmentation of the communities in which the corresponding research is published -- ranging from statistics over machine learning to various applied fields -- many discussions of the algorithms do not reuse established theoretical results and terminology. Similarly, there is no common ``language'' for the software implementations and different solutions are provided by different packages (even within \proglang{R}) with relatively little reuse of code. The \pkg{partykit} tries to address the latter point and improve the computational situation by providing a common unified infrastructure for recursive partytioning in the \proglang{R} system for statistical computing. In particular, \pkg{partykit} provides tools for representing fitted trees along with printing, plotting, and computing predictions. The design principles are: \begin{itemize} \item One `agnostic' base class (\class{party}) which can encompass an extremely wide range of different types of trees. \item Subclasses for important types of trees, e.g., trees with constant fits (\class{constparty}) or with parametric models (\class{modelparty}) in each terminal node (or leaf). \item Nodes are recursive objects, i.e., a node can contain child nodes. \item Keep the (learning) data out of the recursive node and split structure. \item Basic printing, plotting, and predicting for raw node structure. \item Customization via suitable panel or panel-generating functions. \item Coercion from existing object classes in \proglang{R} (\code{rpart}, \code{J48}, etc.) to the new class. \item Usage of simple/fast \proglang{S}3 classes and methods. \end{itemize} In addition to all of this generic infrastructure, two specific tree algorithms are implemented in \pkg{partykit} as well: \fct{ctree} for conditional inference trees \citep{Hothorn+Hornik+Zeileis:2006} and \fct{mob} for model-based recursive partitioning \citep{Zeileis+Hothorn+Hornik:2008}. This vignette (\code{"partykit"}) introduces the basic \class{party} class and associated infrastructure while three further vignettes discuss the tools built on top of it: \code{"constparty"} covers the eponymous class for constant-fit trees along with suitable coercion functions, and \code{"ctree"} and \code{"mob"} discuss the new \fct{ctree} and \fct{mob} implementations, respectively. Each of the vignettes can be viewed within \proglang{R} via \code{vignette(}\emph{``name''}\code{, package = "partykit")}. Normal users reading this vignette will typically be interested only in the motivating example in Section~\ref{sec:intro} while the remaining sections are intended for programmers who want to build infrastructure on top of \pkg{partykit}. \section{Motivating example} \label{sec:intro} \subsection{Data} To illustrate how \pkg{partykit} can be used to represent trees, we employ a simple artificial data set taken from \cite{Witten+Frank:2005}. It concerns the conditions suitable for playing some unspecified game: % <>= data("WeatherPlay", package = "partykit") WeatherPlay @ % To represent the \code{play} decision based on the corresponding weather condition variables one could use the tree displayed in Figure~\ref{fig:weather-plot}. For now, it is ignored how this tree was inferred and it is simply assumed to be given. \setkeys{Gin}{width=0.8\textwidth} \begin{figure}[t!] \centering <>= py <- party( partynode(1L, split = partysplit(1L, index = 1:3), kids = list( partynode(2L, split = partysplit(3L, breaks = 75), kids = list( partynode(3L, info = "yes"), partynode(4L, info = "no"))), partynode(5L, info = "yes"), partynode(6L, split = partysplit(4L, index = 1:2), kids = list( partynode(7L, info = "yes"), partynode(8L, info = "no"))))), WeatherPlay) plot(py) @ \caption{\label{fig:weather-plot} Decision tree for \code{play} decision based on weather conditions in \code{WeatherPlay} data.} \end{figure} \setkeys{Gin}{width=\textwidth} To represent this tree (or recursive partition) in \pkg{partykit}, two basic building blocks are used: splits of class \class{partysplit} and nodes of class \class{partynode}. The resulting recursive partition can then be associated with a data set in an object of class \class{party}. \subsection{Splits} First, we employ the \fct{partysplit} function to create the three splits in the ``play tree'' from Figure~\ref{fig:weather-plot}. The function takes the following arguments \begin{Code} partysplit(varid, breaks = NULL, index = NULL, ..., info = NULL) \end{Code} where \code{varid} is an integer id (column number) of the variable used for splitting, e.g., \code{1L} for \code{outlook}, \code{3L} for \code{humidity}, \code{4L} for \code{windy} etc. Then, \code{breaks} and \code{index} determine which observations are sent to which of the branches, e.g., \code{breaks = 75} for the humidity split. Apart from further arguments not shown above (and just comprised under `\code{...}'), some arbitrary information can be associated with a \class{partysplit} object by passing it to the \code{info} argument. The three splits from Figure~\ref{fig:weather-plot} can then be created via % <>= sp_o <- partysplit(1L, index = 1:3) sp_h <- partysplit(3L, breaks = 75) sp_w <- partysplit(4L, index = 1:2) @ % For the numeric \code{humidity} variable the \code{breaks} are set while for the factor variables \code{outlook} and \code{windy} the information is supplied which of the levels should be associated with which of the branches of the tree. \subsection{Nodes} Second, we use these splits in the creation of the whole decision tree. In \pkg{partykit} a tree is represented by a \class{partynode} object which is recursive in that it may have ``kids'' that are again \class{partynode} objects. These can be created with the function \begin{Code} partynode(id, split = NULL, kids = NULL, ..., info = NULL) \end{Code} where \code{id} is an integer identifier of the node number, \code{split} is a \class{partysplit} object, and \code{kids} is a list of \class{partynode} objects. Again, there are further arguments not shown (\code{...}) and arbitrary information can be supplied in \code{info}. The whole tree from Figure~\ref{fig:weather-plot} can then be created via % <>= pn <- partynode(1L, split = sp_o, kids = list( partynode(2L, split = sp_h, kids = list( partynode(3L, info = "yes"), partynode(4L, info = "no"))), partynode(5L, info = "yes"), partynode(6L, split = sp_w, kids = list( partynode(7L, info = "yes"), partynode(8L, info = "no"))))) @ % where the previously created \class{partysplit} objects are used as splits and the nodes are simply numbered (depth first) from~1 to~8. For the terminal nodes of the tree there are no \code{kids} and the corresponding \code{play} decision is stored in the \code{info} argument. Printing the \class{partynode} object reflects the recursive structure stored. % <>= pn @ % However, the displayed information is still rather raw as it has not yet been associated with the \code{WeatherPlay} data set. \subsection{Trees (or recursive partitions)} Therefore, in a third step the recursive tree structure stored in \code{pn} is coupled with the corresponding data in a \class{party} object. % <>= py <- party(pn, WeatherPlay) print(py) @ % Now, Figure~\ref{fig:weather-plot} can easily be created by % <>= plot(py) @ % In addition to \fct{print} and \fct{plot}, the \fct{predict} method can now be applied, yielding the predicted terminal node IDs. % <>= predict(py, head(WeatherPlay)) @ % In addition to the \class{partynode} and the \class{data.frame}, the function \fct{party} takes several further arguments \begin{Code} party(node, data, fitted = NULL, terms = NULL, ..., info = NULL) \end{Code} i.e., \code{fitted} values, a \code{terms} object, arbitrary additional \code{info}, and again some further arguments comprised in \code{...}. \subsection{Methods and other utilities} The main idea about the \class{party} class is that tedious tasks such as \fct{print}, \fct{plot}, \fct{predict} do not have to be reimplemented for every new kind of decision tree but can simply be reused. However, in addition to these three basic tasks (as already illustrated above) developers of tree model software also need further basic utiltities for working with trees: e.g., functions for querying or subsetting the tree and for customizing printed/plotted output. Below, various utilities provided by the \pkg{partykit} package are introduced. For querying the dimensions of the tree, three basic functions are available: \fct{length} gives the number of kid nodes of the root node, \fct{depth} the depth of the tree and \fct{width} the number of terminal nodes. % <>= length(py) width(py) depth(py) @ % As decision trees can grow to be rather large, it is often useful to inspect only subtrees. These can be easily extracted using the standard \code{[} or \code{[[} operators: % <>= py[6] @ % The resulting object is again a full valid \class{party} tree and can hence be printed (as above) or plotted (via \code{plot(py[6])}, see the left panel of Figure~\ref{fig:plot-customization}). Instead of using the integer node IDs for subsetting, node labels can also be used. By default thise are just (character versions of) the node IDs but other names can be easily assigned: % <>= py2 <- py names(py2) names(py2) <- LETTERS[1:8] py2 @ % The function \fct{nodeids} queries the integer node IDs belonging to a \class{party} tree. By default all IDs are returned but optionally only the terminal IDs (of the leaves) can be extracted. % <>= nodeids(py) nodeids(py, terminal = TRUE) @ % Often functions need to be applied to certain nodes of a tree, e.g., for extracting information. This is accomodated by a new generic function \fct{nodeapply} that follows the style of other \proglang{R} functions from the \code{apply} family and has methods for \class{party} and \class{partynode} objects. Furthermore, it needs a set of node IDs (often computed via \fct{nodeids}) and a function \code{FUN} that is applied to each of the requested \class{partynode} objects, typically for extracting/formatting the \code{info} of the node. % <>= nodeapply(py, ids = c(1, 7), FUN = function(n) n$info) nodeapply(py, ids = nodeids(py, terminal = TRUE), FUN = function(n) paste("Play decision:", n$info)) @ % Similar to the functions applied in a \fct{nodeapply}, the \fct{print}, \fct{predict}, and \fct{plot} methods can be customized through panel function that format certain parts of the tree (such as header, footer, node, etc.). Hence, the same kind of panel function employed above can also be used for predictions: <>= predict(py, FUN = function(n) paste("Play decision:", n$info)) @ As a variation of this approach, an extended formatting with multiple lines can be easily accomodated by supplying a character vector in every node: % <>= print(py, terminal_panel = function(n) c(", then the play decision is:", toupper(n$info))) @ % The same type of approach can also be used in the default \fct{plot} method (with the main difference that the panel function operates on the \code{info} directly rather than on the \class{partynode}). % <>= plot(py, tp_args = list(FUN = function(i) c("Play decision:", toupper(i)))) @ % See the right panel of Figure~\ref{fig:plot-customization} for the resulting graphic. Many more elaborate panel functions are provided in \pkg{partykit}, especially for not only showing text in the visualizations but also statistical graphics. Some of these are briefly illustrated in this and the other package vignettes. Programmers that want to write their own panel functions are advised to inspect the corresponding \proglang{R} source code to see how flexible (but sometimes also complicated) these panel functions are. \setkeys{Gin}{width=0.48\textwidth} \begin{figure}[t!] \centering <>= plot(py[6]) @ <>= <> @ \caption{\label{fig:plot-customization} Visualization of subtree (left) and tree with custom text in terminal nodes (right).} \end{figure} \setkeys{Gin}{width=\textwidth} Finally, an important utility function is \fct{nodeprune} which allows to prune \class{party} trees. It takes a vector of node IDs and prunes all of their kids, i.e., making all the indicated node IDs terminal nodes. <>= nodeprune(py, 2) nodeprune(py, c(2, 6)) @ Note that for the pruned versions of this particular \class{party} tree, the new terminal nodes are displayed with a \code{*} rather than the play decision. This is because we did not store any play decisions in the \code{info} of the inner nodes of \code{py}. We could have of course done so initially, or could do so now, or we might want to do so automatically. For the latter, we would have to know how predictions should be obtained from the data and this is briefly discussed at the end of this vignette and in more detail in \code{vignette("constparty", package = "partykit")}. \section{Technical details} \subsection{Design principles} To facilitate reading of the subsequent sections, two design principles employed in the creation of \pkg{partykit} are briefly explained. % \begin{enumerate} \item Many helper utilities are encapsulated in functions that follow a simple naming convention. To extract/compute some information \emph{foo} from splits, nodes, or trees, \pkg{partykit} provides \emph{foo}\code{_split}, \emph{foo}\code{_node}, \emph{foo}\code{_party} functions (that are applicable to \class{partysplit}, \class{partynode}, and \class{party} objects, repectively). An example for the information \emph{foo} might be \code{kidids} or \code{info}. Hence, in the printing example above using \code{info_node(n)} rather than \code{n$info} for a node \code{n} would have been the preferred syntax; at least when programming new functionality on top of \pkg{partykit}. \item As already illustrated above, printing and plotting relies on \emph{panel functions} that visualize and/or format certain aspects of the resulting display, e.g., that of inner nodes, terminal nodes, headers, footers, etc. Furthermore, arguments like \code{terminal_panel} can also take \emph{panel-generating functions}, i.e., functions that produce a panel function when applied to the \class{party} object. \end{enumerate} \subsection{Splits} \label{sec:splits} \subsubsection{Overview} A split is basically a function that maps data -- or more specifically a partitioning variable -- to daugther nodes. Objects of class \class{partysplit} are designed to represent such functions and are set up by the \fct{partysplit} constructor. For example, a binary split in the numeric partitioning variable \code{humidity} (the 3rd variable in \code{WeatherPlay}) at the breakpoint \code{75} can be created (as above) by % <>= sp_h <- partysplit(3L, breaks = 75) class(sp_h) @ % The internal structure of class \class{partysplit} contains information about the partitioning variable, the splitpoints (or cutpoints or breakpoints), the handling of splitpoints, the treatment of observations with missing values and the kid nodes to send observations to: % <>= unclass(sp_h) @ % Here, the splitting rule is \code{humidity} $\le 75$: % <>= character_split(sp_h, data = WeatherPlay) @ % This representation of splits is completely abstract and, most importantly, independent of any data. Now, data comes into play when we actually want to perform splits: % <>= kidids_split(sp_h, data = WeatherPlay) @ % For each observation in \code{WeatherPlay} the split is performed and the number of the kid node to send this observation to is returned. Of course, this is a very complicated way of saying % <>= as.numeric(!(WeatherPlay$humidity <= 75)) + 1 @ \subsubsection{Mathematical notation} To explain the splitting strategy more formally, we employ some mathematical notation. \pkg{partykit} considers a split to represent a function $f$ mapping an element $x = (x_1, \dots, x_p)$ of a $p$-dimensional sample space $\mathcal{X}$ into a set of $k$ daugther nodes $\mathcal{D} = \{d_1, \dots, d_k\}$. This mapping is defined as a composition $f = h \circ g$ of two functions $g: \mathcal{X} \rightarrow \mathcal{I}$ and $h: \mathcal{I} \rightarrow \mathcal{D}$ with index set $\mathcal{I} = \{1, \dots, l\}, l \ge k$. Let $\mu = (-\infty, \mu_1, \dots, \mu_{l - 1}, \infty)$ denote the split points ($(\mu_1, \dots, \mu_{l - 1})$ = \code{breaks}). We are interested to split according to the information contained in the $i$-th element of $x$ ($i$ = \code{varid}). For numeric $x_i$, the split points are also numeric. If $x_i$ is a factor at levels $1, \dots, K$, the default split points are $\mu = (-\infty, 1, \dots, K - 1, \infty)$. The function $g$ essentially determines, which of the intervals (defined by $\mu$) the value $x_i$ is contained in ($I$ denotes the indicator function here): \begin{eqnarray*} x \mapsto g(x) = \sum_{j = 1}^l j I_{\mathcal{A}(j)}(x_i) \end{eqnarray*} where $\mathcal{A}(j) = (\mu_{j - 1}, \mu_j]$ for \code{right = TRUE} except $\mathcal{A}(l) = (\mu_{l - 1}, \infty)$. If \code{right = FALSE}, then $\mathcal{A}(j) = [\mu_{j - 1}, \mu_j)$ except $\mathcal{A}(1) = (-\infty, \mu_1)$. Note that for a categorical variable $x_i$ and default split points, $g$ is simply the identity. Now, $h$ maps from the index set $\mathcal{I}$ into the set of daugther nodes: \begin{eqnarray*} f(x) = h(g(x)) = d_{\sigma_{g(x)}} \end{eqnarray*} where $\sigma = (\sigma_1, \dots, \sigma_l) \in \{1, \dots, k\}^l$ (\code{index}). By default, $\sigma = (1, \dots, l)$ and $k = l$. If $x_i$ is missing, then $f(x)$ is randomly drawn with $\mathbb{P}(f(x) = d_j) = \pi_j, j = 1, \dots, k$ for a discrete probability distribution $\pi = (\pi_1, \dots, \pi_k)$ over the $k$ daugther nodes (\code{prob}). In the simplest case of a binary split in a numeric variable $x_i$, there is only one split point $\mu_1$ and, with $\sigma = (1, 2)$, observations with $x_i \le \mu_1$ are sent to daugther node $d_1$ and observations with $x_i > \mu_1$ to $d_2$. However, this representation of splits is general enough to deal with more complicated set-ups like surrogate splits, where typically the index needs modification, for example $\sigma = (2, 1)$, categorical splits, i.e., there is one data structure for both ordered and unordered splits, multiway splits, and functional splits. The latter can be implemented by defining a new artificial splitting variable $x_{p + 1}$ by means of a potentially very complex function of $x$ later used for splitting. \subsubsection{Further examples} Consider a split in a categorical variable at three levels where the first two levels go to the left daugther node and the third one to the right daugther node: % <>= sp_o2 <- partysplit(1L, index = c(1L, 1L, 2L)) character_split(sp_o2, data = WeatherPlay) table(kidids_split(sp_o2, data = WeatherPlay), WeatherPlay$outlook) @ % The internal structure of this object contains the \code{index} slot that maps levels to kid nodes. % <>= unclass(sp_o2) @ % This mapping is also useful with splits in ordered variables or when representing multiway splits: % <>= sp_o <- partysplit(1L, index = 1L:3L) character_split(sp_o, data = WeatherPlay) @ % For a split in a numeric variable, the mapping to daugther nodes can also be changed by modifying \code{index}: % <>= sp_t <- partysplit(2L, breaks = c(69.5, 78.8), index = c(1L, 2L, 1L)) character_split(sp_t, data = WeatherPlay) table(kidids_split(sp_t, data = WeatherPlay), cut(WeatherPlay$temperature, breaks = c(-Inf, 69.5, 78.8, Inf))) @ \subsubsection{Further comments} The additional argument \code{prop} can be used to specify a discrete probability distribution over the daugther nodes that is used to map observations with missing values to daugther nodes. Furthermore, the \code{info} argument and slot can take arbitrary objects to be stored with the split (for example split statistics). Currently, no specific structure of the \code{info} is used. Programmers that employ this functionality in their own functions/packages should access the elements of a \class{partysplit} object by the corresponding accessor function (and not just the \code{$} operator as the internal structure might be changed/extended in future release). \subsection{Nodes} \label{sec:nodes} \subsubsection{Overview} Inner and terminal nodes are represented by objects of class \class{partynode}. Each node has a unique identifier \code{id}. A node consisting only of such an identifier (and possibly additional information in \code{info}) is a terminal node: % <>= n1 <- partynode(id = 1L) is.terminal(n1) print(n1) @ % Inner nodes have to have a primary split \code{split} and at least two daugther nodes. The daugther nodes are objects of class \class{partynode} itself and thus represent the recursive nature of this data structure. The daugther nodes are pooled in a list \code{kids}. In addition, a list of \class{partysplit} objects offering surrogate splits can be supplied in argument \code{surrogates}. These are used in case the variable needed for the primary split has missing values in a particular data set. The IDs in a \class{partynode} should be numbered ``depth first'' (sometimes also called ``infix'' or ``pre-order traversal''). This simply means that the root node has identifier 1; the first kid node has identifier 2, whose kid (if present) has identifier 3 and so on. If other IDs are desired, then one can simply set \fct{names} (see above) for the tree; however, internally the depth-first numbering needs to be used. Note that the \fct{partynode} constructor also allows to create \class{partynode} objects with other ID schemes as this is necessary for growing the tree. If one wants to assure the a given \class{partynode} object has the correct IDs, one can simply apply \fct{as.partynode} once more to assure the right order of IDs. Finally, let us emphasize that \class{partynode} objects are not directly connected to the actual data (only indirectly through the associated \class{partysplit} objects). \subsubsection{Examples} Based on the binary split \code{sp_h} defined in the previous section, we set up an inner node with two terminal daugther nodes and print this stump (the data is needed because neither split nor nodes contain information about variable names or levels): % <>= n1 <- partynode(id = 1L, split = sp_o, kids = lapply(2L:4L, partynode)) print(n1, data = WeatherPlay) @ % Now that we have defined this simple tree, we want to assign observations to terminal nodes: % <>= fitted_node(n1, data = WeatherPlay) @ % Here, the \code{id}s of the terminal node each observations falls into are returned. Alternatively, we could compute the position of these daugther nodes in the list \code{kids}: % <>= kidids_node(n1, data = WeatherPlay) @ % Furthermore, the \code{info} argument and slot takes arbitrary objects to be stored with the node (predictions, for example, but we will handle this issue later). The slots can be extracted by means of the corresponding accessor functions. \subsubsection{Methods} A number of methods is defined for \class{partynode} objects: \fct{is.partynode} checks if the argument is a valid \class{partynode} object. \fct{is.terminal} is \code{TRUE} for terminal nodes and \code{FALSE} for inner nodes. The subset method \code{[} returns the \class{partynode} object corresponding to the \code{i}-th kid. The \fct{as.partynode} and \fct{as.list} methods can be used to convert flat list structures into recursive \class{partynode} objects and vice versa. As pointed out above, \fct{as.partynode} applied to \class{partynode} objects also renumbers the recursive nodes starting with root node identifier \code{from}. Furthermore, many of the methods defined for the class \class{party} illustrated above also work for plain \class{partynode} objects. For example, \fct{length} gives the number of kid nodes of the root node, \fct{depth} the depth of the tree and \fct{width} the number of terminal nodes. \subsection{Trees} \label{sec:trees} Although tree structures can be represented by \class{partynode} objects, a tree is more than a number of nodes and splits. More information about (parts of the) corresponding data is necessary for high-level computations on trees. \subsubsection{Trees and data} First, the raw node/split structure needs to be associated with a corresponding data set. % <>= t1 <- party(n1, data = WeatherPlay) t1 @ % Note that the \code{data} may have zero rows (i.e., only contain variable names/classes but not the actual data) and all methods that do not require the presence of any learning data still work fine: % <>= party(n1, data = WeatherPlay[0, ]) @ \subsubsection{Response variables and regression relationships} Second, for decision trees (or regression and classification trees) more information is required: namely, the response variable and its fitted values. Hence, a \class{data.frame} can be supplied in \code{fitted} that has at least one variable \code{(fitted)} containing the terminal node numbers of data used for fitting the tree. For representing the dependence of the response on the partitioning variables, a \code{terms} object can be provided that is leveraged for appropriately preprocessing new data in predictions. Finally, any additional (currently unstructured) information can be stored in \code{info} again. % <>= t2 <- party(n1, data = WeatherPlay, fitted = data.frame( "(fitted)" = fitted_node(n1, data = WeatherPlay), "(response)" = WeatherPlay$play, check.names = FALSE), terms = terms(play ~ ., data = WeatherPlay), ) @ % The information that is now contained in the tree \code{t2} is sufficient for all operations that should typically be performed on constant-fit trees. For this type of trees there is also a dedicated class \class{constparty} that provides some further convenience methods, especially for plotting and predicting. If a suitable \class{party} object like \code{t2} is already available, it just needs to be coerced: % <>= t2 <- as.constparty(t2) t2 @ % \setkeys{Gin}{width=0.6\textwidth} \begin{figure}[t!] \centering <>= plot(t2, tnex = 1.5) @ \caption{\label{fig:constparty-plot} Constant-fit tree for \code{play} decision based on weather conditions in \code{WeatherPlay} data.} \end{figure} \setkeys{Gin}{width=\textwidth} % As pointed out above, \class{constparty} objects have enhanced \fct{plot} and \fct{predict} methods. For example, \code{plot(t2)} now produces stacked bar plots in the leaves (see Figure~\ref{fig:constparty-plot}) as \code{t2} is a classification tree For regression and survival trees, boxplots and Kaplan-Meier curves are employed automatically, respectively. As there is information about the response variable, the \fct{predict} method can now produce more than just the predicted node IDs. The default is to predict the \code{"response"}, i.e., a factor for a classification tree. In this case, class probabilities (\code{"prob"}) are also available in addition to the majority votings. % <>= nd <- data.frame(outlook = factor(c("overcast", "sunny"), levels = levels(WeatherPlay$outlook))) predict(t2, newdata = nd, type = "response") predict(t2, newdata = nd, type = "prob") predict(t2, newdata = nd, type = "node") @ More details on how \class{constparty} objects and their methods work can be found in the corresponding \code{vignette("constparty", package = "partykit")}. \section{Summary} This vignette (\code{"partykit"}) introduces the package \pkg{partykit} that provides a toolkit for computing with recursive partytions, especially decision/regression/classification trees. In this vignette, the basic \class{party} class and associated infrastructure are discussed: splits, nodes, and trees with functions for printing, plotting, and predicting. Further vignettes in the package discuss in more detail the tools built on top of it. \bibliography{party} \end{document} partykit/inst/doc/constparty.Rnw0000644000176200001440000007155714172230001016546 0ustar liggesusers\documentclass[nojss]{jss} %\VignetteIndexEntry{Constant Partying: Growing and Handling Trees with Constant Fits} %\VignetteDepends{partykit, rpart, RWeka, pmml, datasets} %\VignetteKeywords{recursive partitioning, regression trees, classification trees, decision trees} %\VignettePackage{partykit} %% packages \usepackage{amstext} \usepackage{amsfonts} \usepackage{amsmath} \usepackage{thumbpdf} \usepackage{rotating} %% need no \usepackage{Sweave} %% additional commands \newcommand{\squote}[1]{`{#1}'} \newcommand{\dquote}[1]{``{#1}''} \newcommand{\fct}[1]{{\texttt{#1()}}} \newcommand{\class}[1]{\dquote{\texttt{#1}}} \newcommand{\fixme}[1]{\emph{\marginpar{FIXME} (#1)}} %% further commands \renewcommand{\Prob}{\mathbb{P} } \renewcommand{\E}{\mathbb{E}} \newcommand{\V}{\mathbb{V}} \newcommand{\Var}{\mathbb{V}} \hyphenation{Qua-dra-tic} \title{Constant Partying: Growing and Handling Trees with Constant Fits} \author{Torsten Hothorn\\Universit\"at Z\"urich \And Achim Zeileis\\Universit\"at Innsbruck} \Plainauthor{Torsten Hothorn, Achim Zeileis} \Abstract{ This vignette describes infrastructure for regression and classification trees with simple constant fits in each of the terminal nodes. Thus, all observations that are predicted to be in the same terminal node also receive the same prediction, e.g., a mean for numeric responses or proportions for categorical responses. This class of trees is very common and includes all traditional tree variants (AID, CHAID, CART, C4.5, FACT, QUEST) and also more recent approaches like CTree. Trees inferred by any of these algorithms could in principle be represented by objects of class \class{constparty} in \pkg{partykit} that then provides unified methods for printing, plotting, and predicting. Here, we describe how one can create \class{constparty} objects by (a)~coercion from other \proglang{R} classes, (b)~parsing of XML descriptions of trees learned in other software systems, (c)~learning a tree using one's own algorithm. } \Keywords{recursive partitioning, regression trees, classification trees, decision trees} \Address{ Torsten Hothorn\\ Institut f\"ur Epidemiologie, Biostatistik und Pr\"avention \\ Universit\"at Z\"urich \\ Hirschengraben 84\\ CH-8001 Z\"urich, Switzerland \\ E-mail: \email{Torsten.Hothorn@R-project.org}\\ URL: \url{http://user.math.uzh.ch/hothorn/}\\ Achim Zeileis\\ Department of Statistics \\ Faculty of Economics and Statistics \\ Universit\"at Innsbruck \\ Universit\"atsstr.~15 \\ 6020 Innsbruck, Austria \\ E-mail: \email{Achim.Zeileis@R-project.org}\\ URL: \url{http://eeecon.uibk.ac.at/~zeileis/} } \begin{document} \setkeys{Gin}{width=\textwidth} \SweaveOpts{engine=R, eps=FALSE, keep.source=TRUE, eval=TRUE} <>= suppressWarnings(RNGversion("3.5.2")) options(width = 70) library("partykit") set.seed(290875) @ \section{Classes and methods} \label{sec:classes} This vignette describes the handling of trees with constant fits in the terminal nodes. This class of regression models includes most classical tree algorithms like AID \citep{Morgan+Sonquist:1963}, CHAID \citep{Kass:1980}, CART \citep{Breiman+Friedman+Olshen:1984}, FACT \citep{Loh+Vanichsetakul1:988}, QUEST \citep{Loh+Shih:1997}, C4.5 \citep{Quinlan:1993}, CTree \citep{Hothorn+Hornik+Zeileis:2006} etc. In this class of tree models, one can compute simple predictions for new observations, such as the conditional mean in a regression setup, from the responses of those learning sample observations in the same terminal node. Therefore, such predictions can easily be computed if the following pieces of information are available: the observed responses in the learning sample, the terminal node IDs assigned to the observations in the learning sample, and potentially associated weights (if any). In \pkg{partykit} it is easy to create a \class{party} object that contains these pieces of information, yielding a \class{constparty} object. The technical details of the \class{party} class are discussed in detail in Section~3.4 of \code{vignette("partykit", package = "partykit")}. In addition to the elements required for any \class{party}, a \class{constparty} needs to have: variables \code{(fitted)} and \code{(response)} (and \code{(weights)} if applicable) in the \code{fitted} data frame along with the \code{terms} for the model. If such a \class{party} has been created, its properties can be checked and coerced to class \class{constparty} by the \fct{as.constparty} function. Note that with such a \class{constparty} object it is possible to compute all kinds of predictions from the subsample in a given terminal node. For example, instead the mean response the median (or any other quantile) could be employed. Similarly, for a categorical response the predicted probabilities (i.e., relative frequencies) can be computed or the corresponding mode or a ranking of the levels etc. In case the full response from the learning sample is not available but only the constant fit from each terminal node, then a \class{constparty} cannot be set up. Specifically, this is the case for trees saved in the XML format PMML \citep[Predictive Model Markup Language,][]{DMG:2014} that does not provide the full learning sample. To also support such constant-fit trees based on simpler information \pkg{partykit} provides the \class{simpleparty} class. Inspired by the PMML format, this requires that the \code{info} of every node in the tree provides list elements \code{prediction}, \code{n}, \code{error}, and \code{distribution}. For classification trees these should contain the following node-specific information: the predicted single predicted factor, the learning sample size, the misclassification error (in \%), and the absolute frequencies of all levels. For regression trees the contents should be: the predicted mean, the learning sample size, the error sum of squares, and \code{NULL}. The function \fct{as.simpleparty} can also coerce \class{constparty} trees to \class{simpleparty} trees by computing the above summary statistics from the full response associated with each node of the tree. The remainder of this vignette consists of the following parts: In Section~\ref{sec:coerce} we assume that the trees were fitted using some other software (either within or outside of \proglang{R}) and we describe how these models can be coerced to \class{party} objects using either the \class{constparty} or \class{simpleparty} class. Emphasize is given to displaying such trees in textual and graphical ways. Subsequently, in Section~\ref{sec:mytree}, we show a simple classification tree algorithm can be easily implemented using the \pkg{partykit} tools, yielding a \class{constparty} object. Section~\ref{sec:prediction} shows how to compute predictions in both scenarios before Section~\ref{sec:conclusion} finally gives a brief conclusion. \section{Coercing tree objects} \label{sec:coerce} For the illustrations, we use the Titanic data set from package \pkg{datasets}, consisting of four variables on each of the $2201$ Titanic passengers: gender (male, female), age (child, adult), and class (1st, 2nd, 3rd, or crew) set up as follows: <>= data("Titanic", package = "datasets") ttnc <- as.data.frame(Titanic) ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] names(ttnc)[2] <- "Gender" @ The response variable describes whether or not the passenger survived the sinking of the ship. \subsection{Coercing rpart objects} We first fit a classification tree by means of the the \fct{rpart} function from package \pkg{rpart} \citep{rpart} to this data set (make sure to set \code{model = TRUE}; otherwise \code{model.frame.rpart} will return the \code{rpart} object and not the data): <>= library("rpart") (rp <- rpart(Survived ~ ., data = ttnc, model = TRUE)) @ The \class{rpart} object \code{rp} can be coerced to a \class{constparty} by \fct{as.party}. Internally, this transforms the tree structure of the \class{rpart} tree to a \class{partynode} and combines it with the associated learning sample as described in Section~\ref{sec:classes}. All of this is done automatically by <>= (party_rp <- as.party(rp)) @ Now, instead of the print method for \class{rpart} objects the print method for \code{constparty} objects creates a textual display of the tree structure. In a similar way, the corresponding \fct{plot} method produces a graphical representation of this tree, see Figure~\ref{party_plot}. \begin{figure}[p!] \centering <>= plot(rp) text(rp) @ <>= plot(party_rp) @ \caption{\class{rpart} tree of Titanic data plotted using \pkg{rpart} (top) and \pkg{partykit} (bottom) infrastructure. \label{party_plot}} \end{figure} By default, the \fct{predict} method for \class{rpart} objects computes conditional class probabilities. The same numbers are returned by the \fct{predict} method for \Sexpr{class(party_rp)[1L]} objects with \code{type = "prob"} argument (see Section~\ref{sec:prediction} for more details): <>= all.equal(predict(rp), predict(party_rp, type = "prob"), check.attributes = FALSE) @ Predictions are computed based on the \code{fitted} slot of a \class{constparty} object <>= str(fitted(party_rp)) @ which contains the terminal node numbers and the response for each of the training samples. So, the conditional class probabilities for each terminal node can be computed via <>= prop.table(do.call("table", fitted(party_rp)), 1) @ Optionally, weights can be stored in the \code{fitted} slot as well. \subsection{Coercing J48 objects} The \pkg{RWeka} package \citep{RWeka} provides an interface to the \pkg{Weka} machine learning library and we can use the \fct{J48} function to fit a J4.8 tree to the Titanic data <>= if (require("RWeka")) { j48 <- J48(Survived ~ ., data = ttnc) } else { j48 <- rpart(Survived ~ ., data = ttnc) } print(j48) @ This object can be coerced to a \class{party} object using <>= (party_j48 <- as.party(j48)) @ and, again, the print method from the \pkg{partykit} package creates a textual display. Note that, unlike the \class{rpart} trees, this tree includes multiway splits. The \fct{plot} method draws this tree, see Figure~\ref{J48_plot}. \begin{sidewaysfigure} \centering <>= plot(party_j48) @ \caption{\class{J48} tree of Titanic data plotted using \pkg{partykit} infrastructure. \label{J48_plot}} \end{sidewaysfigure} The conditional class probabilities computed by the \fct{predict} methods implemented in packages \pkg{RWeka} and \pkg{partykit} are equivalent: <>= all.equal(predict(j48, type = "prob"), predict(party_j48, type = "prob"), check.attributes = FALSE) @ In addition to \fct{J48} \pkg{RWeka} provides several other tree learners, e.g., \fct{M5P} implementing M5' and \fct{LMT} implementing logistic model trees, respectively. These can also be coerced using \fct{as.party}. However, as these are not constant-fit trees this yields plain \class{party} trees with some character information stored in the \code{info} slot. \subsection{Importing trees from PMML files} The previous two examples showed how trees learned by other \proglang{R} packages can be handled in a unified way using \pkg{partykit}. Additionally, \pkg{partykit} can also be used to import trees from any other software package that supports the PMML (Predictive Model Markup Language) format. As an example, we used \proglang{SPSS} to fit a QUEST tree to the Titanic data and exported this from \proglang{SPSS} in PMML format. This file is shipped along with the \pkg{partykit} package and we can read it as follows: <>= ttnc_pmml <- file.path(system.file("pmml", package = "partykit"), "ttnc.pmml") (ttnc_quest <- pmmlTreeModel(ttnc_pmml)) @ % \begin{figure}[t!] \centering <>= plot(ttnc_quest) @ \caption{QUEST tree for Titanic data, fitted using \proglang{SPSS} and exported via PMML. \label{PMML-Titanic-plot1}} \end{figure} % The object \code{ttnc_quest} is of class \class{simpleparty} and the corresponding graphical display is shown in Figure~\ref{PMML-Titanic-plot1}. As explained in Section~\ref{sec:classes}, the full learning data are not part of the PMML description and hence one can only obtain and display the summarized information provided by PMML. In this particular case, however, we have the learning data available in \proglang{R} because we had exported the data from \proglang{R} to begin with. Hence, for this tree we can augment the \class{simpleparty} with the full learning sample to create a \class{constparty}. As \proglang{SPSS} had reordered some factor levels we need to carry out this reordering as well" <>= ttnc2 <- ttnc[, names(ttnc_quest$data)] for(n in names(ttnc2)) { if(is.factor(ttnc2[[n]])) ttnc2[[n]] <- factor( ttnc2[[n]], levels = levels(ttnc_quest$data[[n]])) } @ % Using this data all information for a \class{constparty} can be easily computed: % <>= ttnc_quest2 <- party(ttnc_quest$node, data = ttnc2, fitted = data.frame( "(fitted)" = predict(ttnc_quest, ttnc2, type = "node"), "(response)" = ttnc2$Survived, check.names = FALSE), terms = terms(Survived ~ ., data = ttnc2) ) ttnc_quest2 <- as.constparty(ttnc_quest2) @ This object is plotted in Figure~\ref{PMML-Titanic-plot2}. \begin{figure}[t!] \centering <>= plot(ttnc_quest2) @ \caption{QUEST tree for Titanic data, fitted using \proglang{SPSS}, exported via PMML, and transformed into a \class{constparty} object. \label{PMML-Titanic-plot2}} \end{figure} Furthermore, we briefly point out that there is also the \proglang{R} package \pkg{pmml} \citep{pmml}, part of the \pkg{rattle} project \citep{rattle}, that allows to export PMML files for \pkg{rpart} trees from \proglang{R}. For example, for the \class{rpart} tree for the Titanic data: <>= library("pmml") tfile <- tempfile() write(toString(pmml(rp)), file = tfile) @ Then, we can simply read this file and inspect the resulting tree <>= (party_pmml <- pmmlTreeModel(tfile)) all.equal(predict(party_rp, newdata = ttnc, type = "prob"), predict(party_pmml, newdata = ttnc, type = "prob"), check.attributes = FALSE) @ Further example PMML files created with \pkg{rattle} are the Data Mining Group web page, e.g., \url{http://www.dmg.org/pmml_examples/rattle_pmml_examples/AuditTree.xml} or \url{http://www.dmg.org/pmml_examples/rattle_pmml_examples/IrisTree.xml}. \section{Growing a simple classification tree} \label{sec:mytree} Although the \pkg{partykit} package offers an extensive toolbox for handling trees along with implementations of various tree algorithms, it does not offer unified infrastructure for \emph{growing} trees. However, once you know how to estimate splits from data, it is fairly straightforward to implement trees. Consider a very simple CHAID-style algorithm (in fact so simple that we would advise \emph{not to use it} for any real application). We assume that both response and explanatory variables are factors, as for the Titanic data set. First we determine the best explanatory variable by means of a global $\chi^2$ test, i.e., splitting up the response into all levels of each explanatory variable. Then, for the selected explanatory variable we search for the binary best split by means of $\chi^2$ tests, i.e., we cycle through all potential split points and assess the quality of the split by comparing the distributions of the response in the so-defined two groups. In both cases, we select the split variable/point with lowest $p$-value from the $\chi^2$ test, however, only if the global test is significant at Bonferroni-corrected level $\alpha = 0.01$. This strategy can be implemented based on the data (response and explanatory variables) and some case weights as follows (\code{response} is just the name of the response and \code{data} is a data frame with all variables): <>= findsplit <- function(response, data, weights, alpha = 0.01) { ## extract response values from data y <- factor(rep(data[[response]], weights)) ## perform chi-squared test of y vs. x mychisqtest <- function(x) { x <- factor(x) if(length(levels(x)) < 2) return(NA) ct <- suppressWarnings(chisq.test(table(y, x), correct = FALSE)) pchisq(ct$statistic, ct$parameter, log = TRUE, lower.tail = FALSE) } xselect <- which(names(data) != response) logp <- sapply(xselect, function(i) mychisqtest(rep(data[[i]], weights))) names(logp) <- names(data)[xselect] ## Bonferroni-adjusted p-value small enough? if(all(is.na(logp))) return(NULL) minp <- exp(min(logp, na.rm = TRUE)) minp <- 1 - (1 - minp)^sum(!is.na(logp)) if(minp > alpha) return(NULL) ## for selected variable, search for split minimizing p-value xselect <- xselect[which.min(logp)] x <- rep(data[[xselect]], weights) ## set up all possible splits in two kid nodes lev <- levels(x[drop = TRUE]) if(length(lev) == 2) { splitpoint <- lev[1] } else { comb <- do.call("c", lapply(1:(length(lev) - 2), function(x) combn(lev, x, simplify = FALSE))) xlogp <- sapply(comb, function(q) mychisqtest(x %in% q)) splitpoint <- comb[[which.min(xlogp)]] } ## split into two groups (setting groups that do not occur to NA) splitindex <- !(levels(data[[xselect]]) %in% splitpoint) splitindex[!(levels(data[[xselect]]) %in% lev)] <- NA_integer_ splitindex <- splitindex - min(splitindex, na.rm = TRUE) + 1L ## return split as partysplit object return(partysplit(varid = as.integer(xselect), index = splitindex, info = list(p.value = 1 - (1 - exp(logp))^sum(!is.na(logp))))) } @ In order to actually grow a tree on data, we have to set up the recursion for growing a recursive \class{partynode} structure: <>= growtree <- function(id = 1L, response, data, weights, minbucket = 30) { ## for less than 30 observations stop here if (sum(weights) < minbucket) return(partynode(id = id)) ## find best split sp <- findsplit(response, data, weights) ## no split found, stop here if (is.null(sp)) return(partynode(id = id)) ## actually split the data kidids <- kidids_split(sp, data = data) ## set up all daugther nodes kids <- vector(mode = "list", length = max(kidids, na.rm = TRUE)) for (kidid in 1:length(kids)) { ## select observations for current node w <- weights w[kidids != kidid] <- 0 ## get next node id if (kidid > 1) { myid <- max(nodeids(kids[[kidid - 1]])) } else { myid <- id } ## start recursion on this daugther node kids[[kidid]] <- growtree(id = as.integer(myid + 1), response, data, w) } ## return nodes return(partynode(id = as.integer(id), split = sp, kids = kids, info = list(p.value = min(info_split(sp)$p.value, na.rm = TRUE)))) } @ A very rough sketch of a formula-based user-interface sets-up the data and calls \fct{growtree}: <>= mytree <- function(formula, data, weights = NULL) { ## name of the response variable response <- all.vars(formula)[1] ## data without missing values, response comes last data <- data[complete.cases(data), c(all.vars(formula)[-1], response)] ## data is factors only stopifnot(all(sapply(data, is.factor))) if (is.null(weights)) weights <- rep(1L, nrow(data)) ## weights are case weights, i.e., integers stopifnot(length(weights) == nrow(data) & max(abs(weights - floor(weights))) < .Machine$double.eps) ## grow tree nodes <- growtree(id = 1L, response, data, weights) ## compute terminal node number for each observation fitted <- fitted_node(nodes, data = data) ## return rich constparty object ret <- party(nodes, data = data, fitted = data.frame("(fitted)" = fitted, "(response)" = data[[response]], "(weights)" = weights, check.names = FALSE), terms = terms(formula)) as.constparty(ret) } @ The call to the constructor \fct{party} sets-up a \class{party} object with the tree structure contained in \code{nodes}, the training samples in \code{data} and the corresponding \code{terms} object. Class \class{constparty} inherits all slots from class \class{party} and has an additional \code{fitted} slot for storing the terminal node numbers for each sample in the training data, the response variable(s) and case weights. The \code{fitted} slot is a \class{data.frame} containing three variables: The fitted terminal node identifiers \code{"(fitted)"}, an integer vector of the same length as \code{data}; the response variables \code{"(response)"} as a vector (or \code{data.frame} for multivariate responses) with the same number of observations; and optionally a vector of weights \code{"(weights)"}. The additional \code{fitted} slot allows to compute arbitrary summary measures for each terminal node by simply subsetting the \code{"(response)"} and \code{"(weights)"} slots by \code{"(fitted)"} before computing (weighted) means, medians, empirical cumulative distribution functions, Kaplan-Meier estimates or whatever summary statistic might be appropriate for a certain response. The \fct{print}, \fct{plot}, and \fct{predict} methods for class \class{constparty} work this way with suitable defaults for the summary statistics depending on the class of the response(s). We now can fit this tree to the Titanic data; the \fct{print} method provides us with a first overview on the resulting model <>= (myttnc <- mytree(Survived ~ Class + Age + Gender, data = ttnc)) @ % \begin{figure}[t!] \centering <>= plot(myttnc) @ \caption{Classification tree fitted by the \fct{mytree} function to the \code{ttnc} data. \label{plottree}} \end{figure} % Of course, we can immediately use \code{plot(myttnc)} to obtain a graphical representation of this tree, the result is given in Figure~\ref{plottree}. The default behavior for trees with categorical responses is simply inherited from \class{constparty} and hence we readily obtain bar plots in all terminal nodes. As the tree is fairly large, we might be interested in pruning the tree to a more reasonable size. For this purpose the \pkg{partykit} package provides the \fct{nodeprune} function that can prune back to nodes with selected IDs. As \fct{nodeprune} (by design) does not provide a specific pruning criterion, we need to determine ourselves which nodes to prune. Here, one idea could be to impose significance at a higher level than the default $10^{-2}$ -- say $10^{-5}$ to obtain a strongly pruned tree. Hence we use \fct{nodeapply} to extract the minimal Bonferroni-corrected $p$-value from all inner nodes: % <>= nid <- nodeids(myttnc) iid <- nid[!(nid %in% nodeids(myttnc, terminal = TRUE))] (pval <- unlist(nodeapply(myttnc, ids = iid, FUN = function(n) info_node(n)$p.value))) @ Then, the pruning of the nodes with the larger $p$-values can be simply carried out by % <>= myttnc2 <- nodeprune(myttnc, ids = iid[pval > 1e-5]) @ % The corresponding visualization is shown in Figure~\ref{prunetree}. \setkeys{Gin}{width=0.85\textwidth} \begin{figure}[t!] \centering <>= plot(myttnc2) @ \caption{Pruned classification tree fitted by the \fct{mytree} function to the \code{ttnc} data. \label{prunetree}} \end{figure} \setkeys{Gin}{width=\textwidth} The accuracy of the tree built using the default options could be assessed by the bootstrap, for example. Here, we want to compare our tree for the Titanic survivor data with a simple logistic regression model. First, we fit this simple GLM and compute the (in-sample) log-likelihood: <>= logLik(glm(Survived ~ Class + Age + Gender, data = ttnc, family = binomial())) @ For our tree, we set-up $25$ bootstrap samples <>= bs <- rmultinom(25, nrow(ttnc), rep(1, nrow(ttnc)) / nrow(ttnc)) @ and implement the log-likelihood of a binomal model <>= bloglik <- function(prob, weights) sum(weights * dbinom(ttnc$Survived == "Yes", size = 1, prob[,"Yes"], log = TRUE)) @ What remains to be done is to iterate over all bootstrap samples, to refit the tree on the bootstrap sample and to evaluate the log-likelihood on the out-of-bootstrap samples based on the trees' predictions (details on how to compute predictions are given in the next section): <>= f <- function(w) { tr <- mytree(Survived ~ Class + Age + Gender, data = ttnc, weights = w) bloglik(predict(tr, newdata = ttnc, type = "prob"), as.numeric(w == 0)) } apply(bs, 2, f) @ We see that the in-sample log-likelihood of the linear logistic regression model is much smaller than the out-of-sample log-likelihood found for our tree and thus we can conclude that our tree-based approach fits data the better than the linear model. \section{Predictions} \label{sec:prediction} As argued in Section~\ref{sec:classes} arbitrary types of predictions can be computed from \class{constparty} objects because the full empirical distribution of the response in the learning sample nodes is available. All of these can be easily computed in the \fct{predict} method for \class{constparty} objects by supplying a suitable aggregation function. However, as certain types of predictions are much more commonly used, these are available even more easily by setting a \code{type} argument. \begin{table}[b!] \centering \begin{tabular}{llll} \hline Response class & \code{type = "node"} & \code{type = "response"} & \code{type = "prob"} \\ \hline \class{factor} & terminal node number & majority class & class probabilities \\ \class{numeric} & terminal node number & mean & ECDF \\ \class{Surv} & terminal node number & median survival time & Kaplan-Meier \\ \hline \end{tabular} \caption{Overview on type of predictions computed by the \fct{predict} method for \class{constparty} objects. For multivariate responses, combinations thereof are returned. \label{predict-type}} \end{table} The prediction \code{type} can either be \code{"node"}, \code{"response"}, or \code{"prob"} (see Table~\ref{predict-type}). The idea is that \code{"response"} always returns a prediction of the same class as the original response and \code{"prob"} returns some object that characterizes the entire empirical distribution. Hence, for different response classes, different types of predictions are produced, see Table~\ref{predict-type} for an overview. Additionally, for \class{numeric} responses \code{type = "quantile"} and \code{type = "density"} is available. By default, these return functions for computing predicted quantiles and probability densities, respectively, but optionally these functions can be directly evaluated \code{at} given values and then return a vector/matrix. Here, we illustrate all different predictions for all possible combinations of the explanatory factor levels. <>= nttnc <- expand.grid(Class = levels(ttnc$Class), Gender = levels(ttnc$Gender), Age = levels(ttnc$Age)) nttnc @ The corresponding predicted nodes, modes, and probability distributions are: <>= predict(myttnc, newdata = nttnc, type = "node") predict(myttnc, newdata = nttnc, type = "response") predict(myttnc, newdata = nttnc, type = "prob") @ Furthermore, the \fct{predict} method features a \code{FUN} argument that can be used to compute customized predictions. If we are, say, interested in the rank of the probabilities for the two classes, we can simply specify a function that implements this feature: <>= predict(myttnc, newdata = nttnc, FUN = function(y, w) rank(table(rep(y, w)))) @ The user-supplied function \code{FUN} takes two arguments, \code{y} is the response and \code{w} is a vector of weights (case weights in this situation). Of course, it would have been easier to do these computations directly on the conditional class probabilities (\code{type = "prob"}), but the approach taken here for illustration generalizes to situations where this is not possible, especially for numeric responses. \section{Conclusion} \label{sec:conclusion} The classes \class{constparty} and \class{simpleparty} introduced here can be used to represent trees with constant fits in the terminal nodes, including most of the traditional tree variants. For a number of implementations it is possible to convert the resulting trees to one of these classes, thus offering unified methods for handling constant-fit trees. User-extensible methods for printing and plotting these trees are available. Also, computing non-standard predictions, such as the median or empirical cumulative distribution functions, is easily possible within this framework. With the infrastructure provided in \pkg{partykit} it is rather straightforward to implement a new (or old) tree algorithm and therefore a prototype implementation of fancy ideas for improving trees is only a couple lines of \proglang{R} code away. \bibliography{party} \end{document} partykit/inst/doc/mob.pdf0000644000176200001440000135055614723350653015142 0ustar liggesusers%PDF-1.5 %¿÷¢þ 1 0 obj << /Type /ObjStm /Length 4946 /Filter /FlateDecode /N 90 /First 762 >> stream xœÝ\YsÛÆ–~Ÿ_·›Ô-¡÷-•ëYÞc;¾’;™ÊEB"bŠPHÈŽó0¿}¾ÓÝàN™bhûÖ˜¦Ð  OŸ­Ï†eÁ UXWè"W˜B(e [ËUáp°¢ð…p.¡Üá /¤R8ŠB« ! éDÀÀB\ºÐÜÊB˜BK‰±¶ÐÚà<æðç}aÝ cp]òÂø` ) «‚*p‹ tós¾.œi g&·… ÆaÒÂKc Üê5ËPx«u¡x¸—…EP^JÁàRE°> ”zm,(ÉD 7€\®8Îi®Aš– E€ 4œ„ Å ­ÐÄ‚B Ú|Cƒ˜äA§d€«dɹÔÕÄ)0—d©@<0†<¾šÃ‹÷wpÌœo‘¯6]‹÷-ÐÐÁZ…Ûttàå‹fð)6¾š4ƒ›~>>~õ¼xÝ"T>úd´Í§óXØ›tìúJÈ`ŒÌGÝœù¶|´ ¬Ì`”ÈG™ÀÈ N)™ùþl´dHà•ÎÓØ„Æìt—±QÆåcº’çc:+[~ë¬^2„Í›–8)3Hž1ä"»ó*3*yré˜QáE22¼Ì)%2<1ÃꤷÕH(›­ó‹jP÷î7-m‚)£·%ÄòQ0Á€Î–ŸVÓæfÒMDУ†4DäkXÜý³ª 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Rather than fitting one global model to a dataset, it estimates local models on subsets of data that are ``learned'' by recursively partitioning. It proceeds in the following way: (1)~fit a parametric model to a data set, (2)~test for parameter instability over a set of partitioning variables, (3)~if there is some overall parameter instability, split the model with respect to the variable associated with the highest instability, (4)~repeat the procedure in each of the resulting subsamples. It is discussed how these steps of the conceptual algorithm are translated into computational tools in an object-oriented manner, allowing the user to plug in various types of parametric models. For representing the resulting trees, the \proglang{R} package \pkg{partykit} is employed and extended with generic infrastructure for recursive partitions where nodes are associated with statistical models. Compared to the previously available implementation in the \pkg{party} package, the new implementation supports more inference options, is easier to extend to new models, and provides more convenience features. } \Address{ Achim Zeileis \\ Department of Statistics \\ Faculty of Economics and Statistics \\ Universit\"at Innsbruck \\ Universit\"atsstr.~15 \\ 6020 Innsbruck, Austria \\ E-mail: \email{Achim.Zeileis@R-project.org} \\ URL: \url{http://eeecon.uibk.ac.at/~zeileis/} \\ Torsten Hothorn\\ Institut f\"ur Epidemiologie, Biostatistik und Pr\"avention \\ Universit\"at Z\"urich \\ Hirschengraben 84\\ CH-8001 Z\"urich, Switzerland \\ E-mail: \email{Torsten.Hothorn@R-project.org}\\ URL: \url{http://user.math.uzh.ch/hothorn/}\\ } \begin{document} \section{Overview} To implement the model-based recursive partitioning (MOB) algorithm of \cite{Zeileis+Hothorn+Hornik:2008} in software, infrastructure for three aspects is required: (1)~statistical ``\emph{models}'', (2)~recursive ``\emph{party}''tions, and (3)~``\emph{mobsters}'' carrying out the MOB algorithm. Along with \cite{Zeileis+Hothorn+Hornik:2008}, an implementation of all three steps was provided in the \pkg{party} package \citep{party} for the \proglang{R} system for statistical computing \citep{R}. This provided one very flexible \code{mob()} function combining \pkg{party}'s \proglang{S}4 classes for representing trees with binary splits and the \proglang{S}4 model wrapper functions from \pkg{modeltools} \citep{modeltools}. However, while this supported many applications of interest, it was somewhat limited in several directions: (1)~The \proglang{S}4 wrappers for the models were somewhat cumbersome to set up. (2)~The tree infrastructure was originally designed for \code{ctree()} and somewhat too narrowly focused on it. (3)~Writing new ``mobster'' interfaces was not easy because of using unexported \proglang{S}4 classes. Hence, a leaner and more flexible interface (based on \proglang{S}3 classes) is now provided in \pkg{partykit} \citep{partykit}: (1)~New models are much easier to provide in a basic version and customization does not require setting up an additional \proglang{S}4 class-and-methods layer anymore. (2)~The trees are built on top of \pkg{partykit}'s flexible `\code{party}' objects, inheriting many useful methods and providing new ones dealing with the fitted models associated with the tree's nodes. (3)~New ``mobsters'' dedicated to specific models, e.g., \code{lmtree()} and \code{glmtree()} for MOBs of (generalized) linear models, are readily provided. The remainder of this vignette is organized as follows: Section~\ref{sec:algorithm} very briefly reviews the original MOB algorithm of \cite{Zeileis+Hothorn+Hornik:2008} and also highlights relevant subsequent work. Section~\ref{sec:implementation} introduces the new \code{mob()} function in \pkg{partykit} in detail, discussing how all steps of the MOB algorithm are implemented and which options for customization are available. For illustration logistic-regression-based recursive partitioning is applied to the Pima Indians diabetes data set from the UCI machine learning repository \citep{mlbench2}. Section~\ref{sec:illustration} and~\ref{sec:mobster} present further illustrative examples \citep[including replications from][]{Zeileis+Hothorn+Hornik:2008} before Section~\ref{sec:conclusion} provides some concluding remarks. \section{MOB: Model-based recursive partitioning} \label{sec:algorithm} First, the theory underling the MOB (model-based recursive partitioning) is briefly reviewed; a more detailed discussion is provided by \cite{Zeileis+Hothorn+Hornik:2008}. To fix notation, consider a parametric model $\mathcal{M}(Y, \theta)$ with (possibly vector-valued) observations $Y$ and a $k$-dimensional vector of parameters $\theta$. This model could be a (possibly multivariate) normal distribution for $Y$, a psychometric model for a matrix of responses $Y$, or some kind of regression model when $Y = (y, x)$ can be split up into a dependent variable $y$ and regressors $x$. An example for the latter could be a linear regression model $y = x^\top \theta$ or a generalized linear model (GLM) or a survival regression. Given $n$ observations $Y_i$ ($i = 1, \dots, n$) the model can be fitted by minimizing some objective function $\sum_{i = 1}^n \Psi(Y_i, \theta)$, e.g., a residual sum of squares or a negative log-likelihood leading to ordinary least squares (OLS) or maximum likelihood (ML) estimation, respectively. If a global model for all $n$ observations does not fit well and further covariates $Z_1, \dots, Z_\ell$ are available, it might be possible to partition the $n$ observations with respect to these variables and find a fitting local model in each cell of the partition. The MOB algorithm tries to find such a partition adaptively using a greedy forward search. The reasons for looking at such local models might be different for different types of models: First, the detection of interactions and nonlinearities in regression relationships might be of interest just like in standard classification and regression trees \citep[see e.g.,][]{Zeileis+Hothorn+Hornik:2008}. Additionally, however, this approach allows to add explanatory variables to models that otherwise do not have regressors or where the link between the regressors and the parameters of the model is inclear \citep[this idea is pursued by][]{Strobl+Wickelmaier+Zeileis:2011}. Finally, the model-based tree can be employed as a thorough diagnostic test of the parameter stability assumption (also termed measurement invariance in psychometrics). If the tree does not split at all, parameter stability (or measurement invariance) cannot be rejected while a tree with splits would indicate in which way the assumption is violated \citep[][employ this idea in psychometric item response theory models]{Strobl+Kopf+Zeileis:2015}. The basic idea is to grow a tee in which every node is associated with a model of type $\mathcal{M}$. To assess whether splitting of the node is necessary a fluctuation test for parameter instability is performed. If there is significant instability with respect to any of the partitioning variables $Z_j$, the node is splitted into $B$ locally optimal segments (the currenct version of the software has $B = 2$ as the default and as the only option for numeric/ordered variables) and then the procedure is repeated in each of the $B$ children. If no more significant instabilities can be found, the recursion stops. More precisely, the steps of the algorithm are % \begin{enumerate} \item Fit the model once to all observations in the current node. \item Assess whether the parameter estimates are stable with respect to every partitioning variable $Z_1, \dots, Z_\ell$. If there is some overall instability, select the variable $Z_j$ associated with the highest parameter instability, otherwise stop. \item Compute the split point(s) that locally optimize the objective function $\Psi$. \item Split the node into child nodes and repeat the procedure until some stopping criterion is met. \end{enumerate} % This conceptual framework is extremely flexible and allows to adapt it to various tasks by choosing particular models, tests, and methods in each of the steps: % \begin{enumerate} \item \emph{Model estimation:} The original MOB introduction \citep{Zeileis+Hothorn+Hornik:2008} discussed regression models: OLS regression, GLMs, and survival regression. Subsequently, \cite{Gruen+Kosmidis+Zeileis:2012} have also adapted MOB to beta regression for limited response variables. Furthermore, MOB provides a generic way of adding covariates to models that otherwise have no regressors: this can either serve as a check whether the model is indeed independent from regressors or leads to local models for subsets. Both views are of interest when employing MOB to detect parameter instabilities in psychometric models for item responses such as the Bradley-Terry or the Rasch model \citep[see][respectively]{Strobl+Wickelmaier+Zeileis:2011,Strobl+Kopf+Zeileis:2015}. \item \emph{Parameter instability tests:} To assess the stability of all model parameters across a certain partitioning variable, the general class of score-based fluctuation tests proposed by \cite{Zeileis+Hornik:2007} is employed. Based on the empirical score function observations (i.e., empirical estimating functions or contributions to the gradient), ordered with respect to the partitioning variable, the fluctuation or instability in the model's parameters can be tested. From this general framework the Andrews' sup\textit{LM} test is used for assessing numerical partitioning variables and a $\chi^2$ test for categorical partitioning variables (see \citealp{Zeileis:2005} and \citealp{Merkle+Zeileis:2013} for unifying views emphasizing regression and psychometric models, respectively). Furthermore, the test statistics for ordinal partitioning variables suggested by \cite{Merkle+Fan+Zeileis:2014} have been added as further options (but are not used by default as the simulation of $p$-values is computationally demanding). \item \emph{Partitioning:} As the objective function $\Psi$ is additive, it is easy to compute a single optimal split point (or cut point or break point). For each conceivable split, the model is estimated on the two resulting subsets and the resulting objective functions are summed. The split that optimizes this segmented objective function is then selected as the optimal split. For optimally splitting the data into $B > 2$ segments, the same idea can be used and a full grid search can be avoided by employing a dynamic programming algorithms \citep{Hawkins:2001,Bai+Perron:2003} but at the moment the latter is not implemented in the software. Optionally, however, categorical partitioning variables can be split into all of their categories (i.e., in that case $B$ is set to the number of levels without searching for optimal groupings). \item \emph{Pruning:} For determining the optimal size of the tree, one can either use a pre-pruning or post-pruning strategy. For the former, the algorithm stops when no significant parameter instabilities are detected in the current node (or when the node becomes too small). For the latter, one would first grow a large tree (subject only to a minimal node size requirement) and then prune back splits that did not improve the model, e.g., judging by information criteria such as AIC or BIC \citep[see e.g.,][]{Su+Wang+Fan:2004}. Currently, pre-pruning is used by default (via Bonferroni-corrected $p$-values from the score-based fluctuation tests) but AIC/BIC-based post-pruning is optionally available (especially for large data sets where traditional significance levels are not useful). \end{enumerate} % In the following it is discussed how most of the options above are embedded in a common computational framework using \proglang{R}'s facilities for model estimation and object orientation. \section[A new implementation in R]{A new implementation in \proglang{R}} \label{sec:implementation} This section introduces a new implementation of the general model-based recursive partitioning (MOB) algorithm in \proglang{R}. Along with \cite{Zeileis+Hothorn+Hornik:2008}, a function \code{mob()} had been introduced to the \pkg{party} package \citep{party} which continues to work but it turned out to be somewhat unflexible for certain applications/extensions. Hence, the \pkg{partykit} package \citep{partykit} provides a completely rewritten (and not backward compatible) implementation of a new \code{mob()} function along with convenience interfaces \code{lmtree()} and \code{glmtree()} for fitting linear model and generalized linear model trees, respectively. The function \code{mob()} itself is intended to be the workhorse function that can also be employed to quickly explore new models -- whereas \code{lmtree()} and \code{glmtree()} will be the typical user interfaces facilitating applications. The new \code{mob()} function has the following arguments: \begin{Code} mob(formula, data, subset, na.action, weights, offset, fit, control = mob_control(), ...) \end{Code} All arguments in the first line are standard for modeling functions in \proglang{R} with a \code{formula} interface. They are employed by \code{mob()} to do some data preprocessing (described in detail in Section~\ref{sec:formula}) before the \code{fit} function is used for parameter estimation on the preprocessed data. The \code{fit} function has to be set up in a certain way (described in detail in Section~\ref{sec:fit}) so that \code{mob()} can extract all information that is needed in the MOB algorithm for parameter instability tests (see Section~\ref{sec:sctest}) and partitioning/splitting (see Section~\ref{sec:split}), i.e., the estimated parameters, the associated objective function, and the score function contributions. A list of \code{control} options can be set up by the \code{mob_control()} function, including options for pruning (see Section~\ref{sec:prune}). Additional arguments \code{...} are passed on to the \code{fit} function. The result is an object of class `\code{modelparty}' inheriting from `\code{party}'. The \code{info} element of the overall `\code{party}' and the individual `\code{node}'s contain various informations about the models. Details are provided in Section~\ref{sec:object}. Finally, a wide range of standard (and some extra) methods are available for working with `\code{modelparty}' objects, e.g., for extracting information about the models, for visualization, computing predictions, etc. The standard set of methods is introduced in Section~\ref{sec:methods}. However, as will be discussed there, it may take some effort by the user to efficiently compute certain pieces of information. Hence, convenience interfaces such as \code{lmtree()} or \code{glmtree()} can alleviate these obstacles considerably, as illustrated in Section~\ref{sec:interface}. \subsection{Formula processing and data preparation} \label{sec:formula} The formula processing within \code{mob()} is essentially done in ``the usual way'', i.e., there is a \code{formula} and \code{data} and optionally further arguments such as \code{subset}, \code{na.action}, \code{weights}, and \code{offset}. These are processed into a \code{model.frame} from which the response and the covariates can be extracted and passed on to the actual \code{fit} function. As there are possibly three groups of variables (response, regressors, and partitioning variables), the \pkg{Formula} package \citep{Formula} is employed for processing these three parts. Thus, the formula can be of type \verb:y ~ x1 + ... + xk | z1 + ... + zl: where the variables on the left of the \code{|} specify the data $Y$ and the variables on the right specify the partitioning variables $Z_j$. As pointed out above, the $Y$ can often be split up into response (\code{y} in the example above) and regressors (\code{x1}, \dots, \code{xk} in the example above). If there are no regressors and just constant fits are employed, then the formula can be specified as \verb:y ~ 1 | z1 + ... + zl:. So far, this formula representation is really just a specification of groups of variables and does not imply anything about the type of model that is to be fitted to the data in the nodes of the tree. The \code{mob()} function does not know anything about the type of model and just passes (subsets of) the \code{y} and \code{x} variables on to the \code{fit} function. Only the partitioning variables \code{z} are used internally for the parameter instability tests (see Section~\ref{sec:sctest}). As different \code{fit} functions will require the data in different formats, \code{mob_control()} allows to set the \code{ytype} and \code{xtype}. The default is to assume that \code{y} is just a single column of the model frame that is extracted as a \code{ytype = "vector"}. Alternatively, it can be a \code{"data.frame"} of all response variables or a \code{"matrix"} set up via \code{model.matrix()}. The options \code{"data.frame"} and \code{"matrix"} are also available for \code{xtype} with the latter being the default. Note that if \code{"matrix"} is used, then transformations (e.g., logs, square roots etc.) and dummy/interaction codings are computed and turned into columns of a numeric matrix while for \code{"data.frame"} the original variables are preserved. By specifying the \code{ytype} and \code{xtype}, \code{mob()} is also provided with the information on how to correctly subset \code{y} and \code{x} when recursively partitioning data. In each step, only the subset of \code{y} and \code{x} pertaining to the current node of the tree is passed on to the \code{fit} function. Similarly, subsets of \code{weights} and \code{offset} are passed on (if specified). \subsubsection*{Illustration} For illustration, we employ the popular benchmark data set on diabetes among Pima Indian women that is provided by the UCI machine learning repository \citep{mlbench2} and available in the \pkg{mlbench} package \citep{mlbench}: % <>= data("PimaIndiansDiabetes", package = "mlbench") @ % Following \cite{Zeileis+Hothorn+Hornik:2008} we want to fit a model for \code{diabetes} employing the plasma glucose concentration \code{glucose} as a regressor. As the influence of the remaining variables on \code{diabetes} is less clear, their relationship should be learned by recursive partitioning. Thus, we employ the following formula: % <>= pid_formula <- diabetes ~ glucose | pregnant + pressure + triceps + insulin + mass + pedigree + age @ % Before passing this to \code{mob()}, a \code{fit} function is needed and a logistic regression function is set up in the following section. \subsection{Model fitting and parameter estimation} \label{sec:fit} The \code{mob()} function itself does not actually carry out any parameter estimation by itself, but assumes that one of the many \proglang{R} functions available for model estimation is supplied. However, to be able to carry out the steps of the MOB algorithm, \code{mob()} needs to able to extract certain pieces of information: especially the estimated parameters, the corresponding objective function, and associated score function contributions. Also, the interface of the fitting function clearly needs to be standardized so that \code{mob()} knows how to invoke the model estimation. Currently, two possible interfaces for the \code{fit} function can be employed: % \begin{enumerate} \item The \code{fit} function can take the following inputs \begin{Code} fit(y, x = NULL, start = NULL, weights = NULL, offset = NULL, ..., estfun = FALSE, object = FALSE) \end{Code} where \code{y}, \code{x}, \code{weights}, \code{offset} are (the subset of) the preprocessed data. In \code{start} starting values for the parameter estimates may be supplied and \code{...} is passed on from the \code{mob()} function. The \code{fit} function then has to return an output list with the following elements: \begin{itemize} \item \code{coefficients}: Estimated parameters $\hat \theta$. \item \code{objfun}: Value of the minimized objective function $\sum_i \Psi(y_i, x_, \hat \theta)$. \item \code{estfun}: Empirical estimating functions (or score function contributions) $\Psi'(y_i, x_i, \hat \theta)$. Only needed if \code{estfun = TRUE}, otherwise optionally \code{NULL}. \item \code{object}: A model object for which further methods could be available (e.g., \code{predict()}, or \code{fitted()}, etc.). Only needed if \code{object = TRUE}, otherwise optionally \code{NULL}. \end{itemize} By making \code{estfun} and \code{object} optional, the fitting function might be able to save computation time by only optimizing the objective function but avoiding further computations (such as setting up covariance matrix, residuals, diagnostics, etc.). \item The \code{fit} function can also of a simpler interface with only the following inputs: \begin{Code} fit(y, x = NULL, start = NULL, weights = NULL, offset = NULL, ...) \end{Code} The meaning of all arguments is the same as above. However, in this case \code{fit} needs to return a classed model object for which methods to \code{coef()}, \code{logLik()}, and \code{estfun()} \citep[see][and the \pkg{sandwich} package]{sandwich} are available for extracting the parameter estimates, the maximized log-likelihood, and associated empirical estimating functions (or score contributions), respectively. Internally, a function of type (1) is set up by \code{mob()} in case a function of type (2) is supplied. However, as pointed out above, a function of type (1) might be useful to save computation time. \end{enumerate} % In either case the \code{fit} function can, of course, choose to ignore any arguments that are not applicable, e.g., if the are no regressors \code{x} in the model or if starting values or not supported. The \code{fit} function of type (2) is typically convenient to quickly try out a new type of model in recursive partitioning. However, when writing a new \code{mob()} interface such as \code{lmtree()} or \code{glmtree()}, it will typically be better to use type (1). Similarly, employing supporting starting values in \code{fit} is then recommended to save computation time. \subsubsection*{Illustration} For recursively partitioning the \code{diabetes ~ glucose} relationship (as already set up in the previous section), we employ a logistic regression model. An interface of type (2) can be easily set up: % <>= logit <- function(y, x, start = NULL, weights = NULL, offset = NULL, ...) { glm(y ~ 0 + x, family = binomial, start = start, ...) } @ % Thus, \code{y}, \code{x}, and the starting values are passed on to \code{glm()} which returns an object of class `\code{glm}' for which all required methods (\code{coef()}, \code{logLik()}, and \code{estfun()}) are available. Using this \code{fit} function and the \code{formula} already set up above the MOB algorithm can be easily applied to the \code{PimaIndiansDiabetes} data: % <>= pid_tree <- mob(pid_formula, data = PimaIndiansDiabetes, fit = logit) @ % The result is a logistic regression tree with three terminal nodes that can be easily visualized via \code{plot(pid_tree)} (see Figure~\ref{fig:pid_tree}) and printed: <>= pid_tree @ % The tree finds three groups of Pima Indian women: \begin{itemize} \item[\#2] Women with low body mass index that have on average a low risk of diabetes, however this increases clearly with glucose level. \item[\#4] Women with average and high body mass index, younger than 30 years, that have a higher avarage risk that also increases with glucose level. \item[\#5] Women with average and high body mass index, older than 30 years, that have a high avarage risk that increases only slowly with glucose level. \end{itemize} Note that the example above is used for illustration here and \code{glmtree()} is recommended over using \code{mob()} plus manually setting up a \code{logit()} function. The same tree structure can be found via: % <>= pid_tree2 <- glmtree(diabetes ~ glucose | pregnant + pressure + triceps + insulin + mass + pedigree + age, data = PimaIndiansDiabetes, family = binomial) @ % However, \code{glmtree()} is slightly faster as it avoids many unnecessary computations, see Section~\ref{sec:interface} for further details. \begin{figure}[p!] \centering \setkeys{Gin}{width=0.8\textwidth} <>= plot(pid_tree) @ \caption{\label{fig:pid_tree} Logistic-regression-based tree for the Pima Indians diabetes data. The plots in the leaves report the estimated regression coefficients.} \setkeys{Gin}{width=\textwidth} <>= plot(pid_tree2, tp_args = list(ylines = 1, margins = c(1.5, 1.5, 1.5, 2.5))) @ \caption{\label{fig:pid_tree2} Logistic-regression-based tree for the Pima Indians diabetes data. The plots in the leaves give spinograms for \code{diabetes} versus \code{glucose}.} \end{figure} Here, we only point out that \code{plot(pid_tree2)} produces a nicer visualization (see Figure~\ref{fig:pid_tree2}). As $y$ is \code{diabetes}, a binary variable, and $x$ is \code{glucose}, a numeric variable, a spinogram is chosen automatically for visualization (using the \pkg{vcd} package, \citealp{vcd}). The x-axis breaks in the spinogram are the five-point summary of \code{glucose} on the full data set. The fitted lines are the mean predicted probabilities in each group. \subsection{Testing for parameter instability} \label{sec:sctest} In each node of the tree, first the parametric model is fitted to all observations in that node (see Section~\ref{sec:fit}). Subsequently it is of interest to find out whether the model parameters are stable over each particular ordering implied by the partitioning variables $Z_j$ or whether splitting the sample with respect to one of the $Z_j$ might capture instabilities in the parameters and thus improve the fit. The tests used in this step belong to the class of generalized M-fluctuation tests \citep{Zeileis:2005,Zeileis+Hornik:2007}. Depending on the class of each of the partitioning variables in \code{z} different types of tests are chosen by \code{mob()}: \begin{enumerate} \item For numeric partitioning variables (of class `\code{numeric}' or `\code{integer}') the sup\textit{LM}~statistic is used which is the maximum over all single-split \textit{LM} statistics. Associated $p$-values can be obtained from a table of critical values \citep[based on][]{Hansen:1997} stored within the package. If there are ties in the partitioning variable, the sequence of \textit{LM} statistics (and hence their maximum) is not unique and hence the results by default may depend to some degree on the ordering of the observations. To explore this, the option \code{breakties = TRUE} can be set in \code{mob_control()} which breaks ties randomly. If there are are only few ties, the influence is often negligible. If there are many ties (say only a dozen unique values of the partitioning variable), then the variable may be better treated as an ordered factor (see below). \item For categorical partitioning variables (of class `\code{factor}'), a $\chi^2$~statistic is employed which captures the fluctuation within each of the categories of the partitioning variable. This is also an \textit{LM}-type test and is asymptotically equivalent to the corresponding likelihood ratio test. However, it is somewhat cheaper to compute the \textit{LM} statistic because the model just has to be fitted once in the current node and not separately for each category of each possible partitioning variable. See also \cite{Merkle+Fan+Zeileis:2014} for a more detailed discussion. \item For ordinal partitioning variables (of class `\code{ordered}' inheriting from `\code{factor}') the same $\chi^2$ as for the unordered categorical variables is used by default \citep[as suggested by][]{Zeileis+Hothorn+Hornik:2008}. Although this test is consistent for any parameter instabilities across ordered variables, it does not exploit the ordering information. Recently, \cite{Merkle+Fan+Zeileis:2014} proposed an adapted max\textit{LM} test for ordered variables and, alternatively, a weighted double maximum test. Both are optionally availble in the new \code{mob()} implementation by setting \code{ordinal = "L2"} or \code{ordinal = "max"} in \code{mob_control()}, respectively. Unfortunately, computing $p$-values from both tests is more costly than for the default \code{ordinal = "chisq"}. For \code{"L2"} suitable tables of critical values have to be simulated on the fly using \code{ordL2BB()} from the \pkg{strucchange} package \citep{strucchange}. For \code{"max"} a multivariate normal probability has to be computed using the \pkg{mvtnorm} package \citep{mvtnorm}. \end{enumerate} All of the parameter instability tests above can be computed in an object-oriented manner as the ``\code{estfun}'' has to be available for the fitted model object. (Either by computing it in the \code{fit} function directly or by providing a \code{estfun()} extractor, see Section~\ref{sec:fit}.) All tests also require an estimate of the corresponding variance-covariance matrix of the estimating functions. The default is to compute this using an outer-product-of-gradients (OPG) estimator. Alternatively, the corrsponding information matrix or sandwich matrix can be used if: (a)~the estimating functions are actually maximum likelihood scores, and (b)~a \code{vcov()} method (based on an estimate of the information) is provided for the fitted model objects. The corresponding option in \code{mob_control()} is to set \code{vcov = "info"} or \code{vcov = "sandwich"} rather than \code{vcov = "opg"} (the default). For each of the $j = 1, \dots, \ell$ partitioning variables in \code{z} the test selected in the control options is employed and the corresponding $p$-value $p_j$ is computed. To adjust for multiple testing, the $p$ values can be Bonferroni adjusted (which is the default). To determine whether there is some overall instability, it is checked whether the minial $p$-value $p_{j^*} = \min_{j = 1, \dots, \ell} p_j$ falls below a pre-specified significance level $\alpha$ (by default $\alpha = 0.05$) or not. If there is significant instability, the variable $Z_{j^*}$ associated with the minimal $p$-value is used for splitting the node. \subsubsection*{Illustration} In the logistic-regression-based MOB \code{pid_tree} computed above, the parameter instability tests can be extracted using the \code{sctest()} function from the \pkg{strucchange} package (for \underline{s}tructural \underline{c}hange \underline{test}). In the first node, the test statistics and Bonferroni-corrected $p$-values are: % <>= library("strucchange") sctest(pid_tree, node = 1) @ % Thus, the body \code{mass} index has the lowest $p$-value and is highly significant and hence used for splitting the data. In the second node, no further significant parameter instabilities can be detected and hence partitioning stops in that branch. % <>= sctest(pid_tree, node = 2) @ % In the third node, however, there is still significant instability associated with the \code{age} variable and hence partitioning continues. % <>= sctest(pid_tree, node = 3) @ % Because no further instabilities can be found in the fourth and fifth node, the recursive partitioning stops there. \subsection{Splitting} \label{sec:split} In this step, the observations in the current node are split with respect to the chosen partitioning variable $Z_{j^*}$ into $B$ child nodes. As pointed out above, the \code{mob()} function currently only supports binary splits, i.e., $B = 2$. For deterimining the split point, an exhaustive search procedure is adopted: For each conceivable split point in $Z_{j^*}$, the two subset models are fit and the split associated with the minimal value of the objective function $\Psi$ is chosen. Computationally, this means that the \code{fit} function is applied to the subsets of \code{y} and \code{x} for each possibly binary split. The ``\code{objfun}'' values are simply summed up (because the objective function is assumed to be additive) and its minimum across splits is determined. In a search over a numeric partitioning variable, this means that typically a lot of subset models have to be fitted and often these will not vary a lot from one split to the next. Hence, the parameter estimates ``\code{coefficients}'' from the previous split are employed as \code{start} values for estimating the coefficients associated with the next split. Thus, if the \code{fit} function makes use of these starting values, the model fitting can often be speeded up. \subsubsection*{Illustration} For the Pima Indians diabetes data, the split points found for \code{pid_tree} are displayed both in the print output and the visualization (see Figure~\ref{fig:pid_tree} and~\ref{fig:pid_tree2}). \subsection{Pruning} \label{sec:prune} By default, the size of \code{mob()} trees is determined only by the significance tests, i.e., when there is no more significant parameter instability (by default at level $\alpha = 0.05$) the tree stops growing. Additional stopping criteria are only the minimal node size (\code{minsize}) and the maximum tree depth (\code{maxdepth}, by default infinity). However, for very large sample size traditional significance levels are typically not useful because even tiny parameter instabilities can be detected. To avoid overfitting in such a situation, one would either have to use much smaller significance levels or add some form of post-pruning to reduce the size of the tree afterwards. Similarly, one could wish to first grow a very large tree (using a large $\alpha$ level) and then prune it afterwards, e.g., using some information criterion like AIC or BIC. To accomodate such post-pruning strategies, \code{mob_control()} has an argument \code{prune} that can be a \code{function(objfun, df, nobs)} that either returns \code{TRUE} if a node should be pruned or \code{FALSE} if not. The arguments supplied are a vector of objective function values in the current node and the sum of all child nodes, a vector of corresponding degrees of freedom, and the number of observations in the current node and in total. For example if the objective function used is the negative log-likelihood, then for BIC-based pruning the \code{prune} function is: \code{(2 * objfun[1] + log(nobs[1]) * df[1]) < (2 * objfun[2] + log(nobs[2]) * df[2])}. As the negative log-likelihood is the default objective function when using the ``simple'' \code{fit} interface, \code{prune} can also be set to \code{"AIC"} or \code{"BIC"} and then suitable functions will be set up internally. Note, however, that for other objective functions this strategy is not appropriate and the functions would have to be defined differently (which \code{lmtree()} does for example). In the literature, there is no clear consensus as to how many degrees of freedom should be assigned to the selection of a split point. Hence, \code{mob_control()} allows to set \code{dfsplit} which by default is \code{dfsplit = TRUE} and then \code{as.integer(dfsplit)} (i.e., 1 by default) degrees of freedom per split are used. This can be modified to \code{dfsplit = FALSE} (or equivalently \code{dfsplit = 0}) or \code{dfsplit = 3} etc.\ for lower or higher penalization of additional splits. \subsubsection*{Illustration} With $n = \Sexpr{nrow(PimaIndiansDiabetes)}$ observations, the sample size is quite reasonable for using the classical significance level of $\alpha = 0.05$ which is also reflected by the moderate tree size with three terminal nodes. However, if we wished to explore further splits, a conceivable strategy could be the following: % <>= pid_tree3 <- mob(pid_formula, data = PimaIndiansDiabetes, fit = logit, control = mob_control(verbose = TRUE, minsize = 50, maxdepth = 4, alpha = 0.9, prune = "BIC")) @ This first grows a large tree until the nodes become too small (minimum node size: 50~observations) or the tree becomes too deep (maximum depth 4~levels) or the significance levels come very close to one (larger than $\alpha = 0.9$). Here, this large tree has eleven nodes which are subsequently pruned based on whether or not they improve the BIC of the model. For this data set, the resulting BIC-pruned tree is in fact identical to the pre-pruned \code{pid_tree} considered above. \subsection[Fitted `party' objects]{Fitted `\texttt{party}' objects} \label{sec:object} The result of \code{mob()} is an object of class `\code{modelparty}' inheriting from `\code{party}'. See the other vignettes in the \pkg{partykit} package \citep{partykit} for more details of the general `\code{party}' class. Here, we just point out that the main difference between a `\code{modelparty}' and a plain `\code{party}' is that additional information about the data and the associated models is stored in the \code{info} elements: both of the overall `\code{party}' and the individual `\code{node}'s. The details are exemplified below. \subsubsection*{Illustration} In the \code{info} of the overall `\code{party}' the following information is stored for \code{pid_tree}: % <>= names(pid_tree$info) @ % The \code{call} contains the \code{mob()} call. The \code{formula} and \code{Formula} are virtually the same but are simply stored as plain `\code{formula}' and extended `\code{Formula}' \citep{Formula} objects, respectively. The \code{terms} contain separate lists of terms for the \code{response} (and regressor) and the \code{partitioning} variables. The \code{fit}, \code{control} and \code{dots} are the arguments that were provided to \code{mob()} and \code{nreg} is the number of regressor variables. Furthermore, each \code{node} of the tree contains the following information: % <>= names(pid_tree$node$info) @ % The \code{coefficients}, \code{objfun}, and \code{object} are the results of the \code{fit} function for that node. In \code{nobs} and \code{p.value} the number of observations and the minimal $p$-value are provided, respectively. Finally, \code{test} contains the parameter instability test results. Note that the \code{object} element can also be suppressed through \code{mob_control()} to save memory space. \subsection{Methods} \label{sec:methods} There is a wide range of standard methods available for objects of class `\code{modelparty}'. The standard \code{print()}, \code{plot()}, and \code{predict()} build on the corresponding methods for `\code{party}' objects but provide some more special options. Furthermore, methods are provided that are typically available for models with formula interfaces: \code{formula()} (optionally one can set \code{extended = TRUE} to get the `\code{Formula}'), \code{getCall()}, \code{model.frame()}, \code{weights()}. Finally, there is a standard set of methods for statistical model objects: \code{coef()}, \code{residuals()}, \code{logLik()} (optionally setting \code{dfsplit = FALSE} suppresses counting the splits in the degrees of freedom, see Section~\ref{sec:prune}), \code{deviance()}, \code{fitted()}, and \code{summary()}. Some of these methods rely on reusing the corresponding methods for the individual model objects in the terminal nodes. Functions such as \code{coef()}, \code{print()}, \code{summary()} also take a \code{node} argument that can specify the node IDs to be queried. Two methods have non-standard arguments to allow for additional flexibility when dealing with model trees. Typically, ``normal'' users do not have to use these arguments directly but they are very flexible and facilitate writing convenience interfaces such as \code{glmtree()} (see Section~\ref{sec:interface}). \begin{itemize} \item The \code{predict()} method has the following arguments: \code{predict(object, newdata = NULL, type = "node", ...)}. The argument \code{type} can either be a function or a character string. More precisely, if \code{type} is a function it should be a \code{function (object, newdata = NULL, ...)} that returns a vector or matrix of predictions from a fitted model \code{object} either with or without \code{newdata}. If \code{type} is a character string, such a function is set up internally as \code{predict(object, newdata = newdata, type = type, ...)}, i.e., it relies on a suitable \code{predict()} method being available for the fitted models associated with the `\code{party}' object. \item The \code{plot()} method has the following arguments: \code{plot(x, terminal_panel = NULL, FUN = NULL)}. This simply calls the \code{plot()} method for `\code{party}' objects with a custom panel function for the terminal panels. By default, \code{node_terminal} is used to include some short text in each terminal node. This text can be set up by \code{FUN} with the default being the number of observations and estimated parameters. However, more elaborate terminal panel functions can be written, as done for the convenience interfaces. \end{itemize} Finally, two \proglang{S}3-style functions are provided without the corresponding generics (as these reside in packages that \pkg{partykit} does not depend on). The \code{sctest.modelparty} can be used in combination with the \code{sctest()} generic from \pkg{strucchange} as illustrated in Section~\ref{sec:sctest}. The \code{refit.modelparty} function extracts (or refits if necessary) the fitted model objects in the specified nodes (by default from all nodes). \subsubsection*{Illustration} The \code{plot()} and \code{print()} methods have already been illustrated for the \code{pid_tree} above. However, here we add that the \code{print()} method can also be used to show more detailed information about particular nodes instead of showing the full tree: % <>= print(pid_tree, node = 3) @ % Information about the model and coefficients can for example be extracted by: % <>= coef(pid_tree) coef(pid_tree, node = 1) ## IGNORE_RDIFF_BEGIN summary(pid_tree, node = 1) ## IGNORE_RDIFF_END @ % As the coefficients pertain to a logistic regression, they can be easily interpreted as odds ratios by taking the \code{exp()}: % <<>>= exp(coef(pid_tree)[,2]) @ % <>= risk <- round(100 * (exp(coef(pid_tree)[,2])-1), digits = 1) @ % i.e., the odds increase by \Sexpr{risk[1]}\%, \Sexpr{risk[2]}\% and \Sexpr{risk[3]}\% with respect to glucose in the three terminal nodes. Log-likelihoods and information criteria are available (which by default also penalize the estimation of splits): <>= logLik(pid_tree) AIC(pid_tree) BIC(pid_tree) @ % Mean squared residuals (or deviances) can be extracted in different ways: <>= mean(residuals(pid_tree)^2) deviance(pid_tree)/sum(weights(pid_tree)) deviance(pid_tree)/nobs(pid_tree) @ % Predicted nodes can also be easily obtained: % <>= pid <- head(PimaIndiansDiabetes) predict(pid_tree, newdata = pid, type = "node") @ % More predictions, e.g., predicted probabilities within the nodes, can also be obtained but require some extra coding if only \code{mob()} is used. However, with the \code{glmtree()} interface this is very easy as shown below. Finally, several methods for `\code{party}' objects are, of course, also available for `\code{modelparty}' objects, e.g., querying width and depth of the tree: % <>= width(pid_tree) depth(pid_tree) @ % Also subtrees can be easily extracted: % <>= pid_tree[3] @ % The subtree is again a completely valid `\code{modelparty}' and hence it could also be visualized via \code{plot(pid_tree[3])} etc. \subsection{Extensions and convenience interfaces} \label{sec:interface} As illustrated above, dealing with MOBs can be carried out in a very generic and object-oriented way. Almost all information required for dealing with recursively partitioned models can be encapsulated in the \code{fit()} function and \code{mob()} does not require more information on what type of model is actually used. However, for certain tasks more detailed information about the type of model used or the type of data it can be fitted to can (and should) be exploited. Notable examples for this are visualizations of the data along with the fitted model or model-based predictions in the leaves of the tree. To conveniently accomodate such specialized functionality, the \pkg{partykit} provides two convenience interfaces \code{lmtree()} and \code{glmtree()} and encourages other packages to do the same (e.g., \code{raschtree()} and \code{bttree()} in \pkg{psychotree}). Furthermore, such a convenience interface can avoid duplicated formula processing in both \code{mob()} plus its \code{fit} function. Specifically, \code{lmtree()} and \code{glmtree()} interface \code{lm.fit()}, \code{lm.wfit()}, and \code{glm.fit()}, respectively, and then provide some extra computations to return valid fitted `\code{lm}' and `\code{glm}' objects in the nodes of the tree. The resulting `\code{modelparty}' object gains an additional class `\code{lmtree}'/`\code{glmtree}' to dispatch to its enhanced \code{plot()} and \code{predict()} methods. \subsubsection*{Illustration} The \code{pid_tree2} object was already created above with \code{glmtree()} (instead of \code{mob()} as for \code{pid_tree}) to illustrate the enhanced plotting capabilities in Figure~\ref{fig:pid_tree2}. Here, the enhanced \code{predict()} method is used to obtain predicted means (i.e., probabilities) and associated linear predictors (on the logit scale) in addition to the previously available predicted nods IDs. % <<>>= predict(pid_tree2, newdata = pid, type = "node") predict(pid_tree2, newdata = pid, type = "response") predict(pid_tree2, newdata = pid, type = "link") @ \section{Illustrations} \label{sec:illustration} In the remainder of the vignette, further empirical illustrations of the MOB method are provided, including replications of the results from \cite{Zeileis+Hothorn+Hornik:2008}: \begin{enumerate} \item An investigation of the price elasticity of the demand for economics journals across covariates describing the type of journal (e.g., its price, its age, and whether it is published by a society, etc.) \item Prediction of house prices in the well-known Boston Housing data set, also taken from the UCI machine learning repository. \item Explore how teaching ratings and beauty scores of professors are associated and how this association changes across further explanatory variables such as age, gender, and native speaker status of the professors. \item Assessment of differences in the preferential treatment of women/children (``women and children first'') across subgroups of passengers on board of the ill-fated maiden voyage of the RMS Titanic. \item Modeling of breast cancer survival by capturing heterogeneity in certain (treatment) effects across patients. \item Modeling of paired comparisons of topmodel candidates by capturing heterogeneity in their attractiveness scores across participants in a survey. \end{enumerate} More details about several of the underlying data sets, previous studies exploring the data, and the results based on MOB can be found in \cite{Zeileis+Hothorn+Hornik:2008}. Here, we focus on using the \pkg{partykit} package to replicate the analysis and explore the resulting trees. The first three illustrations employ the \code{lmtree()} convenience function, the fourth is based on logistic regression using \code{glmtree()}, and the fifth uses \code{survreg()} from \pkg{survival} \citep{survival} in combination with \code{mob()} directly. The sixth and last illustration is deferred to a separate section and shows in detail how to set up new ``mobster'' functionality from scratch. \subsection{Demand for economic journals} The price elasticity of the demand for 180~economic journals is assessed by an OLS regression in log-log form: The dependent variable is the logarithm of the number of US library subscriptions and the regressor is the logarithm of price per citation. The data are provided by the \pkg{AER} package \citep{AER} and can be loaded and transformed via: % <>= data("Journals", package = "AER") Journals <- transform(Journals, age = 2000 - foundingyear, chars = charpp * pages) @ % Subsequently, the stability of the price elasticity across the remaining variables can be assessed using MOB. Below, \code{lmtree()} is used with the following partitioning variables: raw price and citations, age of the journal, number of characters, and whether the journal is published by a scientific society or not. A minimal segment size of 10~observations is employed and by setting \code{verbose = TRUE} detailed progress information about the recursive partitioning is displayed while growing the tree: % <>= j_tree <- lmtree(log(subs) ~ log(price/citations) | price + citations + age + chars + society, data = Journals, minsize = 10, verbose = TRUE) @ % \begin{figure}[t!] \centering \setkeys{Gin}{width=0.75\textwidth} <>= plot(j_tree) @ \caption{\label{fig:Journals} Linear-regression-based tree for the journals data. The plots in the leaves show linear regressions of log(subscriptions) by log(price/citation).} \end{figure} % The resulting tree just has one split and two terminal nodes for young journals (with a somewhat larger price elasticity) and old journals (with an even lower price elasticity), respectively. Figure~\ref{fig:Journals} can be obtained by \code{plot(j_tree)} and the corresponding printed representation is shown below. % <>= j_tree @ % Finally, various quantities of interest such as the coefficients, standard errors and test statistics, and the associated parameter instability tests could be extracted by the following code. The corresponding output is suppressed here. % <>= coef(j_tree, node = 1:3) summary(j_tree, node = 1:3) sctest(j_tree, node = 1:3) @ \subsection{Boston housing data} The Boston housing data are a popular and well-investigated empirical basis for illustrating nonlinear regression methods both in machine learning and statistics. We follow previous analyses by segmenting a bivariate linear regression model for the house values. The data set is available in package \pkg{mlbench} and can be obtained and transformed via: % <>= data("BostonHousing", package = "mlbench") BostonHousing <- transform(BostonHousing, chas = factor(chas, levels = 0:1, labels = c("no", "yes")), rad = factor(rad, ordered = TRUE)) @ % It provides $n = \Sexpr{NROW(BostonHousing)}$ observations of the median value of owner-occupied homes in Boston (in USD~1000) along with $\Sexpr{NCOL(BostonHousing)}$ covariates including in particular the number of rooms per dwelling (\code{rm}) and the percentage of lower status of the population (\code{lstat}). A segment-wise linear relationship between the value and these two variables is very intuitive, whereas the shape of the influence of the remaining covariates is rather unclear and hence should be learned from the data. Therefore, a linear regression model for median value explained by \verb:rm^2: and \verb:log(lstat): is employed and partitioned with respect to all remaining variables. Choosing appropriate transformations of the dependent variable and the regressors that enter the linear regression model is important to obtain a well-fitting model in each segment and we follow in our choice the recommendations of \cite{Breiman+Friedman:1985}. Monotonic transformations of the partitioning variables do not affect the recursive partitioning algorithm and hence do not have to be performed. However, it is important to distinguish between numerical and categorical variables for choosing an appropriate parameter stability test. The variable \code{chas} is a dummy indicator variable (for tract bounds with Charles river) and thus needs to be turned into a factor. Furthermore, the variable \code{rad} is an index of accessibility to radial highways and takes only 9 distinct values. Hence, it is most appropriately treated as an ordered factor. Note that both transformations only affect the parameter stability test chosen (step~2), not the splitting procedure (step~3). % Note that with splittry = 0 (according to old version of mob) there is no % split in dis <>= bh_tree <- lmtree(medv ~ log(lstat) + I(rm^2) | zn + indus + chas + nox + age + dis + rad + tax + crim + b + ptratio, data = BostonHousing) bh_tree @ % The corresponding visualization is shown in Figure~\ref{fig:BostonHousing}. It shows partial scatter plots of the dependent variable against each of the regressors in the terminal nodes. Each scatter plot also shows the fitted values, i.e., a projection of the fitted hyperplane. \setkeys{Gin}{width=\textwidth} \begin{figure}[p!] \centering <>= plot(bh_tree) @ \includegraphics[width=18cm,keepaspectratio,angle=90]{mob-BostonHousing-plot} \caption{\label{fig:BostonHousing} Linear-regression-based tree for the Boston housing data. The plots in the leaves give partial scatter plots for \code{rm} (upper panel) and \code{lstat} (lower panel).} \end{figure} From this visualization, it can be seen that in the nodes~4, 6, 7 and 8 the increase of value with the number of rooms dominates the picture (upper panel) whereas in node~9 the decrease with the lower status population percentage (lower panel) is more pronounced. Splits are performed in the variables \code{tax} (poperty-tax rate) and \code{ptratio} (pupil-teacher ratio). For summarizing the quality of the fit, we could compute the mean squared error, log-likelihood or AIC: % <>= mean(residuals(bh_tree)^2) logLik(bh_tree) AIC(bh_tree) @ \subsection{Teaching ratings data} \cite{Hamermesh+Parker:2005} investigate the correlation of beauty and teaching evaluations for professors. They provide data on course evaluations, course characteristics, and professor characteristics for 463 courses for the academic years 2000--2002 at the University of Texas at Austin. It is of interest how the average teaching evaluation per course (on a scale 1--5) depends on a standardized measure of beauty (as assessed by a committee of six persons based on photos). \cite{Hamermesh+Parker:2005} employ a linear regression, weighted by the number of students per course and adjusting for several further main effects: gender, whether or not the teacher is from a minority, a native speaker, or has tenure, respectively, and whether the course is taught in the upper or lower division. Additionally, the age of the professors is available as a regressor but not considered by \cite{Hamermesh+Parker:2005} because the corresponding main effect is not found to be significant in either linear or quadratic form. Here, we employ a similar model but use the available regressors differently. The basic model is again a linear regression for teaching rating by beauty, estimated by weighted least squares (WLS). All remaining explanatory variables are \emph{not} used as regressors but as partitioning variables because we argue that it is unclear how they influence the correlation between teaching rating and beauty. Hence, MOB is used to adaptively incorporate these further variables and determine potential interactions. First, the data are loaded from the \pkg{AER} package \citep{AER} and only the subset of single-credit courses is excluded. % <>= data("TeachingRatings", package = "AER") tr <- subset(TeachingRatings, credits == "more") @ % The single-credit courses include elective modules that are quite different from the remaining courses (e.g., yoga, aerobics, or dance) and are hence omitted from the main analysis. WLS estimation of the null model (with only an intercept) and the main effects model is carried out in a first step: % <>= tr_null <- lm(eval ~ 1, data = tr, weights = students) tr_lm <- lm(eval ~ beauty + gender + minority + native + tenure + division, data = tr, weights = students) @ % Then, the model-based tree can be estimated with \code{lmtree()} using only \code{beauty} as a regressor and all remaining variables for partitioning. For WLS estimation, we set \code{weights = students} and \code{caseweights = FALSE} because the weights are only proportionality factors and do not signal exactly replicated observations \citep[see][for a discussion of the different types of weights]{Lumley:2020}. % <>= (tr_tree <- lmtree(eval ~ beauty | minority + age + gender + division + native + tenure, data = tr, weights = students, caseweights = FALSE)) @ % \begin{figure}[t!] \setkeys{Gin}{width=\textwidth} <>= plot(tr_tree) @ \caption{\label{fig:tr_tree} WLS-based tree for the teaching ratings data. The plots in the leaves show scatterplots for teaching rating by beauty score.} \end{figure} % The resulting tree can be visualized by \code{plot(tr_tree)} and is shown in Figure~\ref{fig:tr_tree}. This shows that despite age not having a significant main effect \citep[as reported by][]{Hamermesh+Parker:2005}, it clearly plays an important role: While the correlation of teaching rating and beauty score is rather moderate for younger professors, there is a clear correlation for older professors (with the cutoff age somewhat lower for female professors). % <>= coef(tr_lm)[2] coef(tr_tree)[, 2] @ % Th $R^2$ of the tree is also clearly improved over the main effects model: % <>= 1 - c(deviance(tr_lm), deviance(tr_tree))/deviance(tr_null) @ \subsection{Titanic survival data} To illustrate how differences in treatment effects can be captured by MOB, the Titanic survival data is considered: The question is whether ``women and children first'' is applied in the same way for all subgroups of the passengers of the Titanic. Or, in other words, whether the effectiveness of preferential treatment for women/children differed across subgroups. The \code{Titanic} data is provided in base \proglang{R} as a contingency table and transformed here to a `\code{data.frame}' for use with \code{glmtree()}: % <>= data("Titanic", package = "datasets") ttnc <- as.data.frame(Titanic) ttnc <- ttnc[rep(1:nrow(ttnc), ttnc$Freq), 1:4] names(ttnc)[2] <- "Gender" ttnc <- transform(ttnc, Treatment = factor( Gender == "Female" | Age == "Child", levels = c(FALSE, TRUE), labels = c("Male&Adult", "Female|Child"))) @ % The data provides factors \code{Survived} (yes/no), \code{Class} (1st, 2nd, 3rd, crew), \code{Gender} (male, female), and \code{Age} (child, adult). Additionally, a factor \code{Treatment} is added that distinguishes women/children from male adults. To investigate how the preferential treatment effect (\code{Survived ~ Treatment}) differs across the remaining explanatory variables, the following logistic-regression-based tree is considered. The significance level of \code{alpha = 0.01} is employed here to avoid overfitting and separation problems in the logistic regression. % <>= ttnc_tree <- glmtree(Survived ~ Treatment | Class + Gender + Age, data = ttnc, family = binomial, alpha = 0.01) ttnc_tree @ % \begin{figure}[t!] \setkeys{Gin}{width=\textwidth} <>= plot(ttnc_tree, tp_args = list(ylines = 1, margins = c(1.5, 1.5, 1.5, 2.5))) @ \caption{\label{fig:ttnc_tree} Logistic-regression-based tree for the Titanic survival data. The plots in the leaves give spinograms for survival status versus preferential treatment (women or children).} \end{figure} % This shows that the treatment differs strongly across passengers classes, see also the result of \code{plot(ttnc_tree)} in Figure~\ref{fig:ttnc_tree}. The treatment effect is much lower in the 3rd class where women/children still have higher survival rates than adult men but the odds ratio is much lower compared to all remaining classes. The split between the 2nd and the remaining two classes (1st, crew) is due to a lower overall survival rate (intercepts of \Sexpr{round(coef(ttnc_tree)[2, 1], digits = 2)} and \Sexpr{round(coef(ttnc_tree)[3, 1], digits = 2)}, respectively) while the odds ratios associated with the preferential treatment are rather similar (\Sexpr{round(coef(ttnc_tree)[2, 2], digits = 2)} and \Sexpr{round(coef(ttnc_tree)[3, 2], digits = 2)}, respectively). Another option for assessing the class effect would be to immediately split into all four classes rather than using recursive binary splits. This can be obtained by setting \code{catsplit = "multiway"} in the \code{glmtree()} call above. This yields a tree with just a single split but four kid nodes. \subsection{German breast cancer data} To illustrate that the MOB approach can also be used beyond (generalized) linear regression models, it is employed in the following to analyze censored survival times among German women with positive node breast cancer. The data is available in the \pkg{TH.data} package and the survival time is transformed from days to years: % <>= data("GBSG2", package = "TH.data") GBSG2$time <- GBSG2$time/365 @ % For regression a parametric Weibull regression based on the \code{survreg()} function from the \pkg{survival} package \citep{survival} is used. A fitting function for \code{mob()} can be easily set up: % <>= library("survival") wbreg <- function(y, x, start = NULL, weights = NULL, offset = NULL, ...) { survreg(y ~ 0 + x, weights = weights, dist = "weibull", ...) } @ % As the \pkg{survreg} package currently does not provide a \code{logLik()} method for `\code{survreg}' objects, this needs to be added here: % <>= logLik.survreg <- function(object, ...) structure(object$loglik[2], df = sum(object$df), class = "logLik") @ % Without the \code{logLik()} method, \code{mob()} would not know how to extract the optimized objective function from the fitted model. With the functions above available, a censored Weibull-regression-tree can be fitted: The dependent variable is the censored survival time and the two regressor variables are the main risk factor (number of positive lymph nodes) and the treatment variable (hormonal therapy). All remaining variables are used for partitioning: age, tumor size and grade, progesterone and estrogen receptor, and menopausal status. The minimal segment size is set to 80. % <>= gbsg2_tree <- mob(Surv(time, cens) ~ horTh + pnodes | age + tsize + tgrade + progrec + estrec + menostat, data = GBSG2, fit = wbreg, control = mob_control(minsize = 80)) @ % \begin{figure}[p!] \centering \setkeys{Gin}{width=0.6\textwidth} <>= plot(gbsg2_tree) @ \caption{\label{fig:GBSG2} Censored Weibull-regression-based tree for the German breast cancer data. The plots in the leaves report the estimated regression coefficients.} \setkeys{Gin}{width=\textwidth} <>= gbsg2node <- function(mobobj, col = "black", linecol = "red", cex = 0.5, pch = NULL, jitter = FALSE, xscale = NULL, yscale = NULL, ylines = 1.5, id = TRUE, xlab = FALSE, ylab = FALSE) { ## obtain dependent variable mf <- model.frame(mobobj) y <- Formula::model.part(mobobj$info$Formula, mf, lhs = 1L, rhs = 0L) if(isTRUE(ylab)) ylab <- names(y)[1L] if(identical(ylab, FALSE)) ylab <- "" if(is.null(ylines)) ylines <- ifelse(identical(ylab, ""), 0, 2) y <- y[[1L]] ## plotting character and response if(is.null(pch)) pch <- y[,2] * 18 + 1 y <- y[,1] y <- as.numeric(y) pch <- rep(pch, length.out = length(y)) if(jitter) y <- jitter(y) ## obtain explanatory variables x <- Formula::model.part(mobobj$info$Formula, mf, lhs = 0L, rhs = 1L) xnam <- colnames(x) z <- seq(from = min(x[,2]), to = max(x[,2]), length = 51) z <- data.frame(a = rep(sort(x[,1])[c(1, NROW(x))], c(51, 51)), b = z) names(z) <- names(x) z$x <- model.matrix(~ ., data = z) ## fitted node ids fitted <- mobobj$fitted[["(fitted)"]] if(is.null(xscale)) xscale <- range(x[,2]) + c(-0.1, 0.1) * diff(range(x[,2])) if(is.null(yscale)) yscale <- range(y) + c(-0.1, 0.1) * diff(range(y)) ## panel function for scatter plots in nodes rval <- function(node) { ## node index nid <- id_node(node) ix <- fitted %in% nodeids(mobobj, from = nid, terminal = TRUE) ## dependent variable y <- y[ix] ## predictions yhat <- if(is.null(node$info$object)) { refit.modelparty(mobobj, node = nid) } else { node$info$object } yhat <- predict(yhat, newdata = z, type = "quantile", p = 0.5) pch <- pch[ix] ## viewport setup top_vp <- viewport(layout = grid.layout(nrow = 2, ncol = 3, widths = unit(c(ylines, 1, 1), c("lines", "null", "lines")), heights = unit(c(1, 1), c("lines", "null"))), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_scatterplot", nid, sep = "")) pushViewport(top_vp) grid.rect(gp = gpar(fill = "white", col = 0)) ## main title top <- viewport(layout.pos.col = 2, layout.pos.row = 1) pushViewport(top) mainlab <- paste(ifelse(id, paste("Node", nid, "(n = "), ""), info_node(node)$nobs, ifelse(id, ")", ""), sep = "") grid.text(mainlab) popViewport() plot_vp <- viewport(layout.pos.col = 2, layout.pos.row = 2, xscale = xscale, yscale = yscale, name = paste("node_scatterplot", nid, "plot", sep = "")) pushViewport(plot_vp) ## scatterplot grid.points(x[ix,2], y, gp = gpar(col = col, cex = cex), pch = pch) grid.lines(z[1:51,2], yhat[1:51], default.units = "native", gp = gpar(col = linecol)) grid.lines(z[52:102,2], yhat[52:102], default.units = "native", gp = gpar(col = linecol, lty = 2)) grid.xaxis(at = c(ceiling(xscale[1]*10), floor(xscale[2]*10))/10) grid.yaxis(at = c(ceiling(yscale[1]), floor(yscale[2]))) if(isTRUE(xlab)) xlab <- xnam[2] if(!identical(xlab, FALSE)) grid.text(xlab, x = unit(0.5, "npc"), y = unit(-2, "lines")) if(!identical(ylab, FALSE)) grid.text(ylab, y = unit(0.5, "npc"), x = unit(-2, "lines"), rot = 90) grid.rect(gp = gpar(fill = "transparent")) upViewport() upViewport() } return(rval) } class(gbsg2node) <- "grapcon_generator" plot(gbsg2_tree, terminal_panel = gbsg2node, tnex = 2, tp_args = list(xscale = c(0, 52), yscale = c(-0.5, 8.7))) @ \caption{\label{fig:GBSG2-scatter} Censored Weibull-regression-based tree for the German breast cancer data. The plots in the leaves depict censored (hollow) and uncensored (solid) survival time by number of positive lymph nodes along with fitted median survival for patients with (dashed line) and without (solid line) hormonal therapy.} \end{figure} % Based on progesterone receptor, a tree with two leaves is found: % <>= gbsg2_tree coef(gbsg2_tree) logLik(gbsg2_tree) @ % The visualization produced by \code{plot(gbsg2_tree)} is shown in Figure~\ref{fig:GBSG2}. A nicer graphical display using a scatter plot (with indication of censoring) and fitted regression curves is shown in Figure~\ref{fig:GBSG2-scatter}. This uses a custom panel function whose code is too long and elaborate to be shown here. Interested readers are referred to the \proglang{R} code underlying the vignette. The visualization shows that for higher progesterone receptor levels: (1)~survival times are higher overall, (2)~the treatment effect of hormonal therapy is higher, and (3)~the negative effect of the main risk factor (number of positive lymph nodes) is less severe. \section{Setting up a new mobster} \label{sec:mobster} To conclude this vignette, we present another illustration that shows how to set up new mobster functionality from scratch. To do so, we implement the Bradley-Terry tree suggested by \cite{Strobl+Wickelmaier+Zeileis:2011} ``by hand''. The \pkg{psychotree} package already provides an easy-to-use mobster called \code{bttree()} but as an implementation exercise we recreate its functionality here. The only inputs required are a suitable data set with paired comparisons (\code{Topmodel2007} from \pkg{psychotree}) and a parametric model for paired comparison data (\code{btmodel()} from \pkg{psychotools}, implementing the Bradley-Terry model). The latter optionally computes the empirical estimating functions and already comes with a suitable extractor method. <>= data("Topmodel2007", package = "psychotree") library("psychotools") @ % The Bradley-Terry (or Bradley-Terry-Luce) model is a standard model for paired comparisons in social sciences. It parametrizes the probability $\pi_{ij}$ for preferring some object $i$ over another object $j$ in terms of corresponding ``ability'' or ``worth'' parameters $\theta_i$: \begin{eqnarray*} \pi_{ij}\phantom{)} & = & \frac{\theta_i}{\theta_i + \theta_j} \\ \mathsf{logit}(\pi_{ij}) & = & \log(\theta_i) - \log(\theta_j) \end{eqnarray*} This model can be easily estimated by maximum likelihood as a logistic or log-linear GLM. This is the approach used internally by \code{btmodel()}. The \code{Topmodel2007} data provide paired comparisons of attractiveness among the six finalists of the TV show \emph{Germany's Next Topmodel~2007}: Barbara, Anni, Hana, Fiona, Mandy, Anja. The data were collected in a survey with 192~respondents at Universit{\"a}t T{\"u}bingen and the available covariates comprise gender, age, and familiarty with the TV~show. The latter is assess by three by yes/no questions: (1)~Do you recognize the women?/Do you know the show? (2)~Did you watch it regularly? (3)~Did you watch the final show?/Do you know who won? To fit the Bradley-Terry tree to the data, the available building blocks just have to be tied together. First, we set up the basic/simple model fitting interface described in Section~\ref{sec:fit}: % @ <>= btfit1 <- function(y, x = NULL, start = NULL, weights = NULL, offset = NULL, ...) btmodel(y, ...) @ % The function \code{btfit1()} simply calls \code{btmodel()} ignoring all arguments except \code{y} as the others are not needed here. No more processing is required because \class{btmodel} objects come with a \code{coef()}, \code{logLik()}, and \code{estfun()} method. Hence, we can call \code{mob()} now specifying the response and the partitioning variable (and no regressors because there are no regressors in this model). % <>= bt1 <- mob(preference ~ 1 | gender + age + q1 + q2 + q3, data = Topmodel2007, fit = btfit1) @ % An alternative way to fit the exact same tree somewhat more quickly would be to employ the extended interface described in Section~\ref{sec:fit}: % <>= btfit2 <- function(y, x = NULL, start = NULL, weights = NULL, offset = NULL, ..., estfun = FALSE, object = FALSE) { rval <- btmodel(y, ..., estfun = estfun, vcov = object) list( coefficients = rval$coefficients, objfun = -rval$loglik, estfun = if(estfun) rval$estfun else NULL, object = if(object) rval else NULL ) } @ % Still \code{btmodel()} is employed for fitting the model but the quantities \code{estfun} and \code{vcov} are only computed if they are really required. This may save some computation time -- about 20\% on the authors' machine at the time of writing -- when computing the tree: % <>= bt2 <- mob(preference ~ 1 | gender + age + q1 + q2 + q3, data = Topmodel2007, fit = btfit2) @ % The speed-up is not huge but comes almost for free: just a few additional lines of code in \code{btfit2()} are required. For other models where it is more costly to set up a full model (with variance-covariance matrix, predictions, residuals, etc.) larger speed-ups are also possible. Both trees, \code{bt1} and \code{bt2}, are equivalent (except for the details of the fitting function). Hence, in the following we only explore \code{bt2}. However, the same code can be applied to \code{bt1} as well. Many tools come completely for free and are inherited from the general \class{modelparty}/\class{party}. For example, both printing (\code{print(bt2)}) and plotting (\code{plot(bt2)}) shows the estimated parameters in the terminal nodes which can also be extracted by the \code{coef()} method: <>= bt2 coef(bt2) @ The corresponding visualization is shown in the upper panel of Figure~\ref{fig:topmodel-plot1}. In all cases, the estimated coefficients on the logit scale omitting the fixed zero reference level (Anja) are reported. To show the corresponding worth parameters $\theta_i$ including the reference level, one can simply provide a small panel function \code{worthf()}. This applies the \code{worth()} function from \pkg{psychotools} to the fitted-model object stored in the \code{info} slot of each node, yielding the lower panel in Figure~\ref{fig:topmodel-plot1}. % <>= worthf <- function(info) paste(info$object$labels, format(round(worth(info$object), digits = 3)), sep = ": ") plot(bt2, FUN = worthf) @ % \begin{figure}[p!] \centering <>= plot(bt2) @ \vspace*{0.5cm} <>= <> @ \caption{\label{fig:topmodel-plot1} Bradley-Terry-based tree for the topmodel attractiveness data. The default plot (upper panel) reports the estimated coefficients on the log scale while the adapted plot (lower panel) shows the corresponding worth parameters.} \end{figure} % To show a graphical display of these worth parameters rather than printing their numerical values, one can use a simply glyph-style plot. A simply way to generate these is to use the \code{plot()} method for \class{btmodel} objects from \pkg{partykit} and \code{nodeapply} this to all terminal nodes (see Figure~\ref{fig:topmodel-plot2}): % <>= par(mfrow = c(2, 2)) nodeapply(bt2, ids = c(3, 5, 6, 7), FUN = function(n) plot(n$info$object, main = n$id, ylim = c(0, 0.4))) @ % \begin{figure}[t!] \centering <>= <> @ \caption{\label{fig:topmodel-plot2} Worth parameters in the terminal nodes of the Bradley-Terry-based tree for the topmodel attractiveness data.} \end{figure} % Alternatively, one could set up a proper panel-generating function in \pkg{grid} that allows to create the glyphs within the terminal nodes of the tree (see Figure~\ref{fig:topmodel-plot3}). As the code for this panel-generating function \code{node_btplot()} is too complicated to display within the vignette, we refer interested readers to the underlying code. Given this panel-generating function Figure~\ref{fig:topmodel-plot3} can be generated with <>= plot(bt2, drop = TRUE, tnex = 2, terminal_panel = node_btplot(bt2, abbreviate = 1, yscale = c(0, 0.5))) @ \begin{figure}[t!] \centering <>= ## visualization function node_btplot <- function(mobobj, id = TRUE, worth = TRUE, names = TRUE, abbreviate = TRUE, index = TRUE, ref = TRUE, col = "black", linecol = "lightgray", cex = 0.5, pch = 19, xscale = NULL, yscale = NULL, ylines = 1.5) { ## node ids node <- nodeids(mobobj, terminal = FALSE) ## get all coefficients cf <- partykit:::apply_to_models(mobobj, node, FUN = function(z) if(worth) worth(z) else coef(z, all = FALSE, ref = TRUE)) cf <- do.call("rbind", cf) rownames(cf) <- node ## get one full model mod <- partykit:::apply_to_models(mobobj, node = 1L, FUN = NULL) if(!worth) { if(is.character(ref) | is.numeric(ref)) { reflab <- ref ref <- TRUE } else { reflab <- mod$ref } if(is.character(reflab)) reflab <- match(reflab, mod$labels) cf <- cf - cf[,reflab] } ## reference if(worth) { cf_ref <- 1/ncol(cf) } else { cf_ref <- 0 } ## labeling if(is.character(names)) { colnames(cf) <- names names <- TRUE } ## abbreviation if(is.logical(abbreviate)) { nlab <- max(nchar(colnames(cf))) abbreviate <- if(abbreviate) as.numeric(cut(nlab, c(-Inf, 1.5, 4.5, 7.5, Inf))) else nlab } colnames(cf) <- abbreviate(colnames(cf), abbreviate) if(index) { x <- 1:NCOL(cf) if(is.null(xscale)) xscale <- range(x) + c(-0.1, 0.1) * diff(range(x)) } else { x <- rep(0, length(cf)) if(is.null(xscale)) xscale <- c(-1, 1) } if(is.null(yscale)) yscale <- range(cf) + c(-0.1, 0.1) * diff(range(cf)) ## panel function for bt plots in nodes rval <- function(node) { ## node index id <- id_node(node) ## dependent variable setup cfi <- cf[id,] ## viewport setup top_vp <- viewport(layout = grid.layout(nrow = 2, ncol = 3, widths = unit(c(ylines, 1, 1), c("lines", "null", "lines")), heights = unit(c(1, 1), c("lines", "null"))), width = unit(1, "npc"), height = unit(1, "npc") - unit(2, "lines"), name = paste("node_btplot", id, sep = "")) pushViewport(top_vp) grid.rect(gp = gpar(fill = "white", col = 0)) ## main title top <- viewport(layout.pos.col = 2, layout.pos.row = 1) pushViewport(top) mainlab <- paste(ifelse(id, paste("Node", id, "(n = "), ""), info_node(node)$nobs, ifelse(id, ")", ""), sep = "") grid.text(mainlab) popViewport() ## actual plot plot_vpi <- viewport(layout.pos.col = 2, layout.pos.row = 2, xscale = xscale, yscale = yscale, name = paste("node_btplot", id, "plot", sep = "")) pushViewport(plot_vpi) grid.lines(xscale, c(cf_ref, cf_ref), gp = gpar(col = linecol), default.units = "native") if(index) { grid.lines(x, cfi, gp = gpar(col = col, lty = 2), default.units = "native") grid.points(x, cfi, gp = gpar(col = col, cex = cex), pch = pch, default.units = "native") grid.xaxis(at = x, label = if(names) names(cfi) else x) } else { if(names) grid.text(names(cfi), x = x, y = cfi, default.units = "native") else grid.points(x, cfi, gp = gpar(col = col, cex = cex), pch = pch, default.units = "native") } grid.yaxis(at = c(ceiling(yscale[1] * 100)/100, floor(yscale[2] * 100)/100)) grid.rect(gp = gpar(fill = "transparent")) upViewport(2) } return(rval) } class(node_btplot) <- "grapcon_generator" plot(bt2, drop = TRUE, tnex = 2, terminal_panel = node_btplot(bt2, abbreviate = 1, yscale = c(0, 0.5))) @ \caption{\label{fig:topmodel-plot3} Bradley-Terry-based tree for the topmodel attractiveness data with visualizations of the worth parameters in the terminal nodes.} \end{figure} Finally, to illustrate how different predictions can be easily computed, we set up a small data set with three new individuals: % <>= tm <- data.frame(age = c(60, 25, 35), gender = c("male", "female", "female"), q1 = "no", q2 = c("no", "no", "yes"), q3 = "no") tm @ % For these we can easily compute (1)~the predicted node ID, (2)~the corresponding worth parameters, (3)~the associated ranks. <>= tm predict(bt2, tm, type = "node") predict(bt2, tm, type = function(object) t(worth(object))) predict(bt2, tm, type = function(object) t(rank(-worth(object)))) @ This completes the tour of fitting, printing, plotting, and predicting the Bradley-Terry tree model. Convenience interfaces that employ code like shown above can be easily defined and collected in new packages such as \pkg{psychotree}. \section{Conclusion} \label{sec:conclusion} The function \code{mob()} in the \pkg{partykit} package provides a new flexible and object-oriented implementation of the general algorithm for model-based recursive partitioning using \pkg{partykit}'s recursive partytioning infrastructure. New model fitting functions can be easily provided, especially if standard extractor functions (such as \code{coef()}, \code{estfun()}, \code{logLik()}, etc.) are available. The resulting model trees can then learned, visualized, investigated, and employed for predictions. To gain some efficiency in the computations and to allow for further customization (in particular specialized visualization and prediction methods), convenience interfaces \code{lmtree()} and \code{glmtree()} are provided for recursive partitioning based on (generalized) linear models. \bibliography{party} \end{document} partykit/inst/doc/constparty.pdf0000644000176200001440000041235214723350653016563 0ustar liggesusers%PDF-1.5 %¿÷¢þ 1 0 obj << /Type /ObjStm /Length 4242 /Filter /FlateDecode /N 77 /First 646 >> stream xœÕ\[sÛ¸~ï¯à[³Ó qÈÎ63Îu½‰¯d“tv:ŒDÛldÉ+Ñ›¤¿¾ß@‰¤(Yv”îtšœûÀÈ„'*±.ÑInEb!ŒIl"´Ð‰Ã͉$K„U2É‘i•žHΩa"…Ó‰‰Tô^%Ò(”u"sƒ>&Q2GÙ&šg"â³È#8Ú牱ÒXb²<°Ä ‹Î2±Já=Ð2ƒéÄæOœR(ÛÄéÌ%Ò%.£ú,ÉÆ“y’)àŽ&™<%’\p‘æ6³‰RINøÅ<§zL ƒ Ì–+î…ùrmPì¹ÅæÌæÀ›ç˜¢ÆDðŠ'ZâA8™ÐÔ…Â{¹ ã Çê óŃËt¢YäÀ /ñ@oYrkÈR ¯d©@5ÈÒ dis´!*g(bz4Å +ÁA:@Vü#Š+ú¡²Œ'  ¸ˆy¯B+¢# k‚lq],ñ+u,  %aDnH&„QÀÊ/5ØgÙ˜,K0}a¨;„C˜s„Ű` fJ’a(q€l-‡4²u …d›8Ž$+—ê/?þ˜°£².ÆE]$.‡Lž$ìÕu=©¦åÒèËÇÅ9 :^½*öí'³óäÁâ຾˜Í“Ïʳ3ˆ¨æÜâî ®NᢲÁUrŽW\g±žÞg«¶¾~Û€ÆVÅú×8¼7E„EïF«g§«yYÔÕlú¸¨ËäÞã¿K.5˜-Ä]™¿qñWÎÿúCl|ï½(^—ï’ÏU}‘\`^óyy†êçå×ϳùxÑÌÇãf>άæåǵ¡Žps¸ h¡^Çúx§9Òüü3ÝÝj®Kønõì馺}}[ÝjÛ5p<½F‡vï*Öé[Âmø×Ìy'¼À£Ùø&VÏgãëQ ^<;~‘<»˜-êÅh^]ÕPû”ãÚœ^üw9ª“{x~]Õ“²aŒV+$–‚&bYGé1Åå]&¨" \C|b¸ë1НàZÝâÖ;Oø^3DT¾‚ß(€‡·Ã\´]õ#Gí{4»žÖdÆÙó RûO8RÕÌÿ…¹ô·ð.h¸ 2Q¾aPmXÕxoªÃMÆjiã=*Ö«Ø<öV±Z7Ýcmxý[cA‚QiìÇt:« sÑ °òÐ7WáðÈc“€M¦èy1cóˆHpïºAæÑlZ—SŒ » ÜQ9®Š‡³/À† ˜Ü¤äé´H³œzsthÌáI¹˜]ÏG˜ Íã) º‰vs>–5±ãÇO1ñòK ´iÐe¢Œj¾¨“ˆÌ‹ÏYÖ6½Kë;>.õ’çìÝûðÊp¤&ÍÈ)M¯'Âú%‰Æ û)Dó¾®R}Òݾ]öõ-[n»â¹d® \P *P0J Ȩ0ï(C*°3JR—[Ùž¸¥Å˜µœ’ S2jÃ|Oý-Ú@<¦iå:¢±Å·#jÕ7!Û Ö *ö…¨û&DƒèÙÀ_¨çn.Ð× ÈC$ýì‹Îî€þÃbQúîìÕÛwoÞŸüíÅÑÉ처 yÿál2NØ“éh6®¦ç@zðÞ=º(æéû¡aj¼oFè$ôÊ@ù6‚üL¡¯…Ï5íßBýÓjRú% ^½,.Ëâxˆ£LÏá›0÷£j±€pz!‚<âÍi]^¾¥L©-f- ]“û¿¼{ÿêÉr ~ÿ¤<¿ž@t[¢oú¢$zMômOô%¼Àn¢¯)muŒÞ‘®ŒÒL믥 x]$é$²I¤m*ËýÅ›2jèN°v½¨=]«±‘Õ€WH"¥„> _…šXPÖeÆ×)Z¡ u $7GRêûPméîTÀÝÃ0&„ [¬[&tÐT¢¹+n—ïýô¨,ºDO XOïBDõ!’4ïºÓ¥µ¾ÁÊü?þº‚³SÐfÍĘ®‰1=óFæ1{Ò24Ͻ©yÉ^ÁÜüƒs “ó†½e¿²wì½7>Ÿ*çå¢Z´ÌÐhvyY´ŒQ9‹ o“V&i²²JÈÄ/Ê©7NŸ¢yš"à]Ù(r“ò¬Os†‹&Õ°ßÙï׳ºœ,|¦:ùRx$‹·(/«€ò¢ü,ª/l1!\»¶ðz9É?`¿°¯ì?ì?å|Ö1DÍA‰hÖ×"Î=Ñ{²ñ¾K¹Ùníl#Å®6òýÏÏŸÿŒ±ŽfÓÙ ‰„1›LÕêÅÊX*½n,c¬ÒŠìŽÆÒxIÃÓêyWwÆè޹Þg½´ÞzS¾ü}_íñúÚoa5[Úo¥êOz!ÆKd_êûbTUu5—x$]Z|bE åÿXÌÙÇy1úTÖ^ñâsP¶¾eÏ&²•øýº˜}è+û0 W“ëEÛ6­ßªëÓq9_Œfór›²Ë¼QvÕ×öPkhׇy]7}]ߨ»ª:8=¬êì]ä´Ör]?üpô²±1ao­üûcJ¾¦ü»& ήœ—àª㇟ÎìÒ·éÌóØ´c†¦ md!ZÈ[žïnÒ ÔÒø»àϪ(‰W1`î…ÈK dG(x¨Ñ€PؾPlgÎ7;•d â[“Œ¿ýrüƒŸÓÅí…‚¯ …ì âÞGŸ£Ym‡Ã Õ[áŒè0Í›®®Î6ܱ€–­1HÒæ˜‡Òcë³g#…vä ²Ì½óÛO>µ"0B;i°Û–»Ë»çîÆÊMìþ”¡¸=裉1?Ý›+¶â®ÓËiÒT¢·£}P¯Å.¦?ä¿(M·Ù|úÅÒofú~ Œè×Jé7=ÑFoÊ &B•Ñ&)à­pÕHMA‰ÉŠS/‹ MÓ•ÝV bLýlM7>õ-lJ;q?[O×—pcÎN^¬†×Š®ªkŽÌRà»ÒŽh4T#"•CŸõ%~£¶%þ>òÅ-ÖˆßÆOÍæðÂqÁÌÌ|A„B\; 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Reported by Tyson H. Holmes.} } } } \section{Changes in Version 1.2-16 (2022-06-20)}{ \subsection{Buxfixes}{ \itemize{ \item{Address random CRAN errors (honesty checks).} } } } \section{Changes in Version 1.2-15 (2021-08-23)}{ \subsection{Small Improvements}{ \itemize{ \item{Update reference output.} } } } \section{Changes in Version 1.2-14 (2021-04-22)}{ \subsection{Bugfixes}{ \itemize{ \item{\code{cforest} ignored \code{converged} argument.} } } } \section{Changes in Version 1.2-13 (2021-03-03)}{ \subsection{Small Improvements}{ \itemize{ \item{Suggest \pkg{randomForest}.} \item{Test constparty vignette code in tests, to avoid a NOTE about missing \pkg{RWeka} on Solaris.} } } } \section{Changes in Version 1.2-12 (2021-02-08)}{ \subsection{New Features}{ \itemize{ \item{Add \code{method} argument to \code{glmtree}. The default is to use \code{"glm.fit"} (as was hard-coded previously) but this can also be changed, e.g., to \code{"brglmFit"} from \pkg{brglm2} for bias-reduced estimation of generalized linear models.} } } \subsection{Bugfixes}{ \itemize{ \item{Fix LaTeX problem.} \item{Better checks for response classes, fixing a bug reported by John Ogawa.} \item{In \code{lmtree} and \code{glmtree} the \code{"xlevels"} attribute for the regressors is preserved in the models fitted within the trees. Thus, predicting for data whose \code{"xlevels"} do not match, an error is generated now (as opposed to warning and partially incorrect predictions).} } } } \section{Changes in Version 1.2-11 (2020-12-09)}{ \subsection{New Features}{ \itemize{ \item{Add an experimental implementation of honesty.} \item{Add \code{maxvar} argument to \code{ctree_control} for restricting the number of split variables to be used in a tree.} } } \subsection{Bugfixes}{ \itemize{ \item{\code{all.equal} must not check environments.} \item{Non-standard variable names are now handled correctly within \code{extree_data}, prompted by \url{https://stackoverflow.com/questions/64660889/ctree-ignores-variables-with-non-syntactic-names}.} } } } \section{Changes in Version 1.2-10 (2020-10-12)}{ \subsection{Bugfixes}{ \itemize{ \item{Deal with non-integer \code{minsize} in \code{mob}.} \item{Handle NAs in \code{.get_psplits}.} \item{Fix URLs.} } } } \section{Changes in Version 1.2-9 (2020-07-10)}{ \subsection{Bugfixes}{ \itemize{ \item{Fix an issue with printing of tied p-values.} } } } \section{Changes in Version 1.2-8 (2020-06-09)}{ \subsection{Bugfixes}{ \itemize{ \item{pruning of modelparty objects failed to get the fitted slot right.} \item{In R-devel, c() now returns factors, rendering code in .simplify_pred overly pedantic.} } } } \section{Changes in Version 1.2-7 (2020-03-06)}{ \subsection{Bugfixes}{ \itemize{ \item{NAMESPACE fixes: party is only suggested.} } } } \section{Changes in Version 1.2-6 (2020-01-30)}{ \subsection{Bugfixes}{ \itemize{ \item{Remove warning about response not being a factor in \code{predict.cforest}. Reported by Stephen Milborrow.} } } } \section{Changes in Version 1.2-5 (2019-07-17)}{ \subsection{Bugfixes}{ \itemize{ \item{Trying to split in a variable where all observations were missing nevertheless produced a split, as reported by Kevin Ummel.} } } } \section{Changes in Version 1.2-4 (2019-05-17)}{ \subsection{Bugfixes}{ \itemize{ \item{update reference output, fix RNGversion} } } } \section{Changes in Version 1.2-3 (2019-01-28)}{ \subsection{New Features}{ \itemize{ \item{\code{varimp} runs in parallel mode, optionally.} \item{\code{weights} in \code{cforest} can now be used to specify a matrix of weights (number of observations times number of trees) to be used for tree induction (this was always possible in \code{party::cforest}. This was advertised in the documentation but actually not implemented so far.} } } \subsection{Bugfixes}{ \itemize{ \item{\code{predict} did not pay attention to \code{xlev}; this caused problems when empty factor levels were removed prior to tree fitting.} \item{\code{nodeprune} may have got fitted terminal node numbers wrong, spotted by Jason Parker.} } } } \section{Changes in Version 1.2-2 (2018-06-05)}{ \subsection{Bugfixes}{ \itemize{ \item{In \code{mob()} using the \code{cluster} argument with a \code{factor} variable sometimes lead to \code{NA}s in the covariance matrix estimate if empty categories occured in subgroups. The problem had been introduced in version 1.2-0 and has been fixed now.} \item{Methods for the \code{sctest} generic from the \pkg{strucchange} package are now dynamically registered if \pkg{strucchange} is attached. Alternatively, the methods can be called directly using their full names \code{sctest.constparty} and \code{sctest.modelparty}.} \item{The \code{prune.modelparty} function is now fully exported but it is also registered with the \code{prune} generic from \pkg{rpart}.} } } } \section{Changes in Version 1.2-1 (2018-04-20)}{ \subsection{New Features}{ \itemize{ \item{New \code{scale} argument for \code{predict} in \code{cforest}. For simple regression forests, predicting the conditional mean by nearest neighbor weights with \code{scale = TRUE} is now equivalent to the aggregation of means. The unscaled version proposed in can be obtained with \code{scale = FALSE}.} } } \subsection{Bugfixes}{ \itemize{ \item{Bug fix for case weights in \code{mob()} in previous version (1.2-0) introduced a bug in the handling of proportionality weights. Both cases are handled correctly now.} \item{\code{glmtree} can now handle \code{caseweights = TRUE} correctly for \code{vcov} other than the default \code{"opg"}. Internally, the \code{glm} objects are adjusted by correcting the dispersion estimate and the degrees of freedom.} \item{\code{lookahead} did not work in the presence of missing values.} \item{Calling \code{partykit::ctree} did not work when partykit was not attached.} \item{\code{node_inner} now allows to set a different \code{gpar(fontsize = ...)} in the inner nodes compared to the overall tree.} \item{\code{splittest} asked for Monte-Carlo p-values, even when the test statistic was used as criterion.} } } } \section{Changes in Version 1.2-0 (2017-12-18)}{ \subsection{New Features}{ \itemize{ \item{We welcome Heidi Seibold as co-author!} \item{Internal re-organisation for \code{ctree} by means of new extensible tree infrastructure (available in \code{extree_data} and \code{extree_fit}). Certain parts of the new infrastructure are still experimental. \code{ctree} is fully backward compatible.} \item{Use \pkg{libcoin} for computing linear test statistics and p-values for \code{ctree}.} \item{Use \pkg{inum} for binning (the new \code{nmax} argument).} \item{Quadratic test statistics for splitpoint selection are now available for \code{ctree} via \code{ctree_control(splitstat = "quadratic")}.} \item{Maximally selected test statistics for variable selection are now available for \code{ctree} via \code{ctree_control(splittest = TRUE)}.} \item{Missing values can be treated as a separate category, also for splits in numeric variables in \code{ctree} via \code{ctree_control(MIA = TRUE)}.} \item{Permutation variable importance, including conditional variable importance, was added to \pkg{partykit}.} \item{New \code{offset} argument in \code{ctree}.} \item{New \code{get_paths} for computing paths to nodes.} \item{\code{node_barplot} gained a \code{text} argument that can be used to draw text labels for the percentages displayed.} \item{The \code{margins} used in \code{plot.party} can now also be set by the user.} } } \subsection{Bugfixes}{ \itemize{ \item{Bug fix in \code{mob()} if \code{weights} are used and \code{caseweights = TRUE} (the default). The statistics for the parameter instability tests were computed incorrectly and consequently the selection of splitting variables and also the stopping criterion were affected/incorrect.} \item{Avoid log(p) values of \code{-Inf} inside \code{mob()} by replacing weighted averaging with naive averaging in the response surface regression output in case the p values are below machine precision.} \item{The \code{as.party} method for \code{rpart} objects without any splits only returned a naked \code{partynode} rather than a full \code{party}. This has been corrected now.} \item{\code{nodeapply} did not produce the same results for permutations of \code{ids}. Spotted by Heidi Seibold.} \item{Out-of-bag predictions in \code{predict.cforest} were incorrect.} \item{\code{perm} in \code{predict} was only considered when \code{newdata} was given. Spotted by Heidi Seibold.} \item{Don't try to search for binary splits in unordered factors with more than 31 levels. This potentially caused an integer overrun in previous versions. \code{party::ctree()} uses an approximation for binary split searches in unordered factors; thus, using \pkg{party} might be an alternative.} } } } \section{Changes in Version 1.1-1 (2016-09-20)}{ \itemize{ \item{Proper support of quasi-families in \code{glmtree} and hence \code{palmtree}.} \item{NA handling by following the majority was potentially incorrect in \code{ctree}.} \item{Minor speed improvements.} \item{Breaking ties before variable selection was suboptimal for very small log-p-values.} } } \section{Changes in Version 1.1-0 (2016-07-14)}{ \itemize{ \item{Added a new function \code{palmtree} that fits partially additive (generalized) linear model trees. These employ model-based recursive partitioning (\code{mob}) based on (generalized) linear models with some local (i.e., leaf-specific) and some global (i.e., constant throughout the tree) regression coefficients.} \item{Splits in ordinal variables are now represented correctly in the (still internal) \code{list.rule} method.} \item{Kaplan-Meier curves in \code{"constparty"} trees were plotted incorrectly due to use a wrong scaling of the x-axis. Spotted by Peter Calhoun .} \item{Use \code{quote(stats::model.frame)} instead of \code{as.name("model.frame")}.} \item{The \code{as.party} methods for \code{rpart} and \code{Weka_tree} now have a \code{data = TRUE} argument so that by default the data is preserved in the \code{party} object (instead of an empty model frame).} \item{The \code{predict} method for \code{cforest} objects did not work for one-row data frames, fixed now.} \item{Added \code{rot} and \code{just} arguments to \code{node_barplot} for more fine control of x-axis labeling (e.g., with 45 degree rotation).} } } \section{Changes in Version 1.0-5 (2016-02-05)}{ \itemize{ \item{The \pkg{partykit} package has now been published in \emph{Journal of Machine Learning Research}, 16, 3905-3909. \url{https://jmlr.org/papers/v16/hothorn15a.html}} \item{Added support for setting background in panel functions.} \item{The \code{as.list()} method for \code{partynode} objects erroneously created an object \code{thisnode} in the calling environment which is avoided now.} } } \section{Changes in Version 1.0-4 (2015-09-29)}{ \itemize{ \item{Bug fix in \code{plot()} method for \code{constparty} objects. In the previous partykit version clipping was accidentally also applied to the axes labels.} \item{For \code{constparty} objects \code{plot(..., type = "simple")} did not work correctly whereas \code{plot(as.simpleparty(...))} yielded the desired visualization. Now internally \code{as.simpleparty()} is called also in the former case.} \item{The \code{as.simpleparty()} method now preserves p-values from \code{constparty} objects (if any).} \item{Added a \code{getCall()} method for \code{"party"} objects.} \item{In the \code{predict()} method for \code{"lmtree"} and \code{"glmtree"} objects the \code{offset} (if any) was sometimes ignored. It is now always used in the prediction.} } } \section{Changes in Version 1.0-3 (2015-08-14)}{ \itemize{ \item{Import \code{logrank_trafo} from \pkg{coin}.} } } \section{Changes in Version 1.0-2 (2015-07-28)}{ \itemize{ \item{\code{nodeprune(..., ids = 1)} did not prune the tree to the root node. Fixed now.} \item{\code{predict.cforest} used \code{na.omit} instead of \code{na.pass}.} \item{\code{predict.party} now features new \code{perm} argument for permuting splits in specific variables (useful for computing permutation variable importances).} \item{\code{NAMESPACE} updates.} } } \section{Changes in Version 1.0-1 (2015-04-07)}{ \itemize{ \item{The support for (generalized) linear model trees with just a constant regressor has been improved. Now \code{lmtree(y ~ x1 + x2)} is short for \code{lmtree(y ~ 1 | x1 + x2)}, analogously for \code{glmtree()}. Plotting now also works properly in this case.} \item{The \code{as.party()} method for \code{"rpart"} objects did not work if one of the partitioning variables was a \code{"character"} variable rather than a \code{"factor"}. A suitable work-around has been added.} \item{The \code{node_barplot()} panel function can now also be used for multivariate responses, e.g., when all responses are numeric and on the same scale.} \item{The package now also includes a new data set \code{HuntingSpiders} which is essentially a copy of the \code{spider} data from the package \pkg{mvpart} that is currently archived on CRAN. The documentation has been improved somewhat and is likely to change further to explain how the data has been transformed in De'ath (2002).} \item{The survival tree example for the GBSG2 data was broken due to the response being (incorrectly) also part of the explanatory variables. Fixed by using the latest \pkg{Formula} package (at least version 1.2-1).} } } \section{Changes in Version 1.0-0 (2015-02-20)}{ \itemize{ \item{Version 1.0-0 published. This version is described in the MLOSS paper accepted for publication by the Journal of Machine Learning Research today.} \item{The unbiased version of \code{cforest} (with \code{replace = FALSE}) is now the default (as in \pkg{party}).} \item{Register all S3 methods in \code{NAMESPACE}.} } } \section{Changes in Version 0.8-4 (2015-01-06)}{ \itemize{ \item{Extended \code{mob()} interface by a \code{cluster} argument. This can be a vector (numeric, integer, factor) with cluster IDs that are then passed on to the 'fit' function (if supported) and used for clustering the covariance matrix in the parameter stability tests. \code{lmtree()} and \code{glmtree()} hence both gained a \code{cluster} argument which is used only for cluster covariances but not for the model estimation (i.e., corresponding to a working independence model).} \item{Optionally, the parameters' variance-covariance matrix in \code{mob()} can now be estimated by the sandwich matrix instead of the default outer-product-of-gradients (OPG) matrix or the information matrix.} \item{Reimplementation of \code{cforest()} available with extended prediction facilities. Both the internal representation and the user interface are still under development are likely to change in future versions.} \item{Added multicore support to \code{mob()}, \code{ctree()}, and \code{cforest()}. If control argument \code{cores} is specified (e.g., \code{cores = 4}) then the search for the best variable or split point (often involving numerous model fits in \code{mob()} or resampling in \code{ctree()}) is carried out using \code{parallel::mclapply()} rathern than sequential \code{for()} or \code{sapply()}. Additionally, other \code{applyfun}s can be provided, e.g., using networks of workstations etc.} \item{Bug fix in \code{mob()} that occurred when regressor variables and partitioning variables overlapped and were not sorted in the underlying model frame.} } } \section{Changes in Version 0.8-3 (2014-12-15)}{ \itemize{ \item{\pkg{mvpart} was archived 2014-12-15.} } } \section{Changes in Version 0.8-2 (2014-09-12)}{ \itemize{ \item{Fixed an uninitialized memory issue reported by valgrind.} } } \section{Changes in Version 0.8-1 (2014-09-08)}{ \itemize{ \item{partykit now depends on R version >= 3.1.0 in order to import the \code{depth()} generic from the \pkg{grid} package.} \item{The print methods for \code{party}/\code{partynode} objects with only a root node was modified. Now, the terminal panel function is also applied if there is only a root node (while previously it was not).} \item{ \code{ctree()} now catches \code{sum(weights) <= 1} situations before they lead to an error.} \item{ Code from suggested packages is included by using \code{::} syntax as required by recent R versions.} \item{ Argument \code{ytrafo} of \code{ctree()} can now be a function which will be updated in every node.} \item{ A small demo briefly illustrating some memory and speed properties has been added. It can be run interactively via \code{demo("memory-speed", package = "partykit").}} \item{ Section 3 of the "constparty" vignette now shows how properties of a new tree algorithm can be assessed by using \pkg{partykit} building blocks.} } } \section{Changes in Version 0.8-0 (2014-03-27)}{ \itemize{ \item{Major improved version of \pkg{partykit}. The previously existing functions in the package were tested and enhanced, new functions and extensive vignettes added.} \item{Extended and improved introductory documentation. The basic classes and class constructors \code{partynode}/\code{partysplit}/\code{party} are introduced in much more detail now in \code{vignette("partykit", package = "partykit")}.} \item{The class \code{constparty} (inheriting from \code{party}) for representing \code{party} objects with constant fits in the nodes (along with coercion methods for \code{rpart}, \code{J48}, etc.) is now described in more detail in the new \code{vignette("constparty", package = "partykit")}.} \item{The package now includes a reimplementation of the model-based recursive partitioning algorithm (MOB) using \pkg{partykit} infrastructure. The generic algorithm, the corresponding convenience interfaces \code{lmtree()} and \code{glmtree()} as well as various illustrations and possible extensions are described in detail in the new \code{vignette("mob", package = "partykit")}.} \item{Improved implementation of conditional inference trees (CTree), see the new \code{vignette("ctree", package = "partykit")} for details.} \item{New \code{nodeprune()} generic for pruning nodes in all \code{party} trees and \code{partynode} objects.} \item{Deal with empty levels in \code{ctree()} for \code{teststat = "quad"} (bug reported by Wei-Yin Loh ).} \item{In \code{predict()} method for \code{constparty} objects, \code{type = "prob"} now returns ECDF for numeric responses and \code{type = "response"} the (weighted) mean.} \item{New panel function \code{node_ecdf()} for plotting empirical cumulative distribution functions in the terminal leaves of \code{constparty} trees.} } } \section{Changes in Version 0.1-6 (2013-09-03)}{ \itemize{ \item{Bug fix in \code{as.party()} method for J48 trees with ordered factors.} } } \section{Changes in Version 0.1-5 (2013-03-22)}{ \itemize{ \item{Fix C code problems reported by clang under OS X.} } } \section{Changes in Version 0.1-4 (2012-06-05)}{ \itemize{ \item{Added \code{node_surv()} for plotting survival ctrees. Accompanying infrastructure for survival trees was enhanced.} \item{\code{ctree()} now checks for (and does not allow) \code{x >= max(x)} splits.} } } \section{Changes in Version 0.1-3 (2012-01-11)}{ \itemize{ \item{Added \pkg{ipred} to the list of suggested packages due to usage of GlaucomaM and GBSG2 data in tests/examples.} } } \section{Changes in Version 0.1-2 (2011-12-18)}{ \itemize{ \item{The \code{node_terminal()} panel-generating function is now customizable by a FUN argument that is passed to \code{formatinfo()}.} \item{The \code{plot()} method for \code{simpleparty} object now sets up a formatting function passed to \code{formatinfo()}, both in \code{print()} and \code{plot()}.} \item{Fixed bug in \code{pmmlTreeModel()} for processing label IDS in splits when not all levels are present.} \item{Cleaned up unused variables in C code and partial argument matching in R code.} } } \section{Changes in Version 0.1-1 (2011-09-29)}{ \itemize{ \item{First CRAN release.} \item{See \code{vignette("partykit", package = "partykit")} for a (somewhat rough) introduction to the package and its classes/methods.} } } partykit/inst/pmml/0000755000176200001440000000000014723350653014053 5ustar liggesuserspartykit/inst/pmml/bbbc.pmml0000644000176200001440000001226514172227776015647 0ustar liggesusers
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partykit/inst/pmml/iris.pmml0000644000176200001440000001114014172227776015714 0ustar liggesusers
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partykit/inst/pmml/ttnc2.pmml0000644000176200001440000001431114172227776016003 0ustar liggesusers
2014-01-22 11:51:42
"Male" "Male&Adult" "Adult" "Child" "3rd" "1st" "2nd" "Female" "Female|Child" "3rd" "Child" "1st" "2nd" "Crew" "Adult"
partykit/build/0000755000176200001440000000000014723350652013227 5ustar liggesuserspartykit/build/vignette.rds0000644000176200001440000000111414723350652015563 0ustar liggesusers‹½TQoÓ0îšv]˘ž-ži@ŸŒ² ¦ªˆ7×¹´f‰Ùn£¾ñ畳c7iX'T5ñïûî|÷9ß­V«ÝêtÚ­v„ËèÇø?Ç}|Ÿ1)´É©2›ÑTÞÛgFÔ½LÎkæ©Üqã|ûŒoß[F* ¹µA\,Æä£’.1¹ÆGj¦Ð¤àfIv 7Úó¼v5Œí^Ì —‚¦äF$ @0(Á>ò»MÄA¿!Ÿe ©{ϵ¥Çä’|‚Üdy C-‘I9|G5Äd l¥4_ƒ«Øå²õqA¦>Ã(œ×ΤLqI©Їþ¡Çyœì÷¸r¸WfÕcëÛg<­O-Àý̼ÙuóÆ šZŽ©dìúˆ“àÊ:‚1ý wÔ<ËÒ€Š©ÁâÌJ¶^ˆa’‹P×ìzdÃD¯Ôš¯i x¢Z1¶¤b1‘*[¥Sp¶ 0)}.} \item{ytype, xtype}{character. Specification of how \code{mob} should preprocess \code{y} and \code{x} variables. Possible choice are: \code{"vector"} (for \code{y} only), i.e., only one variable; \code{"matrix"}, i.e., the model matrix of all variables; \code{"data.frame"}, i.e., a data frame of all variables.} \item{terminal, inner}{character. Specification of which additional information (\code{"estfun"}, \code{"object"}, or both) should be stored in each node. If \code{NULL}, no additional information is stored.} \item{model}{logical. Should the full model frame be stored in the resulting object?} \item{numsplit}{character indicating how splits for numeric variables should be justified. Because any splitpoint in the interval between the last observation from the left child segment and the first observation from the right child segment leads to the same observed split, two options are available in \code{mob_control}: Either, the split is \code{"left"}-justified (the default for backward compatibility) or \code{"center"}-justified using the midpoint of the possible interval.} \item{catsplit}{character indicating how (unordered) categorical variables should be splitted. By default the best \code{"binary"} split is searched (by minimizing the objective function). Alternatively, if set to \code{"multiway"}, the node is simply splitted into all levels of the categorical variable.} \item{vcov}{character indicating which type of covariance matrix estimator should be employed in the parameter instability tests. The default is the outer product of gradients (\code{"opg"}). Alternatively, \code{vcov = "info"} employs the information matrix and \code{vcov = "sandwich"} the sandwich matrix (both of which are only sensible for maximum likelihood estimation).} \item{ordinal}{character indicating which type of parameter instability test should be employed for ordinal partitioning variables (i.e., ordered factors). This can be \code{"chisq"}, \code{"max"}, or \code{"L2"}. If \code{"chisq"} then the variable is treated as unordered and a chi-squared test is performed. If \code{"L2"}, then a maxLM-type test as for numeric variables is carried out but correcting for ties. This requires simulation of p-values via \code{\link[strucchange]{catL2BB}} and requires some computation time. For \code{"max"} a weighted double maximum test is used that computes p-values via \code{\link[mvtnorm]{pmvnorm}}.} \item{nrep}{numeric. Number of replications in the simulation of p-values for the ordinal \code{"L2"} statistic (if used).} \item{applyfun}{an optional \code{\link[base]{lapply}}-style function with arguments \code{function(X, FUN, \dots)}. It is used for refitting the model across potential sample splits. The default is to use the basic \code{lapply} function unless the \code{cores} argument is specified (see below).} \item{cores}{numeric. If set to an integer the \code{applyfun} is set to \code{\link[parallel]{mclapply}} with the desired number of \code{cores}.} } \details{ See \code{\link{mob}} for more details and references. For post-pruning, \code{prune} can be set to a \code{function(objfun, df, nobs)} which either returns \code{TRUE} to signal that a current node can be pruned or \code{FALSE}. All supplied arguments are of length two: \code{objfun} is the sum of objective function values in the current node and its child nodes, respectively. \code{df} is the degrees of freedom in the current node and its child nodes, respectively. \code{nobs} is vector with the number of observations in the current node and the total number of observations in the dataset, respectively. If the objective function employed in the \code{mob()} call is the negative log-likelihood, then a suitable function is set up on the fly by comparing \code{(2 * objfun + penalty * df)} in the current and the daughter nodes. The penalty can then be set via a numeric or character value for \code{prune}: AIC is used if \code{prune = "AIC"} or \code{prune = 2} and BIC if \code{prune = "BIC"} or \code{prune = log(n)}. } \seealso{\code{\link{mob}}} \value{ A list of class \code{mob_control} containing the control parameters. } \keyword{misc} partykit/man/mob.Rd0000644000176200001440000001715614172230000013737 0ustar liggesusers\name{mob} \alias{mob} \alias{modelparty} \alias{coef.modelparty} \alias{deviance.modelparty} \alias{fitted.modelparty} \alias{formula.modelparty} \alias{getCall.modelparty} \alias{logLik.modelparty} \alias{model.frame.modelparty} \alias{nobs.modelparty} \alias{plot.modelparty} \alias{predict.modelparty} \alias{print.modelparty} \alias{residuals.modelparty} \alias{summary.modelparty} \alias{weights.modelparty} \alias{refit.modelparty} \alias{sctest.modelparty} \title{Model-based Recursive Partitioning} \description{ MOB is an algorithm for model-based recursive partitioning yielding a tree with fitted models associated with each terminal node. } \usage{ mob(formula, data, subset, na.action, weights, offset, cluster, fit, control = mob_control(), \dots) } \arguments{ \item{formula}{symbolic description of the model (of type \code{y ~ z1 + \dots + zl} or \code{y ~ x1 + \dots + xk | z1 + \dots + zl}; for details see below).} \item{data, subset, na.action}{arguments controlling formula processing via \code{\link[stats]{model.frame}}.} \item{weights}{optional numeric vector of weights. By default these are treated as case weights but the default can be changed in \code{\link{mob_control}}.} \item{offset}{optional numeric vector with an a priori known component to be included in the model \code{y ~ x1 + \dots + xk} (i.e., only when \code{x} variables are specified).} \item{cluster}{optional vector (typically numeric or factor) with a cluster ID to be passed on to the \code{fit} function and employed for clustered covariances in the parameter stability tests.} \item{fit}{function. A function for fitting the model within each node. For details see below.} \item{control}{A list with control parameters as returned by \code{\link{mob_control}}.} \item{\dots}{Additional arguments passed to the \code{fit} function.} } \details{ Model-based partitioning fits a model tree using two groups of variables: (1) The model variables which can be just a (set of) response(s) \code{y} or additionally include regressors \code{x1}, \dots, \code{xk}. These are used for estimating the model parameters. (2) Partitioning variables \code{z1}, \dots, \code{zl}, which are used for recursively partitioning the data. The two groups of variables are either specified as \code{y ~ z1 + \dots + zl} (when there are no regressors) or \code{y ~ x1 + \dots + xk | z1 + \dots + zl} (when the model part contains regressors). Both sets of variables may in principle be overlapping. To fit a tree model the following algorithm is used. \enumerate{ \item \code{fit} a model to the \code{y} or \code{y} and \code{x} variables using the observations in the current node \item Assess the stability of the model parameters with respect to each of the partitioning variables \code{z1}, \dots, \code{zl}. If there is some overall instability, choose the variable \code{z} associated with the smallest \eqn{p} value for partitioning, otherwise stop. \item Search for the locally optimal split in \code{z} by minimizing the objective function of the model. Typically, this will be something like \code{\link{deviance}} or the negative \code{\link{logLik}}. \item Refit the \code{model} in both kid subsamples and repeat from step 2. } More details on the conceptual design of the algorithm can be found in Zeileis, Hothorn, Hornik (2008) and some illustrations are provided in \code{vignette("MOB")}. For specifying the \code{fit} function two approaches are possible: (1) It can be a function \code{fit(y, x = NULL, start = NULL, weights = NULL, offset = NULL, \dots)}. The arguments \code{y}, \code{x}, \code{weights}, \code{offset} will be set to the corresponding elements in the current node of the tree. Additionally, starting values will sometimes be supplied via \code{start}. Of course, the \code{fit} function can choose to ignore any arguments that are not applicable, e.g., if the are no regressors \code{x} in the model or if starting values or not supported. The returned object needs to have a class that has associated \code{\link[stats]{coef}}, \code{\link[stats]{logLik}}, and \code{\link[sandwich]{estfun}} methods for extracting the estimated parameters, the maximized log-likelihood, and the empirical estimating function (i.e., score or gradient contributions), respectively. (2) It can be a function \code{fit(y, x = NULL, start = NULL, weights = NULL, offset = NULL, \dots, estfun = FALSE, object = FALSE)}. The arguments have the same meaning as above but the returned object needs to have a different structure. It needs to be a list with elements \code{coefficients} (containing the estimated parameters), \code{objfun} (containing the minimized objective function), \code{estfun} (the empirical estimating functions), and \code{object} (the fitted model object). The elements \code{estfun}, or \code{object} should be \code{NULL} if the corresponding argument is set to \code{FALSE}. Internally, a function of type (2) is set up by \code{mob()} in case a function of type (1) is supplied. However, to save computation time, a function of type (2) may also be specified directly. For the fitted MOB tree, several standard methods are provided such as \code{print}, \code{predict}, \code{residuals}, \code{logLik}, \code{deviance}, \code{weights}, \code{coef} and \code{summary}. Some of these rely on reusing the corresponding methods for the individual model objects in the terminal nodes. Functions such as \code{coef}, \code{print}, \code{summary} also take a \code{node} argument that can specify the node IDs to be queried. Some examples are given below. More details can be found in \code{vignette("mob", package = "partykit")}. An overview of the connections to other functions in the package is provided by Hothorn and Zeileis (2015). } \value{ An object of class \code{modelparty} inheriting from \code{\link{party}}. The \code{info} element of the overall \code{party} and the individual \code{node}s contain various informations about the models. } \references{ Hothorn T, Zeileis A (2015). partykit: A Modular Toolkit for Recursive Partytioning in R. \emph{Journal of Machine Learning Research}, \bold{16}, 3905--3909. Zeileis A, Hothorn T, Hornik K (2008). Model-Based Recursive Partitioning. \emph{Journal of Computational and Graphical Statistics}, \bold{17}(2), 492--514. } \seealso{\code{\link{mob_control}}, \code{\link{lmtree}}, \code{\link{glmtree}}} \examples{ if(require("mlbench")) { ## Pima Indians diabetes data data("PimaIndiansDiabetes", package = "mlbench") ## a simple basic fitting function (of type 1) for a logistic regression logit <- function(y, x, start = NULL, weights = NULL, offset = NULL, ...) { glm(y ~ 0 + x, family = binomial, start = start, ...) } ## set up a logistic regression tree pid_tree <- mob(diabetes ~ glucose | pregnant + pressure + triceps + insulin + mass + pedigree + age, data = PimaIndiansDiabetes, fit = logit) ## see lmtree() and glmtree() for interfaces with more efficient fitting functions ## print tree print(pid_tree) ## print information about (some) nodes print(pid_tree, node = 3:4) ## visualization plot(pid_tree) ## coefficients and summary coef(pid_tree) coef(pid_tree, node = 1) summary(pid_tree, node = 1) ## average deviance computed in different ways mean(residuals(pid_tree)^2) deviance(pid_tree)/sum(weights(pid_tree)) deviance(pid_tree)/nobs(pid_tree) ## log-likelihood and information criteria logLik(pid_tree) AIC(pid_tree) BIC(pid_tree) ## predicted nodes predict(pid_tree, newdata = head(PimaIndiansDiabetes, 6), type = "node") ## other types of predictions are possible using lmtree()/glmtree() } } \keyword{tree} partykit/man/glmtree.Rd0000644000176200001440000000661414172230000014616 0ustar liggesusers\name{glmtree} \alias{glmtree} \alias{plot.glmtree} \alias{predict.glmtree} \alias{print.glmtree} \title{Generalized Linear Model Trees} \description{ Model-based recursive partitioning based on generalized linear models. } \usage{ glmtree(formula, data, subset, na.action, weights, offset, cluster, family = gaussian, epsilon = 1e-8, maxit = 25, method = "glm.fit", \dots) } \arguments{ \item{formula}{symbolic description of the model (of type \code{y ~ z1 + \dots + zl} or \code{y ~ x1 + \dots + xk | z1 + \dots + zl}; for details see below).} \item{data, subset, na.action}{arguments controlling formula processing via \code{\link[stats]{model.frame}}.} \item{weights}{optional numeric vector of weights. By default these are treated as case weights but the default can be changed in \code{\link{mob_control}}.} \item{offset}{optional numeric vector with an a priori known component to be included in the model \code{y ~ x1 + \dots + xk} (i.e., only when \code{x} variables are specified).} \item{cluster}{optional vector (typically numeric or factor) with a cluster ID to be employed for clustered covariances in the parameter stability tests.} \item{family, method}{specification of a family and fitting method for \code{\link[stats]{glm}}.} \item{epsilon, maxit}{control parameters passed to \code{\link[stats]{glm.control}}.} \item{\dots}{optional control parameters passed to \code{\link{mob_control}}.} } \details{ Convenience interface for fitting MOBs (model-based recursive partitions) via the \code{\link{mob}} function. \code{glmtree} internally sets up a model \code{fit} function for \code{mob}, using \code{\link[stats]{glm.fit}}. Then \code{mob} is called using the negative log-likelihood as the objective function. Compared to calling \code{mob} by hand, the implementation tries to avoid unnecessary computations while growing the tree. Also, it provides a more elaborate plotting function. } \value{ An object of class \code{glmtree} inheriting from \code{\link{modelparty}}. The \code{info} element of the overall \code{party} and the individual \code{node}s contain various informations about the models. } \references{ Zeileis A, Hothorn T, Hornik K (2008). Model-Based Recursive Partitioning. \emph{Journal of Computational and Graphical Statistics}, \bold{17}(2), 492--514. } \seealso{\code{\link{mob}}, \code{\link{mob_control}}, \code{\link{lmtree}}} \examples{ if(require("mlbench")) { ## Pima Indians diabetes data data("PimaIndiansDiabetes", package = "mlbench") ## recursive partitioning of a logistic regression model pid_tree2 <- glmtree(diabetes ~ glucose | pregnant + pressure + triceps + insulin + mass + pedigree + age, data = PimaIndiansDiabetes, family = binomial) ## printing whole tree or individual nodes print(pid_tree2) print(pid_tree2, node = 1) ## visualization plot(pid_tree2) plot(pid_tree2, tp_args = list(cdplot = TRUE)) plot(pid_tree2, terminal_panel = NULL) ## estimated parameters coef(pid_tree2) coef(pid_tree2, node = 5) summary(pid_tree2, node = 5) ## deviance, log-likelihood and information criteria deviance(pid_tree2) logLik(pid_tree2) AIC(pid_tree2) BIC(pid_tree2) ## different types of predictions pid <- head(PimaIndiansDiabetes) predict(pid_tree2, newdata = pid, type = "node") predict(pid_tree2, newdata = pid, type = "response") predict(pid_tree2, newdata = pid, type = "link") } } \keyword{tree} partykit/man/ctree_control.Rd0000644000176200001440000002157414172230000016023 0ustar liggesusers\name{ctree_control} \alias{ctree_control} \title{ Control for Conditional Inference Trees } \description{ Various parameters that control aspects of the `ctree' fit. } \usage{ ctree_control(teststat = c("quadratic", "maximum"), splitstat = c("quadratic", "maximum"), splittest = FALSE, testtype = c("Bonferroni", "MonteCarlo", "Univariate", "Teststatistic"), pargs = GenzBretz(), nmax = c(yx = Inf, z = Inf), alpha = 0.05, mincriterion = 1 - alpha, logmincriterion = log(mincriterion), minsplit = 20L, minbucket = 7L, minprob = 0.01, stump = FALSE, maxvar = Inf, lookahead = FALSE, MIA = FALSE, nresample = 9999L, tol = sqrt(.Machine$double.eps),maxsurrogate = 0L, numsurrogate = FALSE, mtry = Inf, maxdepth = Inf, multiway = FALSE, splittry = 2L, intersplit = FALSE, majority = FALSE, caseweights = TRUE, applyfun = NULL, cores = NULL, saveinfo = TRUE, update = NULL, splitflavour = c("ctree", "exhaustive")) } \arguments{ \item{teststat}{ a character specifying the type of the test statistic to be applied for variable selection. } \item{splitstat}{ a character specifying the type of the test statistic to be applied for splitpoint selection. Prior to version 1.2-0, \code{maximum} was implemented only.} \item{splittest}{ a logical changing linear (the default \code{FALSE}) to maximally selected statistics for variable selection. Currently needs \code{testtype = "MonteCarlo"}.} \item{testtype}{ a character specifying how to compute the distribution of the test statistic. The first three options refer to p-values as criterion, \code{Teststatistic} uses the raw statistic as criterion. \code{Bonferroni} and \code{Univariate} relate to p-values from the asymptotic distribution (adjusted or unadjusted). Bonferroni-adjusted Monte-Carlo p-values are computed when both \code{Bonferroni} and \code{MonteCarlo} are given.} \item{pargs}{ control parameters for the computation of multivariate normal probabilities, see \code{\link[mvtnorm]{GenzBretz}}.} \item{nmax}{ an integer of length two defining the number of bins each variable (in the response \code{yx} and the partitioning variables \code{z})) and is divided into prior to tree building. The default \code{Inf} does not apply any binning. Highly experimental, use at your own risk.} \item{alpha}{ a double, the significance level for variable selection.} \item{mincriterion}{ the value of the test statistic or 1 - p-value that must be exceeded in order to implement a split. } \item{logmincriterion}{ the value of the test statistic or 1 - p-value that must be exceeded in order to implement a split on the log-scale. } \item{minsplit}{ the minimum sum of weights in a node in order to be considered for splitting. } \item{minbucket}{ the minimum sum of weights in a terminal node. } \item{minprob}{ proportion of observations needed to establish a terminal node.} \item{stump}{ a logical determining whether a stump (a tree with a maximum of three nodes only) is to be computed. } \item{maxvar}{ maximum number of variables the tree is allowed to split in.} \item{lookahead}{ a logical determining whether a split is implemented only after checking if tests in both daughter nodes can be performed.} \item{MIA}{ a logical determining the treatment of \code{NA} as a category in split, see Twala et al. (2008).} \item{nresample}{ number of permutations for \code{testtype = "MonteCarlo"}.} \item{tol}{tolerance for zero variances.} \item{maxsurrogate}{ number of surrogate splits to evaluate.} \item{numsurrogate}{ a logical for backward-compatibility with party. If \code{TRUE}, only at least ordered variables are considered for surrogate splits.} \item{mtry}{ number of input variables randomly sampled as candidates at each node for random forest like algorithms. The default \code{mtry = Inf} means that no random selection takes place. If \code{\link{ctree_control}} is used in \code{\link{cforest}} this argument is ignored.} \item{maxdepth}{ maximum depth of the tree. The default \code{maxdepth = Inf} means that no restrictions are applied to tree sizes.} \item{multiway}{ a logical indicating if multiway splits for all factor levels are implemented for unordered factors.} \item{splittry}{ number of variables that are inspected for admissible splits if the best split doesn't meet the sample size constraints.} \item{intersplit}{ a logical indicating if splits in numeric variables are simply \code{x <= a} (the default) or interpolated \code{x <= (a + b) / 2}. The latter feature is experimental, see Galili and Meilijson (2016).} \item{majority}{ if \code{FALSE} (the default), observations which can't be classified to a daughter node because of missing information are randomly assigned (following the node distribution). If \code{TRUE}, they go with the majority (the default in the first implementation \code{\link[party]{ctree}}) in package party.} \item{caseweights}{ a logical interpreting \code{weights} as case weights.} \item{applyfun}{an optional \code{\link[base]{lapply}}-style function with arguments \code{function(X, FUN, \dots)}. It is used for computing the variable selection criterion. The default is to use the basic \code{lapply} function unless the \code{cores} argument is specified (see below). If \code{\link{ctree_control}} is used in \code{\link{cforest}} this argument is ignored.} \item{cores}{numeric. If set to an integer the \code{applyfun} is set to \code{\link[parallel]{mclapply}} with the desired number of \code{cores}. If \code{\link{ctree_control}} is used in \code{\link{cforest}} this argument is ignored.} \item{saveinfo}{logical. Store information about variable selection procedure in \code{info} slot of each \code{partynode}.} \item{update}{logical. If \code{TRUE}, the data transformation is updated in every node. The default always was and still is not to update unless \code{ytrafo} is a function.} \item{splitflavour}{use exhaustive search over splits instead of maximally selected statistics (\code{ctree}). This feature may change.} } \details{ The arguments \code{teststat}, \code{testtype} and \code{mincriterion} determine how the global null hypothesis of independence between all input variables and the response is tested (see \code{\link{ctree}}). The variable with most extreme p-value or test statistic is selected for splitting. If this isn't possible due to sample size constraints explained in the next paragraph, up to \code{splittry} other variables are inspected for possible splits. A split is established when all of the following criteria are met: 1) the sum of the weights in the current node is larger than \code{minsplit}, 2) a fraction of the sum of weights of more than \code{minprob} will be contained in all daughter nodes, 3) the sum of the weights in all daughter nodes exceeds \code{minbucket}, and 4) the depth of the tree is smaller than \code{maxdepth}. This avoids pathological splits deep down the tree. When \code{stump = TRUE}, a tree with at most two terminal nodes is computed. The argument \code{mtry > 0} means that a random forest like `variable selection', i.e., a random selection of \code{mtry} input variables, is performed in each node. In each inner node, \code{maxsurrogate} surrogate splits are computed (regardless of any missing values in the learning sample). Factors in test samples whose levels were empty in the learning sample are treated as missing when computing predictions (in contrast to \code{\link[party]{ctree}}. Note also the different behaviour of \code{majority} in the two implementations. } \value{ A list. } \references{ B. E. T. H. Twala, M. C. Jones, and D. J. Hand (2008), Good Methods for Coping with Missing Data in Decision Trees, \emph{Pattern Recognition Letters}, \bold{29}(7), 950--956. Tal Galili, Isaac Meilijson (2016), Splitting Matters: How Monotone Transformation of Predictor Variables May Improve the Predictions of Decision Tree Models, \url{https://arxiv.org/abs/1611.04561}. } \keyword{misc} partykit/man/model.frame.rpart.Rd0000644000176200001440000000105614646201327016512 0ustar liggesusers\name{model_frame_rpart} \alias{model_frame_rpart} \title{ Model Frame Method for rpart } \description{ A model.frame method for rpart objects. } \usage{ model_frame_rpart(formula, \dots) } \arguments{ \item{formula}{ an object of class \code{\link[rpart]{rpart}}.} \item{\dots}{ additional arguments.} } \details{ A \code{\link{model.frame}} method for \code{\link[rpart]{rpart}} objects. Because it is no longer possible to overwrite existing methods, the function name is a little different here. } \value{ A model frame. } \keyword{tree} partykit/man/extree_data.Rd0000644000176200001440000000466714172230000015452 0ustar liggesusers\name{extree_data} \alias{extree_data} %- Also NEED an '\alias' for EACH other topic documented here. \title{ Data Preprocessing for Extensible Trees. } \description{ A routine for preprocessing data before an extensible tree can be grown by \code{extree_fit}. } \usage{ extree_data(formula, data, subset, na.action = na.pass, weights, offset, cluster, strata, scores = NULL, yx = c("none", "matrix"), ytype = c("vector", "data.frame", "matrix"), nmax = c(yx = Inf, z = Inf), ...) } \arguments{ \item{formula}{a formula describing the model of the form \code{y1 + y2 + ... ~ x1 + x2 + ... | z1 + z2 + ...}. } \item{data}{an optional data.frame containing the variables in the model. } \item{subset}{an optional vector specifying a subset of observations to be used in the fitting process. } \item{na.action}{a function which indicates what should happen when the data contain missing values. } \item{weights}{an optional vector of weights. } \item{offset}{an optional offset vector. } \item{cluster}{an optional factor describing clusters. The interpretation depends on the specific tree algorithm. } \item{strata}{an optional factor describing strata. The interpretation depends on the specific tree algorithm. } \item{scores}{an optional named list of numeric scores to be assigned to ordered factors in the \code{z} part of the formula. } \item{yx}{a character indicating if design matrices shall be computed. } \item{ytype}{a character indicating how response variables shall be stored. } \item{nmax}{a numeric vector of length two with the maximal number of bins in the response and \code{x}-part (first element) and the \code{z} part. Use \code{Inf} to switch-off binning. } \item{\dots}{additional arguments. } } \details{ This internal functionality will be the basis of implementations of other tree algorithms in future versions. Currently, only \code{ctree} relies on this function. } \value{An object of class \code{extree_data}. } \examples{ data("iris") ed <- extree_data(Species ~ Sepal.Width + Sepal.Length | Petal.Width + Petal.Length, data = iris, nmax = c("yx" = 25, "z" = 10), yx = "matrix") ### the model.frame mf <- model.frame(ed) all.equal(mf, iris[, names(mf)]) ### binned y ~ x part model.frame(ed, yxonly = TRUE) ### binned Petal.Width ed[[4, type = "index"]] ### response ed$yx$y ### model matrix ed$yx$x } \keyword{tree} partykit/man/panelfunctions.Rd0000644000176200001440000001770614172230000016213 0ustar liggesusers\name{panelfunctions} \alias{panelfunctions} \alias{node_inner} \alias{node_terminal} \alias{edge_simple} \alias{node_barplot} \alias{node_bivplot} \alias{node_boxplot} \alias{node_surv} \alias{node_ecdf} \alias{node_mvar} \title{ Panel-Generators for Visualization of Party Trees } \description{ The plot method for \code{party} and \code{constparty} objects are rather flexible and can be extended by panel functions. Some pre-defined panel-generating functions of class \code{grapcon_generator} for the most important cases are documented here. } \usage{ node_inner(obj, id = TRUE, pval = TRUE, abbreviate = FALSE, fill = "white", gp = gpar()) node_terminal(obj, digits = 3, abbreviate = FALSE, fill = c("lightgray", "white"), id = TRUE, just = c("center", "top"), top = 0.85, align = c("center", "left", "right"), gp = NULL, FUN = NULL, height = NULL, width = NULL) edge_simple(obj, digits = 3, abbreviate = FALSE, justmin = Inf, just = c("alternate", "increasing", "decreasing", "equal"), fill = "white") node_boxplot(obj, col = "black", fill = "lightgray", bg = "white", width = 0.5, yscale = NULL, ylines = 3, cex = 0.5, id = TRUE, mainlab = NULL, gp = gpar()) node_barplot(obj, col = "black", fill = NULL, bg = "white", beside = NULL, ymax = NULL, ylines = NULL, widths = 1, gap = NULL, reverse = NULL, rot = 0, just = c("center", "top"), id = TRUE, mainlab = NULL, text = c("none", "horizontal", "vertical"), gp = gpar()) node_surv(obj, col = "black", bg = "white", yscale = c(0, 1), ylines = 2, id = TRUE, mainlab = NULL, gp = gpar(), \dots) node_ecdf(obj, col = "black", bg = "white", ylines = 2, id = TRUE, mainlab = NULL, gp = gpar(), \dots) node_bivplot(mobobj, which = NULL, id = TRUE, pop = TRUE, pointcol = "black", pointcex = 0.5, boxcol = "black", boxwidth = 0.5, boxfill = "lightgray", bg = "white", fitmean = TRUE, linecol = "red", cdplot = FALSE, fivenum = TRUE, breaks = NULL, ylines = NULL, xlab = FALSE, ylab = FALSE, margins = rep(1.5, 4), mainlab = NULL, \dots) node_mvar(obj, which = NULL, id = TRUE, pop = TRUE, ylines = NULL, mainlab = NULL, varlab = TRUE, bg = "white", ...) } \arguments{ \item{obj}{ an object of class \code{party}.} \item{digits}{ integer, used for formating numbers. } \item{abbreviate}{ logical indicating whether strings should be abbreviated. } \item{col, pointcol, boxcol, linecol}{ a color for points and lines. } \item{fill, boxfill, bg}{ a color to filling rectangles and backgrounds. } \item{id}{ logical. Should node IDs be plotted?} \item{pval}{ logical. Should node p values be plotted (if they are available)?} \item{just}{justification of terminal panel viewport (\code{node_terminal}), or labels (\code{edge_simple}, \code{node_barplot}).} \item{justmin}{minimum average edge label length to employ justification via \code{just} in \code{edge_panel}, otherwise \code{just = "equal"} is used. Thus, by default \code{"equal"} justification is always used but other justifications could be employed for finite \code{justmin}.} \item{top}{in case of top justification, the npc coordinate at which the viewport is justified.} \item{align}{alignment of text within terminal panel viewport.} \item{ylines}{ number of lines for spaces in y-direction. } \item{widths}{ widths in barplots. } \item{boxwidth}{ width in boxplots (called \code{width} in \code{node_boxplot}). } \item{gap}{ gap between bars in a barplot (\code{node_barplot}). } \item{yscale}{ limits in y-direction} \item{ymax}{ upper limit in y-direction} \item{cex, pointcex}{character extension of points in scatter plots.} \item{beside}{ logical indicating if barplots should be side by side or stacked. } \item{reverse}{logical indicating whether the order of levels should be reversed for barplots. } \item{rot}{ arguments passed to \code{\link[grid]{grid.text}} for the x-axis labeling. } \item{gp}{graphical parameters.} \item{FUN}{function for formatting the \code{info}, passed to \code{\link{formatinfo_node}}.} \item{height, width}{ numeric, number of lines/columns for printing text. } \item{mobobj}{an object of class \code{modelparty} as computed by \code{\link{mob}}.} \item{which}{numeric or character. Optional selection of subset of regressor variables. By default one panel for each regressor variable is drawn.} \item{pop}{logical. Should the viewports in the individual nodes be popped after drawing?} \item{fitmean}{logical. Should the fitted mean function be visualized?} \item{cdplot}{logical. Should a CD plot (or a spineplot) be drawn when the response variable is categorical?} \item{fivenum}{logical. Should the five-number summary be used for splitting the x-axis in spineplots?} \item{breaks}{numeric. Optional numeric vector with breaks for the x-axis in splineplots.} \item{xlab, ylab}{character. Optional annotation for x-axis and y-axis.} \item{margins}{numeric. Margins around drawing area in viewport.} \item{mainlab}{character or function. An optional title for the plot. Either a character or a \code{function(id, nobs)}.} \item{varlab}{logical. Should the individual variable labels be attached to the \code{mainlab} for multivariate responses?} \item{text}{logical or character. Should percentage labels be drawn for each bar? The default is \code{"none"} or equivalently \code{FALSE}. Can be set to \code{TRUE} (or \code{"horizontal"}) or alternatively \code{"vertical"}.} \item{\dots}{ additional arguments passed to callies (for example to \code{\link[survival]{survfit}}).} } \details{ The \code{plot} methods for \code{party} and \code{constparty} objects provide an extensible framework for the visualization of binary regression trees. The user is allowed to specify panel functions for plotting terminal and inner nodes as well as the corresponding edges. The panel functions to be used should depend only on the node being visualized, however, for setting up an appropriate panel function, information from the whole tree is typically required. Hence, \pkg{party} adopts the framework of \code{grapcon_generator} (graphical appearance control) from the \pkg{vcd} package (Meyer, Zeileis and Hornik, 2005) and provides several panel-generating functions. For convenience, the panel-generating functions \code{node_inner} and \code{edge_simple} return panel functions to draw inner nodes and left and right edges. For drawing terminal nodes, the functions returned by the other panel functions can be used. The panel generating function \code{node_terminal} is a terse text-based representation of terminal nodes. Graphical representations of terminal nodes are available and depend on the kind of model and the measurement scale of the variables modeled. For univariate regressions (typically fitted by \code{}), \code{node_surv} returns a functions that plots Kaplan-Meier curves in each terminal node; \code{node_barplot}, \code{node_boxplot}, \code{node_hist}, \code{node_ecdf} and \code{node_density} can be used to plot bar plots, box plots, histograms, empirical cumulative distribution functions and estimated densities into the terminal nodes. For multivariate regressions (typically fitted by \code{mob}), \code{node_bivplot} returns a panel function that creates bivariate plots of the response against all regressors in the model. Depending on the scale of the variables involved, scatter plots, box plots, spinograms (or CD plots) and spine plots are created. For the latter two \code{\link[vcd]{spine}} and \code{\link[vcd]{cd_plot}} from the \pkg{vcd} package are re-used. For multivariate responses in \code{\link{ctree}}, the panel function \code{node_mvar} generates one plot for each response. } \references{ Meyer D, Zeileis A, Hornik K (2006). The Strucplot Framework: Visualizing Multi-Way Contingency Tables with vcd. \emph{Journal of Statistical Software}, \bold{17}(3), 1--48. \doi{10.18637/jss.v017.i03} } \keyword{hplot} partykit/man/prune.modelparty.Rd0000644000176200001440000000635314405111440016474 0ustar liggesusers\name{prune.modelparty} \alias{prune.modelparty} \alias{prune.lmtree} \title{Post-Prune \code{modelparty} Objects} \usage{ \method{prune}{modelparty}(tree, type = "AIC", ...) } \description{ Post-pruning of \code{modelparty} objects based on information criteria like AIC, BIC, or related user-defined criteria. } \arguments{ \item{tree}{object of class \code{modelparty}.} \item{type}{pruning type. Can be \code{"AIC"}, \code{"BIC"} or a user-defined function (details below).} \item{\dots}{additional arguments.} } \details{ In \code{\link{mob}}-based model trees, pre-pruning based on p-values is used by default and often no post-pruning is necessary in such trees. However, if pre-pruning is switched off (by using a large \code{alpha}) or does is not sufficient (e.g., possibly in large samples) the \code{prune} method can be used for subsequent post-pruning based on information criteria. The function \code{prune.modelparty} can be called directly but it is also registered as a method for the generic \code{\link[rpart]{prune}} function from the \pkg{rpart} package. Thus, if \pkg{rpart} is attached, \code{prune(tree, type = "AIC", ...)} also works (see examples below). To customize the post-pruning strategy, \code{type} can be set to a \code{function(objfun, df, nobs)} which either returns \code{TRUE} to signal that a current node can be pruned or \code{FALSE}. All supplied arguments are of length two: \code{objfun} is the sum of objective function values in the current node and its child nodes, respectively. \code{df} is the degrees of freedom in the current node and its child nodes, respectively. \code{nobs} is vector with the number of observations in the current node and the total number of observations in the dataset, respectively. For \code{"AIC"} and \code{"BIC"} \code{type} is transformed so that AIC or BIC are computed. However, this assumes that the \code{objfun} used in \code{tree} is actually the negative log-likelihood. The degrees of freedom assumed for a split can be set via the \code{dfsplit} argument in \code{\link{mob_control}} when computing the \code{tree} or manipulated later by changing the value of \code{tree$info$control$dfsplit}. } \value{ An object of class \code{modelparty} where the associated tree is either the same as the original or smaller. } \seealso{ \code{\link[rpart]{prune}}, \code{\link{lmtree}}, \code{\link{glmtree}}, \code{\link{mob}} } \examples{ set.seed(29) n <- 1000 d <- data.frame( x = runif(n), z = runif(n), z_noise = factor(sample(1:3, size = n, replace = TRUE)) ) d$y <- rnorm(n, mean = d$x * c(-1, 1)[(d$z > 0.7) + 1], sd = 3) ## glm versus lm / logLik versus sum of squared residuals fmla <- y ~ x | z + z_noise lm_big <- lmtree(formula = fmla, data = d, maxdepth = 3, alpha = 1) glm_big <- glmtree(formula = fmla, data = d, maxdepth = 3, alpha = 1) AIC(lm_big) AIC(glm_big) ## load rpart for prune() generic ## (otherwise: use prune.modelparty directly) if (require("rpart")) { ## pruning lm_aic <- prune(lm_big, type = "AIC") lm_bic <- prune(lm_big, type = "BIC") width(lm_big) width(lm_aic) width(lm_bic) glm_aic <- prune(glm_big, type = "AIC") glm_bic <- prune(glm_big, type = "BIC") width(glm_big) width(glm_aic) width(glm_bic) } } partykit/man/HuntingSpiders.Rd0000644000176200001440000000621314172230000016120 0ustar liggesusers\name{HuntingSpiders} \alias{HuntingSpiders} \title{Abundance of Hunting Spiders} \description{ Abundances for 12 species of hunting spiders along with environmental predictors, all rated on a 0--9 scale. } \usage{data("HuntingSpiders")} \format{ A data frame containing 28 observations on 18 variables (12 species abundances and 6 environmental predictors). \describe{ \item{arct.lute}{numeric. Abundance of species \emph{Arctosa lutetiana} (on a scale 0--9).} \item{pard.lugu}{numeric. Abundance of species \emph{Pardosa lugubris} (on a scale 0--9).} \item{zora.spin}{numeric. Abundance of species \emph{Zora spinimana} (on a scale 0--9).} \item{pard.nigr}{numeric. Abundance of species \emph{Pardosa nigriceps} (on a scale 0--9).} \item{pard.pull}{numeric. Abundance of species \emph{Pardosa pullata} (on a scale 0--9).} \item{aulo.albi}{numeric. Abundance of species \emph{Aulonia albimana} (on a scale 0--9).} \item{troc.terr}{numeric. Abundance of species \emph{Trochosa terricola} (on a scale 0--9).} \item{alop.cune}{numeric. Abundance of species \emph{Alopecosa cuneata} (on a scale 0--9).} \item{pard.mont}{numeric. Abundance of species \emph{Pardosa monticola} (on a scale 0--9).} \item{alop.acce}{numeric. Abundance of species \emph{Alopecosa accentuata} (on a scale 0--9).} \item{alop.fabr}{numeric. Abundance of species \emph{Alopecosa fabrilis} (on a scale 0--9).} \item{arct.peri}{numeric. Abundance of species \emph{Arctosa perita} (on a scale 0--9).} \item{water}{numeric. Environmental predictor on a scale 0--9.} \item{sand}{numeric. Environmental predictor on a scale 0--9.} \item{moss}{numeric. Environmental predictor on a scale 0--9.} \item{reft}{numeric. Environmental predictor on a scale 0--9.} \item{twigs}{numeric. Environmental predictor on a scale 0--9.} \item{herbs}{numeric. Environmental predictor on a scale 0--9.} } } \details{ The data were originally analyzed by Van der Aart and Smeenk-Enserink (1975). De'ath (2002) transformed all variables to the 0--9 scale and employed multivariate regression trees. } \source{ Package \pkg{mvpart} (currently archived, see \url{https://CRAN.R-project.org/package=mvpart}). } \references{ Van der Aart PJM, Smeenk-Enserink N (1975). Correlations between Distributions of Hunting Spiders (Lycosidae, Ctenidae) and Environmental Characteristics in a Dune Area. \emph{Netherlands Journal of Zoology}, \bold{25}, 1--45. De'ath G (2002). Multivariate Regression Trees: A New Technique for Modelling Species-Environment Relationships. \emph{Ecology}, \bold{83}(4), 1103--1117. } \examples{ ## load data data("HuntingSpiders", package = "partykit") ## fit multivariate tree for 12-dimensional species abundance ## (warnings by mvtnorm are suppressed) suppressWarnings(sptree <- ctree(arct.lute + pard.lugu + zora.spin + pard.nigr + pard.pull + aulo.albi + troc.terr + alop.cune + pard.mont + alop.acce + alop.fabr + arct.peri ~ herbs + reft + moss + sand + twigs + water, data = HuntingSpiders, teststat = "max", minsplit = 5)) plot(sptree, terminal_panel = node_barplot) } \keyword{datasets} partykit/man/WeatherPlay.Rd0000644000176200001440000000276414172230000015406 0ustar liggesusers\name{WeatherPlay} \alias{WeatherPlay} \title{Weather Conditions and Playing a Game} \description{ Artificial data set concerning the conditions suitable for playing some unspecified game. } \usage{data("WeatherPlay")} \format{ A data frame containing 14 observations on 5 variables. \describe{ \item{outlook}{factor.} \item{temperature}{numeric.} \item{humidity}{numeric.} \item{windy}{factor.} \item{play}{factor.} } } \source{ Table 1.3 in Witten and Frank (2011). } \references{ Witten IH, Frank E (2011). \emph{Data Mining: Practical Machine Learning Tools and Techniques}. 3rd Edition, Morgan Kaufmann, San Francisco. } \seealso{\code{\link{party}}, \code{\link{partynode}}, \code{\link{partysplit}}} \examples{ ## load weather data data("WeatherPlay", package = "partykit") WeatherPlay ## construct simple tree pn <- partynode(1L, split = partysplit(1L, index = 1:3), kids = list( partynode(2L, split = partysplit(3L, breaks = 75), kids = list( partynode(3L, info = "yes"), partynode(4L, info = "no"))), partynode(5L, info = "yes"), partynode(6L, split = partysplit(4L, index = 1:2), kids = list( partynode(7L, info = "yes"), partynode(8L, info = "no"))))) pn ## couple with data py <- party(pn, WeatherPlay) ## print/plot/predict print(py) plot(py) predict(py, newdata = WeatherPlay) ## customize printing print(py, terminal_panel = function(node) paste(": play=", info_node(node), sep = "")) } \keyword{datasets} partykit/man/partynode-methods.Rd0000644000176200001440000000763114172230000016625 0ustar liggesusers\name{partynode-methods} \alias{partynode-methods} \alias{is.partynode} \alias{as.partynode} \alias{as.partynode.partynode} \alias{as.partynode.list} \alias{as.list.partynode} \alias{length.partynode} \alias{[.partynode} \alias{[[.partynode} \alias{is.terminal} \alias{is.terminal.partynode} \alias{depth.partynode} \alias{width} \alias{width.partynode} \alias{print.partynode} \alias{nodeprune.partynode} \title{ Methods for Node Objects} \description{ Methods for computing on \code{partynode} objects. } \usage{ is.partynode(x) as.partynode(x, \dots) \method{as.partynode}{partynode}(x, from = NULL, recursive = TRUE, \dots) \method{as.partynode}{list}(x, \dots) \method{as.list}{partynode}(x, \dots) \method{length}{partynode}(x) \method{[}{partynode}(x, i, \dots) \method{[[}{partynode}(x, i, \dots) is.terminal(x, \dots) \method{is.terminal}{partynode}(x, \dots) \method{depth}{partynode}(x, root = FALSE, \dots) width(x, \dots) \method{width}{partynode}(x, \dots) \method{print}{partynode}(x, data = NULL, names = NULL, inner_panel = function(node) "", terminal_panel = function(node) " *", prefix = "", first = TRUE, digits = getOption("digits") - 2, \dots) \method{nodeprune}{partynode}(x, ids, ...) } \arguments{ \item{x}{ an object of class \code{partynode} or \code{list}.} \item{from}{ an integer giving the identifier of the root node.} \item{recursive}{ a logical, if \code{FALSE}, only the id of the root node is checked against \code{from}. If \code{TRUE}, the ids of all nodes are checked.} \item{i}{ an integer specifying the kid to extract.} \item{root}{ a logical. Should the root count be counted in \code{depth}? } \item{data}{ an optional \code{data.frame}.} \item{names}{ a vector of names for nodes.} \item{terminal_panel}{ a panel function for printing terminal nodes.} \item{inner_panel}{ a panel function for printing inner nodes.} \item{prefix}{ lines start with this symbol.} \item{first}{ a logical.} \item{digits}{ number of digits to be printed.} \item{ids}{ a vector of node ids to be pruned-off.} \item{\dots}{ additional arguments.} } \details{ \code{is.partynode} checks if the argument is a valid \code{partynode} object. \code{is.terminal} is \code{TRUE} for terminal nodes and \code{FALSE} for inner nodes. The subset methods return the \code{partynode} object corresponding to the \code{i}th kid. The \code{as.partynode} and \code{as.list} methods can be used to convert flat list structures into recursive \code{partynode} objects and vice versa. \code{as.partynode} applied to \code{partynode} objects renumbers the recursive nodes starting with root node identifier \code{from}. \code{length} gives the number of kid nodes of the root node, \code{depth} the depth of the tree and \code{width} the number of terminal nodes. } \examples{ ## a tree as flat list structure nodelist <- list( # root node list(id = 1L, split = partysplit(varid = 4L, breaks = 1.9), kids = 2:3), # V4 <= 1.9, terminal node list(id = 2L), # V4 > 1.9 list(id = 3L, split = partysplit(varid = 1L, breaks = 1.7), kids = c(4L, 7L)), # V1 <= 1.7 list(id = 4L, split = partysplit(varid = 4L, breaks = 4.8), kids = 5:6), # V4 <= 4.8, terminal node list(id = 5L), # V4 > 4.8, terminal node list(id = 6L), # V1 > 1.7, terminal node list(id = 7L) ) ## convert to a recursive structure node <- as.partynode(nodelist) ## print raw recursive structure without data print(node) ## print tree along with the associated iris data data("iris", package = "datasets") print(node, data = iris) ## print subtree print(node[2], data = iris) ## print subtree, with root node number one print(as.partynode(node[2], from = 1), data = iris) ## number of kids in root node length(node) ## depth of tree depth(node) ## number of terminal nodes width(node) ## convert back to flat structure as.list(node) } \keyword{tree} partykit/man/nodeapply.Rd0000644000176200001440000000551414172230000015150 0ustar liggesusers\name{nodeapply} \alias{nodeapply} \alias{nodeapply.party} \alias{nodeapply.partynode} \title{ Apply Functions Over Nodes } \description{ Returns a list of values obtained by applying a function to \code{party} or \code{partynode} objects. } \usage{ nodeapply(obj, ids = 1, FUN = NULL, \dots) \method{nodeapply}{partynode}(obj, ids = 1, FUN = NULL, \dots) \method{nodeapply}{party}(obj, ids = 1, FUN = NULL, by_node = TRUE, \dots) } \arguments{ \item{obj}{ an object of class \code{\link{partynode}} or \code{\link{party}}.} \item{ids}{ integer vector of node identifiers to apply over.} \item{FUN}{ a function to be applied to nodes. By default, the node itself is returned.} \item{by_node}{ a logical indicating if \code{FUN} is applied to subsets of \code{\link{party}} objects or \code{\link{partynode}} objects (default). } \item{\dots}{ additional arguments.} } \details{ Function \code{FUN} is applied to all nodes with node identifiers in \code{ids} for a \code{partynode} object. The method for \code{party} by default calls the \code{nodeapply} method on it's \code{node} slot. If \code{by_node} is \code{FALSE}, it is applied to a \code{party} object with root node \code{ids}. } \value{ A list of results of length \code{length(ids)}. } \examples{ ## a tree as flat list structure nodelist <- list( # root node list(id = 1L, split = partysplit(varid = 4L, breaks = 1.9), kids = 2:3), # V4 <= 1.9, terminal node list(id = 2L, info = "terminal A"), # V4 > 1.9 list(id = 3L, split = partysplit(varid = 5L, breaks = 1.7), kids = c(4L, 7L)), # V5 <= 1.7 list(id = 4L, split = partysplit(varid = 4L, breaks = 4.8), kids = 5:6), # V4 <= 4.8, terminal node list(id = 5L, info = "terminal B"), # V4 > 4.8, terminal node list(id = 6L, info = "terminal C"), # V5 > 1.7, terminal node list(id = 7L, info = "terminal D") ) ## convert to a recursive structure node <- as.partynode(nodelist) ## return root node nodeapply(node) ## return info slots of terminal nodes nodeapply(node, ids = nodeids(node, terminal = TRUE), FUN = function(x) info_node(x)) ## fit tree using rpart library("rpart") rp <- rpart(Kyphosis ~ Age + Number + Start, data = kyphosis) ## coerce to `constparty' rpk <- as.party(rp) ## extract nodeids nodeids(rpk) unlist(nodeapply(node_party(rpk), ids = nodeids(rpk), FUN = id_node)) unlist(nodeapply(rpk, ids = nodeids(rpk), FUN = id_node)) ## but root nodes of party objects always have id = 1 unlist(nodeapply(rpk, ids = nodeids(rpk), FUN = function(x) id_node(node_party(x)), by_node = FALSE)) } \keyword{tree} partykit/man/ctree.Rd0000644000176200001440000001727614172230000014267 0ustar liggesusers\name{ctree} \alias{ctree} \alias{sctest.constparty} \title{Conditional Inference Trees} \description{ Recursive partitioning for continuous, censored, ordered, nominal and multivariate response variables in a conditional inference framework. } \usage{ ctree(formula, data, subset, weights, na.action = na.pass, offset, cluster, control = ctree_control(\dots), ytrafo = NULL, converged = NULL, scores = NULL, doFit = TRUE, \dots) } \arguments{ \item{formula}{ a symbolic description of the model to be fit. } \item{data}{ a data frame containing the variables in the model. } \item{subset}{ an optional vector specifying a subset of observations to be used in the fitting process.} \item{weights}{ an optional vector of weights to be used in the fitting process. Only non-negative integer valued weights are allowed.} \item{offset}{ an optional vector of offset values.} \item{cluster}{ an optional factor indicating independent clusters. Highly experimental, use at your own risk.} \item{na.action}{a function which indicates what should happen when the data contain missing value.} \item{control}{a list with control parameters, see \code{\link{ctree_control}}.} \item{ytrafo}{an optional named list of functions to be applied to the response variable(s) before testing their association with the explanatory variables. Note that this transformation is only performed once for the root node and does not take weights into account. Alternatively, \code{ytrafo} can be a function of \code{data} and \code{weights}. In this case, the transformation is computed for every node with corresponding weights. This feature is experimental and the user interface likely to change.} \item{converged}{an optional function for checking user-defined criteria before splits are implemented. This is not to be used and very likely to change.} \item{scores}{an optional named list of scores to be attached to ordered factors.} \item{doFit}{a logical, if \code{FALSE}, the tree is not fitted.} \item{\dots}{arguments passed to \code{\link{ctree_control}}.} } \details{ Function \code{partykit::ctree} is a reimplementation of (most of) \code{party::ctree} employing the new \code{\link{party}} infrastructure of the \pkg{partykit} infrastructure. The vignette \code{vignette("ctree", package = "partykit")} explains internals of the different implementations. Conditional inference trees estimate a regression relationship by binary recursive partitioning in a conditional inference framework. Roughly, the algorithm works as follows: 1) Test the global null hypothesis of independence between any of the input variables and the response (which may be multivariate as well). Stop if this hypothesis cannot be rejected. Otherwise select the input variable with strongest association to the response. This association is measured by a p-value corresponding to a test for the partial null hypothesis of a single input variable and the response. 2) Implement a binary split in the selected input variable. 3) Recursively repeate steps 1) and 2). The implementation utilizes a unified framework for conditional inference, or permutation tests, developed by Strasser and Weber (1999). The stop criterion in step 1) is either based on multiplicity adjusted p-values (\code{testtype = "Bonferroni"} in \code{\link{ctree_control}}) or on the univariate p-values (\code{testtype = "Univariate"}). In both cases, the criterion is maximized, i.e., 1 - p-value is used. A split is implemented when the criterion exceeds the value given by \code{mincriterion} as specified in \code{\link{ctree_control}}. For example, when \code{mincriterion = 0.95}, the p-value must be smaller than $0.05$ in order to split this node. This statistical approach ensures that the right-sized tree is grown without additional (post-)pruning or cross-validation. The level of \code{mincriterion} can either be specified to be appropriate for the size of the data set (and \code{0.95} is typically appropriate for small to moderately-sized data sets) or could potentially be treated like a hyperparameter (see Section~3.4 in Hothorn, Hornik and Zeileis, 2006). The selection of the input variable to split in is based on the univariate p-values avoiding a variable selection bias towards input variables with many possible cutpoints. The test statistics in each of the nodes can be extracted with the \code{sctest} method. (Note that the generic is in the \pkg{strucchange} package so this either needs to be loaded or \code{sctest.constparty} has to be called directly.) In cases where splitting stops due to the sample size (e.g., \code{minsplit} or \code{minbucket} etc.), the test results may be empty. Predictions can be computed using \code{\link{predict}}, which returns predicted means, predicted classes or median predicted survival times and more information about the conditional distribution of the response, i.e., class probabilities or predicted Kaplan-Meier curves. For observations with zero weights, predictions are computed from the fitted tree when \code{newdata = NULL}. By default, the scores for each ordinal factor \code{x} are \code{1:length(x)}, this may be changed for variables in the formula using \code{scores = list(x = c(1, 5, 6))}, for example. For a general description of the methodology see Hothorn, Hornik and Zeileis (2006) and Hothorn, Hornik, van de Wiel and Zeileis (2006). } \value{ An object of class \code{\link{party}}. } \references{ Hothorn T, Hornik K, Van de Wiel MA, Zeileis A (2006). A Lego System for Conditional Inference. \emph{The American Statistician}, \bold{60}(3), 257--263. Hothorn T, Hornik K, Zeileis A (2006). Unbiased Recursive Partitioning: A Conditional Inference Framework. \emph{Journal of Computational and Graphical Statistics}, \bold{15}(3), 651--674. Hothorn T, Zeileis A (2015). partykit: A Modular Toolkit for Recursive Partytioning in R. \emph{Journal of Machine Learning Research}, \bold{16}, 3905--3909. Strasser H, Weber C (1999). On the Asymptotic Theory of Permutation Statistics. \emph{Mathematical Methods of Statistics}, \bold{8}, 220--250. } \examples{ ### regression airq <- subset(airquality, !is.na(Ozone)) airct <- ctree(Ozone ~ ., data = airq) airct plot(airct) mean((airq$Ozone - predict(airct))^2) ### classification irisct <- ctree(Species ~ .,data = iris) irisct plot(irisct) table(predict(irisct), iris$Species) ### estimated class probabilities, a list tr <- predict(irisct, newdata = iris[1:10,], type = "prob") ### survival analysis if (require("TH.data") && require("survival") && require("coin") && require("Formula")) { data("GBSG2", package = "TH.data") (GBSG2ct <- ctree(Surv(time, cens) ~ ., data = GBSG2)) predict(GBSG2ct, newdata = GBSG2[1:2,], type = "response") plot(GBSG2ct) ### with weight-dependent log-rank scores ### log-rank trafo for observations in this node only (= weights > 0) h <- function(y, x, start = NULL, weights, offset, estfun = TRUE, object = FALSE, ...) { if (is.null(weights)) weights <- rep(1, NROW(y)) s <- logrank_trafo(y[weights > 0,,drop = FALSE]) r <- rep(0, length(weights)) r[weights > 0] <- s list(estfun = matrix(as.double(r), ncol = 1), converged = TRUE) } ### very much the same tree (ctree(Surv(time, cens) ~ ., data = GBSG2, ytrafo = h)) } ### multivariate responses airct2 <- ctree(Ozone + Temp ~ ., data = airq) airct2 plot(airct2) } \keyword{tree} partykit/man/extree_fit.Rd0000644000176200001440000000313514172230000015310 0ustar liggesusers\name{extree_fit} \alias{extree_fit} %- Also NEED an '\alias' for EACH other topic documented here. \title{ Fit Extensible Trees. } \description{ Basic infrastructure for fitting extensible trees. } \usage{ extree_fit(data, trafo, converged, selectfun = ctrl$selectfun, splitfun = ctrl$splitfun, svselectfun = ctrl$svselectfun, svsplitfun = ctrl$svsplitfun, partyvars, subset, weights, ctrl, doFit = TRUE) } \arguments{ \item{data}{an object of class \code{extree_data}, see \code{\link{extree_data}}. } \item{trafo}{a function with arguments \code{subset}, \code{weights}, \code{info}, \code{estfun} and \code{object}. } \item{converged}{a function with arguments \code{subset}, \code{weights}. } \item{selectfun}{an optional function for selecting variables. } \item{splitfun}{an optional function for selecting splits. } \item{svselectfun}{an optional function for selecting surrogate variables. } \item{svsplitfun}{an optional function for selecting surrogate splits. } \item{partyvars}{a numeric vector assigning a weight to each partitioning variable (\code{z} in \code{\link{extree_data}}. } \item{subset}{a sorted integer vector describing a subset. } \item{weights}{an optional vector of weights. } \item{ctrl}{control arguments. } \item{doFit}{a logical indicating if the tree shall be grown (\code{TRUE}) or not \code{FALSE}. } } \details{ This internal functionality will be the basis of implementations of other tree algorithms in future versions. Currently, only \code{ctree} relies on this function. } \value{An object of class \code{partynode}.} \keyword{tree} partykit/man/partynode.Rd0000644000176200001440000001354114172230000015161 0ustar liggesusers\name{partynode} \alias{partynode} \alias{kidids_node} \alias{fitted_node} \alias{id_node} \alias{split_node} \alias{surrogates_node} \alias{kids_node} \alias{info_node} \alias{formatinfo_node} \title{ Inner and Terminal Nodes } \description{ A class for representing inner and terminal nodes in trees and functions for data partitioning. } \usage{ partynode(id, split = NULL, kids = NULL, surrogates = NULL, info = NULL) kidids_node(node, data, vmatch = 1:ncol(data), obs = NULL, perm = NULL) fitted_node(node, data, vmatch = 1:ncol(data), obs = 1:nrow(data), perm = NULL) id_node(node) split_node(node) surrogates_node(node) kids_node(node) info_node(node) formatinfo_node(node, FUN = NULL, default = "", prefix = NULL, \dots) } \arguments{ \item{id}{ integer, a unique identifier for a node. } \item{split}{ an object of class \code{\link{partysplit}}. } \item{kids}{ a list of \code{partynode} objects. } \item{surrogates}{ a list of \code{partysplit} objects.} \item{info}{ additional information. } \item{node}{ an object of class \code{partynode}.} \item{data}{ a \code{\link{list}} or \code{\link{data.frame}}.} \item{vmatch}{ a permutation of the variable numbers in \code{data}.} \item{obs}{ a logical or integer vector indicating a subset of the observations in \code{data}.} \item{perm}{ a vector of integers specifying the variables to be permuted prior before splitting (i.e., for computing permutation variable importances). The default \code{NULL} doesn't alter the data.} \item{FUN}{ function for formatting the \code{info}, for default see below.} \item{default}{ a character used if the \code{info} in \code{node} is \code{NULL}.} \item{prefix}{ an optional prefix to be added to the returned character. } \item{\dots}{ further arguments passed to \code{\link[utils]{capture.output}}.} } \details{ A node represents both inner and terminal nodes in a tree structure. Each node has a unique identifier \code{id}. A node consisting only of such an identifier (and possibly additional information in \code{info}) is a terminal node. Inner nodes consist of a primary split (an object of class \code{\link{partysplit}}) and at least two kids (daughter nodes). Kid nodes are objects of class \code{partynode} itself, so the tree structure is defined recursively. In addition, a list of \code{partysplit} objects offering surrogate splits can be supplied. Like \code{\link{partysplit}} objects, \code{partynode} objects aren't connected to the actual data. Function \code{kidids_node()} determines how the observations in \code{data[obs,]} are partitioned into the kid nodes and returns the number of the list element in list \code{kids} each observations belongs to (and not it's identifier). This is done by evaluating \code{split} (and possibly all surrogate splits) on \code{data} using \code{\link{kidids_split}}. Function \code{fitted_node()} performs all splits recursively and returns the identifier \code{id} of the terminal node each observation in \code{data[obs,]} belongs to. Arguments \code{vmatch}, \code{obs} and \code{perm} are passed to \code{\link{kidids_split}}. Function \code{formatinfo_node()} extracts the the \code{info} from \code{node} and formats it to a \code{character} vector using the following strategy: If \code{is.null(info)}, the \code{default} is returned. Otherwise, \code{FUN} is applied for formatting. The default function uses \code{as.character} for atomic objects and applies \code{\link[utils]{capture.output}} to \code{print(info)} for other objects. Optionally, a \code{prefix} can be added to the computed character string. All other functions are accessor functions for extracting information from objects of class \code{partynode}. } \value{ The constructor \code{partynode()} returns an object of class \code{partynode}: \item{id}{ a unique integer identifier for a node. } \item{split}{ an object of class \code{\link{partysplit}}. } \item{kids}{ a list of \code{partynode} objects. } \item{surrogates}{ a list of \code{\link{partysplit}} objects.} \item{info}{ additional information. } \code{kidids_split()} returns an integer vector describing the partition of the observations into kid nodes by their position in list \code{kids}. \code{fitted_node()} returns the node identifiers (\code{id}) of the terminal nodes each observation belongs to. } \references{ Hothorn T, Zeileis A (2015). partykit: A Modular Toolkit for Recursive Partytioning in R. \emph{Journal of Machine Learning Research}, \bold{16}, 3905--3909. } \examples{ data("iris", package = "datasets") ## a stump defined by a binary split in Sepal.Length stump <- partynode(id = 1L, split = partysplit(which(names(iris) == "Sepal.Length"), breaks = 5), kids = lapply(2:3, partynode)) ## textual representation print(stump, data = iris) ## list element number and node id of the two terminal nodes table(kidids_node(stump, iris), fitted_node(stump, data = iris)) ## assign terminal nodes with probability 0.5 ## to observations with missing `Sepal.Length' iris_NA <- iris iris_NA[sample(1:nrow(iris), 50), "Sepal.Length"] <- NA table(fitted_node(stump, data = iris_NA, obs = !complete.cases(iris_NA))) ## a stump defined by a primary split in `Sepal.Length' ## and a surrogate split in `Sepal.Width' which ## determines terminal nodes for observations with ## missing `Sepal.Length' stump <- partynode(id = 1L, split = partysplit(which(names(iris) == "Sepal.Length"), breaks = 5), kids = lapply(2:3, partynode), surrogates = list(partysplit( which(names(iris) == "Sepal.Width"), breaks = 3))) f <- fitted_node(stump, data = iris_NA, obs = !complete.cases(iris_NA)) tapply(iris_NA$Sepal.Width[!complete.cases(iris_NA)], f, range) } \keyword{tree} partykit/man/party-methods.Rd0000644000176200001440000000745314172230000015761 0ustar liggesusers\name{party-methods} \alias{party-methods} \alias{length.party} \alias{print.party} \alias{print.simpleparty} \alias{print.constparty} \alias{[.party} \alias{[[.party} \alias{depth.party} \alias{width.party} \alias{getCall.party} \alias{nodeprune} \alias{nodeprune.party} \title{ Methods for Party Objects } \description{ Methods for computing on \code{party} objects. } \usage{ \method{print}{party}(x, terminal_panel = function(node) formatinfo_node(node, default = "*", prefix = ": "), tp_args = list(), inner_panel = function(node) "", ip_args = list(), header_panel = function(party) "", footer_panel = function(party) "", digits = getOption("digits") - 2, \dots) \method{print}{simpleparty}(x, digits = getOption("digits") - 4, header = NULL, footer = TRUE, \dots) \method{print}{constparty}(x, FUN = NULL, digits = getOption("digits") - 4, header = NULL, footer = TRUE, \dots) \method{length}{party}(x) \method{[}{party}(x, i, \dots) \method{[[}{party}(x, i, \dots) \method{depth}{party}(x, root = FALSE, \dots) \method{width}{party}(x, \dots) \method{nodeprune}{party}(x, ids, ...) } \arguments{ \item{x}{ an object of class \code{\link{party}}.} \item{i}{ an integer specifying the root of the subtree to extract.} \item{terminal_panel}{ a panel function for printing terminal nodes.} \item{tp_args}{ a list containing arguments to \code{terminal_panel}.} \item{inner_panel}{ a panel function for printing inner nodes.} \item{ip_args}{ a list containing arguments to \code{inner_panel}.} \item{header_panel}{ a panel function for printing the header.} \item{footer_panel}{ a panel function for printing the footer.} \item{digits}{ number of digits to be printed.} \item{header}{ header to be printed.} \item{footer}{ footer to be printed.} \item{FUN}{ a function to be applied to nodes.} \item{root}{ a logical. Should the root count be counted in \code{depth}? } \item{ids}{ a vector of node ids (or their names) to be pruned-off.} \item{\dots}{ additional arguments.} } \details{ \code{length} gives the number of nodes in the tree (in contrast to the \code{length} method for \code{\link{partynode}} objects which returns the number of kid nodes in the root), \code{depth} the depth of the tree and \code{width} the number of terminal nodes. The subset methods extract subtrees and the \code{print} method generates a textual representation of the tree. \code{nodeprune} prunes-off nodes and makes sure that the node ids of the resulting tree are in pre-order starting with root node id 1. For \code{constparty} objects, the \code{fitted} slot is also changed. } \examples{ ## a tree as flat list structure nodelist <- list( # root node list(id = 1L, split = partysplit(varid = 4L, breaks = 1.9), kids = 2:3), # V4 <= 1.9, terminal node list(id = 2L), # V4 > 1.9 list(id = 3L, split = partysplit(varid = 5L, breaks = 1.7), kids = c(4L, 7L)), # V5 <= 1.7 list(id = 4L, split = partysplit(varid = 4L, breaks = 4.8), kids = 5:6), # V4 <= 4.8, terminal node list(id = 5L), # V4 > 4.8, terminal node list(id = 6L), # V5 > 1.7, terminal node list(id = 7L) ) ## convert to a recursive structure node <- as.partynode(nodelist) ## set up party object data("iris") tree <- party(node, data = iris, fitted = data.frame("(fitted)" = fitted_node(node, data = iris), check.names = FALSE)) names(tree) <- paste("Node", nodeids(tree), sep = " ") ## number of kids in root node length(tree) ## depth of tree depth(tree) ## number of terminal nodes width(tree) ## node number four tree["Node 4"] tree[["Node 4"]] } \keyword{tree} partykit/man/party-coercion.Rd0000644000176200001440000000400614172230000016106 0ustar liggesusers\name{party-coercion} \alias{party-coercion} \alias{as.party} \alias{as.party.rpart} \alias{as.party.Weka_tree} \alias{as.party.XMLNode} \alias{as.constparty} \alias{as.simpleparty} \alias{as.simpleparty.party} \alias{as.simpleparty.simpleparty} \alias{as.simpleparty.XMLNode} \alias{as.simpleparty.constparty} \alias{pmmlTreeModel} \title{Coercion Functions} \description{ Functions coercing various objects to objects of class party. } \usage{ as.party(obj, \dots) \method{as.party}{rpart}(obj, data = TRUE, \dots) \method{as.party}{Weka_tree}(obj, data = TRUE, \dots) \method{as.party}{XMLNode}(obj, \dots) pmmlTreeModel(file, \dots) as.constparty(obj, \dots) as.simpleparty(obj, \dots) \method{as.simpleparty}{party}(obj, \dots) \method{as.simpleparty}{simpleparty}(obj, \dots) \method{as.simpleparty}{constparty}(obj, \dots) \method{as.simpleparty}{XMLNode}(obj, \dots) } \arguments{ \item{obj}{ an object of class \code{\link[rpart]{rpart}}, \code{\link[RWeka:Weka_classifier_trees]{Weka_tree}}, \code{XMLnode} or objects inheriting from \code{party}.} \item{data}{logical. Should the model frame associated with the fitted \code{obj} be included in the \code{data} of the \code{party}?} \item{file}{ a file name of a XML file containing a PMML description of a tree.} \item{\dots}{ additional arguments.} } \details{ Trees fitted using functions \code{\link[rpart]{rpart}} or \code{\link[RWeka:Weka_classifier_trees]{J48}} are coerced to \code{\link{party}} objects. By default, objects of class \code{constparty} are returned. When information about the learning sample is available, \code{\link{party}} objects can be coerced to objects of class \code{constparty} or \code{simpleparty} (see \code{\link{party}} for details). } \value{ All methods return objects of class \code{\link{party}}. } \examples{ ## fit tree using rpart library("rpart") rp <- rpart(Kyphosis ~ Age + Number + Start, data = kyphosis) ## coerce to `constparty' as.party(rp) } \keyword{tree} partykit/man/party-plot.Rd0000644000176200001440000001076214172230000015271 0ustar liggesusers\name{party-plot} \alias{party-plot} \alias{plot.party} \alias{plot.constparty} \alias{plot.simpleparty} \title{ Visualization of Trees } \description{ \code{plot} method for \code{party} objects with extended facilities for plugging in panel functions. } \usage{ \method{plot}{party}(x, main = NULL, terminal_panel = node_terminal, tp_args = list(), inner_panel = node_inner, ip_args = list(), edge_panel = edge_simple, ep_args = list(), drop_terminal = FALSE, tnex = 1, newpage = TRUE, pop = TRUE, gp = gpar(), margins = NULL, \dots) \method{plot}{constparty}(x, main = NULL, terminal_panel = NULL, tp_args = list(), inner_panel = node_inner, ip_args = list(), edge_panel = edge_simple, ep_args = list(), type = c("extended", "simple"), drop_terminal = NULL, tnex = NULL, newpage = TRUE, pop = TRUE, gp = gpar(), \dots) \method{plot}{simpleparty}(x, digits = getOption("digits") - 4, tp_args = NULL, \dots) } \arguments{ \item{x}{ an object of class \code{party} or \code{constparty}.} \item{main}{ an optional title for the plot.} \item{type}{ a character specifying the complexity of the plot: \code{extended} tries to visualize the distribution of the response variable in each terminal node whereas \code{simple} only gives some summary information.} \item{terminal_panel}{ an optional panel function of the form \code{function(node)} plotting the terminal nodes. Alternatively, a panel generating function of class \code{"grapcon_generator"} that is called with arguments \code{x} and \code{tp_args} to set up a panel function. By default, an appropriate panel function is chosen depending on the scale of the dependent variable.} \item{tp_args}{ a list of arguments passed to \code{terminal_panel} if this is a \code{"grapcon_generator"} object.} \item{inner_panel}{ an optional panel function of the form \code{function(node)} plotting the inner nodes. Alternatively, a panel generating function of class \code{"grapcon_generator"} that is called with arguments \code{x} and \code{ip_args} to set up a panel function.} \item{ip_args}{ a list of arguments passed to \code{inner_panel} if this is a \code{"grapcon_generator"} object.} \item{edge_panel}{ an optional panel function of the form \code{function(split, ordered = FALSE, left = TRUE)} plotting the edges. Alternatively, a panel generating function of class \code{"grapcon_generator"} that is called with arguments \code{x} and \code{ip_args} to set up a panel function.} \item{ep_args}{ a list of arguments passed to \code{edge_panel} if this is a \code{"grapcon_generator"} object.} \item{drop_terminal}{ a logical indicating whether all terminal nodes should be plotted at the bottom.} \item{tnex}{a numeric value giving the terminal node extension in relation to the inner nodes.} \item{newpage}{ a logical indicating whether \code{grid.newpage()} should be called. } \item{pop}{ a logical whether the viewport tree should be popped before return. } \item{gp}{graphical parameters.} \item{margins}{numeric vector of margin sizes.} \item{digits}{number of digits to be printed.} \item{\dots}{ additional arguments passed to callies.} } \details{ This \code{plot} method for \code{party} objects provides an extensible framework for the visualization of binary regression trees. The user is allowed to specify panel functions for plotting terminal and inner nodes as well as the corresponding edges. Panel functions for plotting inner nodes, edges and terminal nodes are available for the most important cases and can serve as the basis for user-supplied extensions, see \code{\link{node_inner}}. More details on the ideas and concepts of panel-generating functions and \code{"grapcon_generator"} objects in general can be found in Meyer, Zeileis and Hornik (2005). } \references{ Meyer D, Zeileis A, Hornik K (2006). The Strucplot Framework: Visualizing Multi-Way Contingency Tables with vcd. \emph{Journal of Statistical Software}, \bold{17}(3), 1--48. \doi{10.18637/jss.v017.i03} } \seealso{\code{\link{node_inner}}, \code{\link{node_terminal}}, \code{\link{edge_simple}}, \code{\link{node_barplot}}, \code{\link{node_boxplot}}.} \keyword{hplot} partykit/man/party.Rd0000644000176200001440000001350614172230000014314 0ustar liggesusers\name{party} \alias{party} \alias{names.party} \alias{names<-.party} \alias{node_party} \alias{is.constparty} \alias{is.simpleparty} \alias{data_party} \alias{data_party.default} \title{ Recursive Partytioning } \description{ A class for representing decision trees and corresponding accessor functions. } \usage{ party(node, data, fitted = NULL, terms = NULL, names = NULL, info = NULL) \method{names}{party}(x) \method{names}{party}(x) <- value data_party(party, id = 1L) \method{data_party}{default}(party, id = 1L) node_party(party) is.constparty(party) is.simpleparty(party) } \arguments{ \item{node}{ an object of class \code{\link{partynode}}.} \item{data}{ a (potentially empty) \code{\link{data.frame}}.} \item{fitted}{ an optional \code{\link{data.frame}} with \code{nrow(data)} rows (only if \code{nrow(data) != 0} and containing at least the fitted terminal node identifiers as element \code{(fitted)}. In addition, weights may be contained as element \code{(weights)} and responses as \code{(response)}.} \item{terms}{ an optional \code{\link{terms}} object. } \item{names}{ an optional vector of names to be assigned to each node of \code{node}. } \item{info}{ additional information. } \item{x}{ an object of class \code{party}.} \item{party}{ an object of class \code{party}.} \item{value}{a character vector of up to the same length as \code{x}, or \code{NULL}.} \item{id}{ a node identifier.} } \details{ Objects of class \code{party} basically consist of a \code{\link{partynode}} object representing the tree structure in a recursive way and data. The \code{data} argument takes a \code{data.frame} which, however, might have zero columns. Optionally, a \code{data.frame} with at least one variable \code{(fitted)} containing the terminal node numbers of data used for fitting the tree may be specified along with a \code{\link{terms}} object or any additional (currently unstructured) information as \code{info}. Argument \code{names} defines names for all nodes in \code{node}. Method \code{names} can be used to extract or alter names for nodes. Function \code{node_party} returns the \code{node} element of a \code{party} object. Further methods for \code{party} objects are documented in \code{\link{party-methods}} and \code{\link{party-predict}}. Trees of various flavors can be coerced to \code{party}, see \code{\link{party-coercion}}. Two classes inherit from class \code{party} and impose additional assumptions on the structure of this object: Class \code{constparty} requires that the \code{fitted} slot contains a partitioning of the learning sample as a factor \code{("fitted")} and the response values of all observations in the learning sample as \code{("response")}. This structure is most flexible and allows for graphical display of the response values in terminal nodes as well as for computing predictions based on arbitrary summary statistics. Class \code{simpleparty} assumes that certain pre-computed information about the distribution of the response variable is contained in the \code{info} slot nodes. At the moment, no formal class is used to describe this information. } \value{ The constructor returns an object of class \code{party}: \item{node}{ an object of class \code{\link{partynode}}.} \item{data}{ a (potentially empty) \code{\link{data.frame}}.} \item{fitted}{ an optional \code{\link{data.frame}} with \code{nrow(data)} rows (only if \code{nrow(data) != 0} and containing at least the fitted terminal node identifiers as element \code{(fitted)}. In addition, weights may be contained as element \code{(weights)} and responses as \code{(response)}.} \item{terms}{ an optional \code{\link{terms}} object. } \item{names}{ an optional vector of names to be assigned to each node of \code{node}. } \item{info}{ additional information. } \code{names} can be used to set and retrieve names of nodes and \code{node_party} returns an object of class \code{\link{partynode}}. \code{data_party} returns a data frame with observations contained in node \code{id}. } \references{ Hothorn T, Zeileis A (2015). partykit: A Modular Toolkit for Recursive Partytioning in R. \emph{Journal of Machine Learning Research}, \bold{16}, 3905--3909. } \examples{ ### data ### ## artificial WeatherPlay data data("WeatherPlay", package = "partykit") str(WeatherPlay) ### splits ### ## split in overcast, humidity, and windy sp_o <- partysplit(1L, index = 1:3) sp_h <- partysplit(3L, breaks = 75) sp_w <- partysplit(4L, index = 1:2) ## query labels character_split(sp_o) ### nodes ### ## set up partynode structure pn <- partynode(1L, split = sp_o, kids = list( partynode(2L, split = sp_h, kids = list( partynode(3L, info = "yes"), partynode(4L, info = "no"))), partynode(5L, info = "yes"), partynode(6L, split = sp_w, kids = list( partynode(7L, info = "yes"), partynode(8L, info = "no"))))) pn ### tree ### ## party: associate recursive partynode structure with data py <- party(pn, WeatherPlay) py plot(py) ### variations ### ## tree stump n1 <- partynode(id = 1L, split = sp_o, kids = lapply(2L:4L, partynode)) print(n1, data = WeatherPlay) ## query fitted nodes and kids ids fitted_node(n1, data = WeatherPlay) kidids_node(n1, data = WeatherPlay) ## tree with full data sets t1 <- party(n1, data = WeatherPlay) ## tree with empty data set party(n1, data = WeatherPlay[0, ]) ## constant-fit tree t2 <- party(n1, data = WeatherPlay, fitted = data.frame( "(fitted)" = fitted_node(n1, data = WeatherPlay), "(response)" = WeatherPlay$play, check.names = FALSE), terms = terms(play ~ ., data = WeatherPlay), ) t2 <- as.constparty(t2) t2 plot(t2) } \keyword{tree} partykit/man/cforest.Rd0000644000176200001440000003403614470622331014640 0ustar liggesusers\name{cforest} \alias{cforest} \alias{gettree} \alias{gettree.cforest} \alias{predict.cforest} \encoding{latin1} \title{Conditional Random Forests} \description{ An implementation of the random forest and bagging ensemble algorithms utilizing conditional inference trees as base learners. } \usage{ cforest(formula, data, weights, subset, offset, cluster, strata, na.action = na.pass, control = ctree_control(teststat = "quad", testtype = "Univ", mincriterion = 0, saveinfo = FALSE, \dots), ytrafo = NULL, scores = NULL, ntree = 500L, perturb = list(replace = FALSE, fraction = 0.632), mtry = ceiling(sqrt(nvar)), applyfun = NULL, cores = NULL, trace = FALSE, \dots) \method{predict}{cforest}(object, newdata = NULL, type = c("response", "prob", "weights", "node"), OOB = FALSE, FUN = NULL, simplify = TRUE, scale = TRUE, \dots) \method{gettree}{cforest}(object, tree = 1L, \dots) } \arguments{ \item{formula}{ a symbolic description of the model to be fit. } \item{data}{ a data frame containing the variables in the model. } \item{subset}{ an optional vector specifying a subset of observations to be used in the fitting process.} \item{weights}{ an optional vector of weights to be used in the fitting process. Non-negative integer valued weights are allowed as well as non-negative real weights. Observations are sampled (with or without replacement) according to probabilities \code{weights / sum(weights)}. The fraction of observations to be sampled (without replacement) is computed based on the sum of the weights if all weights are integer-valued and based on the number of weights greater zero else. Alternatively, \code{weights} can be a double matrix defining case weights for all \code{ncol(weights)} trees in the forest directly. This requires more storage but gives the user more control.} \item{offset}{ an optional vector of offset values.} \item{cluster}{ an optional factor indicating independent clusters. Highly experimental, use at your own risk.} \item{strata}{ an optional factor for stratified sampling.} \item{na.action}{a function which indicates what should happen when the data contain missing value.} \item{control}{a list with control parameters, see \code{\link{ctree_control}}. The default values correspond to those of the default values used by \code{\link[party]{cforest}} from the \code{party} package. \code{saveinfo = FALSE} leads to less memory hungry representations of trees. Note that arguments \code{mtry}, \code{cores} and \code{applyfun} in \code{\link{ctree_control}} are ignored for \code{\link{cforest}}, because they are already set.} \item{ytrafo}{an optional named list of functions to be applied to the response variable(s) before testing their association with the explanatory variables. Note that this transformation is only performed once for the root node and does not take weights into account (which means, the forest bootstrap or subsetting is ignored, which is almost certainly not a good idea). Alternatively, \code{ytrafo} can be a function of \code{data} and \code{weights}. In this case, the transformation is computed for every node and the corresponding weights. This feature is experimental and the user interface likely to change.} \item{scores}{an optional named list of scores to be attached to ordered factors.} \item{ntree}{ Number of trees to grow for the forest.} \item{perturb}{ a list with arguments \code{replace} and \code{fraction} determining which type of resampling with \code{replace = TRUE} referring to the n-out-of-n bootstrap and \code{replace = FALSE} to sample splitting. \code{fraction} is the portion of observations to draw without replacement. Honesty (experimental): If \code{fraction} has two elements, the first fraction defines the portion of observations to be used for tree induction, the second fraction defines the portion of observations used for parameter estimation. The sum of both fractions can be smaller than one but most not exceed one. Details can be found in Section 2.4 of Wager and Athey (2018).} \item{mtry}{ number of input variables randomly sampled as candidates at each node for random forest like algorithms. Bagging, as special case of a random forest without random input variable sampling, can be performed by setting \code{mtry} either equal to \code{Inf} or manually equal to the number of input variables.} \item{applyfun}{an optional \code{\link[base]{lapply}}-style function with arguments \code{function(X, FUN, \dots)}. It is used for computing the variable selection criterion. The default is to use the basic \code{lapply} function unless the \code{cores} argument is specified (see below).} \item{cores}{numeric. If set to an integer the \code{applyfun} is set to \code{\link[parallel]{mclapply}} with the desired number of \code{cores}.} \item{trace}{a logical indicating if a progress bar shall be printed while the forest grows.} \item{object}{ An object as returned by \code{cforest}} \item{newdata}{ An optional data frame containing test data.} \item{type}{ a character string denoting the type of predicted value returned, ignored when argument \code{FUN} is given. For \code{"response"}, the mean of a numeric response, the predicted class for a categorical response or the median survival time for a censored response is returned. For \code{"prob"} the matrix of conditional class probabilities (\code{simplify = TRUE}) or a list with the conditional class probabilities for each observation (\code{simplify = FALSE}) is returned for a categorical response. For numeric and censored responses, a list with the empirical cumulative distribution functions and empirical survivor functions (Kaplan-Meier estimate) is returned when \code{type = "prob"}. \code{"weights"} returns an integer vector of prediction weights. For \code{type = "where"}, a list of terminal node ids for each of the trees in the forest ist returned.} \item{OOB}{ a logical defining out-of-bag predictions (only if \code{newdata = NULL}). If the forest was fitted with honesty, this option is ignored.} \item{FUN}{ a function to compute summary statistics. Predictions for each node have to be computed based on arguments \code{(y, w)} where \code{y} is the response and \code{w} are case weights.} \item{simplify}{ a logical indicating whether the resulting list of predictions should be converted to a suitable vector or matrix (if possible).} \item{scale}{a logical indicating scaling of the nearest neighbor weights by the sum of weights in the corresponding terminal node of each tree. In the simple regression forest, predicting the conditional mean by nearest neighbor weights will be equivalent to (but slower!) the aggregation of means.} \item{tree}{ an integer, the number of the tree to extract from the forest.} \item{\dots}{ additional arguments. } } \details{ This implementation of the random forest (and bagging) algorithm differs from the reference implementation in \code{\link[randomForest]{randomForest}} with respect to the base learners used and the aggregation scheme applied. Conditional inference trees, see \code{\link{ctree}}, are fitted to each of the \code{ntree} perturbed samples of the learning sample. Most of the hyper parameters in \code{\link{ctree_control}} regulate the construction of the conditional inference trees. Hyper parameters you might want to change are: 1. The number of randomly preselected variables \code{mtry}, which is fixed to the square root of the number of input variables. 2. The number of trees \code{ntree}. Use more trees if you have more variables. 3. The depth of the trees, regulated by \code{mincriterion}. Usually unstopped and unpruned trees are used in random forests. To grow large trees, set \code{mincriterion} to a small value. The aggregation scheme works by averaging observation weights extracted from each of the \code{ntree} trees and NOT by averaging predictions directly as in \code{\link[randomForest]{randomForest}}. See Hothorn et al. (2004) and Meinshausen (2006) for a description. Predictions can be computed using \code{\link{predict}}. For observations with zero weights, predictions are computed from the fitted tree when \code{newdata = NULL}. Ensembles of conditional inference trees have not yet been extensively tested, so this routine is meant for the expert user only and its current state is rather experimental. However, there are some things available in \code{\link{cforest}} that can't be done with \code{\link[randomForest]{randomForest}}, for example fitting forests to censored response variables (see Hothorn et al., 2004, 2006a) or to multivariate and ordered responses. Using the rich \code{partykit} infrastructure allows additional functionality in \code{cforest}, such as parallel tree growing and probabilistic forecasting (for example via quantile regression forests). Also plotting of single trees from a forest is much easier now. Unlike \code{\link[party]{cforest}}, \code{cforest} is entirely written in R which makes customisation much easier at the price of longer computing times. However, trees can be grown in parallel with this R only implemention which renders speed less of an issue. Note that the default values are different from those used in package \code{party}, most importantly the default for mtry is now data-dependent. \code{predict(, type = "node")} replaces the \code{\link[party]{where}} function and \code{predict(, type = "prob")} the \code{\link[party]{treeresponse}} function. Moreover, when predictors vary in their scale of measurement of number of categories, variable selection and computation of variable importance is biased in favor of variables with many potential cutpoints in \code{\link[randomForest]{randomForest}}, while in \code{\link{cforest}} unbiased trees and an adequate resampling scheme are used by default. See Hothorn et al. (2006b) and Strobl et al. (2007) as well as Strobl et al. (2009). } \value{ An object of class \code{cforest}. } \references{ Breiman L (2001). Random Forests. \emph{Machine Learning}, \bold{45}(1), 5--32. Hothorn T, Lausen B, Benner A, Radespiel-Troeger M (2004). Bagging Survival Trees. \emph{Statistics in Medicine}, \bold{23}(1), 77--91. Hothorn T, Buehlmann P, Dudoit S, Molinaro A, Van der Laan MJ (2006a). Survival Ensembles. \emph{Biostatistics}, \bold{7}(3), 355--373. Hothorn T, Hornik K, Zeileis A (2006b). Unbiased Recursive Partitioning: A Conditional Inference Framework. \emph{Journal of Computational and Graphical Statistics}, \bold{15}(3), 651--674. Hothorn T, Zeileis A (2015). partykit: A Modular Toolkit for Recursive Partytioning in R. \emph{Journal of Machine Learning Research}, \bold{16}, 3905--3909. Meinshausen N (2006). Quantile Regression Forests. \emph{Journal of Machine Learning Research}, \bold{7}, 983--999. Strobl C, Boulesteix AL, Zeileis A, Hothorn T (2007). Bias in Random Forest Variable Importance Measures: Illustrations, Sources and a Solution. \emph{BMC Bioinformatics}, \bold{8}, 25. \doi{10.1186/1471-2105-8-25} Strobl C, Malley J, Tutz G (2009). An Introduction to Recursive Partitioning: Rationale, Application, and Characteristics of Classification and Regression Trees, Bagging, and Random Forests. \emph{Psychological Methods}, \bold{14}(4), 323--348. Stefan Wager & Susan Athey (2018). Estimation and Inference of Heterogeneous Treatment Effects using Random Forests. \emph{Journal of the American Statistical Association}, \bold{113}(523), 1228--1242. \doi{10.1080/01621459.2017.1319839} } \examples{ ## basic example: conditional inference forest for cars data cf <- cforest(dist ~ speed, data = cars) ## prediction of fitted mean and visualization nd <- data.frame(speed = 4:25) nd$mean <- predict(cf, newdata = nd, type = "response") plot(dist ~ speed, data = cars) lines(mean ~ speed, data = nd) ## predict quantiles (aka quantile regression forest) ## Note that this works for integer-valued weight w ## Other weights require weighted quantiles, see for example ## Hmisc::wtd.quantile( myquantile <- function(y, w) quantile(rep(y, w), probs = c(0.1, 0.5, 0.9)) p <- predict(cf, newdata = nd, type = "response", FUN = myquantile) colnames(p) <- c("lower", "median", "upper") nd <- cbind(nd, p) ## visualization with conditional (on speed) prediction intervals plot(dist ~ speed, data = cars, type = "n") with(nd, polygon(c(speed, rev(speed)), c(lower, rev(upper)), col = "lightgray", border = "transparent")) points(dist ~ speed, data = cars) lines(mean ~ speed, data = nd, lwd = 1.5) lines(median ~ speed, data = nd, lty = 2, lwd = 1.5) legend("topleft", c("mean", "median", "10\% - 90\% quantile"), lwd = c(1.5, 1.5, 10), lty = c(1, 2, 1), col = c("black", "black", "lightgray"), bty = "n") \dontrun{ ### honest (i.e., out-of-bag) cross-classification of ### true vs. predicted classes data("mammoexp", package = "TH.data") table(mammoexp$ME, predict(cforest(ME ~ ., data = mammoexp, ntree = 50), OOB = TRUE, type = "response")) ### fit forest to censored response if (require("TH.data") && require("survival")) { data("GBSG2", package = "TH.data") bst <- cforest(Surv(time, cens) ~ ., data = GBSG2, ntree = 50) ### estimate conditional Kaplan-Meier curves print(predict(bst, newdata = GBSG2[1:2,], OOB = TRUE, type = "prob")) print(gettree(bst)) } } } \keyword{tree} partykit/man/nodeids.Rd0000644000176200001440000000442214172230000014577 0ustar liggesusers\name{nodeids} \alias{nodeids} \alias{nodeids.party} \alias{nodeids.partynode} \alias{get_paths} \title{ Extract Node Identifiers } \description{ Extract unique identifiers from inner and terminals nodes of a \code{partynode} object. } \usage{ nodeids(obj, \dots) \method{nodeids}{partynode}(obj, from = NULL, terminal = FALSE, \dots) \method{nodeids}{party}(obj, from = NULL, terminal = FALSE, \dots) get_paths(obj, i) } \arguments{ \item{obj}{ an object of class \code{\link{partynode}} or \code{\link{party}}.} \item{from}{ an integer specifying node to start from.} \item{terminal}{ logical specifying if only node identifiers of terminal nodes are returned. } \item{i}{a vector of node identifiers.} \item{\dots}{ additional arguments.} } \details{ The identifiers of each node are extracted from \code{nodeids}. \code{get_paths} returns the paths for extracting the corresponding nodes using list subsets. } \value{ A vector of node identifiers. } \examples{ ## a tree as flat list structure nodelist <- list( # root node list(id = 1L, split = partysplit(varid = 4L, breaks = 1.9), kids = 2:3), # V4 <= 1.9, terminal node list(id = 2L), # V4 > 1.9 list(id = 3L, split = partysplit(varid = 1L, breaks = 1.7), kids = c(4L, 7L)), # V1 <= 1.7 list(id = 4L, split = partysplit(varid = 4L, breaks = 4.8), kids = 5:6), # V4 <= 4.8, terminal node list(id = 5L), # V4 > 4.8, terminal node list(id = 6L), # V1 > 1.7, terminal node list(id = 7L) ) ## convert to a recursive structure node <- as.partynode(nodelist) ## set up party object data("iris") tree <- party(node, data = iris, fitted = data.frame("(fitted)" = fitted_node(node, data = iris), check.names = FALSE)) tree ### ids of all nodes nodeids(tree) ### ids of all terminal nodes nodeids(tree, terminal = TRUE) ### ids of terminal nodes in subtree with root [3] nodeids(tree, from = 3, terminal = TRUE) ### get paths and extract all terminal nodes tr <- unclass(node_party(tree)) lapply(get_paths(tree, nodeids(tree, terminal = TRUE)), function(path) tr[path]) } \keyword{tree} partykit/man/party-predict.Rd0000644000176200001440000001064714172230000015747 0ustar liggesusers\name{party-predict} \alias{party-predict} \alias{predict.party} \alias{predict_party} \alias{predict_party.default} \alias{predict_party.constparty} \alias{predict_party.simpleparty} \title{ Tree Predictions } \description{ Compute predictions from \code{party} objects. } \usage{ \method{predict}{party}(object, newdata = NULL, perm = NULL, \dots) predict_party(party, id, newdata = NULL, \dots) \method{predict_party}{default}(party, id, newdata = NULL, FUN = NULL, \dots) \method{predict_party}{constparty}(party, id, newdata = NULL, type = c("response", "prob", "quantile", "density", "node"), at = if (type == "quantile") c(0.1, 0.5, 0.9), FUN = NULL, simplify = TRUE, \dots) \method{predict_party}{simpleparty}(party, id, newdata = NULL, type = c("response", "prob", "node"), \dots) } \arguments{ \item{object}{ objects of class \code{\link{party}}. } \item{newdata}{ an optional data frame in which to look for variables with which to predict, if omitted, the fitted values are used.} \item{perm}{an optional character vector of variable names. Splits of nodes with a primary split in any of these variables will be permuted (after dealing with surrogates). Note that surrogate split in the \code{perm} variables will no be permuted.} \item{party}{ objects of class \code{\link{party}}. } \item{id}{ a vector of terminal node identifiers. } \item{type}{ a character string denoting the type of predicted value returned, ignored when argument \code{FUN} is given. For \code{"response"}, the mean of a numeric response, the predicted class for a categorical response or the median survival time for a censored response is returned. For \code{"prob"} the matrix of conditional class probabilities (\code{simplify = TRUE}) or a list with the conditional class probabilities for each observation (\code{simplify = FALSE}) is returned for a categorical response. For numeric and censored responses, a list with the empirical cumulative distribution functions and empirical survivor functions (Kaplan-Meier estimate) is returned when \code{type = "prob"}. \code{"node"} returns an integer vector of terminal node identifiers.} \item{FUN}{ a function to extract (\code{default} method) or compute (\code{constparty} method) summary statistics. For the \code{default} method, this is a function of a terminal node only, for the \code{constparty} method, predictions for each node have to be computed based on arguments \code{(y, w)} where \code{y} is the response and \code{w} are case weights.} \item{at}{ if the return value is a function (as the empirical cumulative distribution function or the empirical quantile function), this function is evaluated at values \code{at} and these numeric values are returned. If \code{at} is \code{NULL}, the functions themselves are returned in a list.} \item{simplify}{ a logical indicating whether the resulting list of predictions should be converted to a suitable vector or matrix (if possible).} \item{\dots}{ additional arguments. } } \details{ The \code{\link{predict}} method for \code{\link{party}} objects computes the identifiers of the predicted terminal nodes, either for new data in \code{newdata} or for the learning samples (only possible for objects of class \code{constparty}). These identifiers are delegated to the corresponding \code{predict_party} method which computes (via \code{FUN} for class \code{constparty}) or extracts (class \code{simpleparty}) the actual predictions. } \value{ A list of predictions, possibly simplified to a numeric vector, numeric matrix or factor. } \examples{ ## fit tree using rpart library("rpart") rp <- rpart(skips ~ Opening + Solder + Mask + PadType + Panel, data = solder, method = 'anova') ## coerce to `constparty' pr <- as.party(rp) ## mean predictions predict(pr, newdata = solder[c(3, 541, 640),]) ## ecdf predict(pr, newdata = solder[c(3, 541, 640),], type = "prob") ## terminal node identifiers predict(pr, newdata = solder[c(3, 541, 640),], type = "node") ## median predictions predict(pr, newdata = solder[c(3, 541, 640),], FUN = function(y, w = 1) median(y)) } \keyword{tree} partykit/man/partysplit.Rd0000644000176200001440000001460214172230000015366 0ustar liggesusers\name{partysplit} \alias{partysplit} \alias{kidids_split} \alias{character_split} \alias{varid_split} \alias{breaks_split} \alias{index_split} \alias{right_split} \alias{prob_split} \alias{info_split} \title{ Binary and Multiway Splits } \description{ A class for representing multiway splits and functions for computing on splits. } \usage{ partysplit(varid, breaks = NULL, index = NULL, right = TRUE, prob = NULL, info = NULL) kidids_split(split, data, vmatch = 1:length(data), obs = NULL) character_split(split, data = NULL, digits = getOption("digits") - 2) varid_split(split) breaks_split(split) index_split(split) right_split(split) prob_split(split) info_split(split) } \arguments{ \item{varid}{ an integer specifying the variable to split in, i.e., a column number in \code{data}. } \item{breaks}{ a numeric vector of split points. } \item{index}{ an integer vector containing a contiguous sequence from one to the number of kid nodes. May contain \code{NA}s.} \item{right}{ a logical, indicating if the intervals defined by \code{breaks} should be closed on the right (and open on the left) or vice versa.} \item{prob}{ a numeric vector representing a probability distribution over kid nodes. } \item{info}{ additional information. } \item{split}{ an object of class \code{partysplit}.} \item{data}{ a \code{\link{list}} or \code{\link{data.frame}}.} \item{vmatch}{ a permutation of the variable numbers in \code{data}.} \item{obs}{ a logical or integer vector indicating a subset of the observations in \code{data}.} \item{digits}{ minimal number of significant digits.} } \details{ A split is basically a function that maps data, more specifically a partitioning variable, to a set of integers indicating the kid nodes to send observations to. Objects of class \code{partysplit} describe such a function and can be set-up via the \code{partysplit()} constructor. The variables are available in a \code{list} or \code{data.frame} (here called \code{data}) and \code{varid} specifies the partitioning variable, i.e., the variable or list element to split in. The constructor \code{partysplit()} doesn't have access to the actual data, i.e., doesn't \emph{estimate} splits. \code{kidids_split(split, data)} actually partitions the data \code{data[obs,varid_split(split)]} and assigns an integer (giving the kid node number) to each observation. If \code{vmatch} is given, the variable \code{vmatch[varid_split(split)]} is used. \code{character_split()} returns a character representation of its \code{split} argument. The remaining functions defined here are accessor functions for \code{partysplit} objects. The numeric vector \code{breaks} defines how the range of the partitioning variable (after coercing to a numeric via \code{\link{as.numeric}}) is divided into intervals (like in \code{\link{cut}}) and may be \code{NULL}. These intervals are represented by the numbers one to \code{length(breaks) + 1}. \code{index} assigns these \code{length(breaks) + 1} intervals to one of at least two kid nodes. Thus, \code{index} is a vector of integers where each element corresponds to one element in a list \code{kids} containing \code{\link{partynode}} objects, see \code{\link{partynode}} for details. The vector \code{index} may contain \code{NA}s, in that case, the corresponding values of the splitting variable are treated as missings (for example factor levels that are not present in the learning sample). Either \code{breaks} or \code{index} must be given. When \code{breaks} is \code{NULL}, it is assumed that the partitioning variable itself has storage mode \code{integer} (e.g., is a \code{\link{factor}}). \code{prob} defines a probability distribution over all kid nodes which is used for random splitting when a deterministic split isn't possible (due to missing values, for example). \code{info} takes arbitrary user-specified information. } \value{ The constructor \code{partysplit()} returns an object of class \code{partysplit}: \item{varid}{ an integer specifying the variable to split in, i.e., a column number in \code{data}, } \item{breaks}{ a numeric vector of split points, } \item{index}{ an integer vector containing a contiguous sequence from one to the number of kid nodes,} \item{right}{ a logical, indicating if the intervals defined by \code{breaks} should be closed on the right (and open on the left) or vice versa} \item{prob}{ a numeric vector representing a probability distribution over kid nodes, } \item{info}{ additional information. } \code{kidids_split()} returns an integer vector describing the partition of the observations into kid nodes. \code{character_split()} gives a character representation of the split and the remaining functions return the corresponding slots of \code{partysplit} objects. } \seealso{\code{\link{cut}}} \references{ Hothorn T, Zeileis A (2015). partykit: A Modular Toolkit for Recursive Partytioning in R. \emph{Journal of Machine Learning Research}, \bold{16}, 3905--3909. } \examples{ data("iris", package = "datasets") ## binary split in numeric variable `Sepal.Length' sl5 <- partysplit(which(names(iris) == "Sepal.Length"), breaks = 5) character_split(sl5, data = iris) table(kidids_split(sl5, data = iris), iris$Sepal.Length <= 5) ## multiway split in numeric variable `Sepal.Width', ## higher values go to the first kid, smallest values ## to the last kid sw23 <- partysplit(which(names(iris) == "Sepal.Width"), breaks = c(3, 3.5), index = 3:1) character_split(sw23, data = iris) table(kidids_split(sw23, data = iris), cut(iris$Sepal.Width, breaks = c(-Inf, 2, 3, Inf))) ## binary split in factor `Species' sp <- partysplit(which(names(iris) == "Species"), index = c(1L, 1L, 2L)) character_split(sp, data = iris) table(kidids_split(sp, data = iris), iris$Species) ## multiway split in factor `Species' sp <- partysplit(which(names(iris) == "Species"), index = 1:3) character_split(sp, data = iris) table(kidids_split(sp, data = iris), iris$Species) ## multiway split in numeric variable `Sepal.Width' sp <- partysplit(which(names(iris) == "Sepal.Width"), breaks = quantile(iris$Sepal.Width)) character_split(sp, data = iris) } \keyword{tree} partykit/man/lmtree.Rd0000644000176200001440000001156214172230000014445 0ustar liggesusers\name{lmtree} \alias{lmtree} \alias{plot.lmtree} \alias{predict.lmtree} \alias{print.lmtree} \title{Linear Model Trees} \description{ Model-based recursive partitioning based on least squares regression. } \usage{ lmtree(formula, data, subset, na.action, weights, offset, cluster, \dots) } \arguments{ \item{formula}{symbolic description of the model (of type \code{y ~ z1 + \dots + zl} or \code{y ~ x1 + \dots + xk | z1 + \dots + zl}; for details see below).} \item{data, subset, na.action}{arguments controlling formula processing via \code{\link[stats]{model.frame}}.} \item{weights}{optional numeric vector of weights. By default these are treated as case weights but the default can be changed in \code{\link{mob_control}}.} \item{offset}{optional numeric vector with an a priori known component to be included in the model \code{y ~ x1 + \dots + xk} (i.e., only when \code{x} variables are specified).} \item{cluster}{optional vector (typically numeric or factor) with a cluster ID to be employed for clustered covariances in the parameter stability tests.} \item{\dots}{optional control parameters passed to \code{\link{mob_control}}.} } \details{ Convenience interface for fitting MOBs (model-based recursive partitions) via the \code{\link{mob}} function. \code{lmtree} internally sets up a model \code{fit} function for \code{mob}, using either \code{\link[stats]{lm.fit}} or \code{\link[stats]{lm.wfit}} (depending on whether weights are used or not). Then \code{mob} is called using the residual sum of squares as the objective function. Compared to calling \code{mob} by hand, the implementation tries to avoid unnecessary computations while growing the tree. Also, it provides a more elaborate plotting function. } \value{ An object of class \code{lmtree} inheriting from \code{\link{modelparty}}. The \code{info} element of the overall \code{party} and the individual \code{node}s contain various informations about the models. } \references{ Zeileis A, Hothorn T, Hornik K (2008). Model-Based Recursive Partitioning. \emph{Journal of Computational and Graphical Statistics}, \bold{17}(2), 492--514. } \seealso{\code{\link{mob}}, \code{\link{mob_control}}, \code{\link{glmtree}}} \examples{ if(require("mlbench")) { ## Boston housing data data("BostonHousing", package = "mlbench") BostonHousing <- transform(BostonHousing, chas = factor(chas, levels = 0:1, labels = c("no", "yes")), rad = factor(rad, ordered = TRUE)) ## linear model tree bh_tree <- lmtree(medv ~ log(lstat) + I(rm^2) | zn + indus + chas + nox + age + dis + rad + tax + crim + b + ptratio, data = BostonHousing, minsize = 40) ## printing whole tree or individual nodes print(bh_tree) print(bh_tree, node = 7) ## plotting plot(bh_tree) plot(bh_tree, tp_args = list(which = "log(lstat)")) plot(bh_tree, terminal_panel = NULL) ## estimated parameters coef(bh_tree) coef(bh_tree, node = 9) summary(bh_tree, node = 9) ## various ways for computing the mean squared error (on the training data) mean((BostonHousing$medv - fitted(bh_tree))^2) mean(residuals(bh_tree)^2) deviance(bh_tree)/sum(weights(bh_tree)) deviance(bh_tree)/nobs(bh_tree) ## log-likelihood and information criteria logLik(bh_tree) AIC(bh_tree) BIC(bh_tree) ## (Note that this penalizes estimation of error variances, which ## were treated as nuisance parameters in the fitting process.) ## different types of predictions bh <- BostonHousing[c(1, 10, 50), ] predict(bh_tree, newdata = bh, type = "node") predict(bh_tree, newdata = bh, type = "response") predict(bh_tree, newdata = bh, type = function(object) summary(object)$r.squared) } if(require("AER")) { ## Demand for economics journals data data("Journals", package = "AER") Journals <- transform(Journals, age = 2000 - foundingyear, chars = charpp * pages) ## linear regression tree (OLS) j_tree <- lmtree(log(subs) ~ log(price/citations) | price + citations + age + chars + society, data = Journals, minsize = 10, verbose = TRUE) ## printing and plotting j_tree plot(j_tree) ## coefficients and summary coef(j_tree, node = 1:3) summary(j_tree, node = 1:3) } if(require("AER")) { ## Beauty and teaching ratings data data("TeachingRatings", package = "AER") ## linear regression (WLS) ## null model tr_null <- lm(eval ~ 1, data = TeachingRatings, weights = students, subset = credits == "more") ## main effects tr_lm <- lm(eval ~ beauty + gender + minority + native + tenure + division, data = TeachingRatings, weights = students, subset = credits == "more") ## tree tr_tree <- lmtree(eval ~ beauty | minority + age + gender + division + native + tenure, data = TeachingRatings, weights = students, subset = credits == "more", caseweights = FALSE) ## visualization plot(tr_tree) ## beauty slope coefficient coef(tr_lm)[2] coef(tr_tree)[, 2] ## R-squared 1 - deviance(tr_lm)/deviance(tr_null) 1 - deviance(tr_tree)/deviance(tr_null) } } \keyword{tree} partykit/man/varimp.Rd0000644000176200001440000001207414172230000014452 0ustar liggesusers\name{varimp} \alias{varimp} \alias{varimp.constparty} \alias{varimp.cforest} \title{ Variable Importance } \description{ Standard and conditional variable importance for `cforest', following the permutation principle of the `mean decrease in accuracy' importance in `randomForest'. } \usage{ \method{varimp}{constparty}(object, nperm = 1L, risk = c("loglik", "misclassification"), conditions = NULL, mincriterion = 0, ...) \method{varimp}{cforest}(object, nperm = 1L, OOB = TRUE, risk = c("loglik", "misclassification"), conditional = FALSE, threshold = .2, applyfun = NULL, cores = NULL, ...) } \arguments{ \item{object}{ an object as returned by \code{cforest}.} \item{mincriterion}{ the value of the test statistic or 1 - p-value that must be exceeded in order to include a split in the computation of the importance. The default \code{mincriterion = 0} guarantees that all splits are included.} \item{conditional}{ a logical determining whether unconditional or conditional computation of the importance is performed. } \item{threshold}{ the value of the test statistic or 1 - p-value of the association between the variable of interest and a covariate that must be exceeded inorder to include the covariate in the conditioning scheme for the variable of interest (only relevant if \code{conditional = TRUE}). } \item{nperm}{ the number of permutations performed.} \item{OOB}{ a logical determining whether the importance is computed from the out-of-bag sample or the learning sample (not suggested).} \item{risk}{ a character determining the risk to be evaluated.} \item{conditions}{ a list of conditions. } \item{applyfun}{an optional \code{\link[base]{lapply}}-style function with arguments \code{function(X, FUN, \dots)}. It is used for computing the variable importances for each tree. The default is to use the basic \code{lapply} function unless the \code{cores} argument is specified (see below). Extra care is needed to ensure correct seeds are used in the parallel runs (\code{RNGkind("L'Ecuyer-CMRG")} for example).} \item{cores}{numeric. If set to an integer the \code{applyfun} is set to \code{\link[parallel]{mclapply}} with the desired number of \code{cores}.} \item{\dots}{additional arguments, not used.} } \details{ NEEDS UPDATE Function \code{varimp} can be used to compute variable importance measures similar to those computed by \code{\link[randomForest]{importance}}. Besides the standard version, a conditional version is available, that adjusts for correlations between predictor variables. If \code{conditional = TRUE}, the importance of each variable is computed by permuting within a grid defined by the covariates that are associated (with 1 - p-value greater than \code{threshold}) to the variable of interest. The resulting variable importance score is conditional in the sense of beta coefficients in regression models, but represents the effect of a variable in both main effects and interactions. See Strobl et al. (2008) for details. Note, however, that all random forest results are subject to random variation. Thus, before interpreting the importance ranking, check whether the same ranking is achieved with a different random seed -- or otherwise increase the number of trees \code{ntree} in \code{\link{ctree_control}}. Note that in the presence of missings in the predictor variables the procedure described in Hapfelmeier et al. (2012) is performed. } \value{ A vector of `mean decrease in accuracy' importance scores. } \references{ Leo Breiman (2001). Random Forests. \emph{Machine Learning}, 45(1), 5--32. Alexander Hapfelmeier, Torsten Hothorn, Kurt Ulm, and Carolin Strobl (2014). A New Variable Importance Measure for Random Forests with Missing Data. \emph{Statistics and Computing}, \bold{24}(1), 21-34. \doi{10.1007/s11222-012-9349-1} Torsten Hothorn, Kurt Hornik, and Achim Zeileis (2006b). Unbiased Recursive Partitioning: A Conditional Inference Framework. \emph{Journal of Computational and Graphical Statistics}, \bold{15}(3), 651-674. \doi{10.1198/106186006X133933} Carolin Strobl, Anne-Laure Boulesteix, Thomas Kneib, Thomas Augustin, and Achim Zeileis (2008). Conditional Variable Importance for Random Forests. \emph{BMC Bioinformatics}, \bold{9}, 307. \doi{10.1186/1471-2105-8-25} } \examples{ set.seed(290875) data("readingSkills", package = "party") readingSkills.cf <- cforest(score ~ ., data = readingSkills, mtry = 2, ntree = 50) # standard importance varimp(readingSkills.cf) # conditional importance, may take a while... varimp(readingSkills.cf, conditional = TRUE) } \keyword{tree} partykit/DESCRIPTION0000644000176200001440000000426114723366102013636 0ustar liggesusersPackage: partykit Title: A Toolkit for Recursive Partytioning Date: 2024-12-02 Version: 1.2-23 Authors@R: c(person(given = "Torsten", family = "Hothorn", role = c("aut", "cre"), email = "Torsten.Hothorn@R-project.org", comment = c(ORCID = "0000-0001-8301-0471")), person(given = "Heidi", family = "Seibold", role = "ctb", email = "heidi@seibold.co", comment = c(ORCID = "0000-0002-8960-9642")), person(given = "Achim", family = "Zeileis", role = "aut", email = "Achim.Zeileis@R-project.org", comment = c(ORCID = "0000-0003-0918-3766"))) Description: A toolkit with infrastructure for representing, summarizing, and visualizing tree-structured regression and classification models. This unified infrastructure can be used for reading/coercing tree models from different sources ('rpart', 'RWeka', 'PMML') yielding objects that share functionality for print()/plot()/predict() methods. Furthermore, new and improved reimplementations of conditional inference trees (ctree()) and model-based recursive partitioning (mob()) from the 'party' package are provided based on the new infrastructure. A description of this package was published by Hothorn and Zeileis (2015) . Depends: R (>= 3.5.0), graphics, grid, libcoin (>= 1.0-0), mvtnorm Imports: grDevices, stats, utils, survival, Formula (>= 1.2-1), inum (>= 1.0-0), rpart (>= 4.1-11) Suggests: XML, pmml, rJava, sandwich, strucchange, vcd, AER, mlbench, TH.data (>= 1.0-3), coin (>= 1.1-0), RWeka (>= 0.4-19), datasets, parallel, psychotools (>= 0.3-0), psychotree, party (>= 1.3-0), randomForest LazyData: yes License: GPL-2 | GPL-3 URL: http://partykit.r-forge.r-project.org/partykit/ RoxygenNote: 6.1.1 NeedsCompilation: yes Packaged: 2024-12-02 15:26:36 UTC; hothorn Author: Torsten Hothorn [aut, cre] (), Heidi Seibold [ctb] (), Achim Zeileis [aut] () Maintainer: Torsten Hothorn Repository: CRAN Date/Publication: 2024-12-02 17:20:02 UTC