DHARMa/0000755000176200001440000000000014704441036011251 5ustar liggesusersDHARMa/tests/0000755000176200001440000000000014704246644012423 5ustar liggesusersDHARMa/tests/manualTests/0000755000176200001440000000000014665273541014725 5ustar liggesusersDHARMa/tests/manualTests/DHARMa-rhub.R0000644000176200001440000000056714665273541017012 0ustar liggesusers library(rhub) # validate_email(email = "florian.hartig@ur.de") rhub::platforms() pltfms = c("ubuntu-rchk") rhub::check(path = "./DHARMa", platform = pltfms) # submitting to winbuilder packageFile = "./DHARMa/" devtools::check_win_devel(packageFile, quiet = T) devtools::check_win_release(packageFile, quiet = T) devtools::check_win_oldrelease(packageFile, quiet = T) DHARMa/tests/manualTests/readme.txt0000644000176200001440000000014014665273541016716 0ustar liggesusersmanual tests moved to https://github.com/florianhartig/DHARMa/tree/master/Code/DHARMaManualTestsDHARMa/tests/testthat/0000755000176200001440000000000014704441036014253 5ustar liggesusersDHARMa/tests/testthat/testModelTypes.R0000644000176200001440000007236714703461527017410 0ustar liggesusers skip_on_cran() #skip_on_ci() set.seed(1234) doPlots = F # Test functions -------------------------------------------------------------- checkOutput <- function(simulationOutput){ # print(simulationOutput) if(any(simulationOutput$scaledResiduals < 0)) stop() if(any(simulationOutput$scaledResiduals > 1)) stop() if(any(is.na(simulationOutput$scaledResiduals))) stop() if(length(simulationOutput$scaledResiduals) != length(simulationOutput$observedResponse)) stop() if(length(simulationOutput$fittedPredictedResponse) != length(simulationOutput$observedResponse)) stop() } expectDispersion <- function(x, answer = T){ res <- simulateResiduals(x) if (answer) expect_lt(testDispersion(res, plot = doPlots)$p.value, 0.05) else expect_gt(testDispersion(res, plot = doPlots)$p.value, 0.05) } runEverything = function(fittedModel, testData, DHARMaData = T, phy = NULL, expectOverdispersion = F){ t = getObservedResponse(fittedModel) expect_true(is.vector(t)) expect_true(is.numeric(t)) x = getSimulations(fittedModel, 1) expect_true(is.matrix(x)) expect_true(ncol(x) == 1) x = getSimulations(fittedModel, 2) expect_true(is.numeric(x)) expect_true(is.matrix(x)) expect_true(ncol(x) == 2) x = getSimulations(fittedModel, 1, type = "refit") expect_true(is.data.frame(x)) x = getSimulations(fittedModel, 2, type = "refit") expect_true(is.data.frame(x)) fittedModel2 = getRefit(fittedModel,x[[1]]) # expect_false(any(getFixedEffects(fittedModel) - # getFixedEffects(fittedModel2) > 0.5)) # doesn't work for some models simulationOutput <- simulateResiduals(fittedModel = fittedModel, n = 200) checkOutput(simulationOutput) if(doPlots) plot(simulationOutput, quantreg = F) expect_gt(testOutliers(simulationOutput, plot = doPlots)$p.value, 0.001) expect_gt(testDispersion(simulationOutput, plot = doPlots)$p.value, 0.001) expect_gt(testUniformity(simulationOutput = simulationOutput, plot = doPlots)$p.value, 0.001) expect_gt(testZeroInflation(simulationOutput = simulationOutput, plot = doPlots)$p.value, 0.001) expect_gt(testTemporalAutocorrelation(simulationOutput = simulationOutput, time = testData$time, plot = doPlots)$p.value, 0.001) expect_gt(testSpatialAutocorrelation(simulationOutput = simulationOutput, x = testData$x, y = testData$y, plot = F)$p.value, 0.001) simulationOutput <- recalculateResiduals(simulationOutput, group = testData$group) expect_gt(testDispersion(simulationOutput, plot = doPlots)$p.value, 0.001) simulationOutput2 <- simulateResiduals(fittedModel = fittedModel, refit = T, n = 100) checkOutput(simulationOutput2) if(doPlots) plot(simulationOutput2, quantreg = F) # note that the pearson test is biased, therefore have to test greater #expect_gt(testDispersion(simulationOutput2, plot = doPlots, alternative = "greater")$p.value, 0.001) x = testDispersion(simulationOutput2, plot = doPlots) simulationOutput3 <- recalculateResiduals(simulationOutput2, group = testData$group) #expect_gt(testDispersion(simulationOutput3, plot = doPlots, alternative = "greater")$p.value, 0.001) x = testDispersion(simulationOutput3, plot = doPlots) } # testData -------------------------------------------------------------------- testData = list() testData$lm = createData(sampleSize = 200, fixedEffects = c(1,0), overdispersion = 0, randomEffectVariance = 0, family = gaussian()) testData$lmm = createData(sampleSize = 200, overdispersion = 0, randomEffectVariance = 0.5, family = gaussian()) testData$binomial_10 = createData(sampleSize = 200, randomEffectVariance = 0, family = binomial()) testData$binomial_yn = createData(sampleSize = 200, fixedEffects = c(1,0), overdispersion = 0, randomEffectVariance = 0, family = binomial(), factorResponse = T) testData$binomial_nk_matrix = createData(sampleSize = 200, overdispersion = 0, randomEffectVariance = 0, family = binomial(), binomialTrials = 20) testData$binomial_nk_weights = createData(sampleSize = 200, overdispersion = 0, randomEffectVariance = 0, family = binomial(), binomialTrials = 20) testData$binomial_nk_weights$prop = testData$binomial_nk_weights$observedResponse1 / 20 testData$binomial_nk_weights2 = createData(sampleSize = 200, overdispersion = 1, randomEffectVariance = 0, family = binomial(), binomialTrials = 20) testData$binomial_nk_weights2$prop = testData$binomial_nk_weights2$observedResponse1 / 20 testData$poisson1 = createData(sampleSize = 500, overdispersion = 0, randomEffectVariance = 0.000, family = poisson()) testData$poisson2 = createData(sampleSize = 200, overdispersion = 2, randomEffectVariance =0.000, family = poisson()) testData$poisson3 = createData(sampleSize = 500, overdispersion = 0.5, randomEffectVariance = 0.000, family = poisson()) testData$poisson_weights = createData(sampleSize = 200, overdispersion = 0.5, randomEffectVariance = 0.5, family = poisson()) testData$weights = rep(c(1,1.1), each = 100) testData$poisson_weights$weights = testData$weights # stats::lm ---------------------------------------------------------------------- test_that("lm works", { fittedModel <- lm(observedResponse ~ Environment1 + Environment2 , data = testData$lm) runEverything(fittedModel, testData = testData$lm) # lm weights are considered in simulate(), should not throw warning fittedModel <- lm(observedResponse ~ Environment1, data = testData$lm, weights = testData$weights) expect_s3_class(simulateResiduals(fittedModel), "DHARMa") } ) # stats::glm ---------------------------------------------------------------------- test_that("glm works", { fittedModel <- glm(observedResponse ~ Environment1, data = testData$lm) runEverything(fittedModel, testData = testData$lm) fittedModel <- glm(observedResponse ~ Environment1, family = "binomial", data = testData$binomial_10) runEverything(fittedModel, testData$binomial_10) fittedModel <- glm(observedResponse ~ Environment1 + Environment2, family = "binomial", data = testData$binomial_yn) runEverything(fittedModel, testData$binomial_yn) fittedModel <- glm(cbind(observedResponse1,observedResponse0) ~ Environment1, family = "binomial", data = testData$binomial_nk_matrix) runEverything(fittedModel, testData$binomial_nk_matrix) fittedModel <- glm(prop ~ Environment1, family = "binomial", data = testData$binomial_nk_weights, weights = rep(20,200)) runEverything(fittedModel, testData$binomial_nk_weights) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData$poisson1) runEverything(fittedModel, testData$poisson1) fittedModel2 <- glm(observedResponse ~ Environment1, family = "poisson", data = testData$poisson2) expectDispersion(fittedModel2) ### Weights checks # glm gaussian still the same fittedModel <- glm(observedResponse ~ Environment1, data = testData$lm, weights = testData$weights) expect_s3_class(simulateResiduals(fittedModel), "DHARMa") # glm behaves nice, throws a warning that simulate ignores weights for poisson fittedModel <- glm(observedResponse ~ Environment1, weights = testData$weights, data = testData$poisson2, family = "poisson") expect_warning(simulateResiduals(fittedModel)) } ) # MASS::glm.nb -------------------------------------------------------------- test_that("glm.nb works", { fittedModel <- MASS::glm.nb(observedResponse ~ Environment1, data = testData$poisson3) runEverything(fittedModel, testData$poisson3) # glm.nb does not warn, does not seem to simulate according to weights fittedModel <- MASS::glm.nb(observedResponse ~ Environment1, data = testData$poisson2, weights = testData$weights) expect_warning(simulateResiduals(fittedModel)) } ) # mgcv::gam -------------------------------------------------------------- test_that("mgcv gam works", { fittedModel <- mgcv::gam(observedResponse ~ Environment1, data = testData$lm) runEverything(fittedModel, testData$lm) fittedModel <- mgcv::gam(observedResponse ~ s(Environment1), data = testData$lm) runEverything(fittedModel, testData$lm) fittedModel <- mgcv::gam(observedResponse ~ Environment1, family = "binomial", data = testData$binomial_10) runEverything(fittedModel, testData$binomial_10) fittedModel <- mgcv::gam(observedResponse ~ Environment1, family = "binomial", data = testData$binomial_yn) runEverything(fittedModel, testData = testData$binomial_yn) fittedModel <- mgcv::gam(cbind(observedResponse1,observedResponse0) ~ Environment1, family = "binomial", data = testData$binomial_nk_matrix) runEverything(fittedModel, testData = testData$binomial_nk_matrix) fittedModel <- mgcv::gam(prop ~ Environment1, family = "binomial", data = testData$binomial_nk_weights, weights = rep(20,200)) runEverything(fittedModel, testData$binomial_nk_weights) fittedModel <- mgcv::gam(observedResponse ~ Environment1, family = "poisson", data = testData$poisson1) runEverything(fittedModel, testData$poisson1) fittedModel2 <- mgcv::gam(observedResponse ~ Environment1, family = "poisson", data = testData$poisson2) expectDispersion(fittedModel2) # mgcv::gam warns about weights fittedModel <- mgcv::gam(observedResponse ~ Environment1, weights = testData$weights, data = testData$poisson_weights, family = "poisson") expect_warning(simulateResiduals(fittedModel)) } ) # lme4::lmer -------------------------------------------------------------- test_that("lme4:lmer works", { fittedModel <- lme4::lmer(observedResponse ~ Environment1 + (1|group), data = testData$lmm) suppressMessages(runEverything(fittedModel, testData$lmm)) # lmer warns! fittedModel <- lme4::lmer(observedResponse ~ Environment1 + (1|group), data = testData$lm, weights = testData$weights) expect_warning(simulateResiduals(fittedModel)) } ) # lme4::glmer -------------------------------------------------------------- test_that("lme4:glmer works", { fittedModel <- lme4::glmer(observedResponse ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_10) suppressMessages(runEverything(fittedModel, testData$binomial_10)) fittedModel <- lme4::glmer(observedResponse ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_yn) suppressMessages( runEverything(fittedModel, testData$binomial_yn)) fittedModel <- lme4::glmer(cbind(observedResponse1,observedResponse0) ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_nk_matrix) suppressMessages(runEverything(fittedModel, testData$binomial_nk_matrix)) fittedModel <- lme4::glmer(prop ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_nk_weights, weights = rep(20,200)) suppressMessages(runEverything(fittedModel, testData$binomial_nk_weights)) fittedModel <- lme4::glmer(observedResponse ~ Environment1 + (1|group) + (1|ID), family = "poisson", data = testData$poisson1, control = lme4::glmerControl(optCtrl = list( maxfun = 20000))) suppressMessages(runEverything(fittedModel, testData$poisson1)) fittedModel2 <- lme4::glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData$poisson2, control = lme4::glmerControl(optCtrl = list( maxfun = 20000))) expectDispersion(fittedModel2) fittedModel <- lme4::glmer.nb(observedResponse ~ Environment1 + (1|group), data = testData$poisson1, control = lme4::glmerControl( optimizer = "bobyqa", optCtrl = list(maxfun=20000))) suppressMessages(runEverything(fittedModel, testData$poisson1)) # lme4::glmer warns, OK fittedModel <- lme4::glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData$poisson_weights, weights = testData$weights) expect_warning(simulateResiduals(fittedModel)) # lme4::glmer.nb warns fittedModel <- lme4::glmer.nb(observedResponse ~ Environment1 + (1|group), data = testData$poisson_weights, weights = testData$weights) expect_warning(simulateResiduals(fittedModel)) } ) # glmmTMB -------------------------------------------------------------- test_that("glmmTMB works", { fittedModel <- glmmTMB::glmmTMB(observedResponse ~ Environment1 + (1|group), data = testData$lmm) runEverything(fittedModel, testData$lmm) fittedModel <- glmmTMB::glmmTMB(observedResponse ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_10) runEverything(fittedModel, testData$binomial_10) fittedModel <- glmmTMB::glmmTMB(observedResponse ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_yn) runEverything(fittedModel, testData$binomial_yn) fittedModel <- glmmTMB::glmmTMB(cbind(observedResponse1, observedResponse0) ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_nk_matrix) runEverything(fittedModel, testData$binomial_nk_matrix) fittedModel <- glmmTMB::glmmTMB(cbind(observedResponse1, observedResponse0) ~ Environment1 + (1|group), family = glmmTMB::betabinomial(), data = testData$binomial_nk_matrix) runEverything(fittedModel, testData$binomial_nk_matrix) fittedModel <- glmmTMB::glmmTMB(prop ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_nk_weights, weights = rep(20,200)) runEverything(fittedModel, testData$binomial_nk_weights) fittedModel <- glmmTMB::glmmTMB(prop ~ Environment1 + (1|group), family = glmmTMB::betabinomial(), data = testData$binomial_nk_weights2, weights = rep(20,200)) runEverything(fittedModel, testData$binomial_nk_weights2) # glmmTMB does not warn, implemented warning in DHARMa fittedModel <- glmmTMB::glmmTMB(observedResponse ~ Environment1, family = "poisson", data = testData$poisson_weights, weights = testData$weights) expect_warning(simulateResiduals(fittedModel)) } ) # spaMM::HLfit -------------------------------------------------------------- test_that("spaMM::HLfit works", { fittedModel <- spaMM::HLfit(observedResponse ~ Environment1 + (1|group), data = testData$lm) runEverything(fittedModel, testData$lm) fittedModel <- spaMM::HLfit(observedResponse ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_10) runEverything(fittedModel, testData$binomial_10) fittedModel <- spaMM::HLfit(observedResponse ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_yn) runEverything(fittedModel, testData$binomial_yn) fittedModel <- spaMM::HLfit(cbind(observedResponse1,observedResponse0) ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_nk_matrix) runEverything(fittedModel, testData$binomial_nk_matrix) # spaMM doesn't support binomial k/n via weights expect_error(spaMM::HLfit(prop ~ Environment1 + (1|group), family = "binomial", data = testData$binomial_nk_weights, prior.weights = rep(20,200))) fittedModel <- spaMM::HLfit(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData$poisson1) runEverything(fittedModel, testData$poisson1) fittedModel <- spaMM::HLfit(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData$poisson2) expectDispersion(fittedModel) # spaMM does not warn, but seems to be simulating with correct (heteroskedastic) variance. # weights cannot be fit with poisson, because spaMM directly interpretes weights as variance # doesn't throw error / warning, but seems intended, see https://github.com/florianhartig/DHARMa/issues/175 expect_error(spaMM::HLfit(observedResponse ~ Environment1 + (1|group), family = negbin(1), data = testData$poisson_weights, prior.weights = weights)) expect_s3_class(simulateResiduals(fittedModel), "DHARMa") } ) # GLMMadaptive -------------------------------------------------------------- test_that("GLMMadaptive works", { # GLMMadaptive does not support gaussian expect_error(GLMMadaptive::mixed_model(fixed = observedResponse ~ Environment1, random = ~ 1 | group, data = testData$lmm, family = gaussian())) fittedModel <- GLMMadaptive::mixed_model(fixed = observedResponse ~ Environment1, random = ~ 1 | group, data = testData$binomial_10, family = binomial()) runEverything(fittedModel, testData$binomial_10) fittedModel <- GLMMadaptive::mixed_model(fixed = observedResponse ~ Environment1, random = ~ 1 | group, data = testData$binomial_yn, family = binomial()) runEverything(fittedModel, testData$binomial_yn) fittedModel <- GLMMadaptive::mixed_model(fixed = cbind(observedResponse1, observedResponse0) ~ Environment1, random = ~ 1 | group, data = testData$binomial_nk_matrix, family = binomial()) # Does not work yet #runEverything(fittedModel, testData) # GLMMadaptive doesn't support binomial k/n via weights #fittedModel <- GLMMadaptive::mixed_model(fixed = observedResponse ~ Environment1, random = ~ 1 | group, data = testData, family = binomial(), weights = rep(20,200)) # does not yet work # runEverything(fittedModel, testData) fittedModel <- GLMMadaptive::mixed_model(fixed = observedResponse ~ Environment1, random = ~ 1 | group, data = testData$poisson1, family = poisson()) runEverything(fittedModel, testData$poisson1) # GLMMadaptive requires weights according to groups weights = rep(c(1,1.1), each = 5) fittedModel <- GLMMadaptive::mixed_model(fixed = observedResponse ~ Environment1, random = ~ 1 | group, data = testData$poisson_weights, family = poisson(), weights = weights) expect_warning(simulateResiduals(fittedModel)) } ) rm(testData) # phylolm::pylolm/phyloglm ----------------------------------------------- # OBS: somehow, the base function update() in getSimulations.phylolm() and # getRefit.phylolm() searches for the objects in the global env, then the # test_that wasn't working. A workaround was to put the objects of the tree and # the dataset in the global env. test_that("phylolm works", { # LM set.seed(123456) tre1 <<- ape::rcoal(60) # global env taxa = sort(tre1$tip.label) b0 = 0; b1 = 1; x <- phylolm::rTrait(n = 1, phy = tre1, model = "BM", parameters = list(ancestral.state = 0, sigma2 = 10)) y <- b0 + b1*x + phylolm::rTrait(n = 1, phy = tre1, model = "lambda", parameters = list(ancestral.state = 0, sigma2 = 1, lambda = 0.5)) testData <<- data.frame(trait = y[taxa], predictor = x[taxa], x = runif(length(y)), y= runif(length(y))) fittedModel = phylolm::phylolm(trait ~ predictor, data = testData, phy = tre1, model = "lambda") runEverything(fittedModel, testData = testData, phy = tre1) }) test_that("phyloglm works", { #GLM set.seed(123456) tre <<- ape::rtree(50) # global env x = phylolm::rTrait(n = 1, phy = tre) X = cbind(rep(1, 50), x) y = phylolm::rbinTrait(n = 1, phy = tre, beta = c(-1,0.5), alpha = 1, X = X) testData <<- data.frame(trait = y, predictor = x, x = runif(length(y)), y = runif(length(y))) fittedModel = phylolm::phyloglm(trait ~ predictor, phy = tre, data = testData) runEverything(fittedModel, testData = testData, phy = tre) }) # isNA works? ------------------------------------------------------------------ # test_that("isNA works", # { # skip_on_cran() # # testData = createData(sampleSize = 200, overdispersion = 0.5, randomEffectVariance = 0.5, family = poisson(), hasNA = T) # # fittedModel <- lm(observedResponse ~ Environment1, data = testData) # expect_true(hasNA(fittedModel)) # # fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) # expect_true(hasNA(fittedModel)) # # fittedModel <- gam(observedResponse ~ Environment1, family = "poisson", data = testData) # expect_true(hasNA(fittedModel)) # # fittedModel <- lme4::glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) # expect_true(hasNA(fittedModel)) # # fittedModel <- lme4::glmer.nb(observedResponse ~ Environment1 + (1|group), data = testData) # expect_true(hasNA(fittedModel)) # # fittedModel <- glm.nb(observedResponse ~ Environment1, data = testData) # expect_true(hasNA(fittedModel)) # # fittedModel <- glmmTMB(observedResponse ~ Environment1, family = "poisson", data = testData) # expect_true(hasNA(fittedModel)) # # fittedModel <- HLfit(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) # expect_true(hasNA(fittedModel)) # # # now without NA # # testData = createData(sampleSize = 200, overdispersion = 0.5, randomEffectVariance = 0.5, family = poisson(), hasNA = F) # # fittedModel <- lm(observedResponse ~ Environment1, data = testData) # expect_false(hasNA(fittedModel)) # # fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) # expect_false(hasNA(fittedModel)) # # fittedModel <- gam(observedResponse ~ Environment1, family = "poisson", data = testData) # expect_false(hasNA(fittedModel)) # # fittedModel <- lme4::glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) # expect_false(hasNA(fittedModel)) # # fittedModel <- lme4::glmer.nb(observedResponse ~ Environment1 + (1|group), data = testData) # expect_false(hasNA(fittedModel)) # # fittedModel <- glm.nb(observedResponse ~ Environment1, data = testData) # expect_false(hasNA(fittedModel)) # # fittedModel <- glmmTMB(observedResponse ~ Environment1, family = "poisson", data = testData) # expect_false(hasNA(fittedModel)) # # fittedModel <- HLfit(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) # expect_false(hasNA(fittedModel)) # # # } # ) # DHARMa/tests/testthat/testSimulateResiduals.R0000644000176200001440000000126114703461527020743 0ustar liggesusers test_that("Rotation of residuals works", { testData = createData(family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) expect_no_error(res1 <- simulateResiduals(fittedModel)) expect_no_error(res2 <- simulateResiduals(fittedModel, rotation = diag(x = rep(1,100)))) expect_equal(res1$scaledResiduals, res2$scaledResiduals) expect_no_error(res3 <- recalculateResiduals(res1, group = testData$group)) expect_no_error(res4 <- recalculateResiduals(res2, group = testData$group, rotation = diag(x = rep(1,10)))) expect_equal(res3$scaledResiduals, res4$scaledResiduals) }) DHARMa/tests/testthat/testDharmaClass.R0000644000176200001440000001130714703461527017470 0ustar liggesusers test_that("createDHARMa works", { testData = createData(sampleSize = 200, family = poisson(), randomEffectVariance = 0, numGroups = 5) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) truth = testData$observedResponse pred = simulationOutput$fittedPredictedResponse simulatedResponse = simulationOutput$simulatedResponse sim = createDHARMa(simulatedResponse = simulatedResponse, observedResponse = truth, fittedPredictedResponse = pred, integerResponse = T) expect_match(class(sim), "DHARMa") expect_message(sim2 <- createDHARMa(simulatedResponse = simulatedResponse, observedResponse = truth), "No fitted predicted") expect_match(class(sim2), "DHARMa") }) test_that("recalcuateResiduals works", { testData = createData(sampleSize = 200, family = poisson(), numGroups = 20, randomEffectVariance = 1) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulationOutput = simulateResiduals(fittedModel) ##### only grouping ##### simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group) expect_true(length(residuals(simulationOutput2)) == simulationOutput2$nGroups) ##### only selection ##### #error expect_error(recalculateResiduals(simulationOutput, sel = 1)) #more than nObs in selection simulationOutput3 = recalculateResiduals(simulationOutput, sel = 1:400) expect_true(length(residuals(simulationOutput3))==simulationOutput3$nObs) #less than nObs in selection expect_true(length(residuals(recalculateResiduals(simulationOutput, sel = 1:2))) == 2) expect_true(length(residuals(recalculateResiduals(simulationOutput, sel = c(1,6,8)))) == 3) expect_true(length(residuals(recalculateResiduals( simulationOutput, sel = testData$group == 1))) == 10) ##### selection and grouping ##### # selection by different variables simulationOutput4 = recalculateResiduals(simulationOutput, sel = testData$group) expect_true(length(residuals(simulationOutput4)) == nlevels(simulationOutput4$sel)) #selecting = float - wrong dimensions (Sel has length 0) expect_true(length(residuals(recalculateResiduals( simulationOutput, sel = 1.0:20.0))) == 20) #just one group within the selection expect_error(recalculateResiduals(simulationOutput, group = testData$group, sel = 1.0:10.0)) expect_true(length(residuals(recalculateResiduals( simulationOutput, sel = 1.5 :10.7))) == 10) # not checking float # simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group, sel = 1.5:10.6) # not working, donĀ“t has to work # selecting = negative Values expect_error(length(residuals(recalculateResiduals( simulationOutput, sel = -10 : 5)))) expect_true(length(residuals(recalculateResiduals(simulationOutput, sel = -10:-5))) == 194) # checking NULL functions simulationOutput3 = recalculateResiduals(simulationOutput, sel = NULL) expect_true(length(residuals(simulationOutput3)) == simulationOutput3$nObs) simulationOutput3 = recalculateResiduals(simulationOutput, group = NULL, sel = NULL) expect_true(length(residuals(simulationOutput3)) == simulationOutput3$nObs) simulationOutput3 = recalculateResiduals(simulationOutput, group = NULL, sel = c(1:5,8,9), method = "PIT") simulationOutput3 = recalculateResiduals(simulationOutput, group = NULL, sel = c(1:5,8,9), method = "traditional") expect_true(length(residuals(simulationOutput3)) == length(simulationOutput3$sel)) # checking for expect_no_error(recalculateResiduals(simulationOutput, group = 1:simulationOutput$nObs, sel = simulationOutput$nObs/2:simulationOutput$nObs, method = "traditional")) expect_no_error(recalculateResiduals(simulationOutput, group = 1:simulationOutput$nObs, sel = simulationOutput$nObs/3.5:simulationOutput$nObs, method = "PIT")) }) DHARMa/tests/testthat/testTests.R0000644000176200001440000002402714703461527016413 0ustar liggesusers test_that("overdispersion recognized", { set.seed(123) testData = createData(sampleSize = 200, overdispersion = 3, pZeroInflation = 0.4, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) x = testUniformity(simulationOutput, plot = F) expect_true( x$p.value < 0.05) x = testOutliers(simulationOutput, plot = F) expect_true( x$p.value < 0.05) x = testDispersion(simulationOutput, alternative = "greater", plot = F) expect_true( x$p.value < 0.05) x = testZeroInflation(simulationOutput, alternative = "greater", plot = F) expect_true( x$p.value < 0.05) }) test_that("tests work", { set.seed(123) # creating test data testData = createData(sampleSize = 200, overdispersion = 0.5, pZeroInflation = 0, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) ###### Distribution tests ##### expect_snapshot(testUniformity(simulationOutput, plot = FALSE)) expect_snapshot(testUniformity(simulationOutput, plot = FALSE, alternative = "less")) expect_snapshot(testUniformity(simulationOutput, plot = FALSE, alternative = "greater")) ###### Dispersion tests ####### expect_snapshot(testDispersion(simulationOutput, plot = FALSE)) expect_snapshot(testDispersion(simulationOutput, plot = FALSE, alternative = "less")) expect_snapshot(testDispersion(simulationOutput, plot = FALSE, alternative = "greater")) expect_snapshot(testDispersion(simulationOutput, plot = FALSE, alternative = "two.sided")) expect_message(testOverdispersion(simulationOutput)) expect_message(testOverdispersionParametric(simulationOutput)) ###### Both together########### expect_snapshot(testResiduals(simulationOutput, plot = FALSE)) expect_message(testSimulatedResiduals(simulationOutput)) ###### zero-inflation ########## # testing zero inflation expect_snapshot(testZeroInflation(simulationOutput, plot = FALSE)) expect_snapshot(testZeroInflation(simulationOutput, plot = FALSE, alternative = "less")) # testing generic summaries # testing for number of 1s countOnes <- function(x) sum(x == 1) expect_snapshot(testGeneric(simulationOutput, summary = countOnes, plot = FALSE)) # 1-inflation expect_snapshot(testGeneric(simulationOutput, summary = countOnes, plot = FALSE, alternative = "less")) # 1-deficit # testing if mean prediction fits means <- function(x) mean(x) expect_snapshot(testGeneric(simulationOutput, summary = means, plot = FALSE)) # testing if mean sd fits spread <- function(x) sd(x) expect_snapshot(testGeneric(simulationOutput, summary = spread, plot = FALSE)) ################################################################## # grouped simulationOutput <- recalculateResiduals(simulationOutput, group = testData$group) ###### Distribution tests ##### expect_snapshot(testUniformity(simulationOutput, plot = FALSE)) expect_snapshot(testUniformity(simulationOutput, plot = FALSE, alternative = "less")) expect_snapshot(testUniformity(simulationOutput, plot = FALSE, alternative = "greater")) ###### Dispersion tests ####### expect_snapshot(testDispersion(simulationOutput, plot = FALSE)) expect_snapshot(testDispersion(simulationOutput, plot = FALSE, alternative = "less")) expect_snapshot(testDispersion(simulationOutput, plot = FALSE, alternative = "greater")) expect_snapshot(testDispersion(simulationOutput, plot = FALSE, alternative = "two.sided")) expect_message(testOverdispersion(simulationOutput)) expect_message(testOverdispersionParametric(simulationOutput)) ###### Both together########### expect_snapshot(testResiduals(simulationOutput, plot = FALSE)) expect_message(testSimulatedResiduals(simulationOutput)) ###### zero-inflation ########## # testing zero inflation expect_snapshot(testZeroInflation(simulationOutput, plot = FALSE)) expect_snapshot(testZeroInflation(simulationOutput, plot = FALSE, alternative = "less")) # testing generic summaries # testing for number of 1s countOnes <- function(x) sum(x == 1) expect_snapshot(testGeneric(simulationOutput, summary = countOnes, plot = FALSE)) # 1-inflation expect_snapshot(testGeneric(simulationOutput, summary = countOnes, plot = FALSE, alternative = "less")) # 1-deficit # testing if mean prediction fits means <- function(x) mean(x) expect_snapshot(testGeneric(simulationOutput, summary = means, plot = FALSE)) # testing if mean sd fits spread <- function(x) sd(x) expect_snapshot(testGeneric(simulationOutput, summary = spread, plot = FALSE)) ###### Refited ############## # if model is refitted, a different test will be called simulationOutput <- simulateResiduals(fittedModel = fittedModel, refit = T) expect_snapshot(testDispersion(simulationOutput, plot = FALSE)) }) ###### Correlation tests ##### test_that("correlation tests work", { set.seed(123) testData = createData(sampleSize = 200, overdispersion = 0.5, pZeroInflation = 0, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # grouped simulationOutputGrouped <- recalculateResiduals(simulationOutput, group = testData$group) ###### testSpatialAutocorrelation ##### # Standard use expect_snapshot(testSpatialAutocorrelation(simulationOutput, x = testData$x, y = testData$y, plot = FALSE)) expect_snapshot(testSpatialAutocorrelation(simulationOutput, x = testData$x, y = testData$y, plot = FALSE, alternative = "two.sided")) # If x and y is not provided, random values will be created expect_error(testSpatialAutocorrelation(simulationOutput)) # Alternatively, one can provide a distance matrix dM = as.matrix(dist(cbind(testData$x, testData$y))) expect_snapshot(testSpatialAutocorrelation(simulationOutput, distMat = dM, plot = FALSE)) expect_snapshot(testSpatialAutocorrelation(simulationOutput, distMat = dM, plot = FALSE, alternative = "two.sided")) # testting when x and y have different length # Error different length expect_snapshot(testSpatialAutocorrelation(simulationOutput, plot = FALSE, x = testData$x[1:10], y = testData$y[1:9]), error = TRUE) # x and y have equal length but unequal to simulationOutput expect_snapshot(testSpatialAutocorrelation(simulationOutput[1:10], plot = FALSE, x = testData$x[1:10], y = testData$y[1:10]), error=TRUE) # see Issue #190 'https://github.com/florianhartig/DHARMa/issues/190' # testing distance matrix and an extra x or y argument expect_snapshot(testSpatialAutocorrelation(simulationOutput, distMat = dM, plot = FALSE, x = testData$x)) expect_snapshot(testSpatialAutocorrelation(simulationOutput, distMat = dM, plot = FALSE, y = testData$y)) ###### testTemporalAutocorrelation ##### # Standard use expect_snapshot(testTemporalAutocorrelation(simulationOutput, plot = FALSE, time = testData$time)) expect_snapshot(testTemporalAutocorrelation(simulationOutput, plot = FALSE, time = testData$time, alternative = "greater")) # error if time is forgotten expect_error(testTemporalAutocorrelation(simulationOutput)) }) ### Test phylogenetic autocorrelation test_that("test phylogenetic autocorrelation", { set.seed(123) tre <<- ape::rcoal(60) b0 = 0; b1 = 1; x <- runif(length(tre$tip.label), 0,1) y <- b0 + b1*x + phylolm::rTrait(n = 1, phy = tre, model = "BM", parameters = list(ancestral.state = 0, sigma2 = 10)) dat <<- data.frame(trait = y, pred = x) fit = lm(trait ~ pred, data = dat) res = simulateResiduals(fit, plot = F) restest <- testPhylogeneticAutocorrelation(res, tree = tre) expect_snapshot(restest) expect_true(restest$p.value <= 0.05) fit2 = phylolm::phylolm(trait ~ pred, data = dat, phy = tre, model = "BM") res2 = simulateResiduals(fit2, plot = F, rotation = "estimated") restest2 <- testPhylogeneticAutocorrelation(res2, tree = tre) expect_snapshot(restest2) expect_true(restest2$p.value > 0.05) }) # Test Outliers test_that("testOutliers", { set.seed(123) testData = createData(sampleSize = 1000, overdispersion = 0, pZeroInflation = 0, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) expect_snapshot(testOutliers(simulationOutput, plot = F, margin = "lower")) expect_snapshot(testOutliers(simulationOutput, plot = F, alternative = "two.sided", margin = "lower")) expect_snapshot(testOutliers(simulationOutput, plot = F, margin = "upper")) }) DHARMa/tests/testthat/testHelper.R0000644000176200001440000000474714703461527016537 0ustar liggesusers test_that("ensureDHARMa", { set.seed(123) testData = createData(sampleSize = 200, overdispersion = 3, pZeroInflation = 0.4, randomEffectVariance = 0) pred = testData$Environment1 fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) expect_error(getSimulations(fittedModel, 1, type = "refdt")) simulationOutput <- simulateResiduals(fittedModel = fittedModel) expect_s3_class(DHARMa:::ensureDHARMa(simulationOutput), "DHARMa") expect_error(DHARMa:::ensureDHARMa(simulationOutput$scaledResiduals), "DHARMa") expect_error(DHARMa:::ensureDHARMa(fittedModel), "DHARMa") expect_s3_class(DHARMa:::ensureDHARMa(simulationOutput, convert = T), "DHARMa") expect_s3_class(DHARMa:::ensureDHARMa(simulationOutput$scaledResiduals, convert = T), "DHARMa") expect_s3_class(DHARMa:::ensureDHARMa(fittedModel, convert = T), "DHARMa") expect_error(DHARMa:::ensureDHARMa(matrix(rnorm(100), nrow = 4), convert = T)) expect_error(DHARMa:::ensureDHARMa(list(c = 1), convert = T)) expect_s3_class(DHARMa:::ensureDHARMa(fittedModel, convert = "Model"), "DHARMa") expect_error(DHARMa:::ensureDHARMa(simulationOutput$scaledResiduals, convert = "Model")) expect_error(DHARMa:::ensureDHARMa(matrix(rnorm(100))), "DHARMa") DHARMa:::ensurePredictor(simulationOutput, predictor = pred) DHARMa:::ensurePredictor(simulationOutput) DHARMa:::ensurePredictor(simulationOutput, predictor = testData$observedResponse) expect_error(DHARMa:::ensurePredictor(simulationOutput, predictor = c(1,2,3))) # testResiduals tests distribution, dispersion and outliers expect_error(testQuantiles(simulationOutput$scaledResiduals)) }) test_that("randomSeed", { runif(1) # testing the function in standard settings currentSeed = .Random.seed x = getRandomState(123) runif(1) x$restoreCurrent() expect_true(all(.Random.seed == currentSeed)) # if no seed was set in env, this will also be restored rm(.Random.seed, envir = globalenv()) # now, there is no random seed x = getRandomState(123) expect_true(exists(".Random.seed")) # TRUE runif(1) x$restoreCurrent() expect_false(exists(".Random.seed")) # False runif(1) # re-create a seed # with seed = false currentSeed = .Random.seed x = getRandomState(FALSE) runif(1) x$restoreCurrent() expect_false(all(.Random.seed == currentSeed)) # with seed = NULL currentSeed = .Random.seed x = getRandomState(NULL) runif(1) x$restoreCurrent() expect_true(all(.Random.seed == currentSeed)) }) DHARMa/tests/testthat/_snaps/0000755000176200001440000000000014703461527015544 5ustar liggesusersDHARMa/tests/testthat/_snaps/testTests.md0000644000176200001440000004054014703473302020065 0ustar liggesusers# tests work Code testUniformity(simulationOutput, plot = FALSE) Output Asymptotic one-sample Kolmogorov-Smirnov test data: simulationOutput$scaledResiduals D = 0.035577, p-value = 0.9619 alternative hypothesis: two-sided --- Code testUniformity(simulationOutput, plot = FALSE, alternative = "less") Output Asymptotic one-sample Kolmogorov-Smirnov test data: simulationOutput$scaledResiduals D^- = 0.035577, p-value = 0.6027 alternative hypothesis: the CDF of x lies below the null hypothesis --- Code testUniformity(simulationOutput, plot = FALSE, alternative = "greater") Output Asymptotic one-sample Kolmogorov-Smirnov test data: simulationOutput$scaledResiduals D^+ = 0.034418, p-value = 0.6226 alternative hypothesis: the CDF of x lies above the null hypothesis --- Code testDispersion(simulationOutput, plot = FALSE) Output DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 1.2578, p-value = 0.096 alternative hypothesis: two.sided --- Code testDispersion(simulationOutput, plot = FALSE, alternative = "less") Output DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 1.2578, p-value = 0.952 alternative hypothesis: less --- Code testDispersion(simulationOutput, plot = FALSE, alternative = "greater") Output DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 1.2578, p-value = 0.048 alternative hypothesis: greater --- Code testDispersion(simulationOutput, plot = FALSE, alternative = "two.sided") Output DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 1.2578, p-value = 0.096 alternative hypothesis: two.sided --- Code testResiduals(simulationOutput, plot = FALSE) Output $uniformity Asymptotic one-sample Kolmogorov-Smirnov test data: simulationOutput$scaledResiduals D = 0.035577, p-value = 0.9619 alternative hypothesis: two-sided $dispersion DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 1.2578, p-value = 0.096 alternative hypothesis: two.sided $outliers DHARMa bootstrapped outlier test data: simulationOutput outliers at both margin(s) = 1, observations = 200, p-value = 0.82 alternative hypothesis: two.sided percent confidence interval: 0.000000 0.012625 sample estimates: outlier frequency (expected: 0.0028 ) 0.005 --- Code testZeroInflation(simulationOutput, plot = FALSE) Output DHARMa zero-inflation test via comparison to expected zeros with simulation under H0 = fitted model data: simulationOutput ratioObsSim = 1.0565, p-value = 0.552 alternative hypothesis: two.sided --- Code testZeroInflation(simulationOutput, plot = FALSE, alternative = "less") Output DHARMa zero-inflation test via comparison to expected zeros with simulation under H0 = fitted model data: simulationOutput ratioObsSim = 1.0565, p-value = 0.784 alternative hypothesis: less --- Code testGeneric(simulationOutput, summary = countOnes, plot = FALSE) Output DHARMa generic simulation test data: simulationOutput ratioObsSim = 0.97457, p-value = 0.808 alternative hypothesis: two.sided --- Code testGeneric(simulationOutput, summary = countOnes, plot = FALSE, alternative = "less") Output DHARMa generic simulation test data: simulationOutput ratioObsSim = 0.97457, p-value = 0.404 alternative hypothesis: less --- Code testGeneric(simulationOutput, summary = means, plot = FALSE) Output DHARMa generic simulation test data: simulationOutput ratioObsSim = 1.0077, p-value = 0.944 alternative hypothesis: two.sided --- Code testGeneric(simulationOutput, summary = spread, plot = FALSE) Output DHARMa generic simulation test data: simulationOutput ratioObsSim = 1.0834, p-value = 0.208 alternative hypothesis: two.sided --- Code testUniformity(simulationOutput, plot = FALSE) Output Exact one-sample Kolmogorov-Smirnov test data: simulationOutput$scaledResiduals D = 0.22547, p-value = 0.613 alternative hypothesis: two-sided --- Code testUniformity(simulationOutput, plot = FALSE, alternative = "less") Output Exact one-sample Kolmogorov-Smirnov test data: simulationOutput$scaledResiduals D^- = 0.16279, p-value = 0.5338 alternative hypothesis: the CDF of x lies below the null hypothesis --- Code testUniformity(simulationOutput, plot = FALSE, alternative = "greater") Output Exact one-sample Kolmogorov-Smirnov test data: simulationOutput$scaledResiduals D^+ = 0.22547, p-value = 0.315 alternative hypothesis: the CDF of x lies above the null hypothesis --- Code testDispersion(simulationOutput, plot = FALSE) Output DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 2.1091, p-value = 0.048 alternative hypothesis: two.sided --- Code testDispersion(simulationOutput, plot = FALSE, alternative = "less") Output DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 2.1091, p-value = 0.976 alternative hypothesis: less --- Code testDispersion(simulationOutput, plot = FALSE, alternative = "greater") Output DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 2.1091, p-value = 0.024 alternative hypothesis: greater --- Code testDispersion(simulationOutput, plot = FALSE, alternative = "two.sided") Output DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 2.1091, p-value = 0.048 alternative hypothesis: two.sided --- Code testResiduals(simulationOutput, plot = FALSE) Output $uniformity Exact one-sample Kolmogorov-Smirnov test data: simulationOutput$scaledResiduals D = 0.22547, p-value = 0.613 alternative hypothesis: two-sided $dispersion DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated data: simulationOutput dispersion = 2.1091, p-value = 0.048 alternative hypothesis: two.sided $outliers DHARMa bootstrapped outlier test data: simulationOutput outliers at both margin(s) = 20, observations = 200, p-value = 0.1 alternative hypothesis: two.sided percent confidence interval: 0.0 0.1 sample estimates: outlier frequency (expected: 0.005 ) 0.1 --- Code testZeroInflation(simulationOutput, plot = FALSE) Output DHARMa zero-inflation test via comparison to expected zeros with simulation under H0 = fitted model data: simulationOutput ratioObsSim = NaN, p-value = 1 alternative hypothesis: two.sided --- Code testZeroInflation(simulationOutput, plot = FALSE, alternative = "less") Output DHARMa zero-inflation test via comparison to expected zeros with simulation under H0 = fitted model data: simulationOutput ratioObsSim = NaN, p-value = 1 alternative hypothesis: less --- Code testGeneric(simulationOutput, summary = countOnes, plot = FALSE) Output DHARMa generic simulation test data: simulationOutput ratioObsSim = NaN, p-value = 1 alternative hypothesis: two.sided --- Code testGeneric(simulationOutput, summary = countOnes, plot = FALSE, alternative = "less") Output DHARMa generic simulation test data: simulationOutput ratioObsSim = NaN, p-value = 1 alternative hypothesis: less --- Code testGeneric(simulationOutput, summary = means, plot = FALSE) Output DHARMa generic simulation test data: simulationOutput ratioObsSim = 1.0077, p-value = 0.944 alternative hypothesis: two.sided --- Code testGeneric(simulationOutput, summary = spread, plot = FALSE) Output DHARMa generic simulation test data: simulationOutput ratioObsSim = 1.4725, p-value = 0.04 alternative hypothesis: two.sided --- Code testDispersion(simulationOutput, plot = FALSE) Output DHARMa nonparametric dispersion test via mean deviance residual fitted vs. simulated-refitted data: simulationOutput dispersion = 1.1231, p-value = 0.248 alternative hypothesis: two.sided # correlation tests work Code testSpatialAutocorrelation(simulationOutput, x = testData$x, y = testData$y, plot = FALSE) Output DHARMa Moran's I test for distance-based autocorrelation data: simulationOutput observed = -0.0166319, expected = -0.0050251, sd = 0.0112750, p-value = 0.3033 alternative hypothesis: Distance-based autocorrelation --- Code testSpatialAutocorrelation(simulationOutput, x = testData$x, y = testData$y, plot = FALSE, alternative = "two.sided") Output DHARMa Moran's I test for distance-based autocorrelation data: simulationOutput observed = -0.0166319, expected = -0.0050251, sd = 0.0112750, p-value = 0.3033 alternative hypothesis: Distance-based autocorrelation --- Code testSpatialAutocorrelation(simulationOutput, distMat = dM, plot = FALSE) Output DHARMa Moran's I test for distance-based autocorrelation data: simulationOutput observed = -0.0166319, expected = -0.0050251, sd = 0.0112750, p-value = 0.3033 alternative hypothesis: Distance-based autocorrelation --- Code testSpatialAutocorrelation(simulationOutput, distMat = dM, plot = FALSE, alternative = "two.sided") Output DHARMa Moran's I test for distance-based autocorrelation data: simulationOutput observed = -0.0166319, expected = -0.0050251, sd = 0.0112750, p-value = 0.3033 alternative hypothesis: Distance-based autocorrelation --- Code testSpatialAutocorrelation(simulationOutput, plot = FALSE, x = testData$x[1:10], y = testData$y[1:9]) Condition Warning in `cbind()`: number of rows of result is not a multiple of vector length (arg 2) Error in `testSpatialAutocorrelation()`: ! Dimensions of x / y coordinates don't match the dimension of the residuals. --- Code testSpatialAutocorrelation(simulationOutput[1:10], plot = FALSE, x = testData$x[ 1:10], y = testData$y[1:10]) Condition Error in `ensureDHARMa()`: ! wrong argument to function, simulationOutput must be a DHARMa object or a numeric vector of quantile residuals! --- Code testSpatialAutocorrelation(simulationOutput, distMat = dM, plot = FALSE, x = testData$ x) Message Both coordinates and distMat provided, calculations will be done based on the distance matrix, coordinates will only be used for plotting. Output DHARMa Moran's I test for distance-based autocorrelation data: simulationOutput observed = -0.0166319, expected = -0.0050251, sd = 0.0112750, p-value = 0.3033 alternative hypothesis: Distance-based autocorrelation --- Code testSpatialAutocorrelation(simulationOutput, distMat = dM, plot = FALSE, y = testData$ y) Message Both coordinates and distMat provided, calculations will be done based on the distance matrix, coordinates will only be used for plotting. Output DHARMa Moran's I test for distance-based autocorrelation data: simulationOutput observed = -0.0166319, expected = -0.0050251, sd = 0.0112750, p-value = 0.3033 alternative hypothesis: Distance-based autocorrelation --- Code testTemporalAutocorrelation(simulationOutput, plot = FALSE, time = testData$ time) Output Durbin-Watson test data: simulationOutput$scaledResiduals ~ 1 DW = 1.9703, p-value = 0.833 alternative hypothesis: true autocorrelation is not 0 --- Code testTemporalAutocorrelation(simulationOutput, plot = FALSE, time = testData$ time, alternative = "greater") Output Durbin-Watson test data: simulationOutput$scaledResiduals ~ 1 DW = 1.9703, p-value = 0.4165 alternative hypothesis: true autocorrelation is greater than 0 # test phylogenetic autocorrelation Code restest Output DHARMa Moran's I test for phylogenetic autocorrelation data: res observed = 0.851667, expected = -0.016949, sd = 0.088733, p-value < 2.2e-16 alternative hypothesis: Phylogenetic autocorrelation --- Code restest2 Output DHARMa Moran's I test for phylogenetic autocorrelation data: res2 observed = 0.047474, expected = -0.016949, sd = 0.088260, p-value = 0.4654 alternative hypothesis: Phylogenetic autocorrelation # testOutliers Code testOutliers(simulationOutput, plot = F, margin = "lower") Output DHARMa outlier test based on exact binomial test with approximate expectations data: simulationOutput outliers at lower margin(s) = 4, observations = 1000, p-value = 0.8037 alternative hypothesis: true probability of success is not equal to 0.003984064 95 percent confidence interval: 0.001090908 0.010209665 sample estimates: frequency of outliers (expected: 0.00398406374501992 ) 0.004 --- Code testOutliers(simulationOutput, plot = F, alternative = "two.sided", margin = "lower") Output DHARMa outlier test based on exact binomial test with approximate expectations data: simulationOutput outliers at lower margin(s) = 4, observations = 1000, p-value = 0.8037 alternative hypothesis: true probability of success is not equal to 0.003984064 95 percent confidence interval: 0.001090908 0.010209665 sample estimates: frequency of outliers (expected: 0.00398406374501992 ) 0.004 --- Code testOutliers(simulationOutput, plot = F, margin = "upper") Output DHARMa outlier test based on exact binomial test with approximate expectations data: simulationOutput outliers at upper margin(s) = 4, observations = 1000, p-value = 0.8037 alternative hypothesis: true probability of success is not equal to 0.003984064 95 percent confidence interval: 0.001090908 0.010209665 sample estimates: frequency of outliers (expected: 0.00398406374501992 ) 0.004 DHARMa/tests/testthat/testPlots.R0000644000176200001440000000546714703461527016421 0ustar liggesusers doClassFunctions <- function(simulationOutput){ print(simulationOutput) expect_true(class(residuals(simulationOutput)) == "numeric") } doPlots <- function(simulationOutput, testData){ plot(simulationOutput, quantreg = T, rank = F, asFactor = T) plot(simulationOutput, quantreg = F, rank = F) plot(simulationOutput, quantreg = T, rank = T) plot(simulationOutput, quantreg = F, rank = T) # qq plot plotQQunif(simulationOutput = simulationOutput) # residual vs. X plots, various options plotResiduals(simulationOutput) plotResiduals(simulationOutput, rank = T, quantreg = F) plotResiduals(simulationOutput, quantiles = 0.5) plotResiduals(simulationOutput, quantiles = c(0.3, 0.6)) plotResiduals(simulationOutput$scaledResiduals, form = simulationOutput$fittedPredictedResponse) # hist hist(simulationOutput) } doTests <- function(simulationOutput, testData){ testUniformity(simulationOutput = simulationOutput) testZeroInflation(simulationOutput = simulationOutput) testTemporalAutocorrelation(simulationOutput = simulationOutput, time = testData$time) testSpatialAutocorrelation(simulationOutput = simulationOutput, x = testData$x, y = testData$y) } # currently not testing the following because of warning #testOverdispersion(simulationOutput) #testOverdispersion(simulationOutput, alternative = "both", plot = T) # simulationOutput2 <- simulateResiduals(fittedModel = fittedModel, refit = T, n = 10) # n=10 is very low, set higher for serious tests # # print(simulationOutput2) # plot(simulationOutput2, quantreg = F) # # testOverdispersion(simulationOutput2) # testOverdispersion(simulationOutput2, alternative = "both", plot = T) # testOverdispersionParametric(fittedModel) test_that("Plots work", { skip_on_cran() testData = createData(sampleSize = 100, overdispersion = 0, randomEffectVariance = 0, family = binomial()) fittedModel <- glm(observedResponse ~ Environment1 , family = "binomial", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) doClassFunctions(simulationOutput) doPlots(simulationOutput, testData) doTests(simulationOutput, testData) testData = createData(sampleSize = 100, overdispersion = 0, randomEffectVariance = 2, numGroups = 4, family = gaussian()) fittedModel <- glm(observedResponse ~ group , data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) doClassFunctions(simulationOutput) doPlots(simulationOutput, testData) plotResiduals(simulationOutput, testData$group) } ) DHARMa/tests/testthat.R0000644000176200001440000000061014703461527014401 0ustar liggesusers# This file is part of the standard setup for testthat. # It is recommended that you do not modify it. # # Where should you do additional test configuration? # Learn more about the roles of various files in: # * https://r-pkgs.org/testing-design.html#sec-tests-files-overview # * https://testthat.r-lib.org/articles/special-files.html library(testthat) library(DHARMa) test_check("DHARMa") DHARMa/MD50000644000176200001440000001441114704441036011562 0ustar liggesusersa637660efc14daf2a2bd94f7c56fb58a *DESCRIPTION 10445a5f9bcdc858ce15778d9b3a9a32 *NAMESPACE 5436910eab101544ca852112d96fb71f *NEWS.md cc0d4370eb9061cc1f213b6bd0674835 *R/DHARMa.R 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789f444a01f6d435959692bc2d0b3009 *tests/testthat/testTests.R 06b940b3a6162b9d5067bde33f3749e2 *vignettes/DHARMa.Rmd 6720e9ba051d92719da97d7a56627a9c *vignettes/DHARMaForBayesians.Rmd 2e9ebf8d3e62710ad6ccb5fcc48a02ce *vignettes/ECDFmotivation.png 7272863a2c73082768e1e36c91a861d3 *vignettes/dispersion.png DHARMa/R/0000755000176200001440000000000014704245735011462 5ustar liggesusersDHARMa/R/transformQuantiles.R0000644000176200001440000000162614677165224015516 0ustar liggesusers#' Transform quantiles to pdf (deprecated) #' #' The purpose of this function was to transform the DHARMa quantile residuals (which have a uniform distribution) to a particular pdf. Since DHARMa 0.3.0, this functionality is integrated in the [residuals.DHARMa] function. Please switch to using this function. #' #' @param res an object with simulated residuals created by [simulateResiduals] #' @param quantileFunction optional - a quantile function to transform the uniform 0/1 scaling of DHARMa to another distribution #' @param outlierValue if a quantile function with infinite support (such as dnorm) is used, residuals that are 0/1 are mapped to -Inf / Inf. outlierValues allows to convert -Inf / Inf values to an optional min / max value. #' #' @export #' transformQuantiles <- function(res, quantileFunction = qnorm, outlierValue = 7){ message("This function is deprecated. Please use residuals() instead") } DHARMa/R/imports.R0000644000176200001440000000312014665273541013300 0ustar liggesusers #### Package car #### # this is copied, slightly modified, from car, to avoid dependencies / S3 clashes when importing car together with lme4 leveneTest_default <- function (y, group, center=median, ...) { # original levene.test if (!is.numeric(y)) stop(deparse(substitute(y)), " is not a numeric variable") if (!is.factor(group)) { warning(deparse(substitute(group)), " coerced to factor.") group <- as.factor(group) } valid <- complete.cases(y, group) meds <- tapply(y[valid], group[valid], center, ...) resp <- abs(y - meds[group]) table <- anova(lm(resp ~ group))[, c(1, 4, 5)] rownames(table)[2] <- " " dots <- deparse(substitute(...)) attr(table, "heading") <- paste("Levene's Test for Homogeneity of Variance (center = ", deparse(substitute(center)), if(!(dots == "NULL")) paste(":", dots), ")", sep="") table } leveneTest_formula <- function(y, data, ...) { form <- y mf <- if (missing(data)) model.frame(form) else model.frame(form, data) if (any(sapply(2:dim(mf)[2], function(j) is.numeric(mf[[j]])))) stop("Levene's test is not appropriate with quantitative explanatory variables.") y <- mf[,1] if(dim(mf)[2]==2) group <- mf[,2] else { if (length(grep("\\+ | \\| | \\^ | \\:",form))>0) stop("Model must be completely crossed formula only.") group <- interaction(mf[,2:dim(mf)[2]]) } leveneTest_default(y=y, group=group, ...) } leveneTest_lm <- function(y, ...) { m <- model.frame(y) m$..y <- model.response(m) f <- formula(y) f[2] <- expression(..y) leveneTest_formula(f, data=m, ...) }DHARMa/R/helper.R0000644000176200001440000002063214703461527013065 0ustar liggesusers#' Modified ECDF function. #' #' @details Ensures symmetric ECDF (standard ECDF is <), and that 0 / 1 values are only produced if the data is strictly < > than the observed data. #' #' @keywords internal DHARMa.ecdf <- function (x) { x <- sort(x) n <- length(x) if (n < 1) stop(paste("DHARMa.ecdf - length vector < 1", x)) vals <- unique(x) rval <- approxfun(vals, cumsum(tabulate(match(x, vals)))/ (n +1), method = "linear", yleft = 0, yright = 1, ties = "ordered") class(rval) <- c("ecdf", "stepfun", class(rval)) assign("nobs", n, envir = environment(rval)) attr(rval, "call") <- sys.call() rval } #' Calculate Residual Quantiles #' #' Calculates residual quantiles from a given simulation. #' #' @param simulations A matrix with simulations from a fitted model. Rows = observations, columns = replicate simulations. #' @param observed A vector with the observed data. #' @param integerResponse Is the response integer-valued? Only has an effect for method = "traditional". #' @param method The quantile randomization method used. See details. #' @param rotation Optional rotation of the residuals. You can either provide as a known or estimated covariance matrix (e.g. when fitting an AR1 model), or use the argument "estimated", in which case the residual covariance will be approximated by simulations. See comments in details. #' #' @details The function calculates residual quantiles from the simulated data. For continuous distributions, this will simply be the value of the ecdf. #' #' **Randomization procedure for discrete data** #' #' For discrete data, there are two options implemented. #' #' The current default (available since DHARMa 0.3.1) are probability integral transform (PIT-) residuals (Smith, 1985; Dunn & Smyth, 1996; see also Warton, et al., 2017). #' #' Before DHARMa 0.3.1, a different randomization procedure was used, in which the a U(-0.5, 0.5) distribution was added on observations and simulations for discrete distributions. For a completely discrete distribution, the two procedures should deliver equivalent results, but the second method has the disadvantage that (a) one has to know if the distribution is discrete (DHARMa tries to recognize this automatically), and (b) that it leads to inefficiencies for some distributions such as the Tweedie, which are partly continuous, partly discrete #' (see e.g. [issue #168](https://github.com/florianhartig/DHARMa/issues/168) on DHARMa GitHub page). #' #' **Rotation (optional)** #' #' The getQuantile function includes an additional option to rotate residuals prior to calculating the quantile residuals. This option should ONLY be used when the fitted model includes a particular residuals covariance structure, such as an AR1 or a spatial or phylogenetic CAR model. #' #' For these models, residuals calculated from unconditional simulations will include the specified covariance structure, which will trigger e.g. temporal autocorrelation tests and can inflate type I errors of other tests. The idea of the rotation is to rotate the residual space according to the covariance structure of the fitted model, such that the rotated residuals are conditional independent (provided the fitted model is correct). #' #' If the residual covariance of the fitted model at the response scale can be extracted (e.g. when fitting gls type models), it would be best to extract it and provide this covariance matrix to the rotation option. If that is not the case, providing the argument "estimated" to rotation will estimate the covariance from the data simulated by the model. This is probably without alternative for GLMMs, where the covariance at the response scale is likely not known / provided, but note, that this approximation will tend to have considerable error and may be slow to compute for high-dimensional data. If you try to estimate the rotation from simulations, you should set n as high as possible! See [testTemporalAutocorrelation] for a practical example. #' #' The rotation of residuals implemented here is similar to the Variogram.lme() and Variongram.gls() functions in nlme package using the argument resType = "normalized". #' #' @references #' #' Smith, J. Q. "Diagnostic checks of non-standard time series models." Journal of Forecasting 4.3 (1985): 283-291. #' #' Dunn, P.K., & Smyth, G.K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics 5, 236-244. #' #' Warton, David I., LoĆÆc Thibaut, and Yi Alice Wang. "The PIT-trapā€”A ā€œmodel-freeā€ bootstrap procedure for inference about regression models with discrete, multivariate responses." PloS one 12.7 (2017). #' #' @export getQuantile <- function(simulations, observed, integerResponse, method = c("PIT", "traditional"), rotation = NULL){ method = match.arg(method) n = length(observed) if(nrow(simulations) != n) stop("DHARMa::getquantile: wrong dimension of simulations") nSim = ncol(simulations) if(method == "traditional"){ if(!is.null(rotation)) stop("rotation can only be used with PIT residuals") if(integerResponse == F){ if(any(duplicated(observed))) message("Model family was recognized or set as continuous, but duplicate values were detected in the response. Consider if you are fitting an appropriate model.") values = as.vector(simulations)[duplicated(as.vector(simulations))] if(length(values) > 0){ if(all(values%%1 == 0)){ integerResponse = T message("Model family was recognized or set as continuous, but duplicate values were detected in the simulation - changing to integer residuals (see ?simulateResiduals for details).") } else { message("Duplicate non-integer values found in the simulation. If this is because you are fitting a non-inter valued discrete response model, note that DHARMa does not perform appropriate randomization for such cases.") } } } scaledResiduals = rep(NA, n) for (i in 1:n){ if(integerResponse == T){ scaledResiduals[i] <- DHARMa.ecdf(simulations[i,] + runif(nSim, -0.5, 0.5))(observed[i] + runif(1, -0.5, 0.5)) }else{ scaledResiduals[i] <- DHARMa.ecdf(simulations[i,])(observed[i]) } } } else { # optional rotation before PIT if(!is.null(rotation)){ if(is.character(rotation) && rotation == "estimated"){ covar = Matrix::nearPD(cov(t(simulations)))$mat L = t(as.matrix(Matrix::chol(covar))) } else if(is.matrix(rotation)) L <- t(chol(rotation)) else stop("DHARMa::getQuantile - wrong argument to rotation parameter.") observed <- solve(L, observed) simulations = apply(simulations, 2, function(a) solve(L, a)) } scaledResiduals = rep(NA, n) for (i in 1:n){ minSim <- mean(simulations[i,] < observed[i]) maxSim <- mean(simulations[i,] <= observed[i]) if (minSim == maxSim) scaledResiduals[i] = minSim else scaledResiduals[i] = runif(1, minSim, maxSim) } } return(scaledResiduals) } # # # testData = createData(sampleSize = 200, family = gaussian(), # randomEffectVariance = 0, numGroups = 5) # fittedModel <- glmmTMB(observedResponse ~ Environment1, # data = testData) # simulationOutput <- simulateResiduals(fittedModel = fittedModel) # # sims = simulationOutput$simulatedResponse # sims[1, c(1,6,8)] = 0 # any(apply(sims, 1, anyDuplicated)) # getQuantile(simulations = sims, observed = testData$observedResponse, n = 200, integerResponse = F, nSim = 250) # # # #' Check dot operator #' #' @param name variable name #' @param default variable default #' #' @details modified from https://github.com/lcolladotor/dots #' #' @keywords internal checkDots <- function(name, default, ...) { args <- list(...) if(!name %in% names(args)) { ## Default value return(default) } else { ## If the argument was defined in the ... part, return it return(args[[name]]) } } securityAssertion <- function(context = "Not provided", stop = F){ generalMessage = "Message from DHARMa: During the execution of a DHARMa function, some unexpected conditions occurred. Even if you didn't get an error, your results may not be reliable. Please check with the help if you use the functions as intended. If you think that the error is not on your side, I would be grateful if you could report the problem at https://github.com/florianhartig/DHARMa/issues \n\n Context:" if (stop == F) warning(paste(generalMessage, context)) else stop(paste(generalMessage, context)) } DHARMa/R/random.R0000644000176200001440000000322114677165224013066 0ustar liggesusers#' Record and restore a random state #' #' The aim of this function is to record, manipulate and restore a random state. #' #' @param seed seed argument to set.seed(), typically a number. Additional options: NULL = no seed is set, but return includes function for restoring random seed. F = function does nothing, i.e. neither seed is changed, nor does the returned function do anything. #' #' @details This function is intended for two (not mutually exclusive tasks): #' #' a) record the current random state. #' #' b) change the current random state in a way that the previous state can be restored. #' #' @return A list with various infos about the random state that after function execution, as well as a function to restore the previous state before the function execution. #' @export #' @example inst/examples/getRandomStateHelp.R #' @author Florian Hartig #' getRandomState <- function(seed = NULL){ # better to explicitly access the global RS? # current = get(".Random.seed", .GlobalEnv, ifnotfound = NULL) current = mget(".Random.seed", envir = .GlobalEnv, ifnotfound = list(NULL))[[1]] if(!is.null(seed) && is.logical(seed) && seed == FALSE){ restoreCurrent <- function(){} }else{ restoreCurrent <- function(){ if(is.null(current)) rm(".Random.seed", envir = .GlobalEnv) else assign(".Random.seed", current , envir = .GlobalEnv) } } # setting seed if(is.numeric(seed)) set.seed(seed) # ensuring that RNG has been initialized if (is.null(current))runif(1) randomState = list(seed, state = get(".Random.seed", globalenv()), kind = RNGkind(), restoreCurrent = restoreCurrent) return(randomState) } DHARMa/R/simulateLRT.R0000644000176200001440000001251714677165224014023 0ustar liggesusers#' Simulated likelihood ratio tests for (generalized) linear mixed models #' #' @description This function uses the DHARMa model wrappers to generate simulated likelihood ratio tests (LRTs) for (generalized) linear mixed models based on a parametric bootstrap. The motivation for using a simulated LRT rather than a standard ANOVA or AIC for model selection in mixed models is that df for mixed models are not clearly defined, thus standard ANOVA based on Chi2 statistics or AIC are unreliable, in particular for models with large contributions of REs to the likelihood. #' #' Interpretation of the results as in a normal LRT: the null hypothesis is that m0 is correct, the tests checks if the increase in likelihood of m1 is higher than expected, using data simulated from m0. #' #' @param m0 null Model. #' @param m1 alternative Model. #' @param n number of simulations. #' @param seed random seed. #' @param plot whether null distribution should be plotted. #' @param suppressWarnings whether to suppress warnings that occur during refitting the models to simulated data. See details for explanations. #' @param saveModels Whether to save refitted models. #' @param ... additional parameters to pass on to the simulate function of the model object. See [getSimulations] for details. #' #' @details The function performs a simulated LRT, which works as follows: #' #' 1. H0: Model 1 is correct. #' 2. Our test statistic is the log LRT of M1/M2. Empirical value will always be > 1 because in a nested setting, the more complex model cannot have a worse likelihood. #' 3. To generate an expected distribution of the test statistic under H0, we simulate new response data under M0, refit M0 and M1 on this data, and calculate the LRs. #' 4. Based on this, calculate p-values etc. in the usual way. #' #' About warnings: warnings such as "boundary (singular) fit: see ?isSingular" will likely occur in this function and are not necessarily the sign of a problem. lme4 warns if RE variances are fit to zero. This is desired / likely in this case, however, because we are simulating data with zero RE variances. Therefore, warnings are turned off per default. For diagnostic reasons, you can turn warnings on, and possibly also inspect fitted models via the parameter saveModels to see if there are any other problems in the re-fitted models. #' #' Data simulations are performed by [getSimulations], which is a wrapper for the respective model functions. The default for all packages, wherever possible, is to generate marginal simulations (meaning that REs are re-simulated as well). I see no sensible reason to change this, but if you want to and if supported by the respective regression package, you could do so by supplying the necessary arguments via ... #' #' @note The logic of an LRT assumes that m0 is nested in m1, which guarantees that the L(M1) > L(M0). The function does not explicitly check if models are nested and will work as long as data can be simulated from M0 that can be refit with M) and M1; however, I would strongly advice against using this for non-nested models unless you have a good statistical reason for doing so. #' #' Also, note that LRTs may be unreliable when fit with REML or some other kind of penalized / restricted ML. Therefore, you should fit model with ML for use in this function. #' #' @author Florian Hartig #' #' @example inst/examples/simulateLRTHelp.R #' @export simulateLRT<-function(m0, m1, n = 250, seed = 123, plot = TRUE, suppressWarnings = TRUE, saveModels = FALSE, ...){ ######## general assertions and startup calculations ########## # identical to simulateResiduals if (n < 2) stop("error in DHARMa::simulateLRT: n > 1 is required to simulate LRT") checkModel(m0) checkModel(m1) randomState <-getRandomState(seed) on.exit({randomState$restoreCurrent()}) ptm <- proc.time() ####### extract model info ############ out = list() out$data.name = paste("m0:", deparse(substitute(m0)), "m1:", deparse(substitute(m1))) out$m0 = m0 out$m1 = m1 out$observedLRT = logLik(m1) - logLik(m0) if(nobs(m0) != nobs(m1)) stop("m0 and m1 seem to have an unequal number of observations. Check for and possibly remove NAs in the data.") out$nObs = nobs(m0) out$nSim = n out$simulatedResponse = getSimulations(m0, nsim = n, type = "refit", ...) out$simulatedLR = rep(NA, n) if(saveModels == TRUE) out$saveModels == list() for (i in 1:n){ simObserved = out$simulatedResponse[[i]] try({ # for testing # if (i==3) stop("x") # Note: also set silent = T for production if(suppressWarnings == TRUE){ invisible(capture.output(suppressWarnings(suppressMessages({ refittedM0 = getRefit(m0, simObserved) refittedM1 = getRefit(m1, simObserved) })))) } else { refittedM0 = getRefit(m0, simObserved) refittedM1 = getRefit(m1, simObserved) } if(saveModels == TRUE) out$saveModels[[i]] = list(refittedM0 = refittedM0, refittedM1 = refittedM1) out$simulatedLR[i] = logLik(refittedM1) - logLik(refittedM0) }, silent = TRUE) } out$statistic = out$observedLRT names(out$statistic) = "LogL(M1/M0)" out$method = "DHARMa simulated LRT" out$alternative = "M1 describes the data better than M0" out$p.value = getP(out$simulatedLR, out$observedLRT, alternative = "greater", plot = plot, xlab="LogL(M1/M0)") class(out) = "htest" return(out) } DHARMa/R/runBenchmarks.R0000644000176200001440000002350314701675644014415 0ustar liggesusers#' Benchmark calculations #' #' This function runs statistical benchmarks, including Power / Type I error simulations for an arbitrary test with a control parameter #' #' @param controlValues optionally, a vector with a control parameter (e.g. to vary the strength of a problem the test should be specific to). See help for an example #' @param calculateStatistics the statistics to be benchmarked. Should return one value, or a vector of values. If controlValues are given, must accept a parameter control #' @param nRep number of replicates per level of the controlValues #' @param alpha significance level #' @param parallel whether to use parallel computations. Possible values are F, T (sets the cores automatically to number of available cores -1), or an integer number for the number of cores that should be used for the cluster #' @param exportGlobal whether the global environment should be exported to the parallel nodes. This will use more memory. Set to true only if you function calculate statistics depends on other functions or global variables. #' @param ... additional parameters to calculateStatistics #' @note The benchmark function in DHARMa are intended for development purposes, and for users that want to test / confirm the properties of functions in DHARMa. If you are running an applied data analysis, they are probably of little use. #' @return A object with list structure of class DHARMaBenchmark. Contains an entry simulations with a matrix of simulations, and an entry summaries with an list of summaries (significant (T/F), mean, p-value for KS-test uniformity). Can be plotted with [plot.DHARMaBenchmark] #' @export #' @author Florian Hartig #' @seealso [plot.DHARMaBenchmark] #' @example inst/examples/runBenchmarksHelp.R runBenchmarks <- function(calculateStatistics, controlValues = NULL, nRep = 10, alpha = 0.05, parallel = FALSE, exportGlobal = FALSE, ...){ start_time <- Sys.time() # Sequential Simulations simulations = list() if(parallel == FALSE){ if(is.null(controlValues)) simulations[[1]] = replicate(nRep, calculateStatistics(), simplify = "array") else for(j in 1:length(controlValues)){ simulations[[j]] = replicate(nRep, calculateStatistics(controlValues[j]), simplify = "array") } # Parallel Simulations }else{ if (parallel == TRUE | parallel == "auto"){ cores <- parallel::detectCores() - 1 message("parallel, set cores automatically to ", cores) } else if (is.numeric(parallel)){ cores <- parallel message("parallel, set number of cores by hand to ", cores) } else stop("wrong argument to parallel") cl <- parallel::makeCluster(cores) # for each # doParallel::registerDoParallel(cl) # # `%dopar%` <- foreach::`%dopar%` # # if(is.null(controlValues)) simulations[[1]] = t(foreach::foreach(i=1:nRep, .packages=c("lme4", "DHARMa"), .combine = rbind) %dopar% calculateStatistics()) # # else for(j in 1:length(controlValues)){ # simulations[[j]] = t(foreach::foreach(i=1:nRep, .packages=c("lme4", "DHARMa"), .combine = rbind) %dopar% calculateStatistics(controlValues[j])) # } # # End for each # doesn't see to work properly loadedPackages = (.packages()) parExectuer = function(x = NULL, control = NULL) calculateStatistics(control) if (exportGlobal == TRUE) parallel::clusterExport(cl = cl, varlist = ls(envir = .GlobalEnv)) parallel::clusterExport(cl = cl, c("parExectuer", "calculateStatistics", "loadedPackages"), envir = environment()) parallel::clusterEvalQ(cl, {for(p in loadedPackages) library(p, character.only=TRUE)}) # parallel::clusterExport(cl = cl, varlist = ls(envir = .GlobalEnv)) # parallel::clusterExport(cl=cl,varlist = c("calculateStatistics"), envir=environment()) # parallel::clusterExport(cl=cl,varlist = c("controlValues", "alpha", envir=environment()) # parallel::clusterExport(cl=cl,varlist = c("calculateStatistics"), envir=environment()) # parallel::clusterExport(cl=cl,varlist = c("controlValues", "alpha", envir=environment()) if(is.null(controlValues)) simulations[[1]] = parallel::parSapply(cl, 1:nRep, parExectuer) else for(j in 1:length(controlValues)){ simulations[[j]] = parallel::parSapply(cl, 1:nRep, parExectuer, control = controlValues[j]) } parallel::stopCluster(cl) } # Calculations of summaries if(is.null(controlValues)) controlValues = c("N") nOutputs = nrow(simulations[[1]]) nControl = length(controlValues) # reducing the list of outputs to a data.frame x = Reduce(rbind, lapply(simulations, t)) x = data.frame(x) x$replicate = rep(1:nRep, length(controlValues)) x$controlValues = rep(controlValues, each = nRep) summary = list() # function for aggregation aggreg <- function(f) { ret <- aggregate(x[,- c(ncol(x) - 1, ncol(x))], by = list(x$controlValues), f) colnames(ret)[1] = "controlValues" return(ret) } sig <- function(x) mean(x < alpha) isUnif <- function(x) ks.test(x, "punif")$p.value summary$propSignificant = aggreg(sig) summary$meanP = aggreg(mean) summary$isUnifP = aggreg(mean) out = list() out$controlValues = controlValues out$simulations = x out$summaries = summary out$time = Sys.time() - start_time out$nSummaries = ncol(x) - 2 out$nReplicates = nRep class(out) = "DHARMaBenchmark" return(out) } #' Plots DHARMa benchmarks #' #' The function plots the result of an object of class DHARMaBenchmark, created by [runBenchmarks]. #' #' @param x object of class DHARMaBenchmark, created by [runBenchmarks]. #' @param ... parameters to pass to the plot function. #' #' @details The function will create two types of plots, depending on whether the run contains only a single value (or no value) of the control parameter, or whether a vector of control values is provided: #' #' If a single or no value of the control parameter is provided, the function will create box plots of the estimated p-values, with the number of significant p-values plotted to the left. #' #' If a control parameter is provided, the function will plot the proportion of significant p-values against the control parameter, with 95% CIs based based on the performed replicates displayed as confidence bands. #' #' @seealso [runBenchmarks] #' @export plot.DHARMaBenchmark <- function(x, ...){ if(length(x$controlValues)== 1){ boxplot(x$simulations[,1:x$nSummaries], col = "grey", ylim = c(-0.3,1), horizontal = TRUE, las = 2, xaxt='n', main = "p distribution", ...) abline(v = 0) abline(v = c(0.25, 0.5, 0.75), lty = 2) text(-0.2, 1:x$nSummaries, labels = x$summaries$propSignificant[-1]) # barplot(as.matrix(x$summaries$propSignificant[-1]), horiz = TRUE, add = TRUE, offset = -0.2, names.arg = "test", width = 0.5, space = 1.4) }else{ res = x$summaries$propSignificant plot(NULL, xlim = range(res$controlValues), ylim = c(0,1), ...) for(i in 1:x$nSummaries){ getCI = function(k) as.vector(binom.test(k,x$nReplicates)$conf.int) CIs = sapply(res[,i+1]*x$nReplicates, getCI) polygon(c(res$controlValues, rev(res$controlValues)), c(CIs[1,], rev(CIs[2,])), col = "#00000020", border = FALSE) lines(res$controlValues, res[,i+1], col = i, lty = i, lwd = 2) } legend("bottomright", colnames(res[,-1]), col = 1:x$nSummaries, lty = 1:x$nSummaries, lwd = 2) } } # this used to be an alternative to the boxplot for control = N plotMultipleHist <- function(x){ lin = ncol(x) histList <- lapply(x, hist, breaks = seq(0,1,0.02), plot = FALSE) plot(NULL, xlim = c(0,1), ylim = c(0, lin), yaxt = 'n', ylab = NULL, xlab = "p-value") abline(h= 0) for(i in 1:lin){ maxD = max(histList[[i]]$density) lines(histList[[i]]$mids, i - 1 + histList[[i]]$density/maxD, type = "l") abline(h= i) abline(h= 1/maxD + i - 1, , col = "red", lty = 2) } abline(v = 1, lty = 2) abline(v = c(0.05, 0), lty = 2, col = "red") } #' Plot distribution of p-values. #' @param x vector of p values. #' @param plot should the values be plotted. #' @param main title for the plot. #' @param ... additional arguments to hist. #' @author Florian Hartig testPDistribution <- function(x, plot = TRUE, main = "p distribution \n expected is flat at 1", ...){ out = suppressWarnings(ks.test(x, 'punif')) hist(x, xlim = c(0,1), breaks = 20, freq = FALSE, main = main, ...) abline(h=1, col = "red") return(out) } # if(plot == TRUE){ # oldpar <- par(mfrow = c(4,4)) # hist(out, breaks = 50, col = "red", main = paste("mean of", nSim, "simulations")) # for (i in 1:min(nSim, 15)) hist(out[i,], breaks = 50, freq = FALSE, main = i) # par(oldpar) # } generateGenerator <- function(mod){ out <- function(){ simulations = simulate(mod, nsim = 1) newData <-model.frame(mod) if(is.vector(simulations[[1]])){ newData[,1] = simulations[[1]] } else { # Hack to make the binomial n/k case work newData[[1]] = NULL newData = cbind(simulations[[1]], newData) } refittedModel = update(mod, data = newData) list(data = newData, model = refittedModel) } } #' Benchmark runtimes of several functions #' @param createModel a function that creates and returns a fitted model. #' @param evaluationFunctions a list of functions that are to be evaluated on the fitted models. #' @param n number of replicates. #' @details This is a small helper function designed to benchmark runtimes of several operations that are to be performed on a list of fitted models. In the example, this is used to benchmark the runtimes of several DHARMa tests. #' @author Florian Hartig #' @example inst/examples/benchmarkRuntimeHelp.R #' @export benchmarkRuntime<- function(createModel, evaluationFunctions, n){ m = length(evaluationFunctions) models = replicate(n, createModel(), simplify = FALSE) runtimes = rep(NA, m) for (i in 1:m){ runtimes[i] = system.time(lapply(models, evaluationFunctions[[i]]))[3] } return(runtimes) } DHARMa/R/DHARMa.R0000644000176200001440000002337014677165224012611 0ustar liggesusers #' @keywords internal #' @references vignette("DHARMa", package="DHARMa") #' @details #' To get started with the package, look at the vignette and start with [simulateResiduals] #' "_PACKAGE" #' Print simulated residuals #' #' @param x an object with simulated residuals created by [simulateResiduals]. #' @param ... optional arguments for compatibility with the generic function, no function implemented. #' @export print.DHARMa <- function(x, ...){ cat(paste("Object of Class DHARMa with simulated residuals based on", x$nSim, "simulations with refit =", x$refit , ". See ?DHARMa::simulateResiduals for help."), "\n", "\n") if (length(x$scaledResiduals) < 20) cat("Scaled residual values:", x$scaledResiduals) else { cat("Scaled residual values:", x$scaledResiduals[1:20], "...") } } #' Return residuals of a DHARMa simulation #' #' @param object an object with simulated residuals created by [simulateResiduals] #' @param quantileFunction optional - a quantile function to transform the uniform 0/1 scaling of DHARMa to another distribution #' @param outlierValues if a quantile function with infinite support (such as dnorm) is used, residuals that are 0/1 are mapped to -Inf / Inf. outlierValues allows to convert -Inf / Inf values to an optional min / max value. #' @param ... optional arguments for compatibility with the generic function, no function implemented #' @details the function accesses the slot $scaledResiduals in a fitted DHARMa object, and optionally transforms the standard DHARMa quantile residuals (which have a uniform distribution) to a particular pdf. #' #' @note some of the papers on simulated quantile residuals transforming the residuals (which are natively uniform) back to a normal distribution. I presume this is because of the larger familiarity of most users with normal residuals. Personally, I never considered this desirable, for the reasons explained in https://github.com/florianhartig/DHARMa/issues/39, but with this function, I wanted to give users the option to plot normal residuals if they so wish. #' #' @export #' @example inst/examples/simulateResidualsHelp.R #' residuals.DHARMa <- function(object, quantileFunction = NULL, outlierValues = NULL, ...){ if(is.null(quantileFunction)){ return(object$scaledResiduals) } else { res = quantileFunction(object$scaledResiduals) if(!is.null(outlierValues)){ res = ifelse(res == -Inf, outlierValues[1], res) res = ifelse(res == Inf, outlierValues[2], res) } return(res) } } #' Return outliers #' #' Returns the outliers of a DHARMa object. #' #' @param object an object with simulated residuals created by [simulateResiduals]. #' @param lowerQuantile lower threshold for outliers. Default is zero = outside simulation envelope. #' @param upperQuantile upper threshold for outliers. Default is 1 = outside simulation envelope. #' @param return wheter to return an indices of outliers or a logical vector. #' #' @details First of all, note that the standard definition of outlier in the DHARMa plots and outlier tests is an observation that is outside the simulation envelope. How far outside that is depends a lot on how many simulations you do. If you have 100 data points and to 100 simulations, you would expect to have one "outlier" on average, even with a perfectly fitting model. This is in fact what the outlier test tests. #' #' Thus, keep in mind that for a small number of simulations, outliers are mostly a technical term: these are points that are outside our simulations, but we don't know how far away they are. #' #' If you are seriously interested in HOW FAR outside the expected distribution a data point is, you should increase the number of simulations in [simulateResiduals] to be sure to get the tail of the data distribution correctly. In this case, it may make sense to adjust lowerQuantile and upperQuantile, e.g. to 0.025, 0.975, which would define outliers as values outside the central 95% of the distribution. #' #' Also, note that outliers are particularly concerning if they have a strong influence on the model fit. One could test the influence, for example, by removing them from the data, or by some meausures of leverage, e.g. generalisations for Cook's distance as in Pinho, L. G. B., Nobre, J. S., & Singer, J. M. (2015). Cookā€™s distance for generalized linear mixed models. Computational Statistics & Data Analysis, 82, 126ā€“136. doi:10.1016/j.csda.2014.08.008. At the moment, however, no such function is provided in DHARMa. #' #' @export #' outliers <- function(object, lowerQuantile = 0, upperQuantile = 1, return = c("index", "logical")){ return = match.arg(return) out = residuals(object) >= upperQuantile | residuals(object) <= lowerQuantile if(return == "logical") return(out) else(return(which(out))) } #' Create a DHARMa object from hand-coded simulations or Bayesian posterior predictive simulations. #' #' @param simulatedResponse matrix of observations simulated from the fitted model - row index for observations and colum index for simulations. #' @param observedResponse true observations. #' @param fittedPredictedResponse optional fitted predicted response. For Bayesian posterior predictive simulations, using the median posterior prediction as fittedPredictedResponse is recommended. If not provided, the mean simulatedResponse will be used. #' @param integerResponse if T, noise will be added at to the residuals to maintain a uniform expectations for integer responses (such as Poisson or Binomial). Unlike in [simulateResiduals], the nature of the data is not automatically detected, so this MUST be set by the user appropriately. #' @param seed the random seed to be used within DHARMa. The default setting, recommended for most users, is keep the random seed on a fixed value 123. This means that you will always get the same randomization and thus teh same result when running the same code. NULL = no new seed is set, but previous random state will be restored after simulation. FALSE = no seed is set, and random state will not be restored. The latter two options are only recommended for simulation experiments. See vignette for details. #' @param method the quantile randomization method used. The two options implemented at the moment are probability integral transform (PIT-) residuals (current default), and the "traditional" randomization procedure, that was used in DHARMa until version 0.3.0. For details, see [getQuantile]. #' @param rotation optional rotation of the residual space to remove residual autocorrelation. See details in [simulateResiduals], section *residual auto-correlation* for an extended explanation, and [getQuantile] for syntax. #' @details The use of this function is to convert simulated residuals (e.g. from a point estimate, or Bayesian p-values) to a DHARMa object, to make use of the plotting / test functions in DHARMa. #' @note Either scaled residuals or (simulatedResponse AND observed response) have to be provided. #' @example inst/examples/createDharmaHelp.R #' @export createDHARMa <- function(simulatedResponse , observedResponse , fittedPredictedResponse = NULL, integerResponse = FALSE, seed = 123, method = c("PIT", "traditional"), rotation = NULL){ randomState <-getRandomState(seed) on.exit({randomState$restoreCurrent()}) match.arg(method) out = list() out$simulatedResponse = simulatedResponse out$refit = F out$integerResponse = integerResponse out$observedResponse = observedResponse if(!is.matrix(simulatedResponse) & !is.null(observedResponse)) stop("either scaled residuals or simulations and observations have to be provided.") if(ncol(simulatedResponse) < 2) stop("simulatedResponse with less than 2 simulations provided - cannot calculate residuals on that.") if(ncol(simulatedResponse) < 10) warning("simulatedResponse with less than 10 simulations provided. This rarely makes sense.") out$nObs = length(observedResponse) if (out$nObs < 3) stop("warning - number of observations < 3 ... this rarely makes sense.") if(! (out$nObs == nrow(simulatedResponse))) stop("dimensions of observedResponse and simulatedResponse do not match.") out$nSim = ncol(simulatedResponse) out$scaledResiduals = getQuantile(simulations = simulatedResponse , observed = observedResponse , integerResponse = integerResponse, method = method, rotation = rotation) # makes sure that DHARM plots that rely on this vector won't crash if(is.null(fittedPredictedResponse)){ message("No fitted predicted response provided, using the mean of the simulations") fittedPredictedResponse = apply(simulatedResponse, 1, mean) } out$fittedPredictedResponse = fittedPredictedResponse out$randomState = randomState class(out) = "DHARMa" return(out) } #' Ensures that an object is of class DHARMa #' #' @param simulationOutput a DHARMa simulation output or an object that can be converted into a DHARMa simulation output #' @param convert if TRUE, attempts to convert model + numeric to DHARMa, if "Model", converts only supported models to DHARMa #' @details The #' @return an object of class DHARMa #' @keywords internal ensureDHARMa <- function(simulationOutput, convert = FALSE){ if(inherits(simulationOutput, "DHARMa")){ return(simulationOutput) } else { if(convert == FALSE) stop("wrong argument to function, simulationOutput must be a DHARMa object!") else { if (class(simulationOutput)[1] %in% getPossibleModels()){ if (convert == "Model" | convert == TRUE) return(simulateResiduals(simulationOutput)) } else if(is.vector(simulationOutput, mode = "numeric") & convert == TRUE) { out = list() out$scaledResiduals = simulationOutput out$nObs = length(out$scaledResiduals) class(out) = "DHARMa" return(out) } } } stop("wrong argument to function, simulationOutput must be a DHARMa object or a numeric vector of quantile residuals!") } DHARMa/R/startup.R0000644000176200001440000000056614701671620013307 0ustar liggesusersprintDHARMaStartupInfo <- function() { version <- packageVersion('DHARMa') hello <- paste("This is DHARMa ",version,". For overview type '?DHARMa'. For recent changes, type news(package = 'DHARMa')" ,sep="") packageStartupMessage(hello) } .onLoad <- function(...) { options(DHARMaSignalColor = "red") } .onAttach <- function(...) { printDHARMaStartupInfo() } DHARMa/R/data.R0000644000176200001440000000352014677165224012521 0ustar liggesusers#' Hurricanes #' #' A data set on hurricane strength and fatalities in the US between 1950 and 2012. The data originates from the study by Jung et al., PNAS, 2014, who claim that the masculinity / femininity of a hurricane name has a causal effect on fatalities, presumably through a different perception of danger caused by the names. #' #' @name hurricanes #' @aliases hurricanes #' @docType data #' #' @references Jung, K., Shavitt, S., Viswanathan, M., & Hilbe, J. M. (2014). Female hurricanes are deadlier than male hurricanes. Proceedings of the National Academy of Sciences, 111(24), 8782-8787. #' #' @format A 'data.frame': 92 obs. of 14 variables #' \describe{ #' \item{Year}{Year of the hurricane (1950-2012) } #' \item{Name}{Name of the hurricane } #' \item{MasFem}{Masculinity-femininity rating of the hurricane's name in the range 1 = very masculine, 11 = very feminine.} #' \item{MinPressure_before}{Minimum air pressure (909-1002).} #' \item{Minpressure_Updated_2014}{Updated minimum air pressure (909-1003).} #' \item{Gender_MF}{Binary gender categorization based on MasFem (male = 0, female = 1).} #' \item{Category}{Strength of the hurricane in categories (1:7). (1 = not at all, 7 = very intense).} #' \item{alldeaths}{Human deaths occured (1:256).} #' \item{NDAM}{Normalized damage in millions (1:75.000). The raw (dollar) amounts of property damage caused by hurricanes were obtained, and the unadjusted dollar amounts were normalized to 2013 monetary values by adjusting them to inflation, wealth and population density.} #' \item{Elapsed_Yrs}{Elapsed years since the occurrence of hurricanes (1:63).} #' \item{Source}{MWR/wikipedia ()} #' \item{ZMasFem}{Scaled (MasFem)} #' \item{ZMinPressure_A}{Scaled (Minpressure_Updated_2014)} #' \item{ZNDAM}{Scaled (NDAM)} #' ... #' } #' @example inst/examples/hurricanes.R NULL DHARMa/R/createData.R0000644000176200001440000001446214677165224013654 0ustar liggesusers#' Simulate test data #' @description This function creates synthetic dataset with various problems such as overdispersion, zero-inflation, etc. #' @param sampleSize sample size of the dataset. #' @param intercept intercept (linear scale). #' @param fixedEffects vector of fixed effects (linear scale). #' @param quadraticFixedEffects vector of quadratic fixed effects (linear scale). #' @param numGroups number of groups for the random effect. #' @param randomEffectVariance variance of the random effect (intercept). #' @param overdispersion if this is a numeric value, it will be used as the sd of a random normal variate that is added to the linear predictor. Alternatively, a random function can be provided that takes as input the linear predictor. #' @param family family. #' @param scale scale if the distribution has a scale (e.g. sd for the Gaussian) #' @param cor correlation between predictors. #' @param roundPoissonVariance if set, this creates a uniform noise on the possion response. The aim of this is to create heteroscedasticity. #' @param pZeroInflation probability to set any data point to zero. #' @param binomialTrials Number of trials for the binomial. Only active if family == binomial. #' @param temporalAutocorrelation strength of temporalAutocorrelation. #' @param spatialAutocorrelation strength of spatial Autocorrelation. #' @param factorResponse should the response be transformed to a factor (inteded to be used for 0/1 data). #' @param replicates number of datasets to create. #' @param hasNA should an NA be added to the environmental predictor (for test purposes). #' @export #' @example /inst/examples/createDataHelp.R createData <- function(sampleSize = 100, intercept = 0, fixedEffects = 1, quadraticFixedEffects = NULL, numGroups = 10, randomEffectVariance = 1, overdispersion = 0, family = poisson(), scale = 1, cor = 0, roundPoissonVariance = NULL, pZeroInflation = 0, binomialTrials = 1, temporalAutocorrelation = 0, spatialAutocorrelation = 0, factorResponse = FALSE, replicates = 1, hasNA = FALSE){ nPredictors = length(fixedEffects) out = list() time = sample.int(sampleSize) #change to random order because of issue #436 x = runif(sampleSize) y = runif(sampleSize) for (i in 1:replicates){ ######################################################################## # Create predictors predictors = matrix(runif(nPredictors*sampleSize, min = -1), ncol = nPredictors) if (cor != 0){ predTemp <- runif(sampleSize, min = -1) predictors = (1-cor) * predictors + cor * matrix(rep(predTemp, nPredictors), ncol = nPredictors) } colnames(predictors) = paste("Environment", 1:nPredictors, sep = "") ######################################################################## # Create random effects group = rep(1:numGroups, each = sampleSize/numGroups) groupRandom = rnorm(numGroups, sd = sqrt(randomEffectVariance)) ######################################################################## # Creation of linear prediction linearResponse = intercept + predictors %*% fixedEffects + groupRandom[group] if(!is.null(quadraticFixedEffects)){ linearResponse = linearResponse + predictors^2 %*% quadraticFixedEffects } ######################################################################## # Overdispersion on linear predictor if(is.numeric(overdispersion)) linearResponse = linearResponse + rnorm(sampleSize, sd = overdispersion) if(is.function(overdispersion)) linearResponse = linearResponse + overdispersion(linearResponse) ######################################################################## # Autocorrelation if(!(temporalAutocorrelation == 0)){ distMat <- as.matrix(dist(time)) invDistMat <- 1/distMat * 5000 diag(invDistMat) <- 0 invDistMat = sfsmisc::posdefify(invDistMat) temporalError <- MASS::mvrnorm(n = 1, mu = rep(0,sampleSize), Sigma = invDistMat) linearResponse = linearResponse + temporalAutocorrelation * temporalError } if(!(spatialAutocorrelation == 0)) { distMat <- as.matrix(dist(cbind(x, y))) invDistMat <- 1/distMat * 5000 diag(invDistMat) <- 0 invDistMat = sfsmisc::posdefify(invDistMat) spatialError <- MASS::mvrnorm(n = 1, mu = rep(0,sampleSize), Sigma = invDistMat) linearResponse = linearResponse + spatialAutocorrelation * spatialError } ######################################################################## # Link and distribution linkResponse = family$linkinv(linearResponse) if (family$family == "gaussian") observedResponse = rnorm(n = sampleSize, mean = linkResponse, sd = scale) # need checking else if (family$family == "gamma") observedResponse = rgamma(n = sampleSize, shape = linkResponse / scale, scale = scale) else if (family$family == "binomial"){ observedResponse = rbinom(n = sampleSize, binomialTrials, prob = linkResponse) if (binomialTrials > 1) observedResponse = cbind(observedResponse1 = observedResponse, observedResponse0 = binomialTrials - observedResponse) } else if (family$family == "poisson") { if(is.null(roundPoissonVariance)) observedResponse = rpois(n = sampleSize, lambda = linkResponse) else observedResponse = round(rnorm(n = length(linkResponse), mean = linkResponse, sd = roundPoissonVariance)) } else if (grepl("Negative Binomial",family$family)) { theta = as.numeric(gsub("[\\(\\)]", "", regmatches(family$family, gregexpr("\\(.*?\\)", family$family))[[1]])) observedResponse = MASS::rnegbin(linkResponse, theta = theta) } else stop("wrong link argument supplied") ######################################################################## # Zero-inflation if(pZeroInflation != 0){ artificialZeros = rbinom(n = length(observedResponse), size = 1, prob = 1-pZeroInflation) observedResponse = observedResponse * artificialZeros } if(factorResponse) observedResponse = factor(observedResponse) # add spatialError? out[[i]] <- data.frame(ID = 1:sampleSize, observedResponse, predictors, group = as.factor(group), time, x, y) } if(length(out) == 1) out = out[[1]] if(hasNA) out[1,3] = NA return(out) } #createData() DHARMa/R/simulateResiduals.R0000644000176200001440000005116314704245735015312 0ustar liggesusers#' Create simulated residuals #' #' The function creates scaled residuals by simulating from the fitted model. Residuals can be extracted with [residuals.DHARMa]. See [testResiduals] for an overview of residual tests, [plot.DHARMa] for an overview of available plots. #' #' @param fittedModel A fitted model of a class supported by DHARMa. #' @param n Number of simulations. The smaller the number, the higher the stochastic error on the residuals. Also, for very small n, discretization artefacts can influence the tests. Default is 250, which is a relatively safe value. You can consider increasing to 1000 to stabilize the simulated values. #' @param refit If FALSE, new data will be simulated and scaled residuals will be created by comparing observed data with new data. If TRUE, the model will be refitted on the simulated data (parametric bootstrap), and scaled residuals will be created by comparing observed with refitted residuals. #' @param integerResponse If TRUE, noise will be added at to the residuals to maintain a uniform expectations for integer responses (such as Poisson or Binomial). Usually, the model will automatically detect the appropriate setting, so there is no need to adjust this setting. #' @param plot If TRUE, [plotResiduals] will be directly run after the residuals have been calculated. #' @param ... Further parameters to pass on to the simulate function of the model object. An important use of this is to specify whether simulations should be conditional on the current random effect estimates, e.g. via re.form. Note that not all models support syntax to specify conditional or unconditional simulations. See details and [getSimulations]. #' @param seed The random seed to be used within DHARMa. The default setting, recommended for most users, is keep the random seed on a fixed value 123. This means that you will always get the same randomization and thus the same result when running the same code. If NULL, no new seed is set, but previous random state will be restored after simulation. If FALSE, no seed is set, and random state will not be restored. The latter two options are only recommended for simulation experiments. See vignette for details. #' @param method For refit = FALSE, the quantile randomization method is used. The two options implemented at the moment are probability integral transform (PIT-) residuals (current default), and the "traditional" randomization procedure, that was used in DHARMa until version 0.3.0. refit = T will always use "traditional", respectively of the value of method. For details, see [getQuantile]. #' @param rotation Optional rotation of the residual space prior to calculating the quantile residuals. The main purpose of this is to account for residual covariance as created by temporal, spatial or phylogenetic autocorrelation. See details below, section *residual autocorrelation* as well as the help of [getQuantile] and, for a practical example, [testTemporalAutocorrelation]. #' #' @details There are a number of important considerations when simulating from a more complex (hierarchical) model: #' #' \strong{Re-simulating random effects / hierarchical structure}: in a hierarchical model, we have several stochastic processes aligned on top of each other. Specifically, in a GLMM, we have a lower level stochastic process (random effect), whose result enters into a higher level (e.g. Poisson distribution). For other hierarchical models such as state-space models, similar considerations apply. #' #' In such a situation, we have to decide if we want to re-simulate all stochastic levels, or only a subset of those. For example, in a GLMM, it is common to only simulate the last stochastic level (e.g. Poisson) conditional on the fitted random effects. This is often referred to as a conditional simulation. For controlling how many levels should be re-simulated, the simulateResidual function allows to pass on parameters to the simulate function of the fitted model object. Please refer to the help of the different simulate functions (e.g. ?simulate.merMod) for details. For merMod (lme4) model objects, the relevant parameters are parameters are use.u and re.form. For glmmTMB model objects, the package version 1.1.10 has a temporary solution to simulate conditional to all random effects (see [glmmTMB::set_simcodes] val = "fix", and issue [#888](https://github.com/glmmTMB/glmmTMB/issues/888) in glmmTMB GitHub repository. #' #' If the model is correctly specified, the simulated residuals should be flat regardless how many hierarchical levels we re-simulate. The most thorough procedure would therefore be to test all possible options. If testing only one option, I would recommend to re-simulate all levels, because this essentially tests the model structure as a whole. This is the default setting in the DHARMa package. A potential drawback is that re-simulating the lower-level random effects creates more variability, which may reduce power for detecting problems in the upper-level stochastic processes. In particular dispersion tests may produce different results when switching from conditional to unconditional simulations, and often the conditional simulation is more sensitive. #' #' \strong{Refitting or not}: a third issue is how residuals are calculated. simulateResiduals has two options that are controlled by the refit parameter: #' #' 1. if refit = FALSE (default), new data is simulated from the fitted model, and residuals are calculated by comparing the observed data to the new data. #' #' 2. if refit = TRUE, a parametric bootstrap is performed, meaning that the model is refit on the new data, and residuals are created by comparing observed residuals against refitted residuals. I advise against using this method per default (see more comments in the vignette), unless you are really sure that you need it. #' #' \strong{Residuals per group}: In many situations, it can be useful to look at residuals per group, e.g. to see how much the model over / underpredicts per plot, year or subject. To do this, use [recalculateResiduals], together with a grouping variable (see also help). #' #' \strong{Transformation to other distributions}: DHARMa calculates residuals for which the theoretical expectation (assuming a correctly specified model) is uniform. To transform this residuals to another distribution (e.g. so that a correctly specified model will have normal residuals) see [residuals.DHARMa]. #' #' \strong{Integer responses}: this is only relevant if method = "traditional", in which case it activates the randomization of the residuals. Usually, this does not need to be changed, as DHARMa will try to automatically check if the fitted model has an integer or discrete distribution via the family argument. However, in some cases the family does not allow to uniquely identify the distribution type. For example, a tweedie distribution can be interger or continuous. Therefore, DHARMa will additionally check the simulation results for repeated values, and will change the distribution type if repeated values are found (a message is displayed in this case). #' #' \strong{Residual autocorrelation}: a common problem is residual autocorrelation. Spatial, temporal and phylogenetic autocorrelation can be tested with [testSpatialAutocorrelation], [testTemporalAutocorrelation] and [testPhylogeneticAutocorrelation]. If simulations are unconditional, residual correlations will be maintained, even if the autocorrelation is addressed by an appropriate CAR structure. This may be a problem, because autocorrelation may create apparently systematic patterns in plots or tests such as [testUniformity]. To reduce this problem, either simulate conditional on fitted correlated REs, or rotate residuals via the rotation parameter (the latter will likely only work in approximately linear models). See [getQuantile] for details on the rotation. #' #' @return An S3 class of type "DHARMa". Implemented S3 functions include [plot.DHARMa], [print.DHARMa] and [residuals.DHARMa]. For other functions that can be used on a DHARMa object, see section "See Also" below. #' #' @seealso [testResiduals], [plotResiduals], [recalculateResiduals], [outliers] #' #' @example inst/examples/simulateResidualsHelp.R #' @import stats #' @export simulateResiduals <- function(fittedModel, n = 250, refit = FALSE, integerResponse = NULL, plot = FALSE, seed = 123, method = c("PIT", "traditional"), rotation = NULL, ...){ ######## general assertions and startup calculations ########## if (n < 2) stop("error in DHARMa::simulateResiduals: n > 1 is required to calculate scaled residuals") checkModel(fittedModel) match.arg(method) randomState <- getRandomState(seed) on.exit({randomState$restoreCurrent()}) ptm <- proc.time() ####### extract model info ############ out = list() family = getFamily(fittedModel) out$fittedModel = fittedModel out$modelClass = class(fittedModel)[1] out$additionalParameters = list(...) out$nObs = nobs(fittedModel) out$nSim = n out$refit = refit out$observedResponse = getObservedResponse(fittedModel) # this is to check for problem #325 if (out$nObs < length(out$observedResponse)) stop("DHARMA::simulateResiduals: nobs(model) < nrow(model.frame). A possible reason is that you have observation with zero prior weights (in binomial with n=0) in your data. Calculating residuals in this case wouldn't be sensible. Please remove zero-weight observations from your data and re-fit your model! If you believe that this is not the reason, please file an issue under https://github.com/florianhartig/DHARMa/issues") if(is.null(integerResponse)){ if (family$family %in% c("integer-valued", "binomial", "poisson", "quasibinomial", "quasipoisson", "Negative Binom", "nbinom2", "nbinom1", "genpois", "compois", "truncated_poisson", "truncated_nbinom2", "truncated_nbinom1", "betabinomial", "Poisson", "Tpoisson", "COMPoisson", "negbin", "Tnegbin") | grepl("Negative Binomial",family$family) ) integerResponse = TRUE else integerResponse = FALSE } out$integerResponse = integerResponse out$problems = list() out$fittedPredictedResponse = getFitted(fittedModel) out$fittedFixedEffects = getFixedEffects(fittedModel) out$fittedResiduals = getResiduals(fittedModel) ######## refit = F ################## if (refit == FALSE){ out$method = method out$simulatedResponse <- getSimulations(fittedModel, nsim = n, type = "normal", ...) checkSimulations(out$simulatedResponse, out$nObs, out$nSim) out$scaledResiduals <- getQuantile(simulations = out$simulatedResponse , observed = out$observedResponse , integerResponse = integerResponse, method = method, rotation = rotation) ######## refit = T ################## } else { out$method = "traditional" # Adding new outputs out$refittedPredictedResponse <- matrix(nrow = out$nObs, ncol = n ) out$refittedFixedEffects <- matrix(nrow = length(out$fittedFixedEffects), ncol = n ) #out$refittedRandomEffects <- matrix(nrow = length(out$fittedRandomEffects), ncol = n ) out$refittedResiduals <- matrix(nrow = out$nObs, ncol = n) out$refittedPearsonResiduals <- matrix(nrow = out$nObs, ncol = n) out$simulatedResponse <- getSimulations(fittedModel, nsim = n, type = "refit", ...) for (i in 1:n){ simObserved <- out$simulatedResponse[[i]] try({ # for testing # if (i==3) stop("x") # Note: also set silent = T for production refittedModel <- getRefit(fittedModel, simObserved, ...) out$refittedPredictedResponse[,i] <- getFitted(refittedModel) out$refittedFixedEffects[,i] <- getFixedEffects(refittedModel) out$refittedResiduals[,i] <- getResiduals(refittedModel) out$refittedPearsonResiduals[,i] <- residuals(refittedModel, type = "pearson") #out$refittedRandomEffects[,i] <- ranef(refittedModel) }, silent = TRUE) } ######### residual checks ########### if(anyNA(out$refittedResiduals)) warning("DHARMa::simulateResiduals warning: on refit = TRUE, at least one of the refitted models produced an error. Inspect the refitted model values. Results may not be reliable.") ## check for convergence problems dup = sum(duplicated(out$refittedFixedEffects, MARGIN = 2)) if (dup > 0){ if (dup < n/3){ warning(paste("There were", dup, "of", n ,"duplicate parameter estimates in the refitted models. This may hint towards a problem with optimizer convergence in the fitted models. Results may not be reliable. The suggested action is to not use the refitting procedure, and diagnose with tools available for the normal (not refitted) simulated residuals. If you absolutely require the refitting procedure, try changing tolerance / iterations in the optimizer settings.")) } else { warning(paste("There were", dup, "of", n ,"duplicate parameter estimates in the refitted models. This may hint towards a problem with optimizer convergence in the fitted models. Results are likely not reliable. The suggested action is to not use the refitting procedure, and diagnose with tools available for the normal (not refitted) simulated residuals. If you absolutely require the refitting procedure, try changing tolerance / iterations in the optimizer settings.")) out$problems[[length(out$problems)+ 1]] = "error in refit" } } ######### residual calculations ########### out$scaledResiduals = getQuantile(simulations = out$refittedResiduals, observed = out$fittedResiduals, integerResponse = integerResponse, method = "traditional", rotation = rotation) } ########### Wrapup ############ out$time = proc.time() - ptm out$randomState = randomState class(out) = "DHARMa" if(plot == TRUE) plot(out) return(out) } #' Check simulated data #' #' The function checks if the simulated data seems fine. #' #' @param simulatedResponse the simulated response #' @param nObs number of observations #' @param nSim number of simulations #' #' @keywords internal checkSimulations <- function(simulatedResponse, nObs, nSim){ if(!inherits(simulatedResponse, "matrix")) securityAssertion("Simulation from the model produced wrong class.", stop = TRUE) if(any(dim(simulatedResponse) != c(nObs, nSim) )) securityAssertion("Simulation from the model do not have the same dimension as nObs.", stop = FALSE) if(any(!is.finite(simulatedResponse))) message("Simulations from your fitted model produce infinite values. Consider if this is sensible.") if(any(is.nan(simulatedResponse))) securityAssertion("Simulations from your fitted model produce NaN values. DHARMa cannot calculated residuals for this. This is nearly certainly an error of the regression package you are using.", stop = TRUE) if(any(is.na(simulatedResponse))) securityAssertion("Simulations from your fitted model produce NA values. DHARMa cannot calculated residuals for this. This is nearly certainly an error of the regression package you are using.", stop = TRUE) } #' Recalculate residuals with grouping #' #' The purpose of this function is to recalculate scaled residuals per group, based on the simulations done by [simulateResiduals]. #' #' @param simulationOutput an object with simulated residuals created by [simulateResiduals]. #' @param group group of each data point. #' @param aggregateBy function for the aggregation. Default is sum. This should only be changed if you know what you are doing. Note in particular that the expected residual distribution might not be flat any more if you choose general functions, such as sd etc. #' @param sel an optional vector for selecting the data to be aggregated. #' @param seed the random seed to be used within DHARMa. The default setting, recommended for most users, is keep the random seed on a fixed value 123. This means that you will always get the same randomization and thus teh same result when running the same code. NULL = no new seed is set, but previous random state will be restored after simulation. FALSE = no seed is set, and random state will not be restored. The latter two options are only recommended for simulation experiments. See vignette for details. #' @param method the quantile randomization method used. The two options implemented at the moment are probability integral transform (PIT-) residuals (current default), and the "traditional" randomization procedure, that was used in DHARMa until version 0.3.0. For details, see [getQuantile]. #' @param rotation optional rotation of the residual space to remove residual autocorrelation. See details in [simulateResiduals], section *residual auto-correlation* for an extended explanation, and [getQuantile] for syntax. #' @return an object of class DHARMa, similar to what is returned by [simulateResiduals], but with additional outputs for the new grouped calculations. Note that the relevant outputs are 2x in the object, the first is the grouped calculations (which is returned by $name access), and later another time, under identical name, the original output. Moreover, there is a function 'aggregateByGroup', which can be used to aggregate predictor variables in the same way as the variables calculated here. #' #' @details The function aggregates the observed and simulated data per group according to the function provided by the aggregateBy option. DHARMa residuals are then calculated exactly as for a single data point (see [getQuantile] for details). #' #' @example inst/examples/simulateResidualsHelp.R #' @export recalculateResiduals <- function(simulationOutput, group = NULL, aggregateBy = sum, sel = NULL, seed = 123, method = c("PIT", "traditional"), rotation = NULL){ randomState <- getRandomState(seed) on.exit({randomState$restoreCurrent()}) match.arg(method) # ensures that the base simulation is always used for recalculate if(!is.null(simulationOutput$original)) simulationOutput = simulationOutput$original out = list() out$original = simulationOutput out$group = group out$method = method out$aggregateBy = aggregateBy if(is.null(group) & is.null(sel)) return(simulationOutput) else { if(is.null(group)) group = 1:simulationOutput$nObs group = as.factor(group) out$nGroups = nlevels(group) if(is.null(sel)) sel = 1:simulationOutput$nObs out$sel = sel aggregateByGroup <- function(x) aggregate(x[sel], by = list(group[sel]), FUN=aggregateBy)[,2] out$observedResponse = aggregateByGroup(simulationOutput$observedResponse) out$fittedPredictedResponse = aggregateByGroup(simulationOutput$fittedPredictedResponse) if (simulationOutput$refit == FALSE){ out$simulatedResponse = apply(simulationOutput$simulatedResponse, 2, aggregateByGroup) out$scaledResiduals = getQuantile(simulations = out$simulatedResponse , observed = out$observedResponse, integerResponse = simulationOutput$integerResponse, method = method, rotation = rotation) ######## refit = T ################## } else { out$refittedPredictedResponse <- apply(simulationOutput$refittedPredictedResponse, 2, aggregateByGroup) out$fittedResiduals = aggregateByGroup(simulationOutput$fittedResiduals) out$refittedResiduals = apply(simulationOutput$refittedResiduals, 2, aggregateByGroup) out$refittedPearsonResiduals = apply(simulationOutput$refittedPearsonResiduals, 2, aggregateByGroup) out$scaledResiduals = getQuantile(simulations = out$refittedResiduals , observed = out$fittedResiduals , integerResponse = simulationOutput$integerResponse, method = method, rotation = rotation) } # hack - the c here will result in both old and new outputs to be present resulting output, but a named access should refer to the new, grouped calculations # question to myself - what's the use of that, why not erase the old outputs? they are anyway saved in the old object out$aggregateByGroup = aggregateByGroup out = c(out, simulationOutput) out$randomState = randomState class(out) = "DHARMa" return(out) } } DHARMa/R/plots.R0000644000176200001440000004613614703461527012756 0ustar liggesusers#' DHARMa standard residual plots #' #' This S3 function creates standard plots for the simulated residuals contained in an object of class DHARMa, using [plotQQunif] (left panel) and [plotResiduals] (right panel) #' #' @param x An object of class DHARMa with simulated residuals created by [simulateResiduals]. #' @param ... Further options for [plotResiduals]. Consider in particular parameters quantreg, rank and asFactor. xlab, ylab and main cannot be changed when using plot.DHARMa, but can be changed when using [plotResiduals]. #' @param title The title for both panels (plotted via mtext, outer = TRUE). #' #' @details The function creates a plot with two panels. The left panel is a uniform qq plot (calling [plotQQunif]), and the right panel shows residuals against predicted values (calling [plotResiduals]), with outliers highlighted in red (default color but see Note). #' #' Very briefly, we would expect that a correctly specified model shows: #' #' a) a straight 1-1 line, as well as non-significance of the displayed tests in the qq-plot (left) -> evidence for an the correct overall residual distribution (for more details on the interpretation of this plot, see [plotQQunif]) #' #' b) visual homogeneity of residuals in both vertical and horizontal direction, as well as n.s. of quantile tests in the res ~ predictor plot (for more details on the interpretation of this plot, see [plotResiduals]) #' #' Deviations from these expectations can be interpreted similar to a linear regression. See the vignette for detailed examples. #' #' Note that, unlike [plotResiduals], plot.DHARMa command uses the default rank = T. #' #' @note The color for highlighting outliers and significant tests can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. This is convenient for a color-blind friendly display, since red and black are difficult for some people to separate. #' #' @seealso [plotResiduals], [plotQQunif] #' @example inst/examples/plotsHelp.R #' @import graphics #' @import utils #' @export plot.DHARMa <- function(x, title = "DHARMa residual", ...){ oldpar <- par(mfrow = c(1,2), oma = c(0,1,2,1)) on.exit(par(oldpar)) plotQQunif(x) plotResiduals(x, ...) mtext(title, outer = TRUE) } #' Histogram of DHARMa residuals #' #' The function produces a histogram from a DHARMa output. Outliers are marked red. #' #' @param x A DHARMa simulation output (class DHARMa) #' @param breaks Breaks for hist() function. #' @param col Color for histogram bars. #' @param main Plot title. #' @param xlab Plot x-axis label. #' @param cex.main Plot cex.main. #' @param ... Other arguments to be passed on to hist(). #' @details The function calls hist() to create a histogram of the scaled residuals. Outliers are marked red as default but it can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. #' @seealso [plotSimulatedResiduals], [plotResiduals] #' @example inst/examples/plotsHelp.R #' @export hist.DHARMa <- function(x, breaks = seq(-0.02, 1.02, len = 53), col = c(.Options$DHARMaSignalColor,rep("lightgrey",50), .Options$DHARMaSignalColor), main = "Hist of DHARMa residuals", xlab = "Residuals (outliers are marked red)", cex.main = 1, ...){ x = ensureDHARMa(x, convert = TRUE) val = x$scaledResiduals val[val == 0] = -0.01 val[val == 1] = 1.01 hist(val, breaks = breaks, col = col, main = main, xlab = xlab, cex.main = cex.main, ...) } #' DHARMa standard residual plots #' #' DEPRECATED, use plot() instead #' #' @param simulationOutput an object with simulated residuals created by [simulateResiduals] #' @param ... further options for [plotResiduals]. Consider in particular parameters quantreg, rank and asFactor. xlab, ylab and main cannot be changed when using plotSimulatedResiduals, but can be changed when using plotResiduals. #' @note This function is deprecated. Use [plot.DHARMa] #' #' @seealso [plotResiduals], [plotQQunif] #' @export plotSimulatedResiduals <- function(simulationOutput, ...){ message("plotSimulatedResiduals is deprecated, please switch your code to simply using the plot() function") plot(simulationOutput, ...) } #' Quantile-quantile plot for a uniform distribution #' #' The function produces a uniform quantile-quantile plot from a DHARMa output. Optionally, tests for uniformity, outliers and dispersion can be added. #' #' @param simulationOutput A DHARMa simulation output (class DHARMa). #' @param testUniformity If T, the function [testUniformity] will be called and the result will be added to the plot. #' @param testOutliers If T, the function [testOutliers] will be called and the result will be added to the plot. #' @param testDispersion If T, the function [testDispersion] will be called and the result will be added to the plot. #' @param ... Arguments to be passed on to [gap::qqunif]. #' #' @details The function calls qqunif() from the R package gap to create a quantile-quantile plot for a uniform distribution, and overlays tests for particular distributional problems as specified. #' When tests are displayed, significant p-values are highlighted in the color red by default. This can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. #' @seealso [plotSimulatedResiduals], [plotResiduals] #' @example inst/examples/plotsHelp.R #' @export plotQQunif <- function(simulationOutput, testUniformity = TRUE, testOutliers = TRUE, testDispersion = TRUE, ...){ a <- list(...) a$pch = checkDots("pch", 2, ...) a$bty = checkDots("bty", "n", ...) a$logscale = checkDots("logscale", F, ...) a$col = checkDots("col", "black", ...) a$main = checkDots("main", "QQ plot residuals", ...) a$cex.main = checkDots("cex.main", 1, ...) a$xlim = checkDots("xlim", c(0,1), ...) a$ylim = checkDots("ylim", c(0,1), ...) simulationOutput = ensureDHARMa(simulationOutput, convert = "Model") do.call(gap::qqunif, append(list(simulationOutput$scaledResiduals), a)) if(testUniformity == TRUE){ temp = testUniformity(simulationOutput, plot = FALSE) legend("topleft", c(paste("KS test: p=", round(temp$p.value, digits = 5)), paste("Deviation ", ifelse(temp$p.value < 0.05, "significant", "n.s."))), text.col = ifelse(temp$p.value < 0.05, .Options$DHARMaSignalColor, "black" ), bty="n") } if(testOutliers == TRUE){ temp = testOutliers(simulationOutput, plot = FALSE) legend("bottomright", c(paste("Outlier test: p=", round(temp$p.value, digits = 5)), paste("Deviation ", ifelse(temp$p.value < 0.05, "significant", "n.s."))), text.col = ifelse(temp$p.value < 0.05, .Options$DHARMaSignalColor, "black" ), bty="n") } if(testDispersion == TRUE){ temp = testDispersion(simulationOutput, plot = FALSE) legend("center", c(paste("Dispersion test: p=", round(temp$p.value, digits = 5)), paste("Deviation ", ifelse(temp$p.value < 0.05, "significant", "n.s."))), text.col = ifelse(temp$p.value < 0.05, .Options$DHARMaSignalColor, "black" ), bty="n") } } #' Generic res ~ pred scatter plot with spline or quantile regression on top #' #' The function creates a generic residual plot with either spline or quantile regression to highlight patterns in the residuals. Outliers are highlighted in red by default (but see Details). #' #' @param simulationOutput An object, usually a DHARMa object, from which residual values can be extracted. Alternatively, a vector with residuals or a fitted model can be provided, which will then be transformed into a DHARMa object. #' @param form Optional predictor against which the residuals should be plotted. Default is to used the predicted(simulationOutput). #' @param quantreg Whether to perform a quantile regression based on [testQuantiles] or a smooth spline around the mean. Default NULL chooses T for nObs < 2000, and F otherwise. #' @param rank If T, the values provided in form will be rank transformed. This will usually make patterns easier to spot visually, especially if the distribution of the predictor is skewed. If form is a factor, this has no effect. #' @param asFactor Should a numeric predictor provided in form be treated as a factor. Default is to choose this for < 10 unique values, as long as enough predictions are available to draw a boxplot. #' @param smoothScatter if T, a smooth scatter plot will plotted instead of a normal scatter plot. This makes sense when the number of residuals is very large. Default NULL chooses T for nObs > 10000, and F otherwise. #' @param quantiles For a quantile regression, which quantiles should be plotted. Default is 0.25, 0.5, 0.75. #' @param absoluteDeviation If T, switch from displaying normal quantile residuals to absolute deviation from the mean expectation of 0.5 (calculated as 2 * abs(res - 0.5)). The purpose of this is to test explicitly for heteroskedasticity, see details. #' @param ... Additional arguments to plot / boxplot. #' @details The function plots residuals against a predictor (by default against the fitted value, extracted from the DHARMa object, or any other predictor). #' #' Outliers are highlighted in red as default (for information on definition and interpretation of outliers, see [testOutliers]). This can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. #' #' To provide a visual aid for detecting deviations from uniformity in the y-direction, the plot function calculates an (optional) quantile regression of the residuals, by default for the 0.25, 0.5 and 0.75 quantiles. Since the residuals should be uniformly distributed for a correctly specified model, the theoretical expectations for these regressions are straight lines at 0.25, 0.5 and 0.75, shown as dashed black lines on the plot. However, even for a perfect model, some deviation from these expectations is to be expected by chance, especially if the sample size is small. The function therefore tests whether the deviation of the fitted quantile regression from the expectation is significant, using [testQuantiles]. If so, the significant quantile regression is highlighted in red (as default) and a warning is displayed in the plot. #' #' Overdispersion typically manifests itself as Q1 (0.25) deviating towards 0 and Q3 (0.75) deviating towards 1. Heteroskedasticity manifests itself as non-parallel quantile lines. To diagnose heteroskedasticity and overdispersion, it can be helpful to additionally plot the absolute deviation of the residuals from the mean expectation of 0.5, using the option absoluteDeviation = T. In this case, we would again expect Q1-Q3 quantile lines at 0.25, 0.5, 0.75, but greater dispersion (also locally in the case of heteroskedasticity) always manifests itself in deviations towards 1. #' #' The quantile regression can take some time to calculate, especially for larger data sets. For this reason, quantreg = F can be set to generate a smooth spline instead. This is the default for n > 2000. #' #' If form is a factor, a boxplot will be plotted instead of a scatter plot. The distribution for each factor level should be uniformly distributed, so the box should go from 0.25 to 0.75, with the median line at 0.5 (within-group). To test if deviations from those expecations are significant, KS-tests per group and a Levene test for homogeneity of variances is performed. See [testCategorical] for details. #' #' @note If nObs > 10000, the scatter plot is replaced by graphics::smoothScatter #' #' #' @note The color for highlighting outliers and quantile lines/splines with significant tests can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. This is convenient for a color-blind friendly display, since red and black are difficult for some people to separate. #' #' @return If quantile tests are performed, the function returns them invisibly. #' #' @seealso [plotQQunif], [testQuantiles], [testOutliers] #' @example inst/examples/plotsHelp.R #' @export plotResiduals <- function(simulationOutput, form = NULL, quantreg = NULL, rank = TRUE, asFactor = NULL, smoothScatter = NULL, quantiles = c(0.25, 0.5, 0.75), absoluteDeviation = FALSE, ...){ ##### Checks ##### a <- list(...) yAxis = ifelse(absoluteDeviation == TRUE, "Residual spread [2*abs(res - 0.5)]", "DHARMa residual") a$ylab = checkDots("ylab", yAxis , ...) a$xlab = checkDots("xlab", ifelse(is.null(form), "Model predictions", gsub(".*[$]","",deparse(substitute(form)))), ...) if(rank == TRUE) a$xlab = paste(a$xlab, "(rank transformed)") simulationOutput = ensureDHARMa(simulationOutput, convert = TRUE) res = simulationOutput$scaledResiduals if(absoluteDeviation == TRUE){ res = 2 * abs(res - 0.5) } if(inherits(form, "DHARMa"))stop("DHARMa::plotResiduals > argument form cannot be of class DHARMa. Note that the syntax of plotResiduals has changed since DHARMa 0.3.0. See ?plotResiduals.") pred = ensurePredictor(simulationOutput, form) ##### Rank transform and factor conversion##### if(!is.factor(pred)){ if (rank == TRUE){ pred = rank(pred, ties.method = "average") pred = pred / max(pred) a$xlim = checkDots("xlim", c(0,1), ...) } nuniq = length(unique(pred)) ndata = length(pred) if(is.null(asFactor)) asFactor = (nuniq == 1) | (nuniq < 10 & ndata / nuniq > 10) if (asFactor) pred = factor(pred) } ##### Residual scatter plots ##### if(is.null(quantreg)) if (length(res) > 2000) quantreg = FALSE else quantreg = TRUE switchScatter = 10000 if(is.null(smoothScatter)) if (length(res) > switchScatter) smoothScatter = TRUE else smoothScatter = FALSE blackcol = rgb(0,0,0, alpha = max(0.1, 1 - 3 * length(res) / switchScatter)) # Note to self: wrapped in do.call because of the check dots, needs to be consolidate, e.g. for testCategorical # categorical plot if(is.factor(pred)){ testCategorical(simulationOutput = simulationOutput, catPred = pred, quantiles = quantiles) } # smooth scatter else if (smoothScatter == TRUE) { defaultCol = ifelse(res == 0 | res == 1, 2,blackcol) do.call(graphics::smoothScatter, append(list(x = pred, y = res , ylim = c(0,1), axes = FALSE, colramp = colorRampPalette(c("white", "darkgrey"))),a)) points(pred[defaultCol == 2], res[defaultCol == 2], col = .Options$DHARMaSignalColor, cex = 0.5) axis(1) axis(2, at=c(0, quantiles, 1)) } # normal plot else{ defaultCol = ifelse(res == 0 | res == 1, 2,blackcol) defaultPch = ifelse(res == 0 | res == 1, 8,1) a$col = checkDots("col", defaultCol, ...) a$pch = checkDots("pch", defaultPch, ...) do.call(plot, append(list(res ~ pred, ylim = c(0,1), axes = FALSE), a)) axis(1) axis(2, at=c(0, quantiles, 1)) } ##### Quantile regressions ##### main = checkDots("main", ifelse(is.null(form), paste(yAxis, "vs. predicted"), paste(yAxis, "Residual vs. predictor")), ...) out = NULL if(is.numeric(pred)){ if(quantreg == FALSE){ title(main = main, cex.main = 1) abline(h = quantiles, col = "black", lwd = 0.5, lty = 2) try({ lines(smooth.spline(pred, res, df = 10), lty = 2, lwd = 2, col = .Options$DHARMaSignalColor) abline(h = 0.5, col = .Options$DHARMaSignalColor, lwd = 2) }, silent = TRUE) }else{ out = testQuantiles(res, pred, quantiles = quantiles, plot = FALSE) if(is.na(out$p.value)){ main = paste(main, "Some quantile regressions failed", sep = "\n") maincol = .Options$DHARMaSignalColor } else{ if(any(out$pvals < 0.05, na.rm = TRUE)){ main = paste(main, "Quantile deviations detected (red curves)", sep ="\n") if(out$p.value <= 0.05){ main = paste(main, "Combined adjusted quantile test significant", sep ="\n") } else { main = paste(main, "Combined adjusted quantile test n.s.", sep ="\n") } maincol = .Options$DHARMaSignalColor } else { main = paste(main, "No significant problems detected", sep ="\n") maincol = "black" } } title(main = main, cex.main = 0.8, col.main = maincol) for(i in 1:length(quantiles)){ lineCol = ifelse(out$pvals[i] <= 0.05 & !(is.na(out$pvals[i])), .Options$DHARMaSignalColor, "black") filCol = ifelse(out$pvals[i] <= 0.05 & !(is.na(out$pvals[i])), "#FF000040", "#00000020") abline(h = quantiles[i], col = lineCol, lwd = 0.5, lty = 2) polygon(c(out$predictions$pred, rev(out$predictions$pred)), c(out$predictions[,2*i] - out$predictions[,2*i+1], rev(out$predictions[,2*i] + out$predictions[,2*i+1])), col = "#00000020", border = FALSE) lines(out$predictions$pred, out$predictions[,2*i], col = lineCol, lwd = 2) } } } invisible(out) } #' Ensures the existence of a valid predictor to plot residuals against #' #' @param simulationOutput A DHARMa simulation output or an object that can be converted into a DHARMa simulation output. #' @param predictor An optional predictor. If no predictor is provided, will try to extract the fitted value. #' @keywords internal ensurePredictor <- function(simulationOutput, predictor = NULL){ if(!is.null(predictor)){ if(length(predictor) != length(simulationOutput$scaledResiduals)) stop("DHARMa: residuals and predictor do not have the same length. The issue is possibly that you have NAs in your predictor that were removed during the model fit. Remove the NA values from your predictor.") if(is.character(predictor)) { predictor = factor(predictor) warning("DHARMa:::ensurePredictor: character string was provided as predictor. DHARMa has converted to factor automatically. To remove this warning, please convert to factor before attempting to plot with DHARMa.") } } else { predictor = simulationOutput$fittedPredictedResponse if(is.null(predictor)) stop("DHARMa: can't extract predictor from simulationOutput, and no predictor provided.") } return(predictor) } #plotConventionalResiduals(fittedModel) #' Conventional residual plot #' #' Convenience function to draw conventional residual plots #' #' @param fittedModel a fitted model object #' @export plotConventionalResiduals <- function(fittedModel){ opar <- par(mfrow = c(1,3), oma = c(0,1,2,1)) on.exit(par(opar)) plot(predict(fittedModel), resid(fittedModel, type = "deviance"), main = "Deviance" , ylab = "Residual", xlab = "Predicted") plot(predict(fittedModel), resid(fittedModel, type = "pearson") , main = "Pearson", ylab = "Residual", xlab = "Predicted") plot(predict(fittedModel), resid(fittedModel, type = "response") , main = "Raw residuals" , ylab = "Residual", xlab = "Predicted") mtext("Conventional residual plots", outer = TRUE) } DHARMa/R/tests.R0000644000176200001440000015010114703461527012743 0ustar liggesusers#' DHARMa general residual test #' #' Calls uniformity, dispersion and outliers tests. #' #' This function is a wrapper for the various test functions implemented in DHARMa. Currently, this function calls the functions [testUniformity], [testDispersion], and [testOutliers]. All other tests (see list below) have to be called by hand. #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param plot if TRUE, plots functions of the tests are called. #' @author Florian Hartig #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @example inst/examples/testsHelp.R #' @export testResiduals <- function(simulationOutput, plot = TRUE){ opar = par(mfrow = c(1,3)) on.exit(par(opar)) out = list() out$uniformity = testUniformity(simulationOutput, plot = plot) out$dispersion = testDispersion(simulationOutput, plot = plot) out$outliers = testOutliers(simulationOutput, plot = plot) #print(out) # do we need it? return(out) } #' Residual tests #' #' @details Deprecated, switch your code to using the [testResiduals] function #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @author Florian Hartig #' @export testSimulatedResiduals <- function(simulationOutput){ message("testSimulatedResiduals is deprecated, switch your code to using the testResiduals function") testResiduals(simulationOutput) } #' Test for overall uniformity #' #' This function tests the overall uniformity of the simulated residuals in a DHARMa object #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param alternative a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis. See [stats::ks.test] for details #' @param plot if TRUE, plots calls [plotQQunif] as well #' @details The function applies a [stats::ks.test] for uniformity on the simulated residuals. #' @author Florian Hartig #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @example inst/examples/testsHelp.R #' @export testUniformity <- function(simulationOutput, alternative = c("two.sided", "less", "greater"), plot = TRUE){ simulationOutput = ensureDHARMa(simulationOutput, convert = T) out <- suppressWarnings(ks.test(simulationOutput$scaledResiduals, 'punif', alternative = alternative)) if(plot == T) plotQQunif(simulationOutput = simulationOutput) return(out) } # Experimental testBivariateUniformity <- function(simulationOutput, alternative = c("two.sided", "less", "greater"), plot = TRUE){ simulationOutput = ensureDHARMa(simulationOutput, convert = T) #out <- suppressWarnings(ks.test(simulationOutput$scaledResiduals, 'punif', alternative = alternative)) #if(plot == T) plotQQunif(simulationOutput = simulationOutput) out = NULL return(out) } #' Test for quantiles #' #' This function tests #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param predictor an optional predictor variable to be used, instead of the predicted response (default) #' @param quantiles the quantiles to be tested #' @param plot if TRUE, the function will create an additional plot #' @details The function fits quantile regressions (via package qgam) on the residuals, and compares their location to the expected location (because of the uniform distributionm, the expected location is 0.5 for the 0.5 quantile). #' #' A significant p-value for the splines means the fitted spline deviates from a flat line at the expected location (p-values of intercept and spline are combined via Benjamini & Hochberg adjustment to control the FDR) #' #' The p-values of the splines are combined into a total p-value via Benjamini & Hochberg adjustment to control the FDR. #' #' @author Florian Hartig #' @example inst/examples/testQuantilesHelp.R #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @export testQuantiles <- function(simulationOutput, predictor = NULL, quantiles = c(0.25,0.5,0.75), plot = TRUE){ if(plot == F){ out = list() out$data.name = deparse(substitute(simulationOutput)) simulationOutput = ensureDHARMa(simulationOutput, convert = T) res = simulationOutput$scaledResiduals pred = ensurePredictor(simulationOutput, predictor) dat = data.frame(res = simulationOutput$scaledResiduals, pred = pred) quantileFits <- list() pval = rep(NA, length(quantiles)) predictions = data.frame(pred = sort(dat$pred)) predictions = cbind(predictions, matrix(ncol = 2 * length(quantiles), nrow = nrow(dat))) for(i in 1:length(quantiles)){ datTemp = dat datTemp$res = datTemp$res - quantiles[i] # settings for k = the dimension of the basis used to represent the smooth term. # see https://github.com/mfasiolo/qgam/issues/37 dimSmooth = min(length(unique(datTemp$pred)), 10) quantResult = try(capture.output(quantileFits[[i]] <- qgam::qgam(res ~ s(pred, k = dimSmooth), data = datTemp, qu = quantiles[i])), silent = T) if(inherits(quantResult, "try-error")){ message("\n DHARMa: qgam was unable to calculate quantile regression for quantile ", quantiles[i], ". Possibly to few (unique) data points / predictions. The quantile will be ommited in plots and significance calculations. \n") } else { x = summary(quantileFits[[i]]) pval[i] = min(p.adjust(c(x$p.table[1,4], x$s.table[1,4]), method = "BH")) # correction for test on slope and intercept quantPre = predict(quantileFits[[i]], newdata = predictions, se = T) predictions[, 2*i] = quantPre$fit + quantiles[i] predictions[, 2*i + 1] = quantPre$se.fit } } out$method = "Test for location of quantiles via qgam" out$alternative = "both" out$pvals = pval out$p.value = min(p.adjust(pval, method = "BH")) # correction for multiple quantile tests out$predictions = predictions out$qgamFits = quantileFits class(out) = "htest" } else if(plot == T) { out <- plotResiduals(simulationOutput = simulationOutput, form = predictor, quantiles = quantiles, quantreg = TRUE) } return(out) } #unif.2017YMi(X, type = c("Q1", "Q2", "Q3"), lower = rep(0, ncol(X)),upper = rep(1, ncol(X))) #' Test for outliers #' #' This function tests if the number of observations outside the simulatio envelope are larger or smaller than expected #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param alternative a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" (default) compared to the simulated null hypothesis #' @param margin whether to test for outliers only at the lower, only at the upper, or both sides (default) of the simulated data distribution #' @param type either default, bootstrap or binomial. See details #' @param nBoot number of boostrap replicates. Only used ot type = "bootstrap" #' @param plot if TRUE, the function will create an additional plot #' @param plotBoostrap if plot should be produced of outlier frequencies calculated under the bootstrap #' @details DHARMa residuals are created by simulating from the fitted model, and comparing the simulated values to the observed data. It can occur that all simulated values are higher or smaller than the observed data, in which case they get the residual value of 0 and 1, respectively. I refer to these values as simulation outliers, or simply outliers. #' #' Because no data was simulated in the range of the observed value, we don't know "how strongly" these values deviate from the model expectation, so the term "outlier" should be used with a grain of salt. It is not a judgment about the magnitude of the residual deviation, but simply a dichotomous sign that we are outside the simulated range. Moreover, the number of outliers will decrease as we increase the number of simulations. #' #' To test if the outliers are a concern, testOutliers implements 2 options (bootstrap, binomial), which can be chosen via the parameter "type". The third option (default) chooses bootstrap for integer-valued distribubtions with nObs < 500, and else binomial. #' #' The binomial test considers that under the null hypothesis that the model is correct, and for continuous distributions (i.e. data and the model distribution are identical and continous), the probability that a given observation is higher than all simulations is 1/(nSim +1), and binomial distributed. The testOutlier function can test this null hypothesis via type = "binomial". In principle, it would be nice if we could extend this idea to integer-valued distributions, which are randomized via the PIT procedure (see [simulateResiduals]), the rate of "true" outliers is more difficult to calculate, and in general not 1/(nSim +1). The testOutlier function implements a small tweak that calculates the rate of residuals that are closer than 1/(nSim+1) to the 0/1 border, which roughly occur at a rate of nData /(nSim +1). This approximate value, however, is generally not exact, and may be particularly off non-bounded integer-valued distributions (such as Poisson or Negative Binomial). #' #' For this reason, the testOutlier function implements an alternative procedure that uses the bootstrap to generate a simulation-based expectation for the outliers. It is recommended to use the bootstrap for integer-valued distributions (and integer-valued only, because it has no advantage for continuous distributions, ideally with reasonably high values of nSim and nBoot (I recommend at least 1000 for both). Because of the high runtime, however, this option is switched off for type = default when nObs > 500. #' #' Both binomial or bootstrap generate a null expectation, and then test for an excess or lack of outliers. Per default, testOutliers() looks for both, so if you get a significant p-value, you have to check if you have to many or too few outliers. An excess of outliers is to be interpreted as too many values outside the simulation envelope. This could be caused by overdispersion, or by what we classically call outliers. A lack of outliers would be caused, for example, by underdispersion. #' #' #' @author Florian Hartig #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @export testOutliers <- function(simulationOutput, alternative = c("two.sided", "greater", "less"), margin = c("both", "upper", "lower"), type = c("default","bootstrap", "binomial"), nBoot = 100, plot = TRUE, plotBoostrap = FALSE){ # check inputs alternative = match.arg(alternative) margin = match.arg(margin) type = match.arg(type) data.name = deparse(substitute(simulationOutput)) # remember: needs to be called before ensureDHARMa simulationOutput = ensureDHARMa(simulationOutput, convert = "Model") if(type == "default"){ if(simulationOutput$integerResponse == FALSE) type = "binomial" else{ if(simulationOutput$nObs > 500) type = "binomial" else type = "bootstrap" } } # using the binomial test, not exact if(type == "binomial"){ # calculation of outliers if(margin == "both") outliers = sum(simulationOutput$scaledResiduals < (1/(simulationOutput$nSim+1))) + sum(simulationOutput$scaledResiduals > (1-1/(simulationOutput$nSim+1))) if(margin == "upper") outliers = sum(simulationOutput$scaledResiduals > (1-1/(simulationOutput$nSim+1))) if(margin == "lower") outliers = sum(simulationOutput$scaledResiduals < (1/(simulationOutput$nSim+1))) # calculations of trials and H0 outFreqH0 = 1/(simulationOutput$nSim +1) * ifelse(margin == "both", 2, 1) trials = simulationOutput$nObs out = binom.test(outliers, trials, p = outFreqH0, alternative = alternative) # overwrite information in binom.test out$method = "DHARMa outlier test based on exact binomial test with approximate expectations" out$data.name = data.name out$margin = margin names(out$statistic) = paste("outliers at", margin, "margin(s)") names(out$parameter) = "observations" names(out$estimate) = paste("frequency of outliers (expected:", out$null.value,")") if (simulationOutput$integerResponse == T & out$p.value < 0.05) message("DHARMa:testOutliers with type = binomial may have inflated Type I error rates for integer-valued distributions. To get a more exact result, it is recommended to re-run testOutliers with type = 'bootstrap'. See ?testOutliers for details") if(plot == T) { hist(simulationOutput, main = "") main = ifelse(out$p.value <= 0.05, "Outlier test significant", "Outlier test n.s.") title(main = main, cex.main = 1, col.main = ifelse(out$p.value <= 0.05, "red", "black")) } } else { if(margin == "both") outliers = mean(simulationOutput$scaledResiduals == 0) + mean(simulationOutput$scaledResiduals == 1) if(margin == "upper") outliers = mean(simulationOutput$scaledResiduals == 1) if(margin == "lower") outliers = mean(simulationOutput$scaledResiduals == 0) # Bootstrapping to compare to expected simIndices = 1:simulationOutput$nSim nSim = simulationOutput$nSim if(simulationOutput$refit == T){ simResp = simulationOutput$refittedResiduals } else { simResp = simulationOutput$simulatedResponse } resMethod = simulationOutput$method resInteger = simulationOutput$integerResponse if (nBoot > nSim){ message("DHARMa::testOutliers: nBoot > nSim does not make much sense, thus changed to nBoot = nSim. If you want to increase nBoot, increase nSim in DHARMa::simulateResiduals as well.") nBoot = nSim } frequBoot <- rep(NA, nBoot) for (i in 1:nBoot){ #sel = -i sel = sample(simIndices[-i], size = nSim, replace = T) residuals <- getQuantile(simulations = simResp[,sel], observed = simResp[,i], integerResponse = resInteger, method = resMethod) if(margin == "both") frequBoot[i] = mean(residuals == 1) + mean(residuals == 0) else if(margin == "upper") frequBoot[i] = mean(residuals == 1) else if(margin == "lower") frequBoot[i] = mean(residuals == 0) } out = list() class(out) = "htest" out$alternative = alternative out$p.value = getP(frequBoot, outliers, alternative = alternative) out$conf.int = quantile(frequBoot, c(0.025, 0.975)) out$data.name = data.name out$margin = margin out$method = "DHARMa bootstrapped outlier test" out$statistic = outliers * simulationOutput$nObs names(out$statistic) = paste("outliers at", margin, "margin(s)") out$parameter = simulationOutput$nObs names(out$parameter) = "observations" out$estimate = outliers names(out$estimate) = paste("outlier frequency (expected:", mean(frequBoot),")") if(plotBoostrap == T){ hist(frequBoot, xlim = range(frequBoot, outliers), col = "lightgrey", main = "Bootstrapped outlier frequency") abline(v = mean(frequBoot), col = 1, lwd = 2) abline(v = outliers, col = "red", lwd = 2) # legend("center", c(paste("p=", round(out$p.value, digits = 5)), paste("Deviation ", ifelse(out$p.value < 0.05, "significant", "n.s."))), text.col = ifelse(out$p.value < 0.05, "red", "black" )) } if(plot == T) { hist(simulationOutput, main = "") main = ifelse(out$p.value <= 0.05, "Outlier test significant", "Outlier test n.s.") title(main = main, cex.main = 1, col.main = ifelse(out$p.value <= 0.05, "red", "black")) } } return(out) } #' Test for categorical dependencies #' #' This function tests if there are probles in a res ~ group structure. It performs two tests: test for within-group uniformity, and test for between-group homogeneity of variances #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param catPred a categorical predictor with the same dimensions as the residuals in simulationOutput #' @param quantiles whether to draw the quantile lines. #' @param plot if TRUE, the function will create an additional plot #' @details The function tests for two common problems: are residuals within each group distributed according to model assumptions, and is the variance between group heterogeneous. #' #' The test for within-group uniformity is performed via multipe KS-tests, with adjustment of p-values for multiple testing. If the plot is drawn, problematic groups are highlighted in red, and a corresponding message is displayed in the plot. #' #' The test for homogeneity of variances is done with a Levene test. A significant p-value means that group variances are not constant. In this case, you should consider modelling variances, e.g. via ~dispformula in glmmTMB. #' #' @author Florian Hartig #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @example inst/examples/testsHelp.R #' @export testCategorical <- function(simulationOutput, catPred, quantiles = c(0.25, 0.5, 0.75), plot = TRUE){ simulationOutput = ensureDHARMa(simulationOutput, convert = T) catPred = as.factor(catPred) out = list() out$uniformity$details = suppressWarnings(by(simulationOutput$scaledResiduals, catPred, ks.test, 'punif', simplify = TRUE)) out$uniformity$p.value = rep(NA, nlevels(catPred)) for(i in 1:nlevels(catPred)) out$uniformity$p.value[i] = out$uniformity$details[[i]]$p.value out$uniformity$p.value.cor = p.adjust(out$uniformity$p.value) if(nlevels(catPred) > 1) out$homogeneity = leveneTest_formula(simulationOutput$scaledResiduals ~ catPred) if(plot == T){ boxplot(simulationOutput$scaledResiduals ~ catPred, ylim = c(0,1), axes = FALSE, col = ifelse(out$uniformity$p.value.cor < 0.05, "red", "lightgrey")) axis(1, at = 1:nlevels(catPred), levels(catPred)) axis(2, at=c(0, quantiles, 1)) abline(h = quantiles, lty = 2) } mtext(ifelse(any(out$uniformity$p.value.cor < 0.05), "Within-group deviations from uniformity significant (red)", "Within-group deviation from uniformity n.s."), col = ifelse(any(out$uniformity$p.value.cor < 0.05), "red", "black"), line = 1) if(length(out) > 1) { mtext(ifelse(out$homogeneity$`Pr(>F)`[1] < 0.05, "Levene Test for homogeneity of variance significant", "Levene Test for homogeneity of variance n.s."), col = ifelse(out$homogeneity$`Pr(>F)`[1] < 0.05, "red", "black")) } return(out) } #' DHARMa dispersion tests #' #' This function performs simulation-based tests for over/underdispersion. If type = "DHARMa" (default and recommended), simulation-based dispersion tests are performed. Their behavior differs depending on whether simulations are done with refit = F, or refit = T, and whether data is simulated conditional (e.g. re.form ~0 in lme4) (see below). If type = "PearsonChisq", a chi2 test on Pearson residuals is performed. #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param alternative a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis. Greater corresponds to testing only for overdispersion. It is recommended to keep the default setting (testing for both over and underdispersion) #' @param plot whether to provide a plot for the results #' @param type which test to run. Default is DHARMa, other options are PearsonChisq (see details) #' @param ... arguments to pass on to [testGeneric] #' #' @details Over / underdispersion means that the observed data is more / less dispersed than expected under the fitted model. There is no unique way to test for dispersion problems, and there are a number of different dispersion tests implemented in various R packages. #' #' The testDispersion function implements several dispersion tests: #' #' **Simulation-based dispersion tests (type == "DHARMa")** #' #' If type = "DHARMa" (default and recommended), simulation-based dispersion tests are performed. Their behavior differs depending on whether simulations are done with refit = F, or refit = T #' #' #' **Important:** for either refit = T or F, the results of type = "DHARMa" dispersion test will differ depending on whether simulations are done conditional (= conditional on fitted random effects) or unconditional (= REs are re-simulated). How to change between conditional or unconditional simulations is discussed in [simulateResiduals]. The general default in DHARMa is to use unconditional simulations, because this has advantages in other situations, but dispersion tests for models with strong REs specifically may increase substantially in power / sensitivity when switching to conditional simulations. I therefore recommend checking dispersion with conditional simulations if supported by the used regression package. #' #' If refit = F, the function uses [testGeneric] to compare the variance of the observed raw residuals (i.e. var(observed - predicted), displayed as a red line) against the variance of the simulated residuals (i.e. var(simulated - predicted), histogram). The variances are scaled to the mean simulated variance. A significant ratio > 1 indicates overdispersion, a significant ratio < 1 underdispersion. #' #' If refit = T, the function compares the approximate deviance (via squared pearson residuals) with the same quantity from the models refitted with simulated data. Applying this is much slower than the previous alternative. Given the computational cost, I would suggest that most users will be satisfied with the standard dispersion test. #' #' ** Analytical dispersion tests (type == "PearsonChisq")** #' #' This is the test described in https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#overdispersion, identical to performance::check_overdispersion. Works only if the fitted model provides df.residual and Pearson residuals. #' #' The test statistics is biased to lower values under quite general conditions, and will therefore tend to test significant for underdispersion. It is recommended to use this test only for overdispersion, i.e. use alternative == "greater". Also, obviously, it requires that Pearson residuals are available for the chosen model, which will not be the case for all models / packages. #' #' @note For particular model classes / situations, there may be more powerful and thus preferable over the DHARMa test. The advantage of the DHARMa test is that it directly targets the spread of the data (unless other tests such as dispersion/df, which essentially measure fit and may thus be triggered by problems other than dispersion as well), and it makes practically no assumptions about the fitted model, other than the availability of simulations. #' #' @author Florian Hartig #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @example inst/examples/testDispersionHelp.R #' @export testDispersion <- function(simulationOutput, alternative = c("two.sided", "greater", "less"), plot = T, type = c("DHARMa", "PearsonChisq"), ...){ alternative <- match.arg(alternative) type <- match.arg(type) out = list() out$data.name = deparse(substitute(simulationOutput)) if(type == "DHARMa"){ simulationOutput = ensureDHARMa(simulationOutput, convert = "Model") # if(class(simulationOutput$fittedModel) %in% c("glmerMod", "lmerMod"){ # if(!"re.form" %in% names(simulationOutput$additionalParameters) & is.null(simulationOutput$additionalParameters$re.form)) message("recommended to run conditional simulations for dispersion test, see help") #} if(simulationOutput$refit == F){ expectedVar = sd(simulationOutput$simulatedResponse)^2 spread <- function(x) var(x - simulationOutput$fittedPredictedResponse) / expectedVar out = testGeneric(simulationOutput, summary = spread, alternative = alternative, methodName = "DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated", plot = plot, ...) names(out$statistic) = "dispersion" } else { observed = tryCatch(sum(residuals(simulationOutput$fittedModel, type = "pearson")^2), error = function(e) { message(paste("DHARMa: the requested tests requires pearson residuals, but your model does not implement these calculations. Test will return NA. Error message:", e)) return(NA) }) if(is.na(observed)) return(NA) expected = apply(simulationOutput$refittedPearsonResiduals^2 , 2, sum) out$statistic = c(dispersion = observed / mean(expected)) names(out$statistic) = "dispersion" out$method = "DHARMa nonparametric dispersion test via mean deviance residual fitted vs. simulated-refitted" p = getP(simulated = expected, observed = observed, alternative = alternative) out$alternative = alternative out$p.value = p class(out) = "htest" if(plot == T) { #plotTitle = gsub('(.{1,50})(\\s|$)', '\\1\n', out$method) xLabel = paste("Simulated values, red line = fitted model. p-value (",out$alternative, ") = ", out$p.value, sep ="") hist(expected, xlim = range(expected, observed, na.rm=T ), col = "lightgrey", main = "", xlab = xLabel, breaks = 20, cex.main = 1) abline(v = observed, lwd= 2, col = "red") main = ifelse(out$p.value <= 0.05, "Dispersion test significant", "Dispersion test n.s.") title(main = main, cex.main = 1, col.main = ifelse(out$p.value <= 0.05, "red", "black")) } } } else if(type == "PearsonChisq"){ if("DHARMa" %in% class(simulationOutput)){ model = simulationOutput$fittedModel } else model = simulationOutput if(! alternative == "greater") message("Note that the chi2 test on Pearson residuals is biased for MIXED models towards underdispersion. Tests with alternative = two.sided or less are therefore not reliable. If you have random effects in your model, I recommend to test only with alternative = 'greater', i.e. test for overdispersion, or else use the DHARMa default tests which are unbiased. See help for details.") rdf <- df.residual(model) rp <- getPearsonResiduals(model) Pearson.chisq <- sum(rp^2) prat <- Pearson.chisq/rdf if(alternative == "greater") pval <- pchisq(Pearson.chisq, df=rdf, lower.tail=FALSE) else if (alternative == "less") pval <- pchisq(Pearson.chisq, df=rdf, lower.tail=TRUE) else if (alternative == "two.sided") pval <- min(min(pchisq(Pearson.chisq, df=rdf, lower.tail=TRUE), pchisq(Pearson.chisq, df=rdf, lower.tail=FALSE)) * 2,1) out$statistic = prat names(out$statistic) = "dispersion" out$parameter = rdf names(out$parameter) = "df" out$method = "Parametric dispersion test via mean Pearson-chisq statistic" out$alternative = alternative out$p.value = pval class(out) = "htest" # c(chisq=Pearson.chisq,ratio=prat,rdf=rdf,p=pval) return(out) } return(out) } #' Simulated overdisperstion tests #' #' @details Deprecated, switch your code to using the [testDispersion] function #' #' @param simulationOutput an object of class DHARMa with simulated quantile residuals, either created via [simulateResiduals] or by [createDHARMa] for simulations created outside DHARMa #' @param ... additional arguments to [testDispersion] #' @export testOverdispersion <- function(simulationOutput, ...){ message("testOverdispersion is deprecated, switch your code to using the testDispersion function") testDispersion(simulationOutput, ...) } #' Parametric overdisperstion tests #' #' @details Deprecated, switch your code to using the [testDispersion] function. #' #' @param ... arguments will be ignored, the parametric tests is no longer recommend #' @export testOverdispersionParametric <- function(...){ message("testOverdispersionParametric is deprecated - switch your code to using the testDispersion function") return(0) } #' Tests for zero-inflation #' #' This function compares the observed number of zeros with the zeros expected from simulations. #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param ... further arguments to [testGeneric] #' @details Zero-inflation means that the observed data contain more zeros than would be expected under the fitted model. Zero-inflation must always be accessed with respect to a particular model, so the mere fact that there are many zeros in the observed data is not an indication of zero-inflation, see Warton, D. I. (2005). Many zeros does not mean zero inflation: comparing the goodness-of-fit of parametric models to multivariate abundance data. Environmetrics 16(3), 275-289. #' #' The testZeroInflation function simulates new datasets from the fitted model and compares this null distribution (gray histogram in the plot) with the observed values (red line in the plot). Technically, it is a wrapper for [testGeneric], with the summary argument set to function(x) sum(x == 0). The test statistic is the ratio of observed to simulated zeros. A value < 1 means that the observed data have fewer zeros than expected, a value > 1 means that they have more zeros than expected (aka zero inflation). By default, the function tests both sides, so it would also test for fewer zeros than expected. #' #' @note Zero-inflation can occur for a number of reasons other than an underlying data generating process corresponding to a ZIP model. Vice versa, it is very well possible that no zero-inflation will be observed when fitting models to data derived from a ZIP process. The latter is due to the fact that excess zeros can often be explained by other model parameters, such as the theta parameter in the negative binomial. #' #' For this reason, results of the zero-inflation test should be interpreted as a residual pattern that can have many reasons, not as a decision criterion for whether or not to fit a ZIP model. To decide whether to add a ZIP term, I would advise relying on appropriate model selection techniques such as AIC, BIC, WAIC, Bayes factor, or LRT. Note that these tests are often not reliable in GLMMs because it is difficult to determine the df spent by the different models. The [simulateLRT] function in DHARMa provides a nonparametric alternative to obtain p-values for LRT is nested models with unknown df. #' #' @author Florian Hartig #' @example inst/examples/testsHelp.R #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @export testZeroInflation <- function(simulationOutput, ...){ countZeros <- function(x) sum( x == 0) testGeneric(simulationOutput = simulationOutput, summary = countZeros, methodName = "DHARMa zero-inflation test via comparison to expected zeros with simulation under H0 = fitted model", ... ) } #' Test for a generic summary statistic based on simulated data #' #' This function tests if a user-defined summary differs when applied to simulated / observed data. #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param summary a function that can be applied to simulated / observed data. See examples below #' @param alternative a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis #' @param plot whether to plot the simulated summary #' @param methodName name of the test (will be used in plot) #' #' @details This function applies a user-defined summary to the simulated/observed data of a DHARMa object and then performs a hypothesis test using the ratio Obs / Sim as the test statistic. #' #' The summary is applied directly to the data and not to the residuals, but it can easily be remodeled to apply summaries to the residuals by simply defining something like f = function(x) summary (x - predictions), as done in [testDispersion] #' #' @note The summary function you specify will be applied to the data as it appears in your fitted model, which may not always be what you want. #' #' As an example, consider the case where we want to test for n-inflation in k/n data. If you provide your data via cbind (k, n-k), you have to test for n-inflation, but if you provide your data via k/n and weights = n, you should test for 1-inflation. When in doubt, check how the data is represented internally in model.frame(model) or via simulate(model). #' #' @export #' @author Florian Hartig #' @example inst/examples/testsHelp.R #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] testGeneric <- function(simulationOutput, summary, alternative = c("two.sided", "greater", "less"), plot = T, methodName = "DHARMa generic simulation test"){ out = list() out$data.name = deparse(substitute(simulationOutput)) simulationOutput = ensureDHARMa(simulationOutput, convert = "Model") alternative <- match.arg(alternative) observed = summary(simulationOutput$observedResponse) simulated = apply(simulationOutput$simulatedResponse, 2, summary) p = getP(simulated = simulated, observed = observed, alternative = alternative) out$statistic = c(ratioObsSim = observed / mean(simulated)) out$method = methodName out$alternative = alternative out$p.value = p class(out) = "htest" if(plot == T) { plotTitle = gsub('(.{1,50})(\\s|$)', '\\1\n', methodName) xLabel = paste("Simulated values, red line = fitted model. p-value (",out$alternative, ") = ", out$p.value, sep ="") hist(simulated, xlim = range(simulated, observed, na.rm=T ), col = "lightgrey", main = plotTitle, xlab = xLabel, breaks = max(round(simulationOutput$nSim / 5), 20), cex.main = 0.8) abline(v = observed, lwd= 2, col = "red") } return(out) } #' Test for temporal autocorrelation #' #' This function performs a standard test for temporal autocorrelation on the simulated residuals #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or by [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param time the time, in the same order as the data points. #' @param alternative a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis #' @param plot whether to plot output #' @details The function performs a Durbin-Watson test on the uniformly scaled residuals, and plots the residuals against time. The DB test was originally be designed for normal residuals. In simulations, I didn't see a problem with this setting though. The alternative is to transform the uniform residuals to normal residuals and perform the DB test on those. #' #' Testing for temporal autocorrelation requires unique time values - if you have several observations per time value, either use [recalculateResiduals] function to aggregate residuals per time step, or extract the residuals from the fitted object, and plot / test each of them independently for temporally repeated subgroups (typical choices would be location / subject etc.). Note that the latter must be done by hand, outside testTemporalAutocorrelation. #' #' @note Standard DHARMa simulations from models with (temporal / spatial / phylogenetic) conditional autoregressive terms will still have the respective temporal / spatial / phylogenetic correlation in the DHARMa residuals, unless the package you are using is modelling the autoregressive terms as explicit REs and is able to simulate conditional on the fitted REs. This has two consequences #' #' 1. If you check the residuals for such a model, they will still show significant autocorrelation, even if the model fully accounts for this structure. #' #' 2. Because the DHARMa residuals for such a model are not statistically independent any more, other tests (e.g. dispersion, uniformity) may have inflated type I error, i.e. you will have a higher likelihood of spurious residual problems. #' #' There are three (non-exclusive) routes to address these issues when working with spatial / temporal / other autoregressive models: #' #' 1. Simulate conditional on the fitted CAR structures (see conditional simulations in the help of [simulateResiduals]) #' #' 2. Rotate simulations prior to residual calculations (see parameter rotation in [simulateResiduals]) #' #' 3. Use custom tests / plots that explicitly compare the correlation structure in the simulated data to the correlation structure in the observed data. #' #' @author Florian Hartig #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @example inst/examples/testTemporalAutocorrelationHelp.R #' @export testTemporalAutocorrelation <- function(simulationOutput, time, alternative = c("two.sided", "greater", "less"), plot = TRUE){ simulationOutput = ensureDHARMa(simulationOutput, convert = T) # actually not sure if this is neccessary for dwtest, but seems better to aggregate if(any(duplicated(time))) stop("testing for temporal autocorrelation requires unique time values - if you have several observations per time value, either use the recalculateResiduals function to aggregate residuals per time step, or extract the residuals from the fitted object, and plot / test each of them independently for temporally repeated subgroups (typical choices would be location / subject etc.). Note that the latter must be done by hand, outside testTemporalAutocorrelation.") alternative <- match.arg(alternative) if(is.null(time)){ time = sample.int(simulationOutput$nObs, simulationOutput$nObs) message("DHARMa::testTemporalAutocorrelation - no time argument provided, using random times for each data point") } # To avoid Issue #190 if (length(time) != length(residuals(simulationOutput))) stop("Dimensions of time don't match the dimension of the residuals") out = lmtest::dwtest(simulationOutput$scaledResiduals ~ 1, order.by = time, alternative = alternative) if(plot == T) { oldpar <- par(mfrow = c(1,2)) on.exit(par(oldpar)) plot(simulationOutput$scaledResiduals[order(time)] ~ time[order(time)], type = "l", ylab = "Scaled residuals", xlab = "Time", main = "Residuals vs. time", ylim = c(0,1)) abline(h=c(0.5)) abline(h=c(0,0.25,0.75,1), lty = 2 ) acf(simulationOutput$scaledResiduals[order(time)], main = "Autocorrelation", ylim = c(-1,1)) legend("topright", c(paste(out$method, " p=", round(out$p.value, digits = 5)), paste("Deviation ", ifelse(out$p.value < 0.05, "significant", "n.s."))), text.col = ifelse(out$p.value < 0.05, "red", "black" ), bty="n") } return(out) } #' Test for distance-based spatial (or similar type) autocorrelation #' #' This function performs a Moran's I test for distance-based spatial (or similar type) autocorrelation on the calculated quantile residuals. #' #' @param simulationOutput An object of class DHARMa, either created via [simulateResiduals] for supported models or via [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param x The x coordinate, in the same order as the data points. Must be specified unless distMat is provided. #' @param y The y coordinate, in the same order as the data points. Must be specified unless distMat is provided. #' @param distMat Optional distance matrix. If not provided, euclidean distances based on x and y will be calculated. See details for explanation. #' @param alternative A character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis. #' @param plot If T, and if x and y is provided, plot the output (see Details). #' #' @details The function performs Moran.I test from the package ape on the DHARMa residuals. If a distance matrix (distMat) is provided, calculations will be based on this distance matrix, and x,y coordinates will only used for the plotting (if provided). If distMat is not provided, the function will calculate the euclidean distances between x,y coordinates, and test Moran.I based on these distances. #' #' If plot = T, a plot will be produced showing each residual with at its x,y position, colored according to the residual value. Residuals with 0.5 are colored white, everything below 0.5 is colored increasinly red, everything above 0.5 is colored increasingly blue. #' #' Testing for spatial autocorrelation requires unique x,y values - if you have several observations per location, either use the [recalculateResiduals] function to aggregate residuals per location, or extract the residuals from the fitted object, and plot / test each of them independently for spatially repeated subgroups (a typical scenario would repeated spatial observation, in which case one could plot / test each time step separately for temporal autocorrelation). Note that the latter must be done by hand, outside [testSpatialAutocorrelation]. #' #' @note Standard DHARMa simulations from models with (temporal / spatial / phylogenetic) conditional autoregressive terms will still have the respective temporal / spatial / phylogenetic correlation in the DHARMa residuals, unless the package you are using is modelling the autoregressive terms as explicit REs and is able to simulate conditional on the fitted REs. This has two consequences: #' #' 1. If you check the residuals for such a model, they will still show significant autocorrelation, even if the model fully accounts for this structure. #' #' 2. Because the DHARMa residuals for such a model are not statistically independent any more, other tests (e.g. dispersion, uniformity) may have inflated type I error, i.e. you will have a higher likelihood of spurious residual problems. #' #' There are three (non-exclusive) routes to address these issues when working with spatial / temporal / phylogenetic / other autoregressive models: #' #' 1. Simulate conditional on the fitted CAR structures (see conditional simulations in the help of [simulateResiduals]). #' #' 2. Rotate simulations prior to residual calculations (see parameter rotation in [simulateResiduals]). #' #' 3. Use custom tests / plots that explicitly compare the correlation structure in the simulated data to the correlation structure in the observed data. #' #' @author Florian Hartig #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @import grDevices #' @example inst/examples/testSpatialAutocorrelationHelp.R #' @export testSpatialAutocorrelation <- function(simulationOutput, x = NULL, y = NULL, distMat = NULL, alternative = c("two.sided", "greater", "less"), plot = TRUE){ alternative <- match.arg(alternative) data.name = deparse(substitute(simulationOutput)) # needs to be before ensureDHARMa simulationOutput = ensureDHARMa(simulationOutput, convert = T) # Assertions if(any(duplicated(cbind(x,y)))) stop("Testing for spatial autocorrelation requires unique x,y values - if you have several observations per location, either use the recalculateResiduals function to aggregate residuals per location, or extract the residuals from the fitted object, and plot / test each of them independently for spatially repeated subgroups (a typical scenario would repeated spatial observation, in which case one could plot / test each time step separately for temporal autocorrelation). Note that the latter must be done by hand, outside testSpatialAutocorrelation.") if( (!is.null(x) | !is.null(y)) & !is.null(distMat) ) message("Both coordinates and distMat provided, calculations will be done based on the distance matrix, coordinates will only be used for plotting.") if( (is.null(x) | is.null(y)) & is.null(distMat) ) stop("You need to provide either x,y, coordinates or a distMatrix.") if(is.null(distMat) & (length(x) != length(residuals(simulationOutput)) | length(y) != length(residuals(simulationOutput)))) # To avoid Issue #190 if (!is.null(x) & length(x) != length(residuals(simulationOutput)) | !is.null(y) & length(y) != length(residuals(simulationOutput))) stop("Dimensions of x / y coordinates don't match the dimension of the residuals.") # if not provided, create distance matrix based on x and y if(is.null(distMat)) distMat <- as.matrix(dist(cbind(x, y))) invDistMat <- 1/distMat diag(invDistMat) <- 0 MI = ape::Moran.I(simulationOutput$scaledResiduals, weight = invDistMat, alternative = alternative) out = list() out$statistic = c(observed = MI$observed, expected = MI$expected, sd = MI$sd) out$method = "DHARMa Moran's I test for distance-based autocorrelation" out$alternative = "Distance-based autocorrelation" out$p.value = MI$p.value out$data.name = data.name class(out) = "htest" if(plot == T & !is.null(x) & !is.null(y)) { opar <- par(mfrow = c(1,1)) on.exit(par(opar)) col = colorRamp(c("red", "white", "blue"))(simulationOutput$scaledResiduals) plot(x,y, col = rgb(col, maxColorValue = 255), main = out$method, cex.main = 0.8 ) # TODO implement correlogram } return(out) } #' Test for phylogenetic autocorrelation #' #' This function performs a Moran's I test for phylogenetic autocorrelation on the calculated quantile residuals. #' #' @param simulationOutput an object of class DHARMa, either created via [simulateResiduals] for supported models or via [createDHARMa] for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case. #' @param tree A phylogenetic tree object. #' @param alternative A character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis of no phylogenetic correlation. #' #' @details The function performs Moran.I test from the package ape on the DHARMa residuals, based on the phylogenetic distance matrix internally created from the provided tree. For custom distance matrices, you can use [testSpatialAutocorrelation]. #' #' @note Standard DHARMa simulations from models with (temporal / spatial / phylogenetic) conditional autoregressive terms will still have the respective temporal / spatial / phylogenetic correlation in the DHARMa residuals, unless the package you are using is modelling the autoregressive terms as explicit REs and is able to simulate conditional on the fitted REs. This has two consequences: #' #' 1. If you check the residuals for such a model, they will still show significant autocorrelation, even if the model fully accounts for this structure. #' #' 2. Because the DHARMa residuals for such a model are not statistically independent any more, other tests (e.g. dispersion, uniformity) may have inflated type I error, i.e. you will have a higher likelihood of spurious residual problems. #' #' There are three (non-exclusive) routes to address these issues when working with spatial / temporal / phylogenetic autoregressive models: #' #' 1. Simulate conditional on the fitted CAR structures (see conditional simulations in the help of [simulateResiduals]). #' #' 2. Rotate simulations prior to residual calculations (see parameter rotation in [simulateResiduals]). #' #' 3. Use custom tests / plots that explicitly compare the correlation structure in the simulated data to the correlation structure in the observed data. #' #' @author Florian Hartig #' @seealso [testResiduals], [testUniformity], [testOutliers], [testDispersion], [testZeroInflation], [testGeneric], [testTemporalAutocorrelation], [testSpatialAutocorrelation], [testQuantiles], [testCategorical] #' @example inst/examples/testPhylogeneticAutocorrelationHelp.R #' @export testPhylogeneticAutocorrelation <- function(simulationOutput, tree, alternative = c("two.sided", "greater", "less")){ alternative <- match.arg(alternative) data.name = deparse(substitute(simulationOutput)) # needs to be before ensureDHARMa simulationOutput = ensureDHARMa(simulationOutput, convert = T) # calculate distance matrix distMat <- cophenetic(tree) invDistMat <- 1/distMat diag(invDistMat) <- 0 MI = ape::Moran.I(simulationOutput$scaledResiduals, weight = invDistMat, alternative = alternative) out = list() out$statistic = c(observed = MI$observed, expected = MI$expected, sd = MI$sd) out$method = "DHARMa Moran's I test for phylogenetic autocorrelation" out$alternative = "Phylogenetic autocorrelation" out$p.value = MI$p.value out$data.name = data.name class(out) = "htest" return(out) } getP <- function(simulated, observed, alternative, plot = FALSE, ...){ if(alternative == "greater") p = mean(simulated >= observed) if(alternative == "less") p = mean(simulated <= observed) if(alternative == "two.sided") p = min(min(mean(simulated <= observed), mean(simulated >= observed) ) * 2,1) if(plot == T){ hist(simulated, xlim = range(simulated, observed), col = "lightgrey", main = "Distribution of test statistic \n grey = simulated, red = observed", ...) abline(v = mean(simulated), col = 1, lwd = 2) abline(v = observed, col = "red", lwd = 2) } return(p) } DHARMa/R/compatibility.R0000644000176200001440000006230014704245735014457 0ustar liggesusers# General notes ----------------------------------------------------------- # This file contains the wrappers for the models supported by DHARMa. # The design philosophy is that DHARMa interacts with packages ONLY via the wrappers, # so that the internal package functions can rely on a standardized interface. # # The currently supported models can be returned via getPossibleModels(). # # Below, you find under the section "Generic S3 Wrappers" the 6 Wrapper # functions that need to be implemented to add a model to DHARMa. # # Each of these generics has a default, which may already work with a given # model class. The general approach for integrating a package in DHARMa is # # i) test if the default DHARMa wrappers work as intended. # ii) if not, define new class-specific S3 wrapper (e.g. getSimulations.gam). # See comments in the help of the generic S3 functions for guidance about how to implement each function. # Checks ----------------------------------------------------------- #' Check if the fitted model is supported by DHARMa #' #' The function checks if the fitted model is supported by DHARMa, and if there are other issues that could create problems. #' #' @param fittedModel a fitted model. #' @param stop whether to throw an error if the model is not supported by DHARMa. #' #' @details The main purpose of this function os to check if the fitted model class is supported by DHARMa. The function additionally checks for properties of the fitted model that could create problems for calculating residuals or working with the resuls in DHARMa. #' #' #' @keywords internal checkModel <- function(fittedModel, stop = F){ out = T if(!(class(fittedModel)[1] %in% getPossibleModels())){ if(stop == FALSE) warning("DHARMa: fittedModel not in class of supported models. Absolutely no guarantee that this will work!") else stop("DHARMa: fittedModel not in class of supported models.") } # if(hasNA(fittedModel)) message("It seems there were NA values in the data used for fitting the model. This can create problems if you supply additional data to DHARMa functions. See ?checkModel for details") # TODO: check as implemented does not work reliably, check if there is any other option to check for NA # #' @example inst/examples/checkModelHelp.R # NA values in the data: checkModel will detect if there were NA values in the data frame. For NA values, most regression models will remove the entire observation from the data. This is not a problem for DHARMa - residuals are then only calculated for non-NA rows in the data. However, if you provide additional predictors to DHARMa, for example to plot residuals against a predictor, you will have to remove all NA rows that were also removed in the model. For most models, you can get the rows of the data that were actually used in the fit via rownames(model.frame(fittedModel)) #if (class(fittedModel)[1] == "gam" ) if (class(fittedModel$family)[1] == "extended.family") stop("It seems you are trying to fit a model from mgcv that was fit with an extended.family. Simulation functions for these families are not yet implemented in DHARMa. See issue https://github.com/florianhartig/DHARMa/issues/11 for updates about this") } #' get possible models #' #' returns a list of supported model classes #' #' @keywords internal getPossibleModels<-function()c("lm", "glm", "negbin", "lmerMod", "lmerModLmerTest", "glmerMod", "gam", "bam", "glmmTMB", "HLfit", "MixMod", "phylolm", "phyloglm") weightsWarning = "Model was fit with prior weights. These will be ignored in the simulation. See ?getSimulations for details." ######### Generic S3 Wrappers ############# #' Get model response #' #' Extract the response of a fitted model. #' #' The purpose of this function is to safely extract the observed response (dependent variable) of the fitted model classes. #' #' #' @param object a fitted model. #' @param ... additional parameters. #' #' @example inst/examples/wrappersHelp.R #' #' @seealso [getRefit], [getSimulations], [getFixedEffects], [getFitted] #' @author Florian Hartig #' @export getObservedResponse <- function (object, ...) { UseMethod("getObservedResponse", object) } #' Get model simulations #' #' @description Wrapper to simulate from a fitted model. #' #' @param object a fitted model. #' @param nsim number of simulations. #' @param type if simulations should be prepared for getQuantile or for refit. #' @param ... additional parameters to be passed on, usually to the simulate function of the respective model class. #' #' @return A matrix with simulations. #' @example inst/examples/wrappersHelp.R #' #' @seealso [getObservedResponse], [getRefit], [getFixedEffects], [getFitted] #' #' @details The purpose of this function is to wrap or implement the simulate function of different model classes and thus return simulations from fitted models in a standardized way. #' #' Note: GLMM and other regression packages often differ in how simulations are produced, and which parameters can be used to modify this behavior. #' #' One important difference is how to modifiy which hierarchical levels are held constant, and which are re-simulated. In lme4, this is controlled by the re.form argument (see [lme4::simulate.merMod]). In glmmTMB, the package version 1.1.10 has a temporary solution to simulate conditional to all random effects (see [glmmTMB::set_simcodes] val = "fix", and issue [#888](https://github.com/glmmTMB/glmmTMB/issues/888) in glmmTMB GitHub repository. For other packages, please consult the help. #' #' If the model was fit with weights and the respective model class does not include the weights in the simulations, getSimulations will throw a warning. The background is if weights are used on the likelihood directly, then what is fitted is effectively a pseudo likelihood, and there is no way to directly simulate from the specified likelihood. Whether or not residuals can be used in this case depends very much on what is tested and how weights are used. I'm sorry to say that it is hard to give a general recommendation, you have to consult someone that understands how weights are processed in the respective model class. #' #' @author Florian Hartig #' @export getSimulations <- function (object, nsim = 1 , type = c("normal", "refit"), ...) { UseMethod("getSimulations", object) } #' Extract fixed effects of a supported model #' #' A wrapper to extract fixed effects of a supported model. #' #' @param object a fitted model. #' @param ... additional parameters. #' @example inst/examples/wrappersHelp.R #' @seealso [getObservedResponse], [getSimulations], [getRefit], [getFitted] #' @export getFixedEffects <- function(object, ...){ UseMethod("getFixedEffects", object) } #' Get model refit #' #' Wrapper to refit a fitted model. #' #' @param object a fitted model. #' @param newresp the new response that should be used to refit the model. #' @param ... additional parameters to be passed on to the refit or update class that is used to refit the model. #' #' @details The purpose of this wrapper is to standardize the refit of a model. The behavior of this function depends on the supplied model. When available, it uses the refit method, otherwise it will use update. For glmmTMB: since version 1.0, glmmTMB has a refit function, but this didn't work, so I switched back to this implementation, which is a hack based on the update function. #' #' @example inst/examples/wrappersHelp.R #' #' @seealso [getObservedResponse], [getSimulations], [getFixedEffects] #' @author Florian Hartig #' @export getRefit <- function (object, newresp, ...) { UseMethod("getRefit", object) } #' Get fitted/predicted values #' #' Wrapper to get the fitted/predicted response of model at the response scale. #' #' The purpose of this wrapper is to standardize extract the fitted values, which is implemented via predict(model, type = "response") for most model classes. #' #' If you implement this function for a new model class, you should include an option to modifying which random effects (REs) are included in the predictions. If this option is not available, it is essential that predictions are provided marginally/unconditionally, i.e. without the RE estimates (because of https://github.com/florianhartig/DHARMa/issues/43), which corresponds to re-form = ~0 in lme4. #' #' @param object A fitted model. #' @param ... Additional parameters to be passed on, usually to the simulate function of the respective model class. #' #' @example inst/examples/wrappersHelp.R #' #' @seealso [getObservedResponse], [getSimulations], [getRefit], [getFixedEffects] #' #' @author Florian Hartig #' @export getFitted <- function (object, ...) { UseMethod("getFitted", object) } # NOTE - a bit unclear if fitted or predict should be used #' Get model residuals #' #' Wrapper to get the residuals of a fitted model. #' #' The purpose of this wrapper is to standardize the extraction of model residuals. Similar to some other functions, a key question is whether to calculate those conditional or unconditional on the fitted Random Effects. #' #' @param object a fitted model. #' @param ... additional parameters to be passed on, usually to the residual function of the respective model class. #' #' @example inst/examples/wrappersHelp.R #' #' @seealso [getObservedResponse], [getSimulations], [getRefit], [getFixedEffects], [getFitted] #' #' @author Florian Hartig #' @export getResiduals <- function (object, ...) { UseMethod("getResiduals", object) } # NOTE - a bit unclear if fitted or predict should be used #' Get Pearson residuals #' #' Wrapper to get the Pearson residuals of a fitted model. #' #' The purpose of this wrapper is to extract the Pearson residuals of a fitted model. #' #' @param object a fitted model. #' @param ... additional parameters to be passed on, usually to the residual function of the respective model class. #' #' @example inst/examples/wrappersHelp.R #' #' @seealso [getObservedResponse], [getSimulations], [getRefit], [getFixedEffects], [getFitted] #' #' @author Florian Hartig #' @export getPearsonResiduals <- function (object, ...) { UseMethod("getPearsonResiduals", object) } #' Get model family #' #' Wrapper to get the family of a fitted model. #' #' @param object a fitted model. #' @param ... additional parameters to be passed on. #' #' @seealso [getObservedResponse], [getSimulations], [getRefit], [getFixedEffects], [getFitted] #' #' @author Florian Hartig #' @export getFamily <- function (object, ...) { UseMethod("getFamily", object) } # nObs # default ----------------------------------------------------------------- #' @rdname getObservedResponse #' @export getObservedResponse.default <- function (object, ...){ out = model.frame(object)[,1] # observation is factor - unlike lme4 and older, glmmTMB simulates nevertheless as numeric if(is.factor(out)) out = as.numeric(out) - 1 # check for weights in k/n case if(family(object)$family %in% c("binomial", "betabinomial") & "(weights)" %in% colnames(model.frame(object))){ x = model.frame(object) out = out * x$`(weights)` } if(is.matrix(out)){ # case scaled variables or something like that if(ncol(out) == 1){ out = as.vector(out) } else if(ncol(out) == 2) { # case k/n binomial if(!(family(object)$family %in% c("binomial", "betabinomial"))) securityAssertion("nKcase - wrong family") out = out[,1] } else securityAssertion("Response in the model is a matrix with > 2 dim") } return(out) } #' @rdname getRefit #' @importFrom lme4 refit #' @export getRefit.default <- function (object, newresp, ...){ refit(object, newresp, ...) } #' @rdname getSimulations #' @export getSimulations.default <- function (object, nsim = 1, type = c("normal", "refit"), ...){ type <- match.arg(type) out = simulate(object, nsim = nsim , ...) if (type == "normal"){ if(family(object)$family %in% c("binomial", "betabinomial")){ if(is.factor(out[[1]])){ if(nlevels(out[[1]]) != 2){ warning("The fitted model has a factorial response with number of levels not equal to 2 - there is currently no sensible application in DHARMa that would lead to this situation. Likely, you are trying something that doesn't work.") } else{ out = data.matrix(out) - 1 } } if("(weights)" %in% colnames(model.frame(object))){ x = model.frame(object) out = out * x$`(weights)` } else if (is.matrix(out[[1]])){ # this is for the k/n binomial case out = as.matrix(out)[,seq(1, (2*nsim), by = 2)] } } if(!is.matrix(out)) out = data.matrix(out) } else{ if(family(object)$family %in% c("binomial", "betabinomial")){ if (!is.matrix(out[[1]]) & !is.numeric(out)) data.frame(data.matrix(out)-1) } } return(out) } #' @rdname getFixedEffects #' @importFrom lme4 fixef #' @export getFixedEffects.default <- function(object, ...){ if(class(object)[1] %in% c("glm", "lm", "gam", "bam", "negbin") ){ out = coef(object) } else if(class(object)[1] %in% c("glmerMod", "lmerMod", "HLfit", "lmerTest")){ out = fixef(object) } else if(class(object)[1] %in% c("glmmTMB")){ out = glmmTMB::fixef(object) out = out$cond } else { out = coef(object) if(is.null(out)) out = fixef(object) } return(out) } #' @rdname getFitted #' @export getFitted.default <- function (object,...){ out = predict(object, type = "response", re.form = ~0) out = as.vector(out) # introduced because of phyr error } #' @rdname getResiduals #' @export getResiduals.default <- function (object, ...){ residuals(object, type = "response", ...) } #' @rdname getPearsonResiduals #' @export getPearsonResiduals.default <- function (object, ...){ residuals(object, type = "pearson", ...) } # #' has NA # #' # #' checks if the fitted model excluded NA values. # #' # #' @param object a fitted model. # #' # #' @details Checks if the fitted model excluded NA values. # #' # #' @export # hasNA <- function(object){ # x = rownames(model.frame(object)) # if(length(x) < as.numeric(x[length(x) ])) return(TRUE) # else return(FALSE) # } # #' @rdname getFamily #' @export getFamily.default <- function (object,...){ family(object) } ######### LM ############# #' @rdname getRefit #' @export getRefit.lm <- function(object, newresp, ...){ newData <-model.frame(object) if(is.vector(newresp)){ newData[,1] = newresp } else if (is.factor(newresp)){ # Hack to make the factor binomial case work newData[,1] = as.numeric(newresp) - 1 } else { # Hack to make the binomial n/k case work newData[[1]] = NULL newData = cbind(newresp, newData) } refittedModel = update(object, data = newData) return(refittedModel) } hasWeigths.lm <- function(object, ...){ if(length(unique(object$prior.weights)) != 1) return(TRUE) else return(FALSE) } ######### GLM ############# #' @rdname getSimulations #' @export getSimulations.negbin<- function (object, nsim = 1, type = c("normal", "refit"), ...){ type <- match.arg(type) if("(weights)" %in% colnames(model.frame(object))) warning(weightsWarning) getSimulations.default(object = object, nsim = nsim, type = type, ...) } ######## MGCV ############ # This function overwrites the standard fitted function for GAM #' @rdname getFitted #' @export getFitted.gam <- function(object, ...){ class(object) = "glm" out = stats::fitted(object, ...) names(out) = as.character(1:length(out)) out } # Check that this works # plot(fitted(fittedModelGAM), predict(fittedModelGAM, type = "response")) #' @rdname getPearsonResiduals #' @export #' @details This needed to be adopted because for some reason, mgcv uses the argument "scaled.pearson" for what most packags define as "pearson". See comments in ?residuals.gam. #' getPearsonResiduals.gam <- function (object, ...){ residuals(object, type = "scaled.pearson", ...) } # Get Simulations of gam object #' @rdname getSimulations #' @param mgcViz whether simulations should be created with mgcViz (if mgcViz is available) #' @export getSimulations.gam <- function(object, nsim = 1, type = c("normal", "refit"), mgcViz = TRUE, ...){ type <- match.arg(type) if(length(find.package("mgcViz")) > 0 & mgcViz == T){ if("(weights)" %in% colnames(model.frame(object)) & ! family(object)$family %in% c("binomial", "betabinomial")) warning(weightsWarning) # use mgcViz if available out = mgcViz::simulate.gam(object, nsim = nsim , ...) out = as.data.frame(out) # from here to end identical to default if (type == "normal"){ if(family(object)$family %in% c("binomial", "betabinomial")){ if("(weights)" %in% colnames(model.frame(object))){ x = model.frame(object) out = out * x$`(weights)` } else if (is.matrix(model.frame(object)[[1]])){ # this is for the k/n binomial case out = out * rowSums(model.frame(object)[[1]]) } } if(!is.matrix(out)) out = data.matrix(out) } else{ if(family(object)$family %in% c("binomial", "betabinomial")){ if (is.matrix(model.frame(object)[[1]])){ # need to convert to k,n-k format for refit. Syntax here is from # https://stackoverflow.com/questions/6143697/data-frame-with-a-column-containing-a-matrix-in-r trials = rowSums(model.frame(object)[[1]]) oldnames = names(out) oldrownames = row.names(out) out = out * trials out = as.list(out) for(i in 1:length(out)){ out[[i]] = cbind(out[[i]], trials - out[[i]]) colnames(out[[i]]) = colnames(model.frame(object)[[1]]) } class(out) = "data.frame" names(out) = oldnames row.names(out) = oldrownames } } } } else { message("It seems you don't have mgcViz installed on this computer. When using DHARMa with mgcv objects, it is highly recommended to also install mgcViz, which will extend the ability of DHARMa to simulate from various gam objects. Withoug mgcViz, simulations will fail in various situations. See vignette for details!") out = getSimulations.default(object, nsim, type, ...) } return(out) } ######## lme4 ############ #' @rdname getSimulations #' @export getSimulations.lmerMod <- function (object, nsim = 1, type = c("normal", "refit"), ...){ if("(weights)" %in% colnames(model.frame(object))) warning(weightsWarning) getSimulations.default(object = object, nsim = nsim, type = type, ...) } ######## glmmTMB ###### #' @rdname getRefit #' @export getRefit.glmmTMB <- function(object, newresp, ...){ newData <-model.frame(object) # hack to make update work - for some reason, glmmTMB wants the matrix embedded in the df for update to work ... should be solved ideally, see https://github.com/glmmTMB/glmmTMB/issues/549 if(is.matrix(newresp)){ tmp = colnames(newData[[1]]) newData[[1]] = NULL newData = cbind(newresp, newData) colnames(newData)[1:2] = tmp } else { newData[[1]] = newresp } refittedModel = update(object, data = newData) return(refittedModel) } # glmmTMB simulates normal counts (and not proportions in any case, so the check for the other models is not needed), see #158 # note that if observation is factor - unlike lme4 and older, glmmTMB simulates nevertheless as numeric #' @rdname getSimulations #' @export getSimulations.glmmTMB <- function (object, nsim = 1, type = c("normal", "refit"), ...){ type <- match.arg(type) if("(weights)" %in% colnames(model.frame(object)) & ! family(object)$family %in% c("binomial", "betabinomial")) warning(weightsWarning) type <- match.arg(type) out = simulate(object, nsim = nsim, ...) if (type == "normal"){ if (is.matrix(out[[1]])){ # this is for the k/n binomial case out = as.matrix(out)[,seq(1, (2*nsim), by = 2)] } if(!is.matrix(out)) out = data.matrix(out) }else{ # check for weights in k/n case if(family(object)$family %in% c("binomial", "betabinomial")){ if("(weights)" %in% colnames(model.frame(object))){ w = model.frame(object) w = w$`(weights)` tmp <- function(x)x/w out = apply(out, 2, tmp) out = as.data.frame(out) } else if(is.matrix(out[[1]]) & !is.matrix(model.frame(object)[[1]])){ out = as.data.frame(as.matrix(out)[,seq(1, (2*nsim), by = 2)]) } } # matrixResp = # # if(matrixResp & !is.null(ncol(newresp))){ # # Hack to make the factor binomial case work # tmp = colnames(newData[[1]]) # newData[[1]] = NULL # newData = cbind(newresp, newData) # colnames(newData)[1:2] = tmp # } else if(!is.null(ncol(newresp))){ # newData[[1]] = newresp[,1] # } else { # newData[[1]] = newresp # } # if (out$modelClass == "glmmTMB" & ncol(simulations) == 2*n) simObserved = simulations[,(1+(2*(i-1))):(2+(2*(i-1)))] } # else securityAssertion("Simulation results produced unsupported data structure", stop = TRUE) return(out) } ####### spaMM ######### #' @rdname getObservedResponse #' @export getObservedResponse.HLfit <- function(object, ...){ out = spaMM::response(object, ...) nKcase = is.matrix(out) if(nKcase){ if(! (family(object) %in% c("binomial", "betabinomial"))) securityAssertion("nKcase - wrong family") if(! (ncol(out)==2)) securityAssertion("nKcase - wrong dimensions of response") out = out[,1] } if(!is.numeric(out)) out = as.numeric(out) return(out) } #' @rdname getSimulations #' @export getSimulations.HLfit <- function(object, nsim = 1, type = c("normal", "refit"), ...){ type <- match.arg(type) capture.output({out = simulate(object, nsim = nsim, ...)}) if(type == "normal"){ if(!is.matrix(out)) out = data.matrix(out) }else{ out = as.data.frame(out) } return(out) } #' @rdname getRefit #' @export getRefit.HLfit <- function(object, newresp, ...) { spaMM::update_resp(object, newresp, evaluate = TRUE) } #' @rdname getFitted #' @export getFitted.HLfit <- function (object,...){ predict(object, type = "response", re.form = ~0)[,1L] } ####### GLMMadaptive ######### ### getObservedResponse - seems getObservedResponse.default is working #' @rdname getSimulations #' @export getSimulations.MixMod <- function(object, nsim = 1, type = c("normal", "refit"), ...){ if ("weights" %in% names(object)) warning(weightsWarning) type <- match.arg(type) out = simulate(object, nsim = nsim , ...) if(type == "normal"){ if(!is.matrix(out)) out = data.matrix(out) }else{ out = as.data.frame(out) } return(out) } #' @rdname getFixedEffects #' @export getFixedEffects.MixMod <- function(object, ...){ out <- fixef(object, sub_model = "main") return(out) } # TODO: this could go wrong if the DF has no column names, although I guess then one couldn't use formula # TODO: goes wrong for k/n binomial with c(s,f) ~ pred syntax #' @rdname getRefit #' @export getRefit.MixMod <- function(object, newresp, ...) { responsename = colnames(model.frame(object))[1] newDat = object$data newDat[, match(responsename,names(newDat))] = newresp update(object, data = newDat) } #' @rdname getFitted #' @export getFitted.MixMod <- function (object,...){ predict(object, type = "mean_subject") } #' @rdname getResiduals #' @export getResiduals.MixMod <- function (object,...){ residuals(object, type = "subject_specific") } ####### phylolm / phyloglm ######### #' @rdname getObservedResponse #' @export getObservedResponse.phylolm <- function (object, ...){ out = object$y return(out) } #' @rdname getSimulations #' @export getSimulations.phylolm <- function(object, nsim = 1, type = c("normal", "refit"), ...){ type <- match.arg(type) fitBoot = update(object, boot = nsim, save = T, ...) out = fitBoot$bootdata if(type == "normal"){ if(!is.matrix(out)) out = data.matrix(out) }else{ out = as.data.frame(out) } return(out) } #' @rdname getRefit #' @export getRefit.phylolm <- function(object, newresp, ...){ newData <- model.frame(object) newData[,1] = newresp refittedModel = update(object, data = newData, ...) } #' @rdname getFitted #' @export getFitted.phylolm <- function (object,...){ return(object$fitted.values) } #' @rdname getFamily #' @export getFamily.phylolm <- function (object,...){ out = list() out$family = "gaussian" return(out) } #' @rdname getObservedResponse #' @export getObservedResponse.phyloglm <- function (object, ...){ out = object$y return(out) } #' @rdname getSimulations #' @export getSimulations.phyloglm <- function(object, nsim = 1, type = c("normal", "refit"), ...){ type <- match.arg(type) fitBoot = update(object, boot = nsim, save = T, ...) out = fitBoot$bootdata if(type == "normal"){ if(!is.matrix(out)) out = data.matrix(out) }else{ out = as.data.frame(out) } return(out) } #' @rdname getRefit #' @export getRefit.phyloglm <- function(object, newresp, ...){ #object phyloglm doesn't have a model.frame object terms <- as.character(formula(object))[-1] newData <- model.frame(object$y ~ object$X[,-1]) names(newData) <- terms newData[,1] = newresp refittedModel = update(object, data = newData, ...) return(refittedModel) } #' @rdname getFitted #' @export getFitted.phyloglm <- function (object,...){ return(object$fitted.values) } #' @rdname getFamily #' @export getFamily.phyloglm <- function (object,...){ out = list() # 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}€±£Ÿż×ļū‘åµ¾ė„sÜ=ętĻ§fiīó›>fÜźv,Ęo,ÓfćČśKśØ$Ȍņn£iŪQ}_Ó¶M›vQżQĄ‚Zzõ’”ųóa’‰?@^MüłCū@}$ž@…$ž@…$ž@…$ž@…$ž@…$ž@…$ž@…$ž@…–Ÿūßæ’wŁŌ<Š™„מO B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B Bą’µoĒƒü­§±£<`Hü€!ń†Ä`Hü€!ń†ī"¦ÕméEIEND®B`‚DHARMa/vignettes/DHARMaForBayesians.Rmd0000644000176200001440000002276214665273541017252 0ustar liggesusers--- title: "DHARMa for Bayesians" author: "Florian Hartig, Theoretical Ecology, University of Regensburg [website](https://www.uni-regensburg.de/biologie-vorklinische-medizin/theoretische-oekologie/mitarbeiter/hartig/)" date: "`r Sys.Date()`" output: rmarkdown::html_vignette: toc: true vignette: > %\VignetteIndexEntry{DHARMa for Bayesians} \usepackage[utf8]{inputenc} %\VignetteEngine{knitr::rmarkdown} abstract: "The 'DHARMa' package uses a simulation-based approach to create readily interpretable scaled (quantile) residuals for fitted (generalized) linear mixed models. This Vignette describes how to user DHARMa vor checking Bayesian models. It is recommended to read this AFTER the general DHARMa vignette, as all comments made there (in pacticular regarding the interpretation of the residuals) also apply to Bayesian models. \n \n \n" editor_options: chunk_output_type: console --- ```{r global_options, include=FALSE} knitr::opts_chunk$set(fig.width=8.5, fig.height=5.5, fig.align='center', warning=FALSE, message=FALSE) ``` ```{r, echo = F, message = F} library(DHARMa) set.seed(123) ``` # Basic workflow In principle, DHARMa residuals can be calculated and interpreted for Bayesian models in very much the same way as for frequentist models. Therefore, all comments regarding tests, residual interpretation etc. from the main vignette are equally valid for Bayesian model checks. There are some minor differences regarding the expected null distribution of the residuals, in particular in the low data limit, but I believe that for most people, these are of less concern. The main difference for a Bayesian user is that, unlike for users of directly supported regression packages such as lme4 or glmmTMB, most Bayesian users will have to create the simulations for the fitted model themselves and then feed them into DHARMa by hand. The basic workflow for Bayesians that work with BUGS, JAGS, STAN or similar is: 1. Create posterior predictive simulations for your model 2. Read these in with the createDHARMa function 3. Interpret those as described in the main vignette This is more easy as it sounds. For the major Bayesian samplers (e.g. BUGS, JAGS, STAN), it amounts to adding a block with data simulations to the model, and observing those during the MCMC sampling. Then, feed the simulations into DHARMa via createDHARMa, and all else will work pretty much the same as in the main vignette. ## Example in Jags Here is an example, with JAGS ```{r, eval = F} library(rjags) library(BayesianTools) set.seed(123) dat <- DHARMa::createData(200, overdispersion = 0.2) Data = as.list(dat) Data$nobs = nrow(dat) Data$nGroups = length(unique(dat$group)) modelCode = "model{ for(i in 1:nobs){ observedResponse[i] ~ dpois(lambda[i]) # poisson error distribution lambda[i] <- exp(eta[i]) # inverse link function eta[i] <- intercept + env*Environment1[i] # linear predictor } intercept ~ dnorm(0,0.0001) env ~ dnorm(0,0.0001) # Posterior predictive simulations for (i in 1:nobs) { observedResponseSim[i]~dpois(lambda[i]) } }" jagsModel <- jags.model(file= textConnection(modelCode), data=Data, n.chains = 3) para.names <- c("intercept","env", "lambda", "observedResponseSim") Samples <- coda.samples(jagsModel, variable.names = para.names, n.iter = 5000) x = BayesianTools::getSample(Samples) colnames(x) # problem: all the variables are in one array - this is better in STAN, where this is a list - have to extract the right columns by hand posteriorPredDistr = x[,3:202] # this is the uncertainty of the mean prediction (lambda) posteriorPredSim = x[,203:402] # these are the simulations sim = createDHARMa(simulatedResponse = t(posteriorPredSim), observedResponse = dat$observedResponse, fittedPredictedResponse = apply(posteriorPredDistr, 2, median), integerResponse = T) plot(sim) ``` In the created plots, you will see overdispersion, which is completely expected, as the simulated data has overdispersion and a RE, which is not accounted for by the Jags model. ## Exercise As an exercise, you could now: * Add a RE * Account for overdispersion, e.g. via an OLRE or a negative Binomial And check how the residuals improve. # Conditional vs. unconditional simulations in hierarchical models The most important consideration in using DHARMa with Bayesian models is how to create the simulations. You can see in my jags code that the block ```{r, eval=F} # Posterior predictive simulations for (i in 1:nobs) { observedResponseSim[i]~dpois(lambda[i]) } ``` performs the posterior predictive simulations. Here, we just take the predicted lambda (mean perdictions) during the MCMC simulations and sample from the assumed distribution. This will works for any non-hierarchical model. When we move to hierarchical or multi-level models, including GLMMs, the issue of simulation becomes a bit more complicated. In a hierarchical model, there are several random processes that sit on top of each other. In the same way as explained in the main vignette at the point conditional / unconditional simulations, we will have to decide which of these random processes should be included in the posterior predictive simulations. As an example, imagine we add a RE in the likelihood of the previous model, to account for the group structure in the data. ```{r, eval = F} for(i in 1:nobs){ observedResponse[i] ~ dpois(lambda[i]) # poisson error distribution lambda[i] <- exp(eta[i]) # inverse link function eta[i] <- intercept + env*Environment1[i] + RE[group[i]] # linear predictor } for(j in 1:nGroups){ RE[j] ~ dnorm(0,tauRE) } ``` The predictions lambda[i] now depend on a lower-level stochastic effect, which is described by RE[j] ~ dnorm(0,tauRE). We can now decide to create posterior predictive simulations conditional on posterior estimates RE[j] (conditional simulations), in which case we would have to change nothing in the block for the posterior predictive simulations. Alternatively, we can decide that we want to re-simulate the RE (unconditional simulations), in which case we have to copy the entire structure of the likelihood in the predictions ```{r, eval=F} for(j in 1:nGroups){ RESim[j] ~ dnorm(0,tauRE) } for (i in 1:nobs) { observedResponseSim[i] ~ dpois(lambdaSim[i]) lambdaSim[i] <- exp(etaSim[i]) etaSim[i] <- intercept + env*Environment1[i] + RESim[group[i]] } ``` Essentially, you can remember that if you want full (uncoditional) simulations, you basically have to copy the entire likelihood of the hierarchical model, minus the priors, and sample along the hierarchical model structure. If you want to condition on a part of this structure, just cut the DAG at the point on which you want to condition on. # Statistical differences between Bayesian vs. MLE quantile residuals A common question is if there are differences between Bayesian and MLE quantile residuals. First of all, note that MLE and Bayesian quantile residuals are not exactly identical. The main difference is in how the simulation of the data under the fitted model are performed: * For models fitted by MLE, simulations in DHARMa are with the MLE (point estimate) * For models fitted with Bayes, simulations are practically always performed while also drawing from the posterior parameter uncertainty (as a point estimate is not available). Thus, Bayesian posterior predictive simulations include the parametric uncertainty of the model, additionally to the sampling uncertainty. From this we can directly conclude that Bayesian and MLE quantile residuals are asymptotically identical (and via the usual arguments uniformly distributed), but become more different the smaller n becomes. To examine what those differences are, let's imagine that we start with a situation of infinite data. In this case, we have a "sharp" posterior that can be viewed as identical to the MLE. If we reduce the number of data, there are two things happening 1. The posterior gets wider, with the likelihood component being normally distributed, at least initially 2. The influence of the prior increases, the faster the stronger the prior is. Thus, if we reduce the data, for weak / uninformative priors, we will simulate data while sampling parameters from a normal distribution around the MLE, while for strong priors, we will effectively sample data while drawing parameters of the model from the prior. In particular in the latter case (prior dominates, which can be checked via prior sensitivity analysis), you may see residual patterns that are caused by the prior, even though the model structure is correct. In some sense, you could say that the residuals check if the combination of prior + structure is compatible with the data. It's a philosophical debate how to react on such a deviation, as the prior is not really negotiable in a Bayesian analysis. Of course, also the MLE distribution might get problems in low data situations, but I would argue that MLE is usually only used anyway if the MLE is reasonably sharp. In practice, I have self experienced problems with MLE estimates. It's a bit different in the Bayesian case, where it is possible and often done to fit very complex models with limited data. In this case, many of the general issues in defining null distributions for Bayesian p-values (as, e.g., reviewed in [Conn et al., 2018](https://esajournals.onlinelibrary.wiley.com/doi/10.1002/ecm.1314)) apply. I would add though that while I find it important that users are aware of those differences, I have found that in practice these issues are small, and usually overruled by the much stronger effects of model error. DHARMa/vignettes/DHARMa.Rmd0000644000176200001440000017254014704245735014742 0ustar liggesusers--- title: "DHARMa: residual diagnostics for hierarchical (multi-level/mixed) regression models" author: "Florian Hartig, Theoretical Ecology, University of Regensburg [website](https://www.uni-regensburg.de/biologie-vorklinische-medizin/theoretische-oekologie/mitarbeiter/hartig/)" date: "`r Sys.Date()`" output: rmarkdown::html_vignette: toc: true pdf_document: toc: true vignette: > %\VignetteIndexEntry{The import package} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} abstract: "The 'DHARMa' package uses a simulation-based approach to create readily interpretable scaled (quantile) residuals for fitted generalized linear (mixed) models. Currently supported are linear and generalized linear (mixed) models from 'lme4' (classes 'lmerMod', 'glmerMod'), 'glmmTMB', 'GLMMadaptive' and 'spaMM'; phylogenetic linear models from 'phylolm' (classes 'phylolm' and 'phyloglm'); generalized additive models ('gam' from 'mgcv'); 'glm' (including 'negbin' from 'MASS', but excluding quasi-distributions) and 'lm' model classes. Moreover, externally created simulations, e.g. posterior predictive simulations from Bayesian software such as 'JAGS', 'STAN', or 'BUGS' can be processed as well. The resulting residuals are standardized to values between 0 and 1 and can be interpreted as intuitively as residuals from a linear regression. The package also provides a number of plot and test functions for typical model misspecification problems, such as over/underdispersion, zero-inflation, and residual spatial, temporal and phylogenetic autocorrelation. \n \n \n" editor_options: chunk_output_type: console --- ```{r global_options, include=FALSE} knitr::opts_chunk$set(fig.width=6.5, fig.height=4.5, fig.align='center', warning=FALSE, message=FALSE, cache = T) ``` ```{r, echo = F, message = F} library(DHARMa) set.seed(123) ``` # Motivation The interpretation of conventional residuals for generalized linear (mixed) and other hierarchical statistical models is often problematic. As an example, here the result of conventional Deviance, Pearson and raw residuals for two Poisson GLMMs, one that is lacking a quadratic effect, and one that fits the data perfectly. Could you tell which is the correct model? ```{r, echo = F, fig.width=6, fig.height=3} library(lme4) overdispersedData = createData(sampleSize = 250, overdispersion = 0, quadraticFixedEffects = -2, family = poisson()) fittedModelOverdispersed <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = overdispersedData) plotConventionalResiduals(fittedModelOverdispersed) testData = createData(sampleSize = 250, intercept = 0, overdispersion = 0, family = poisson(), randomEffectVariance = 0) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = testData) plotConventionalResiduals(fittedModel) ``` Just for completeness - it was the second one. But don't get too excited if you got it right. Probably you were just lucky - I can't really tell a difference. But even so, would you have added a quadratic effect, instead of adding an overdispersion correction? The point here is that misspecifications in GL(M)Ms cannot reliably be diagnosed with standard residual plots, and thus GLMMs are often not as thoroughly checked as they should. One reason why GL(M)Ms residuals are harder to interpret is that the expected distribution of the data (aka predictive distribution) changes with the fitted values. Reweighting with the expected dispersion, as done in Pearson residuals, or using deviance residuals, helps to some extent, but it does not lead to visually homogenous residuals, even if the model is correctly specified. As a result, standard residual plots, when interpreted in the same way as for linear models, seem to show all kind of problems, such as non-normality, heteroscedasticity, even if the model is correctly specified. Questions on the R mailing lists and forums show that practitioners are regularly confused about whether such patterns in GL(M)M residuals are a problem or not. But even experienced statistical analysts currently have few options to diagnose misspecification problems in GLMMs. In my experience, the current standard practice is to eyeball the residual plots for major misspecifications, potentially have a look at the random effect distribution, and then run a test for overdispersion, which is usually positive, after which the model is modified towards an overdispersed / zero-inflated distribution. This approach, however, has a number of drawbacks, notably: - Overdispersion is often the result of missing predictors or a misspecified model structure. Standard residual plots make it difficult to identify these problems by examining residual correlations or patterns of residuals against predictors. - Not all overdispersion is the same. For count data, the negative binomial creates a different distribution than adding observation-level random effects to the Poisson. Once overdispersion is corrected for, such violations of distributional assumptions are not detectable with standard overdispersion tests (because the tests only looks at total dispersion), and nearly impossible to see visually from standard residual plots. - Dispersion frequently varies with predictors (heteroscedasticity). This can have a significant effect on the inference. While it is standard to tests for heteroscedasticity in linear regressions, heteroscedasticity is currently hardly ever tested for in GLMMs, although it is likely as frequent and influential. - Moreover, if residuals are checked, they are usually checked conditional on the fitted random effect estimates. Thus, standard checks only check the final level of the random structure in a GLMM. One can perform extra checks on the random effects, but it is somewhat unsatisfactory that there is no check on the entire model structure. DHARMa aims at solving these problems by creating readily interpretable residuals for generalized linear (mixed) models that are standardized to values between 0 and 1, and that can be interpreted as intuitively as residuals for the linear model. This is achieved by a simulation-based approach, similar to the Bayesian p-value or the parametric bootstrap, that transforms the residuals to a standardized scale. The basic steps are: 1. Simulate new response data from the fitted model for each observation. 2. For each observation, calculate the empirical cumulative density function for the simulated observations, which describes the possible values (and their probability) at the predictor combination of the observed value, assuming the fitted model is correct. 3. The residual is then defined as the value of the empirical density function at the value of the observed data, so a residual of 0 means that all simulated values are larger than the observed value, and a residual of 0.5 means half of the simulated values are larger than the observed value. These steps are visualized in the following figure The key advantage of this definition is that the so-defined residuals always have the same, known distribution, independent of the model that is fit, if the model is correctly specified. To see this, note that, if the observed data was created from the same data-generating process that we simulate from, all values of the cumulative distribution should appear with equal probability. That means we expect the distribution of the residuals to be flat, regardless of the model structure (Poisson, binomial, random effects and so on). I currently prepare a more exact statistical justification for the approach in an accompanying paper, but if you must provide a reference in the meantime, I would suggest citing - Dunn, K. P., and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics 5, 1-10. - Gelman, A. & Hill, J. Data analysis using regression and multilevel/hierarchical models Cambridge University Press, 2006 p.s.: DHARMa stands for "Diagnostics for HierArchical Regression Models" - which, strictly speaking, would make DHARM. But in German, Darm means intestines; plus, the meaning of DHARMa in Hinduism makes the current abbreviation so much more suitable for a package that tests whether your model is in harmony with your data: > From Wikipedia, 28/08/16: In Hinduism, dharma signifies behaviours that are considered to be in accord with rta, the order that makes life and universe possible, and includes duties, rights, laws, conduct, virtues and 'right way of living'. # Workflow in DHARMa ## Installing, loading and citing the package If you haven't installed the package yet, either run ```{r, eval = F} install.packages("DHARMa") ``` Or follow the instructions on to install a development version. Loading and citation ```{r} library(DHARMa) citation("DHARMa") ``` ## Calculating scaled residuals Let's assume we have a fitted model that is supported by DHARMa. ```{r} testData = createData(sampleSize = 250) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = testData) ``` Most functions in DHARMa can be calculated directly on the fitted model object. For example, if you are only interested in testing for dispersion problems, you could run ```{r, results = "hide", fig.show='hide'} testDispersion(fittedModel) ``` In this case, the randomized quantile residuals are calculated on the fly inside the function call. If you work in this way, however, residual calculation will be repeated by every test / plot you call, and this can take a while. It is therefore highly recommended to first calculate the residuals once, using the simulateResiduals() function ```{r} simulationOutput <- simulateResiduals(fittedModel = fittedModel, plot = F) ``` which calculates randomized quantile residuals according to the algorithm discussed above. The function returns an object of class DHARMa, containing the simulations and the scaled residuals, which can later be passed on to all other plots and test functions. When specifying the optional argument plot = T, the standard DHARMa residual plot is displayed directly. The interpretation of the plot will be discussed below. Using the simulateResiduals function has the added benefit that you can modify the way in which residuals are calculated. For example, you may want to change the number of simulations, or the REs to condition on. See ?simulateResiduals and section "simulation options" below for details. The calculated (scaled) residuals can be plotted and tested via a number of DHARMa functions (see below), or accessed directly via ```{r, results = "hide"} residuals(simulationOutput) ``` To interpret the residuals, remember that a scaled residual value of 0.5 means that half of the simulated data are higher than the observed value, and half of them lower. A value of 0.99 would mean that nearly all simulated data are lower than the observed value. The minimum/maximum values for the residuals are 0 and 1. For a correctly specified model we would expect asymptotically - a uniform (flat) distribution of the scaled residuals - uniformity in y direction if we plot against any predictor. Note: the uniform distribution is the only differences to "conventional" residuals as calculated for a linear regression. If you cannot get used to this, you can transform the uniform distribution to another distribution, for example normal, via ```{r, eval = F} residuals(simulationOutput, quantileFunction = qnorm, outlierValues = c(-7,7)) ``` These normal residuals will behave exactly like the residuals of a linear regression. However, for reasons of a) numeric stability with low number of simulations, which makes it neccessary to descide on which value outliers are to be transformed and b) my conviction that it is much easier to visually detect deviations from uniformity than normality, DHARMa checks all residuals in the uniform space, and I would personally advice against using the transformation. ## Plotting the scaled residuals The main plot function for the calculated DHARMa object produced by simulateResiduals() is the plot.DHARMa() function ```{r} plot(simulationOutput) ``` The function creates two plots, which can also be called separately, and provide extended explanations / examples in the help ```{r, eval = F} plotQQunif(simulationOutput) # left plot in plot.DHARMa() plotResiduals(simulationOutput) # right plot in plot.DHARMa() ``` - plotQQunif (left panel) creates a qq-plot to detect overall deviations from the expected distribution, by default with added tests for correct distribution (KS test), dispersion and outliers. Note that outliers in DHARMa are values that are by default defined as values outside the simulation envelope, not in terms of a particular quantile. Thus, which values will appear as outliers will depend on the number of simulations. If you want outliers in terms of a particuar quantile, you can use the outliers() function. - plotResiduals (right panel) produces a plot of the residuals against the predicted value (or alternatively, other variable). Simulation outliers (data points that are outside the range of simulated values) are highlighted as red stars. These points should be carefully interpreted, because we actually don't know "how much" these values deviate from the model expectation. Note also that the probability of an outlier depends on the number of simulations, so whether the existence of outliers is a reason for concern depends also on the number of simulations. To provide a visual aid in detecting deviations from uniformity in y-direction, the plot function calculates an (optional default) quantile regression, which compares the empirical 0.25, 0.5 and 0.75 quantiles in y direction (red solid lines) with the theoretical 0.25, 0.5 and 0.75 quantiles (dashed black line), and provides a p-value for the deviation from the expected quantile. The significance of the deviation to the expected quantiles is tested and displayed visually, and can be additionally extracted with the testQuantiles function. By default, plotResiduals plots against predicted values. However, you can also use it to plot residuals against a specific other predictors (highly recommend). ```{r, eval = F} plotResiduals(simulationOutput, form = YOURPREDICTOR) ``` If the predictor is a factor, or if there is just a small number of observations on the x axis, plotResiduals will plot a box plot with additional tests instead of a scatter plot. ```{r, eval = F} plotResiduals(simulationOutput, form = testData$group) ``` See ?plotResiduas for details, but very shortly: under H0 (perfect model), we would expect those boxes to range homogeneously from 0.25-0.75. To see whether there are deviations from this expecation, the plot calculates a test for uniformity per box, and a test for homogeneity of variances between boxes. A positive test will be highlighted in red. ## Goodness-of-fit tests on the scaled residuals To support the visual inspection of the residuals, the DHARMa package provides a number of specialized goodness-of-fit tests on the simulated residuals: - testUniformity() - tests if the overall distribution conforms to expectations. - testOutliers() - tests if there are more simulation outliers than expected. - testDispersion() - tests if the simulated dispersion is equal to the observed dispersion. - testQuantiles() - fits a quantile regression or residuals against a predictor (default predicted value), and tests of this conforms to the expected quantile. - testCategorical(simulationOutput, catPred = testData\$group) tests residuals against a categorical predictor. - testZeroinflation() - tests if there are more zeros in the data than expected from the simulations. - testGeneric() - test if a generic summary statistics (user-defined) deviates from model expectations. - testTemporalAutocorrelation() - tests for temporal autocorrelation in the residuals. - testSpatialAutocorrelation() - tests for spatial autocorrelation in the residuals. Can also be used with a generic distance function. - testPhylogeneticAutocorrelation() - tests for phylogenetic signal in the residuals. See the help of the functions and further comments below for a more detailed description. ## Simulation options There are a few important technical details regarding how the simulations are performed, in particular regarding the treatments of random effects and integer responses. It is strongly recommended to read the help of ```{r, eval = F} ?simulateResiduals ``` #### Refit ```{r, eval= F} simulationOutput <- simulateResiduals(fittedModel = fittedModel, refit = T) ``` - if refit = F (default), new datasets are simulated from the fitted model, and residuals are calculated by comparing the observed data to the new data - if refit = T, a parametric bootstrap is performed, meaning that the model is refit to all new datasets, and residuals are created by comparing observed residuals against refitted residuals The second option is much much slower, and also seemed to have lower power in some tests I ran. **It is therefore not recommended for standard residual diagnostics!** I only recommend using it if you know what you are doing, and have particular reasons, for example if you estimate that the tested model is biased. A bias could, for example, arise in small data situations, or when estimating models with shrinkage estimators that include a purposeful bias, such as ridge/lasso, random effects or the splines in GAMs. My idea was then that simulated data would not fit to the observations, but that residuals for model fits on simulated data would have the same patterns/bias than model fits on the observed data. Note also that refit = T can sometimes run into numerical problems, if the fitted model does not converge on the newly simulated data. #### Conditinal vs. unconditinal simulations The second option is the treatment of the stochastic hierarchy. In a hierarchical model, several layers of stochasticity are placed on top of each other. Specifically, in a GLMM, we have a lower level stochastic process (random effect), whose result enters into a higher level (e.g. Poisson distribution). For other hierarchical models, such as state-space models, similar considerations apply, but the hierarchy can be more complex. When simulating, we have to decide if we want to re-simulate all stochastic levels, or only a subset of those. For example, in a GLMM, it is common to only simulate the last stochastic level (e.g. Poisson) conditional on the fitted random effects, meaning that the random effects are set on the fitted values. For controlling how many levels should be re-simulated, the simulateResidual function allows to pass on parameters to the simulate function of the fitted model object. Please refer to the help of the different simulate functions (e.g. ?simulate.merMod) for details. For merMod (lme4) model objects, the relevant parameters are "use.u", and "re.form", as, e.g., in ```{r, eval= F} simulationOutput <- simulateResiduals(fittedModel = fittedModel, n = 250, use.u = T) ``` If the model is correctly specified and the fitting procedure is unbiased (disclaimer: GLMM estimators are not always unbiased), the simulated residuals should be flat regardless how many hierarchical levels we re-simulate. The most thorough procedure would be therefore to test all possible options. If testing only one option, I would recommend to re-simulate all levels, because this essentially tests the model structure as a whole. This is the default setting in the DHARMa package. A potential drawback is that re-simulating the random effects creates more variability, which may reduce power for detecting problems in the upper-level stochastic processes, in particular overdispersion (see section on dispersion tests below). *Note:* Although unconditional residuals implicitly also test the normal distribution of the REs, it is probably not a bad idea to look addditionally check for normality of the RE distribution. As this is not based on quantile residuals, there is no special DHARMa function for this, so you should just extract the REs, and then run e.g. a Shapiro test. #### Integer treatment / randomization A third option is the treatment of integer responses. The background of this option is that, for integer-valued variables, some additional steps are necessary to make sure that the residual distribution becomes flat (essentially, we have to smoothen away the integer nature of the data). The idea is explained in - Dunn, K. P., and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics 5, 1-10. DHARMa currently implements two procedures for randomization. The default procedure will randomize automatically. The second option requires knowledge about whether the model is integer-valued, which is usually implemented automatically. See ?simulateResiduals for details. Usually, these options should simply be kept at their defaults. #### Calculating residuals for groups or subsets In many situations, it can be useful to look at residuals per group, e.g. to see how much the model over / underpredicts per plot, year or subject. To do this, use the recalculateResiduals() function, together with a grouping variable (group) or a subsetting variable (sel), which can also be used in combination. ```{r, eval= F} simulationOutput = recalculateResiduals(simulationOutput, group = testData$group) ``` Note, however, that you will have to change the selection of variables that you provide to plots and tests (e.g. in plotResiduals or testSpatialAutocorrelation) accordingly when you group or subset residuals. #### Reproducibility notes, random seed and random state As DHARMa uses simulations to calculate the residuals, a naive implementation of the algorithm would mean that residuals would look slightly different each time a DHARMa calculation is executed. This might both be confusing and bear the danger that a user would run the simulation several times and take the result that looks better (which would amount to multiple testing / p-hacking). By default, DHARMa therefore fixes the random seed to the same value every time a simulation is run, and afterwards restores the random state to the old value. This means that you will get exactly the same residual plot each time. If you want to avoid this behavior, for example for simulation experiments on DHARMa, use seed = NULL -\> no seed set, but random state will be restored, or seed = F -\> no seed set, and random state will not be restored. Whether or not you fix the seed, the setting for the random seed and the random state are stored in ```{r, eval = F} simulationOutput$randomState ``` If you want to reproduce simulations for such a run, set the variable .Random.seed by hand, and simulate with seed = NULL. Moreover (general advice), to ensure reproducibility, it's advisable to add a set.seed() at the beginning, and a session.info() at the end of your script. The latter will list the version number of R and all loaded packages. # Interpreting residuals and recognizing misspecification problems ## General remarks on interperting residual patterns and tests So far, all shown DHARMa results were calculated for a correctly specified model, resulting in "perfect" residual plots and diagnostics. In this section, we discuss how to recognize and interpret diagnostics that indicate a misspecified model. Before going into the details, note, however, that 1. **No residual pattern does not "prove" that the model is correct**: The fact that none of the DHARMa tests indicate a problem does not "prove" that the model is correctly specified. For any model, there are likely a large number of structural problems that do not create a pattern in the DHARMa diagnostics. In good old Popper fashion, you should interpret no residual problems as your working hypothesis not being rejected in that particular test, which increases confidence in the model, but does not constitute a conclusive proof. So, keep your skepticism alive, and if you find the results fishy, keep searching and testing. 2. **Once a residual effect is statistically significant, look at the magnitude to decide if there is a problem**: It is crucial to note that significance is NOT a measure of the strength of the residual pattern, it is a measure of the signal/noise ratio, i.e. whether you are sure there is a pattern at all. Significance in hypothesis tests depends on at least 2 ingredients: the strength of the signal and the number of data points. If you have a lot of data points, residual diagnostics will nearly inevitably become significant, because having a perfectly fitting model is very unlikely. That, however, doesn't necessarily mean that you need to change your model. The p-values confirm that there is a deviation from your null hypothesis. It is, however, in your discretion to decide whether this deviation is worth worrying about. For example, if you see a dispersion parameter of 1.01, I would not worry, even if the dispersion test is significant. A significant value of 5, however, is clearly a reason to move to a model that accounts for overdispersion. 3. **A residual pattern does not indicate that the model is unusable**: While a significant pattern in the residuals indicates with good reliability that the observed data did likely not originate from the fitted model, this doesn't necessarily imply that the inferential results from this wrong model are not usable. There are many situations in statistics where it is common practice to work with "wrong models". For example, many statistical models use shrinkage estimators, which purposefully bias parameter estimates to certain values. Random effects are a special case of this. If DHARMa residuals for these estimators are calculated, they will often show a slight pattern in the residuals even if the model is correctly specified, and tests for this can get significant for large sample sizes. For this reason, DHARMa is excluding RE estimates in the predictions when plotting res \~ pred. Another example is data that is missing at random (MAR). Since it is known that this phenomenon does not create a bias on the fixed effects estimates, it is common practice to fit these data with standard mixed models. Nevertheless, DHARMa recognizes that the observed data looks different from what would be expected from the model assumptions, and flags the model as problematic (see [here](https://github.com/florianhartig/DHARMa/issues/101)). **Important conclusion: DHARMa only flags a difference between the observed and expected data - the user has to decide whether this difference is actually a problem for the analysis!** ## Recognizing over/underdispersion GL(M)Ms often display over/underdispersion, which means that residual variance is larger/smaller than expected under the fitted model. This phenomenon is most common for GLM families with constant (fixed) dispersion, in particular for Poisson and binomial models, but it can also occur in GLM families that adjust the variance (such as the beta or negative binomial) when distribution assumptions are violated. A few general rules of thumb about dealing with dispersion problems: - Dispersion is a property of the residuals, i.e. you can detect dispersion problems only AFTER fitting the model. It doesn't make sense to look at the dispersion of your response variable - Overdispersion is more common than underdispersion - If overdispersion is present, the main effect is that confidence intervals tend to be too narrow, and p-values to small, leading to inflated type I error. The opposite is true for underdispersion, i.e. the main issue of underdispersion is that you loose power. - A common reason for overdispersion is a misspecified model. When overdispersion is detected, one should therefore first search for problems in the model specification (e.g. by plotting residuals against predictors with DHARMa), and only if this doesn't lead to success, overdispersion corrections such as individual-level random effects or changes in the distribution should be applied ### Residual patterns of over/underdispersion This this is how **overdispersion** looks like in the DHARMa residuals. Note that we get more residuals around 0 and 1, which means that more residuals are in the tail of distribution than would be expected under the fitted model. ```{r} testData = createData(sampleSize = 200, overdispersion = 1.5, family = poisson()) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` If you see this pattern, note that overdispersion is often caused by model misfit. Thus, before moving to a GLM with variable dispersion (for count data this would typically be a negative binomial), you should check your model for misfit, e.g. by plotting residuals against all predictors using plotResiduals(). Next, this is an example of underdispersion. Here, we get too many residuals around 0.5, which means that we are not getting as many residuals as we would expect in the tail of the distribution than expected from the fitted model. ```{r} testData = createData(sampleSize = 500, intercept=0, fixedEffects = 2, overdispersion = 0, family = poisson(), roundPoissonVariance = 0.001, randomEffectVariance = 0) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` If you see this pattern, note that a common reason for underdispersion is overfitting, i.e. your model is too complex. Other possible explanations to check for include zero-inflation (best to check by comparing to a ZIP model, but see also DHARMa::testZeroInflation), non-independence of the data (e.g. temporal autocorrelation, check via DHARMa:: testTemporalAutocorrelation) that your predictors can use to overfit, or that your data-generating process is simply not a Poisson process. From a technical side, underdispersion is not as concerning as over dispersion, as it will usually bias p-values to the conservative side, but if your goal is to get a good power, you may want to consider a simpler model. If that is not helping, you can move to a distribution for underdispersed count data (e.g. Conway-Maxwell-Poisson, generalized Poisson). ### Formal tests for over/underdispersion Although, as discussed above, over/underdispersion will show up in the residuals, and it's possible to detect it with the testUniformity function, simulations show that this test is less powerful than more targeted tests. DHARMa contains several overdispersion tests that compare the dispersion of simulated residuals to the observed residuals. 1. *default:* a non-parametric test that compares the variance of the simulated residuals to the observed residuals (default), which has some analogy to the variance test implemented in aer::dispersiontest 2. *PearsonChisq:* alternatively, DHARMa implements the Pearson-chi2 test that is popular in the literature, suggested in the glmm Wiki, and implemented in some other R packages such as performance::check_overdispersion 3. *refit* if residual simulations are done via refit, DHARMa will compare the the Pearson residuals of the re-fitted simulations to the original Pearson residuals. This is essentially a nonparametric version of test 2. All of these tests are included in the testDispersion function, see ?testDispersion for details. ```{r overDispersionTest, echo = T, fig.width=4, fig.height=4} testDispersion(simulationOutput) ``` IMPORTANT INFO: we have made extensive simulations, which have shown that the various tests have certain advantages and disadvantages. The basic results are that: - The most powerful and reliable test is option 3, but this costs a lot of time and is not available for all regression packages, as it requires that Pearson residuals are available - Option 2, the parametric Pearson-chi2 is fast if Pearson residuals are available, but based on a naive expectation of df (counts RE as 1 df) and the test statistic is thus biased towards underdispersion for mixed models. Similar to the df approximation, Bias increasing with the number of RE levels. When testing only for overdispersion (alternative = "greater"), this makes the test more conservative, but it also costs power. - The DHARMa default option 1 is fast, nearly unbiased (i.e. you can test under and overdispersion), and only slightly less powerful as test 3, PROVIDED that simulations are made conditional on the fitted REs. Note that the latter is not the DHARMa default, so you have to actively request conditional simulations, e.g. for lme4 by specifying re.form = NULL. Power compared to the parametric Pearson-chi2 test depends on the number of RE levels, it will be more powerful for typical number of RE levels. As support for these statements, here results of the simulation, which compares the uniform (KS) test with the standard simuation-based test (conditional and unconditional) and the Pearson-chi2 test (two-sided and greater) for an n=200 Poisson GLMM with 30 RE levels. Thus, my current recommendation is: for most users, use the default DHARMa test, but create simulations conditionally. ## Zero-inflation / k-inflation or deficits A common special case of overdispersion is zero-inflation, which is the situation when more zeros appear in the observation than expected under the fitted model. Zero-inflation requires special correction steps. More generally, we can also have too few zeros, or too much or too few of any other values. We'll discuss that at the end of this section. ### Residual patterns Here an example of a typical zero-inflated count dataset, plotted against the environmental predictor ```{r} testData = createData(sampleSize = 500, intercept = 2, fixedEffects = c(1), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3), randomEffectVariance = 0, pZeroInflation = 0.6) par(mfrow = c(1,2)) plot(testData$Environment1, testData$observedResponse, xlab = "Envrionmental Predictor", ylab = "Response") hist(testData$observedResponse, xlab = "Response", main = "") ``` We see a hump-shaped dependence of the environment, but with too many zeros. In the normal DHARMa residual plots, zero-inflation will look pretty much like overdispersion ```{r, fig.height=5.5} fittedModel <- glmer(observedResponse ~ Environment1 + I(Environment1^2) + (1|group) , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` The reason is that the model will usually try to find a compromise between the zeros, and the other values, which will lead to excess variance in the residuals. ### Formal tests for zero-inflation DHARMa also has a special test for zero-inflation, which compares the distribution of expected zeros in the data against the observed zeros ```{r, fig.width=4, fig.height=4} testZeroInflation(simulationOutput) ``` This test is likely better suited for detecting zero-inflation than the standard plot, but note that also overdispersion will lead to excess zeros, so only seeing too many zeros is not a reliable diagnostics for moving towards a zero-inflated model. A reliable differentiation between overdispersion and zero-inflation will usually only be possible when directly comparing alternative models, e.g. through residual comparison / model selection of a model with / without zero-inflation, or by simply fitting a model with zero-inflation and looking at the parameter estimate for the zero-inflation. A good option is the R package glmmTMB, which is also supported by DHARMa. We can use this to fit ```{r, eval= F} # requires glmmTMB fittedModel <- glmmTMB(observedResponse ~ Environment1 + I(Environment1^2) + (1|group), ziformula = ~1 , family = "poisson", data = testData) summary(fittedModel) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` ### Testing generic summary statistics, e.g. for k-inflation or deficits To test for generic excess / deficits of particular values, we have the function testGeneric, which compares the values of a generic, user-provided summary statistics Choose one of alternative = c("greater", "two.sided", "less") to test for inflation / deficit or both. Default is "greater" = inflation. ```{r, fig.width=4.5, fig.height=4.5} countOnes <- function(x) sum(x == 1) # testing for number of 1s testGeneric(simulationOutput, summary = countOnes, alternative = "greater") # 1-inflation ``` ## Heteroscedasticity So far, most of the things that we have tested could also have been detected with parametric tests. Here, we come to the first issue that is difficult to detect with current tests, and that is usually neglected. Heteroscedasticity means that there is a systematic dependency of the dispersion / variance on another variable in the model. It is not sufficiently appreciated that also binomial or Poisson models can show heteroscedasticity. Basically, it means that the level of over/underdispersion depends on another parameter. Here an example where we create such data ```{r} testData = createData(sampleSize = 500, intercept = -1.5, overdispersion = function(x){return(rnorm(length(x), sd = 1 * abs(x)))}, family = poisson(), randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` The exact p-values for the quantile lines in the plot can be displayed via ```{r, eval = F} testQuantiles(simulationOutput) ``` As mentioned above, the equivalent test for categorical predictors (plot function will switch automatically) would be ```{r, eval = F} testCategorical(simulationOutput, catPred = testData$group) ``` Adding a simple overdispersion correction will try to find a compromise between the different levels of dispersion in the model. The qq plot looks better now, but there is still a pattern in the residuals ```{r} testData = createData(sampleSize = 500, intercept = 0, overdispersion = function(x){return(rnorm(length(x), sd = 2*abs(x)))}, family = poisson(), randomEffectVariance = 0) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) + (1|ID), family = "poisson", data = testData) # plotConventionalResiduals(fittedModel) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` To remove this pattern, you would need to make the dispersion parameter dependent on a predictor (e.g. in JAGS), or apply a transformation on the data. ## Detecting missing predictors or wrong functional assumptions A second test that is typically run for LMs, but not for GL(M)Ms is to plot residuals against the predictors in the model (or potentially predictors that were not in the model) to detect possible misspecifications. Doing this is *highly recommended*. For that purpose, you can retrieve the residuals via ```{r, eval = F} simulationOutput$scaledResiduals ``` Note again that the residual values are scaled between 0 and 1. If you plot the residuals against predictors, space or time, the resulting plots should not only show no systematic dependency of those residuals on the covariates, but they should also again be flat for each fixed situation. That means that if you have, for example, a categorical predictor: treatment / control, the distribution of residuals for each predictor alone should be flat as well. Here an example with a missing quadratic effect in the model and 2 predictors ```{r} testData = createData(sampleSize = 200, intercept = 1, fixedEffects = c(1,2), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3,0)) fittedModel <- glmer(observedResponse ~ Environment1 + Environment2 + (1|group), family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # plotConventionalResiduals(fittedModel) plot(simulationOutput, quantreg = T) # testUniformity(simulationOutput = simulationOutput) ``` It is difficult to see that there is a problem at all in the general plot, but it becomes clear if we plot against the environment ```{r} par(mfrow = c(1,2)) plotResiduals(simulationOutput, testData$Environment1) plotResiduals(simulationOutput, testData$Environment2) ``` ## Residual correlation structures (temporal, spatial, phylogenetic) If a distance between residuals can be defined (temporal, spatial, phylogenetic), you should check if there is a distance-dependence in the residuals, which would suggest to move to a GLS (generalized least squares) structure for analysis. The three functions to test for this in DHARMa are: - testTemporalAutocrrelation based on the Durbin-Watson test. - testSpatialAutocorrelation, based on Moran's I, can also be used for generic distance functions. - testPhylogeneticAutocorrelation, based on Moran's I test from `Moran.I` function on package `ape`. Here a short example for the spatial case, see help of the functions for extended examples. ```{r, fig.width=4, fig.height=4} testData = createData(sampleSize = 100, family = poisson(), spatialAutocorrelation = 3, numGroups = 1, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , data = testData, family = poisson() ) simulationOutput <- simulateResiduals(fittedModel = fittedModel) testSpatialAutocorrelation(simulationOutput = simulationOutput, x = testData$x, y= testData$y) # plot(simulationOutput) ``` Note that all these tests are most sensitive against homogeneous residual structure, and might miss local and heterogeneous (non-stationary) residual structures. Additional visual checks can be useful. However, standard DHARMa simulations from models with temporal / spatial / phylogenetic conditional autoregressive terms will still have the respective correlation in the DHARMa residuals, unless the package you are using is modelling the autoregressive terms as explicit REs and is able to simulate conditional on the fitted REs. It means that the residuals will still show significant autocorrelation, even if the model fully accounts for this strucuture, and other tests, such as dispersion, uniformity, may have inflated type I error. See the example below with a `glmmTMB` model with a spatial autocorrelation structure: ```{r, fig.width=4, fig.height=4} library(glmmTMB) testData$pos <- numFactor(testData$x, testData$y) fittedModel2 <- glmmTMB(observedResponse ~ Environment1 + exp(pos + 0|group), data = testData, family = poisson()) simulationOutput2 <- simulateResiduals(fittedModel = fittedModel2) testSpatialAutocorrelation(simulationOutput = simulationOutput2, x = testData$x, y= testData$y) # plot(simulationOutput2) ``` One of the options to solve it and get correct tests and no residual pattern (if the model is correct) is to rotate the residual space according to the coariance structure of the fitted model, such that the rotated residuals are conditionally independent. The argument rotation in `simulateResiduals` does it (see also `?getQuantile` for details about the rotation options): ```{r, fig.width=4, fig.height=4} # rotation of the residuals simulationOutput3 <- simulateResiduals(fittedModel = fittedModel2, rotation = "estimated") testSpatialAutocorrelation(simulationOutput = simulationOutput3, x = testData$x, y= testData$y) # plot(simulationOutput3) ``` # Case studies and examples **Note:** More real-world examples can be found on the DHARMa GitHub repository. ## Budworm example (count-proportion n/k binomial) This example comes from [Jochen Fruend](https://jochenfruend.wordpress.com/). Measured are the number of parasitized observations, with population density as a covariate: ```{r, echo = F} data = structure(list(N_parasitized = c(226, 689, 481, 960, 1177, 266, 46, 4, 884, 310, 19, 4, 7, 1, 3, 0, 365, 388, 369, 829, 532, 5), N_adult = c(1415, 2227, 2854, 3699, 2094, 376, 8, 1, 1379, 323, 2, 2, 11, 2, 0, 1, 1394, 1392, 1138, 719, 685, 3), density.attack = c(216.461273226486, 214.662143448767, 251.881252132684, 400.993643475831, 207.897856251888, 57.0335141562012, 6.1642552100285, 0.503930659141302, 124.673812637575, 27.3764667492035, 0.923453215863429, 0.399890030241684, 0.829818131526174, 0.146640466903247, 0.216795117773948, 0.215498663908284, 110.635445098884, 91.3766566822467, 126.157080458047, 82.9699108890686, 61.0476207779938, 0.574539291305784), Plot = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L ), .Label = c("1", "2", "3", "4"), class = "factor"), PY = c("p1y82", "p1y83", "p1y84", "p1y85", "p1y86", "p1y87", "p1y88", "p1y89", "p2y86", "p2y87", "p2y88", "p2y89", "p2y90", "p2y91", "p2y92", "p2y93", "p3y88", "p3y89", "p3y90", "p3y91", "p3y92", "p3y93" ), Year = c(82, 83, 84, 85, 86, 87, 88, 89, 86, 87, 88, 89, 90, 91, 92, 93, 88, 89, 90, 91, 92, 93), ID = 1:22), .Names = c("N_parasitized", "N_adult", "density.attack", "Plot", "PY", "Year", "ID"), row.names = c("p1y82", "p1y83", "p1y84", "p1y85", "p1y86", "p1y87", "p1y88", "p1y89", "p2y86", "p2y87", "p2y88", "p2y89", "p2y90", "p2y91", "p2y92", "p2y93", "p3y88", "p3y89", "p3y90", "p3y91", "p3y92", "p3y93" ), class = "data.frame") data$logDensity = log10(data$density.attack+1) ``` ```{r, fig.height=4, fig.width=4} plot(N_parasitized / (N_adult + N_parasitized ) ~ logDensity, xlab = "Density", ylab = "Proportion infected", data = data) ``` Let's fit the data with a regular binomial n/k glm ```{r} mod1 <- glm(cbind(N_parasitized, N_adult) ~ logDensity, data = data, family=binomial) simulationOutput <- simulateResiduals(fittedModel = mod1) plot(simulationOutput) ``` We see various signals of overdispersion - QQ: s-shaped QQ plot, distribution test (KS) signficant - QQ: Dispersion test is significant - QQ: Outlier test significant - Res \~ predicted: Quantile fits are spread out too far OK, so let's add overdispersion through an individual-level random effect ```{r} mod2 <- glmer(cbind(N_parasitized, N_adult) ~ logDensity + (1|ID), data = data, family=binomial) simulationOutput <- simulateResiduals(fittedModel = mod2) plot(simulationOutput) ``` The overdispersion looks better, but you can see that the residuals still look a bit irregular (although tests are n.s.). The raw data looks a bit humped-shaped, so we might be tempted to add a quadratic effect. ```{r} mod3 <- glmer(cbind(N_parasitized, N_adult) ~ logDensity + I(logDensity^2) + (1|ID), data = data, family=binomial) simulationOutput <- simulateResiduals(fittedModel = mod3) plot(simulationOutput) ``` The residuals look perfect now. That being said, we dont' have a lot of data, and we have to be sure we're not overfitting. A likelihood ratio test tells us that the quadratic effect is not significantly supported. ```{r} anova(mod2, mod3) ``` Also AIC differences are small, although slightly in favor of model 3 ```{r} AIC(mod2) AIC(mod3) ``` I guess you could use either Model 2 or 3 - the broader point is: increasing model complexity will nearly always improve the residuals, but according to standard statistical arguments (power, bias-variance trade-off) it's not always advisable to get them perfect, just good enough! ## Owl example (count data) The next examples uses the fairly well known Owl dataset which is provided in glmmTMB (see ?Owls for more info about the data). The following shows a sequence of models, all checked with DHARMa. The example is discussed in a talk at ISEC 2018, see slides [here](https://www.slideshare.net/florianhartig/mon-c5hartig2493). ```{r, error=TRUE} library(glmmTMB) m1 <- glm(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)), data=Owls , family = poisson) res <- simulateResiduals(m1) plot(res) ``` OK, this is highly overdispersed. Let's add a RE on nest: ```{r, error=TRUE} m2 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), data=Owls , family = poisson) res <- simulateResiduals(m2) plot(res) ``` Somewhat better, but not good. Move to neg binom, to adjust dispersion, and checking dispersion and residuals against FoodTreatment predictor: ```{r, error=TRUE} m3 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), data=Owls , family = nbinom1) res <- simulateResiduals(m3, plot = T) par(mfrow = c(1,2)) testDispersion(res) plotResiduals(res, Owls$FoodTreatment) ``` We see underdispersion now. In a model with variable dispersion, this is often the signal that some other distributional assumptions are violated. Let's check for zero-inflation: ```{r, fig.height=4, fig.width=4} testZeroInflation(res) ``` It looks as if there is some zero-inflation, although non-significant. Fitting a zero-inflated model: ```{r, error=TRUE} m4 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), ziformula = ~ FoodTreatment + SexParent, data=Owls , family = nbinom1) res <- simulateResiduals(m4, plot = T) ``` ```{r, error=TRUE, fig.width=7} par(mfrow = c(1,3)) plotResiduals(res, Owls$FoodTreatment) testDispersion(res) testZeroInflation(res) ``` This looks a lot better. Trying a slightly different model specification, adding a dispersion model as well: ```{r, error=TRUE} m5 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), dispformula = ~ FoodTreatment + SexParent , ziformula = ~ FoodTreatment + SexParent, data=Owls , family = nbinom1) res <- simulateResiduals(m5, plot = T) ``` ```{r, error=TRUE, fig.width=7} par(mfrow = c(1,3)) plotResiduals(res, Owls$FoodTreatment) testDispersion(res) testZeroInflation(res) ``` but that does not seem to make things better. Both models would be acceptable in terms of their fit to the data. Which one should you prefer? This is not a question for residual checks. Residual checks tell you which models can be rejected with the data. Which of the typically many acceptable models you should fit must be decided by your scientific question, and/or possibly by model selection methods. In doubt, I would tend towards the simpler model though. # Notes on particular data types ## Poisson data The main concern in Poisson data is dispersion. See comments in the section on the dispersion test, in particular regarding the advantage of conditional simulations in this case. To address overdispersion, I would recommend to prefer the negative binomial model over observation-level random effects, because this mode will be easier to test in DHARMa and its dispersion can be easier modeled, e.g. with glmmTMB. The third option would be quasi models, but there are few advantages, except runtime. Note also that quasi models cannot be tested with DHARMa. Once dispersion is adjusted, you should check for heteroscedasticity (via standard plot, also against all predictors), and for zero-inflation. As noted, zero-inflation tests are often negative, and rather show up as underdispersion. Work through the owl example below. ## Proportional data Proportional data expressed as percentage or fractions of a whole, i.e. non-count-based data, is often modeled with beta regressions. Those can be tested with DHARMa. Note that beta regressions are often 0 or 1 inflated. Both should be tested with testZeroInflation or testGeneric. techniques for analysing continuous (also called non-count-based or non-binomial) proportions (e.g. percent cover, fraction time spent on an activity) Note: discrete proportions, i.e. count-based proportions, of the type k/n should NOT be modeled with the beta regression. Use the binomial (see below). ## Binomial data Binomial data behave slightly different depending on whether we have a 0/1 response (Bernoulli) or a k/n response (true binomial). A k/n response, in particular when n is large, will behave similar to the Poisson, in that it approaches a normal distribution with fixed dispersion for large n and becomes more assymetric at its borders (for k = 0 or n). You should check for dispersion and consider a beta-binomial in cases of overdispersion. Things are a bit different for the 0/1 response. Let's look at the residuals of a clearly misspecified binomial model (missing predictor) with 0/1 response data. ```{r} testData = createData(sampleSize = 500, overdispersion = 0, fixedEffects = 5, family = binomial(), randomEffectVariance = 3, numGroups = 25) fittedModel <- glm(observedResponse ~ 1, family = "binomial", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) ``` If you would do the same with a binomial k/n response or count data, such a misspecification would produce overdispersion (try it out). For the 0/1 response we see neither dispersion problems nor a misfit in the general res \~ predicted plot. ```{r} plot(simulationOutput, asFactor = T) ``` Even though the misfit is clearly visible if we plot the residuals against the missing predictor. ```{r, fig.width=4, fig.height=4} plotResiduals(simulationOutput, testData$Environment1, quantreg = T) ``` However, we can see the overdispersion arising from the misfit if we group our residuals, which basically transforms the 0/1 response in a k/n response. To show this, let's look at the dispersion test for the same model, once ungrouped (left), and grouped according to the variable group which was in the data (right). ```{r} par(mfrow = c(1,2)) testDispersion(simulationOutput) simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group) testDispersion(simulationOutput2) ``` In general, you can group according to any variable that you like, including continous variables or space. However, some variables make more sense than others. To understand this, consider a simulation where we create binonial data with true probabilities p, drawn from a uniform distribution: ```{r} n = 1000 p = runif(n, 0.1, 0.9) # true probabilities obs = rbinom(n, 1, p) ``` The important thing to note here is that `rbinom(n, 1, p)` will generate an identical overall distribution as `rbinom(1, n, mean(p))`. What that means: a misfit of the prediction will not show up unless they are wrong in the overall mean. Consequenly, if we fit: ```{r} fit <- glm(obs ~ 1, family = "binomial") # wrong model, assumes equal probabilities library(DHARMa) res <- simulateResiduals(fit, plot = T) # nothing to see ``` We see no misfit, and neither do we see a misfit when we group the data points randomly, as the mean of a random group is still fit well by the overall mean. ```{r} res2 <- recalculateResiduals(res, group = rep(1:20, each = 10)) plot(res2) ``` However, we see thes misfit / overdispersion if we aggregate according to something that is correlated to the misfit. For our example, let's just group according to the true means: ```{r} grouping = cut(p, breaks = quantile(p, seq(0,1,0.02))) res3 <- recalculateResiduals(res, group = grouping) plot(res3) ``` In this case, the groups have a different mean than the fitted grand mean, and the misfit shows up in the residuals. Thus, what we are looking for in the grouping is variables that may correlate with the misfit. If you don't have a natural grouping variable, you can introduce arbitrary grouping variables, e.g. via discretising a predictor or the response (usually preferable), and grouping according to that, or via discretising space (e.g. group observation in spatial blocks). The pattern appears only, however, if the grouping variable correlates with the model error. Consider the following example: We create data and fit a model with a missing predictor (Environment2): ```{r} set.seed(123) testData = createData(sampleSize = 500, overdispersion = 0, fixedEffects = c(0,3), family = binomial(), randomEffectVariance = 3, numGroups = 50) ``` Apparently, no problem with the residuals for the misfitted model: ```{r} res <- simulateResiduals(fittedModel = fittedModel) fittedModel <- glm(observedResponse ~ Environment1, family = "binomial", data = testData) plot(res) ``` 1. Grouping according to the RE produces overdispersion because RE is missing in the first model: ```{r} res2 = recalculateResiduals(res , group = testData$group) plot(res2) ``` 2. Grouping according to a random factor does not produce an effect. In this respect, the model has correct dispersion: ```{r} grouping = as.factor(sample.int(50, 500, replace = T)) res2 = recalculateResiduals(res , group = grouping) plot(res2) ``` 3. Grouping according to the response doesn't create a pattern: ```{r} x = predict(fittedModel) grouping = cut(x, breaks = quantile(x, seq(0,1,0.02))) res2 = recalculateResiduals(res , group = grouping) plot(res2) ``` 4. Grouping according to the missing variable creates pattern, because in relation to this variable, the model is overdispersed: ```{r} x = testData$Environment2 grouping = cut(x, breaks = quantile(x, seq(0,1,0.02))) res2 = recalculateResiduals(res , group = grouping) plot(res2) ``` 5. Grouping according to space does not create a pattern, because there is no missing spatial predictor: ```{r} x = testData$x grouping = cut(x, breaks = quantile(x, seq(0,1,0.02))) res3 = recalculateResiduals(res , group = grouping) plot(res3) ``` **Conclusions:** if you see overdispersion or a pattern after grouping, it highlights a model error that is structured by group. As the pattern usually highlights a model misfit, rather than a dispersion problem akin to what happens in an overdispersed binomial (which has major impacts on p-values and CIs), I view this binomial grouping pattern as less critical. Likely, most conclusions will not change if you ignore the problem. Nevertheless, you should try to understand the reason for it. When the group is spatial, it could be the sign of residual spatial autocorrelation which could be addressed by a spatial RE or a spatial model. When grouped by a continuous variable, it could be the sign of a nonlinear effect. # Supported packages and frameworks ## lm and glm lm and glm and MASS::glm.nb are fully supported. ## lme4 lme4 model classes are fully supported. Possible to condition on REs via re.form, see help of predict.merMod ## mgcv When using mgcv with DHARMa, it is highly recommended to also install mgcViz. Since version 0.4.5, this will allow DHARMa to fall back on the simulate.gam function in mgcViz, which is more general than the default simulate function. For example, without mgcViz, it will not be possible to simulate from mgcv::gam objects fitted with extended families. If you absolutely want to use DHARMa without mgcViz, you should make sure that simulate(model) works correctly for the model object for which you want to calculate DHARMa residuals. ## gamm4 Models fitted with gamm4 return a list that contains a lme4 object under the name "mer". You can test this object like an lme4 model, so e.g. simulateResiduals(myGamm4Model\$mer). All remarks regarding lme4 objects apply. ## glmmTMB glmmTMB is nearly fully supported since DHARMa 0.2.7 and glmmTMB 1.0.0. A remaining limitation is that you can't adjust whether simulation are conditional or not, so simulateResiduals(model, re.form = NULL) will have no effect, simulations will always be done from the full model. ## spaMM spaMM is supported by DHARMa since 0.2.1 ## GLMMadaptive GLMMadaptive is supported by DHARMa since 0.3.4. ## phylolm phylom (version \>= 2.6.5) is supported by DHARMa since 0.4.7 for both model classes phylolm and phyloglm. ## phyr DHARMa residuals work with phyr, but the correct implementation is not fully tested as of DHARMa 0.4.2. See also ## brms brms can be made to work together with DHARMa, see ## Unsupported packages If confronted with an unsupported package, DHARMa will try to use standard S3 functions such as coef(), simulate() etc. to perform simulations. If no error occurs, a residual object will be calculated, and a warning will be provided that this package has not been checked for full functionality. In many cases, the results can be used though (but no guarantee, maybe check with null simulations if the results are OK). Other than that, see my general comments about [adding new R packages to DHARMa](https://github.com/florianhartig/DHARMa/wiki/Adding-new-R-packages-to-DHARMA) ## Importing external simulations (e.g. from Bayesian software or unsupported packages) DHARMa can also import external simulations from a fitted model via createDHARMa(), which will be interesting for unsupported packages and for Bayesians. **Bayesians should note the extra Vignette on "DHARMa for Bayesians" regarding the interpretation of these residuals.** Here, an example for how to create simulations for a Poisson glm. Of course, it doesn't make sense to do this as glm is a supported model class, but you could do the same in case you want to check a model class that is currently not supported by DHARMa. ```{r, eval = T} testData = createData(sampleSize = 200, overdispersion = 0.5, family = poisson()) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulatePoissonGLM <- function(fittedModel, n){ pred = predict(fittedModel, type = "response") nObs = length(pred) sim = matrix(nrow = nObs, ncol = n) for(i in 1:n) sim[,i] = rpois(nObs, pred) return(sim) } sim = simulatePoissonGLM(fittedModel, 100) DHARMaRes = createDHARMa(simulatedResponse = sim, observedResponse = testData$observedResponse, fittedPredictedResponse = predict(fittedModel), integerResponse = T) plot(DHARMaRes, quantreg = F) ``` DHARMa/vignettes/dispersion.png0000644000176200001440000013131714665273541016166 0ustar liggesusers‰PNG  IHDRæ&›ž=„ 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This is a good option for color-blind friendly plots. * Documentation: improved help files and vignette. # DHARMa 0.4.6 ## New Features * new function benchmarkRuntime() for checking runtime of functions * new function simulatedLRT() to generate a simulated likelihood ratio test ## Bugfixes * fixed issue with parallelization in runBenchmarks * various minor bugfixed and help improvements # DHARMa 0.4.5 ## Minor changes * included option to simulate mgcv models using the functions implemented in mgcViz which should improve mgcv compatibility with DHARMa * Added option to include plot title in plot() #320 ## Bugfixes * fixed issues with plotting, see #313 and #274 # DHARMa 0.4.4 ## Major changes * remodelled tests so that all tested packages can be used conditionally ## Minor changes * re-introduced glmmTMB to suggests * phyr moved to enhances * re-modelled package unit tests * added RStan, CmdStanR, rjags, BayesianTools to enhances, as they could be used with DHARMa * moved parallel calculations in runBenchmark to R native parallel functions ## New features * Added rotation option to all functions that create residuals (simulateResiduals, recalculateResiduals, createDHARMa) ## Documentation * Added help comments about autocorrelation structures, in particular in simulateResiduals, testSpatialAutocorrelation, testTemporalAutocorrelation * Added example about the use of rotation in testTemporalAutocorrelation * Improved help of dispersion test # DHARMa 0.4.3 ## Bugfixes * Removed glmmTMB completely, see #289 # DHARMa 0.4.2 ## Bugfixes * Moved glmmTMB from suggest to import because this package is used in the vignette, see #289 ## Minor changes * Added hurricane dataset * Help and vignette updates * phyr added in suggests # DHARMa 0.4.1 ## Bugfixes * Force method = traditional for refit = T, as it turns out that the PIT method is not a good idea on the residuals, see #272 # DHARMa 0.4.0 This is actually a bugfix release for 0.3.4, but on reflection I decided that 0.4.0 should have been a minor release, so I pushed the version number up to 0.4.0 ## Bugfixes * bugfix in getResiduals, which had consequences for quantile residual calculations with refit = T # DHARMa 0.3.4 0.3.4 is a relatively important release with various minor improvements a smaller new features, most noteworthy the support of glmmAdaptive ## New features * added parametric dispersion test in testDispersion (0.3.3.2) * support for glmmAdaptive (0.3.3.1) * new plot for categorical predictors * new plots for result of runBenchmarks ## Major changes ## Minor changes * changed test statistics in standard dispersion test to standardized variance, to be more in line with standard dispersion parameters * defaults for plot function unified * removed option to provide no x,y / time in the correlation tests * recalculateResiduals now allows subsetting #246 * better input checking in correlation tests #190 ## Bugfixes * bugfix in runBenchmarks included in https://github.com/florianhartig/DHARMa/pull/247 * bugfix in testQuantiles https://github.com/florianhartig/DHARMa/pull/261 * bugfix in getRandomState https://github.com/florianhartig/DHARMa/issues/254 # DHARMa 0.3.3 ## Bugfixes * bugfix in testOutliers, see https://github.com/florianhartig/DHARMa/issues/197 * bugfix in the ecdf / PIT residual function, see https://github.com/florianhartig/DHARMa/issues/195 # DHARMa 0.3.2 ## Bugfixes * bugfix in testOutliers, see https://github.com/florianhartig/DHARMa/issues/182 # DHARMa 0.3.1 ## Major changes * added PIT quantile calculations based on suggestion in #168. For details see ?getQuantiles ## Bugfixes * bugfix for passing on parameters to plot.default through plotR.DHARMa and plotResiduals ## Minor changes * added checks / warnings for models fit with weights # DHARMa 0.3.0 ## New features * quantile regressions switched to qgam, which also calculates p-values on the quantile estimates * new testQuantiles function, based on the qgam quantile regressions ## Changes * syntax change for plotResiduals, see ?plotResiduals * transformQuantiles is deprecated, functionality included in residuals() * nearly all functions can now also be called directly with a fitted model (for computational efficiency, however, it is still recommended to calculate the residuals first) * qqPlot now shows disribution, dispersion and outlier test ## Bugfixes * bugfix #158 for fitting glmmTMB binomial with proportions # DHARMa 0.2.7 ## New features * added smooth scatter in plotResiduals https://github.com/florianhartig/DHARMa/commit/da01d8c7a9a74558817e4a73fe826084164cf05d * glmmTMB now fully supported through new compulsory version 1.0 of glmmTMB, which includes the re.form argument in the simulations required by DHARMa https://github.com/florianhartig/DHARMa/pull/140 # DHARMa 0.2.6 ## Bugfixes * return of plotResiduals set to invisible # DHARMa 0.2.5 ## New features * transformQuantiles function added to transform uniform DHARMa residuals to normal or other residuals ## Minor changes * several smaller corrections to help # DHARMa 0.2.4 ## Bugfixes * corrected issues in the vignette * small corrections to help # DHARMa 0.2.3 ## Bugfixes * added missing distributions https://github.com/florianhartig/DHARMa/pull/104 * bugfix in simulate residuals https://github.com/florianhartig/DHARMa/issues/107 # DHARMa 0.2.2 ## Bugfixes * fixes bug in Vignette (header lost) # DHARMa 0.2.1 ## New features * Outlier highlighting (in plots) and formal outlier test, implemented in https://github.com/florianhartig/DHARMa/pull/99 * Supporting now also models fit with the spaMM package ## Major changes * Remodelled createDHARMa function * option to directly provide scaled residuals was removed * Rewrote ecdf function for DHARMa to get fully balanced scale, in the course of https://github.com/florianhartig/DHARMa/pull/99 ## Minor changes * a number of smaller updates, mostly to help files ## Bugfixes * fixes #82 / Bug in recalculateResiduals # DHARMa 0.2.0 ## New features * support for glmmTMB https://github.com/florianhartig/DHARMa/issues/16, implemented since https://github.com/florianhartig/DHARMa/releases/tag/v0.1.6.2 * support for grouping of residuals, see https://github.com/florianhartig/DHARMa/issues/22 * residual function for DHARMa ## Major changes * remodeled benchmarks functions in https://github.com/florianhartig/DHARMa/releases/tag/v0.1.6.3 * remodeled dispersion testsin https://github.com/florianhartig/DHARMa/releases/tag/v0.1.6.4, adresses https://github.com/florianhartig/DHARMa/issues/62 ## Minor changes * changed plot function names in https://github.com/florianhartig/DHARMa/releases/tag/v0.1.6.1 ## Bugfixes * fixed bug with zeroinflation test for k/n binomial data https://github.com/florianhartig/DHARMa/issues/55 * fixed bug with p-value calculation via ecdf https://github.com/florianhartig/DHARMa/issues/55 # DHARMa 0.1.6 ## New features * option to apply rank tranformation of x values in plotResiduals, see https://github.com/florianhartig/DHARMa/issues/44 * option to convert predictor to factor * random seed is fixed, random state is recorded ## Minor changes * changed syntax in tests for sptial / temporal autocorrlation * null provides now random. Also, custom distance matrices can be provided to testSpatialAutocorrelation * slight changes to plot layout ## Bugfixes * error catching for crashes in plot function https://github.com/florianhartig/DHARMa/issues/42 * bugfix for glmer.nb parametricOverdispersinTest https://github.com/florianhartig/DHARMa/issues/47 # DHARMa 0.1.5 ## Minor changes * fixes a bug in version 0.1.4 that occurred when running simulateResiduals with refit = T. Apologies for any inconvenience. # DHARMa 0.1.4 ## Major changes * new experimental non-parametric dispersion test on simulated residuals. Extended simulations to compare dispersion tests ## Minor changes * supports for binomial with response coded as factor * error catching for refit procedure https://github.com/florianhartig/DHARMa/issues/18 * warnings in case the refit procedure fails or produces identical parameter values https://github.com/florianhartig/DHARMa/issues/20 # DHARMa 0.1.3 ## Major changes * includes support for model class 'gam' from package 'mgcv'. Required overwriting the 'fitted' function for gam, see https://github.com/florianhartig/DHARMa/issues/12 ## Minor changes * plotResiduals includes support for factors * updates to the help # DHARMa 0.1.2 * This bugfix release fixes an issue with backwards compatibility introduced in the 0.1.1 release, which used the 'startsWith' function that is only available in R base since 3.3.0. In 0.1.2, all occurences of 'startsWith' were replaced with 'grepl', which restores the compatibility with older R versions. # DHARMa 0.1.1 * including now the negative binomial models from MASS and lme4, as well as the possibility to create synthetic data from the negative binomial family * includes a createDHARMa function that allows using the plot functions of DHARMa also with externally created simualtions, for example for Bayesian predictive simulations # DHARMA 0.1.0 * initial release, with support for lm, glm, lme4 DHARMa/inst/0000755000176200001440000000000014704246643012235 5ustar liggesusersDHARMa/inst/examples/0000755000176200001440000000000014703461527014052 5ustar liggesusersDHARMa/inst/examples/simulateLRTHelp.R0000644000176200001440000000135514665273541017223 0ustar liggesusers library(DHARMa) library(lme4) # create test data set.seed(123) dat <- createData(sampleSize = 200, randomEffectVariance = 1) # define Null and alternative model (should be nested) m1 = glmer(observedResponse ~ Environment1 + (1|group), data = dat, family = "poisson") m0 = glm(observedResponse ~ Environment1 , data = dat, family = "poisson") \dontrun{ # run LRT - n should be increased to at least 250 for a real study out = simulateLRT(m0, m1, n = 10) # To inspect warnings thrown during the refits: out = simulateLRT(m0, m1, saveModels = TRUE, suppressWarnings = FALSE, n = 10) summary(out$saveModels[[2]]$refittedM1) # RE SD = 0, no problem # If there are warnings that seem problematic, # could try changing the optimizer or iterations } DHARMa/inst/examples/testDispersionHelp.R0000644000176200001440000000323414665273541020033 0ustar liggesuserslibrary(lme4) set.seed(123) testData = createData(sampleSize = 100, overdispersion = 0.5, randomEffectVariance = 1) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # default DHARMa dispersion test - simulation-based testDispersion(simulationOutput) testDispersion(simulationOutput, alternative = "less", plot = FALSE) # only underdispersion testDispersion(simulationOutput, alternative = "greater", plot = FALSE) # only oversispersion # for mixed models, the test is usually more powerful if residuals are calculated # conditional on fitted REs simulationOutput <- simulateResiduals(fittedModel = fittedModel, re.form = NULL) testDispersion(simulationOutput) # DHARMa also implements the popular Pearson-chisq test that is also on the glmmWiki by Ben Bolker # The issue with this test is that it requires the df of the model, which are not well defined # for GLMMs. It is biased towards underdispersion, with bias getting larger with the number # of RE groups. In doubt, only test for overdispersion testDispersion(simulationOutput, type = "PearsonChisq", alternative = "greater") # if refit = TRUE, a different test on simulated Pearson residuals will calculated (see help) simulationOutput2 <- simulateResiduals(fittedModel = fittedModel, refit = TRUE, seed = 12, n = 20) testDispersion(simulationOutput2) # often useful to test dispersion per group (in particular for binomial data, see vignette) simulationOutputAggregated = recalculateResiduals(simulationOutput2, group = testData$group) testDispersion(simulationOutputAggregated) DHARMa/inst/examples/testQuantilesHelp.R0000644000176200001440000000174114665273541017662 0ustar liggesuserstestData = createData(sampleSize = 200, overdispersion = 0.0, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # run the quantile test x = testQuantiles(simulationOutput) x # the test shows a combined p-value, corrected for multiple testing \dontrun{ # accessing results of the test x$pvals # pvalues for the individual quantiles x$qgamFits # access the fitted quantile regression summary(x$qgamFits[[1]]) # summary of the first fitted quantile # possible to test user-defined quantiles testQuantiles(simulationOutput, quantiles = c(0.7)) # example with missing environmental predictor fittedModel <- glm(observedResponse ~ 1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) testQuantiles(simulationOutput, predictor = testData$Environment1) plot(simulationOutput) plotResiduals(simulationOutput) } DHARMa/inst/examples/createDataHelp.R0000644000176200001440000000237014665273541017051 0ustar liggesuserstestData = createData(sampleSize = 500, intercept = 2, fixedEffects = c(1), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3), randomEffectVariance = 0) par(mfrow = c(1,2)) plot(testData$Environment1, testData$observedResponse) hist(testData$observedResponse) # with zero-inflation testData = createData(sampleSize = 500, intercept = 2, fixedEffects = c(1), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3), randomEffectVariance = 0, pZeroInflation = 0.6) par(mfrow = c(1,2)) plot(testData$Environment1, testData$observedResponse) hist(testData$observedResponse) # binomial with multiple trials testData = createData(sampleSize = 40, intercept = 2, fixedEffects = c(1), overdispersion = 0, family = binomial(), quadraticFixedEffects = c(-3), randomEffectVariance = 0, binomialTrials = 20) plot(observedResponse1 / observedResponse0 ~ Environment1, data = testData, ylab = "Proportion 1") # spatial / temporal correlation testData = createData(sampleSize = 100, family = poisson(), spatialAutocorrelation = 3, temporalAutocorrelation = 3) plot(log(observedResponse) ~ time, data = testData) plot(log(observedResponse) ~ x, data = testData) DHARMa/inst/examples/wrappersHelp.R0000644000176200001440000000112014665273541016647 0ustar liggesuserstestData = createData(sampleSize = 400, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) # response that was used to fit the model getObservedResponse(fittedModel) # predictions of the model for these points getFitted(fittedModel) # extract simulations from the model as matrix getSimulations(fittedModel, nsim = 2) # extract simulations from the model for refit (often requires different structure) x = getSimulations(fittedModel, nsim = 2, type = "refit") getRefit(fittedModel, x[[1]]) getRefit(fittedModel, getObservedResponse(fittedModel)) DHARMa/inst/examples/checkModelHelp.R0000644000176200001440000000074414665273541017055 0ustar liggesusers testData = createData(sampleSize = 200, overdispersion = 0.5, randomEffectVariance = 0.5, family = gaussian(), hasNA = TRUE) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) res <- simulateResiduals(fittedModel) # throws NA message # get the indices of the rows that were used to fit the model sel = as.numeric(rownames(model.frame(fittedModel))) # now use the indices when plotting against other variables plotResiduals(res, form = testData$Environment1[sel]) DHARMa/inst/examples/testsHelp.R0000644000176200001440000000300614677165224016154 0ustar liggesuserstestData = createData(sampleSize = 100, overdispersion = 0.5, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # the plot function shows 2 plots and runs 4 tests # i) KS test i) Dispersion test iii) Outlier test iv) quantile test plot(simulationOutput, quantreg = TRUE) # testResiduals tests distribution, dispersion and outliers testResiduals(simulationOutput) ####### Individual tests ####### # KS test for correct distribution of residuals testUniformity(simulationOutput) # KS test for correct distribution within and between groups testCategorical(simulationOutput, testData$group) # Dispersion test - for details see ?testDispersion testDispersion(simulationOutput) # tests under and overdispersion # Outlier test (number of observations outside simulation envelope) # Use type = "boostrap" for exact values, see ?testOutliers testOutliers(simulationOutput, type = "binomial") # testing zero inflation testZeroInflation(simulationOutput) # testing generic summaries countOnes <- function(x) sum(x == 1) # testing for number of 1s testGeneric(simulationOutput, summary = countOnes) # 1-inflation testGeneric(simulationOutput, summary = countOnes, alternative = "less") # 1-deficit means <- function(x) mean(x) # testing if mean prediction fits testGeneric(simulationOutput, summary = means) spread <- function(x) sd(x) # testing if mean sd fits testGeneric(simulationOutput, summary = spread) DHARMa/inst/examples/testSpatialAutocorrelationHelp.R0000644000176200001440000000625314703461527022404 0ustar liggesuserstestData = createData(sampleSize = 40, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1, data = testData) res = simulateResiduals(fittedModel) # Standard use testSpatialAutocorrelation(res, x = testData$x, y = testData$y) # Alternatively, one can provide a distance matrix dM = as.matrix(dist(cbind(testData$x, testData$y))) testSpatialAutocorrelation(res, distMat = dM) # You could add a spatial variogram via # library(gstat) # dat = data.frame(res = residuals(res), x = testData$x, y = testData$y) # coordinates(dat) = ~x+y # vario = variogram(res~1, data = dat, alpha=c(0,45,90,135)) # plot(vario, ylim = c(-1,1)) # if there are multiple observations with the same x values, # create first ar group with unique values for each location # then aggregate the residuals per location, and calculate # spatial autocorrelation on the new group # modifying x, y, so that we have the same location per group # just for completeness testData$x = as.numeric(testData$group) testData$y = as.numeric(testData$group) # calculating x, y positions per group groupLocations = aggregate(testData[, 6:7], list(testData$group), mean) # calculating residuals per group res2 = recalculateResiduals(res, group = testData$group) # running the spatial test on grouped residuals testSpatialAutocorrelation(res2, groupLocations$x, groupLocations$y) # careful when using REs to account for spatially clustered (but not grouped) # data. this originates from https://github.com/florianhartig/DHARMa/issues/81 # Assume our data is divided into clusters, where observations are close together # but not at the same point, and we suspect that observations in clusters are # autocorrelated clusters = 100 subsamples = 10 size = clusters * subsamples testData = createData(sampleSize = size, family = gaussian(), numGroups = clusters ) testData$x = rnorm(clusters)[testData$group] + rnorm(size, sd = 0.01) testData$y = rnorm(clusters)[testData$group] + rnorm(size, sd = 0.01) # It's a good idea to use a RE to take out the cluster effects. This accounts # for the autocorrelation within clusters library(lme4) fittedModel <- lmer(observedResponse ~ Environment1 + (1|group), data = testData) # DHARMa default is to re-simulate REs - this means spatial pattern remains # because residuals are still clustered res = simulateResiduals(fittedModel) testSpatialAutocorrelation(res, x = testData$x, y = testData$y) # However, it should disappear if you just calculate an aggregate residuals per cluster # Because at least how the data are simulated, cluster are spatially independent res2 = recalculateResiduals(res, group = testData$group) testSpatialAutocorrelation(res2, x = aggregate(testData$x, list(testData$group), mean)$x, y = aggregate(testData$y, list(testData$group), mean)$x) # For lme4, it's also possible to simulated residuals conditional on fitted # REs (re.form). Conditional on the fitted REs (i.e. accounting for the clusters) # the residuals should now be indepdendent. The remaining RSA we see here is # probably due to the RE shrinkage res = simulateResiduals(fittedModel, re.form = NULL) testSpatialAutocorrelation(res, x = testData$x, y = testData$y) DHARMa/inst/examples/hurricanes.R0000644000176200001440000000155614665273541016353 0ustar liggesusers\dontrun{ # Loading hurricanes dataset library(DHARMa) data(hurricanes) str(hurricanes) # this is the model fit by Jung et al. library(glmmTMB) originalModelGAM = glmmTMB(alldeaths ~ scale(MasFem) * (scale(Minpressure_Updated_2014) + scale(NDAM)), data = hurricanes, family = nbinom2) # no significant deviation in the general DHARMa plot res <- simulateResiduals(originalModelGAM) plot(res) # but residuals ~ NDAM looks funny, which was pointed # out by Bob O'Hara in a blog post after publication of the paper plotResiduals(res, hurricanes$NDAM) # we also find temporal autocorrelation res2 = recalculateResiduals(res, group = hurricanes$Year) testTemporalAutocorrelation(res2, time = unique(hurricanes$Year)) # task: try to address these issues - in many instances, this will # make the MasFem predictor n.s. }DHARMa/inst/examples/testPhylogeneticAutocorrelationHelp.R0000644000176200001440000000140514703461527023433 0ustar liggesusers\dontrun{ library(DHARMa) library(phylolm) set.seed(123) tre = rcoal(60) b0 = 0; b1 = 1; x <- runif(length(tre$tip.label), 0, 1) y <- b0 + b1*x + rTrait(n = 1, phy = tre,model="BM", parameters = list(ancestral.state = 0, sigma2 = 10)) dat = data.frame(trait = y, pred = x) fit = lm(trait ~ pred, data = dat) res = simulateResiduals(fit, plot = T) testPhylogeneticAutocorrelation(res, tree = tre) fit = phylolm(trait ~ pred, data = dat, phy = tre, model = "BM") summary(fit) # phylogenetic autocorrelation still present in residuals res = simulateResiduals(fit, plot = T) # with "rotation" the residual autcorrelation is gone, see ?simulateResiduals. res = simulateResiduals(fit, plot = T, rotation = "estimated") } DHARMa/inst/examples/plotsHelp.R0000644000176200001440000000342014665273541016152 0ustar liggesuserstestData = createData(sampleSize = 200, family = poisson(), randomEffectVariance = 1, numGroups = 10) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) ######### main plotting function ############# # for all functions, quantreg = T will be more # informative, but slower plot(simulationOutput, quantreg = FALSE) ############# Distribution ###################### plotQQunif(simulationOutput = simulationOutput, testDispersion = FALSE, testUniformity = FALSE, testOutliers = FALSE) hist(simulationOutput ) ############# residual plots ############### # rank transformation, using a simulationOutput plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE) # smooth scatter plot - usually used for large datasets, default for n > 10000 plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE, smoothScatter = TRUE) # residual vs predictors, using explicit values for pred, residual plotResiduals(simulationOutput, form = testData$Environment1, quantreg = FALSE) # if pred is a factor, or if asFactor = TRUE, will produce a boxplot plotResiduals(simulationOutput, form = testData$group) # to diagnose overdispersion and heteroskedasticity it can be useful to # display residuals as absolute deviation from the expected mean 0.5 plotResiduals(simulationOutput, absoluteDeviation = TRUE, quantreg = FALSE) # All these options can also be provided to the main plotting function # If you want to plot summaries per group, use simulationOutput = recalculateResiduals(simulationOutput, group = testData$group) plot(simulationOutput, quantreg = FALSE) # we see one residual point per RE DHARMa/inst/examples/createDharmaHelp.R0000644000176200001440000000173514665273541017400 0ustar liggesusers## READING IN HAND-CODED SIMULATIONS testData = createData(sampleSize = 50, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1, data = testData, family = "poisson") # in DHARMA, using the simulate.glm function of glm sims = simulateResiduals(fittedModel) plot(sims, quantreg = FALSE) # Doing the same with a handcoded simulate function. # of course this code will only work with a 1-par glm model simulateMyfit <- function(n=10, fittedModel){ int = coef(fittedModel)[1] slo = coef(fittedModel)[2] pred = exp(int + slo * testData$Environment1) predSim = replicate(n, rpois(length(pred), pred)) return(predSim) } sims = simulateMyfit(250, fittedModel) dharmaRes <- createDHARMa(simulatedResponse = sims, observedResponse = testData$observedResponse, fittedPredictedResponse = predict(fittedModel, type = "response"), integer = TRUE) plot(dharmaRes, quantreg = FALSE) DHARMa/inst/examples/testOutliersHelp.R0000644000176200001440000000275714665273541017533 0ustar liggesusersset.seed(123) testData = createData(sampleSize = 200, overdispersion = 1, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # default outlier test (with plot) testOutliers(simulationOutput) # default test uses "bootstrap" for nObs <= 500, or else binomial # binomial is faster, but not exact for integer-valued distributions, see help testOutliers(simulationOutput, type = "binomial") testOutliers(simulationOutput, type = "bootstrap") # note that default is to test outliers at BOTH margins for both an excess AND a lack # of outliers. In the case above, the test reported an excess of outliers (you) # can see this because expected frequency < observed. Moreover, if we plot the residuals plotResiduals(simulationOutput, quantreg = FALSE) # we see that we mostly have an excess of outliers at the upper margin. # Let's see what would have happened if we would just have checked the lower margin # (lower margin means residuals with value 0, i.e. lower tail of the simualtion # envelope) testOutliers(simulationOutput, margin = "lower", plot = FALSE) # OK, now the frequency of outliers is 0, so we have too few, but this is n.s. against # the expectation # just for completeness, what would have happened if we would have checked both # margins, but just for a lack of outliers (sign of underdispersion) testOutliers(simulationOutput, alternative = "less", plot = FALSE) DHARMa/inst/examples/testTemporalAutocorrelationHelp.R0000644000176200001440000001425114665273541022573 0ustar liggesuserstestData = createData(sampleSize = 40, family = gaussian(), randomEffectVariance = 0) fittedModel <- lm(observedResponse ~ Environment1, data = testData) res = simulateResiduals(fittedModel) # Standard use testTemporalAutocorrelation(res, time = testData$time) # If you have several observations per time step, e.g. # because you have several locations, you will have to # aggregate timeSeries1 = createData(sampleSize = 40, family = gaussian(), randomEffectVariance = 0) timeSeries1$location = 1 timeSeries2 = createData(sampleSize = 40, family = gaussian(), randomEffectVariance = 0) timeSeries2$location = 2 testData = rbind(timeSeries1, timeSeries2) fittedModel <- lm(observedResponse ~ Environment1, data = testData) res = simulateResiduals(fittedModel) # Will not work because several residuals per time # testTemporalAutocorrelation(res, time = testData$time) # aggregating residuals by time res = recalculateResiduals(res, group = testData$time) testTemporalAutocorrelation(res, time = unique(testData$time)) # testing only subgroup location 1, could do same with loc 2 res = recalculateResiduals(res, sel = testData$location == 1) testTemporalAutocorrelation(res, time = unique(testData$time)) # example to demonstrate problems with strong temporal correlations and # how to possibly remove them by rotating residuals # note that if your model allows to condition on estimated REs, this may # be preferable! \dontrun{ set.seed(123) # Gaussian error # Create AR data with 5 observations per time point n <- 100 x <- MASS::mvrnorm(mu = rep(0,n), Sigma = .9 ^ as.matrix(dist(1:n)) ) y <- rep(x, each = 5) + 0.2 * rnorm(5*n) times <- factor(rep(1:n, each = 5), levels=1:n) levels(times) group <- factor(rep(1,n*5)) dat0 <- data.frame(y,times,group) # fit model / would be similar for nlme::gls and similar models model = glmmTMB(y ~ ar1(times + 0 | group), data=dat0) # Note that standard residuals still show problems because of autocorrelation res <- simulateResiduals(model) plot(res) # The reason is that most (if not all) autoregressive models treat the # autocorrelated error as random, i.e. the autocorrelated error structure # is not used for making predictions. If you then make predictions based # on the fixed effects and calculate residuals, the autocorrelation in the # residuals remains. We can see this if we again calculate the auto- # correlation test res2 <- recalculateResiduals(res, group=dat0$times) testTemporalAutocorrelation(res2, time = 1:length(res2$scaledResiduals)) # so, how can we check then if the current model correctly removed the # autocorrelation? # Option 1: rotate the residuals in the direction of the autocorrelation # to make the independent. Note that this only works perfectly for gls # type models as nonlinear link function make the residuals covariance # different from a multivariate normal distribution # this can be either done by extracting estimated AR1 covariance cov <- VarCorr(model) cov <- cov$cond$group # extract covariance matrix of REs # grouped according to times, rotated with estimated Cov - how all fine! res3 <- recalculateResiduals(res, group=dat0$times, rotation=cov) plot(res3) testTemporalAutocorrelation(res3, time = 1:length(res2$scaledResiduals)) # alternatively, you can let DHARMa estimate the covariance from the # simulations res4 <- recalculateResiduals(res, group=dat0$times, rotation="estimated") plot(res4) testTemporalAutocorrelation(res3, time = 1:length(res2$scaledResiduals)) # Alternatively, in glmmTMB, we can condition on the estimated correlated # residuals. Unfortunately, in this case, we will have to do simulations by # hand as glmmTMB does not allow to simulate conditional on a fitted # correlation structure # re.form = NULL creates predictions conditional on the fitted temporally # autocorreated REs pred = predict(model, re.form = NULL) # now we simulate data, conditional on the autocorrelation part, with the # uncorrelated residual error simulations = sapply(1:250, function(i) rnorm(length(pred), pred, summary(model)$sigma)) res5 = createDHARMa(simulations, dat0$y, pred) plot(res5) res5b <- recalculateResiduals(res5, group=dat0$times) testTemporalAutocorrelation(res5b, time = 1:length(res5b$scaledResiduals)) # Poisson error # note that for GLMMs, covariances will be estimated at the scale of the # linear predictor, while residual covariance will be at the responses scale # and thus further distorted by the link. Thus, for GLMMs with a nonlinear # link, there will be no exact rotation for a given covariance structure set.seed(123) # Create AR data with 5 observations per time point n <- 100 x <- MASS::mvrnorm(mu = rep(0,n), Sigma = .9 ^ as.matrix(dist(1:n)) ) y <- rpois(n = n*5, lambda = exp(rep(x, each = 5))) times <- factor(rep(1:n, each = 5), levels=1:n) levels(times) group <- factor(rep(1,n*5)) dat0 <- data.frame(y,times,group) # fit model model = glmmTMB(y ~ ar1(times + 0 | group), data=dat0, family = poisson) res <- simulateResiduals(model) # grouped according to times, unrotated res2 <- recalculateResiduals(res, group=dat0$times) testTemporalAutocorrelation(res2, time = 1:length(res2$scaledResiduals)) # grouped according to times, rotated with estimated Cov - problems remain cov <- VarCorr(model) cov <- cov$cond$group # extract covariance matrix of REs res3 <- recalculateResiduals(res, group=dat0$times, rotation=cov) testTemporalAutocorrelation(res3, time = 1:length(res2$scaledResiduals)) # grouped according to times, rotated with covariance estimated from residual # simulations at the response scale res4 <- recalculateResiduals(res, group=dat0$times, rotation="estimated") testTemporalAutocorrelation(res4, time = 1:length(res2$scaledResiduals)) } DHARMa/inst/examples/runBenchmarksHelp.R0000644000176200001440000000371514665273541017622 0ustar liggesusers# define a function that will run a simulation and return a number of statistics, typically p-values returnStatistics <- function(control = 0){ testData = createData(sampleSize = 20, family = poisson(), overdispersion = control, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1, data = testData, family = poisson()) res <- simulateResiduals(fittedModel = fittedModel, n = 250) out <- c(testUniformity(res, plot = FALSE)$p.value, testDispersion(res, plot = FALSE)$p.value) return(out) } # testing a single return returnStatistics() # running benchmark for a fixed simulation, increase nRep for sensible results out = runBenchmarks(returnStatistics, nRep = 5) # plotting results depend on whether a vector or a single value is provided for control plot(out) \dontrun{ # running benchmark with varying control values out = runBenchmarks(returnStatistics, controlValues = c(0,0.5,1), nRep = 100) plot(out) # running benchmark can be done using parallel cores out = runBenchmarks(returnStatistics, nRep = 100, parallel = TRUE) out = runBenchmarks(returnStatistics, controlValues = c(0,0.5,1), nRep = 10, parallel = TRUE) # Alternative plot function using vioplot, provides nicer pictures plot.DHARMaBenchmark <- function(x, ...){ if(length(x$controlValues)== 1){ vioplot::vioplot(x$simulations[,x$nSummaries:1], las = 2, horizontal = TRUE, side = "right", areaEqual = FALSE, main = "p distribution under H0", ylim = c(-0.15,1), ...) abline(v = 1, lty = 2) abline(v = c(0.05, 0), lty = 2, col = "red") text(-0.1, x$nSummaries:1, labels = x$summaries$propSignificant[-1]) }else{ res = x$summaries$propSignificant matplot(res$controlValues, res[,-1], type = "l", main = "Power analysis", ylab = "Power", ...) legend("bottomright", colnames(res[,-1]), col = 1:x$nSummaries, lty = 1:x$nSummaries, lwd = 2) } } } DHARMa/inst/examples/getRandomStateHelp.R0000644000176200001440000000127214665273541017735 0ustar liggesusers set.seed(13) runif(1) # testing the function in standard settings currentSeed = .Random.seed x = getRandomState(123) runif(1) x$restoreCurrent() all(.Random.seed == currentSeed) # if no seed was set in env, this will also be restored rm(.Random.seed) # now, there is no random seed x = getRandomState(123) exists(".Random.seed") # TRUE runif(1) x$restoreCurrent() exists(".Random.seed") # False runif(1) # re-create a seed # with seed = false currentSeed = .Random.seed x = getRandomState(FALSE) runif(1) x$restoreCurrent() all(.Random.seed == currentSeed) # with seed = NULL currentSeed = .Random.seed x = getRandomState(NULL) runif(1) x$restoreCurrent() all(.Random.seed == currentSeed) DHARMa/inst/examples/simulateResidualsHelp.R0000644000176200001440000000212014665273541020504 0ustar liggesuserslibrary(lme4) testData = createData(sampleSize = 100, overdispersion = 0.5, family = poisson()) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # standard plot plot(simulationOutput) # one of the possible test, for other options see ?testResiduals / vignette testDispersion(simulationOutput) # the calculated residuals can be accessed via residuals(simulationOutput) # transform residuals to other pdf, see ?residuals.DHARMa for details residuals(simulationOutput, quantileFunction = qnorm, outlierValues = c(-7,7)) # get residuals that are outside the simulation envelope outliers(simulationOutput) # calculating aggregated residuals per group simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group) plot(simulationOutput2, quantreg = FALSE) # calculating residuals only for subset of the data simulationOutput3 = recalculateResiduals(simulationOutput, sel = testData$group == 1 ) plot(simulationOutput3, quantreg = FALSE) DHARMa/inst/examples/benchmarkRuntimeHelp.R0000644000176200001440000000105514665273541020311 0ustar liggesusers createModel = function(){ testData = createData(family = poisson(), overdispersion = 1, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1, data = testData, family = poisson()) return(fittedModel) } a = function(m){ testUniformity(m, plot = FALSE)$p.value } b = function(m){ testDispersion(m, plot = FALSE)$p.value } c = function(m){ testDispersion(m, plot = FALSE, type = "PearsonChisq")$p.value } evaluationFunctions = list(a,b, c) benchmarkRuntime(createModel, evaluationFunctions, 2) DHARMa/inst/doc/0000755000176200001440000000000014704246643013002 5ustar liggesusersDHARMa/inst/doc/DHARMaForBayesians.html0000644000176200001440000006405014704246643017177 0ustar liggesusers DHARMa for Bayesians

DHARMa for Bayesians

Florian Hartig, Theoretical Ecology, University of Regensburg website

2024-10-17

Abstract

The ā€˜DHARMaā€™ package uses a simulation-based approach to create readily interpretable scaled (quantile) residuals for fitted (generalized) linear mixed models. This Vignette describes how to user DHARMa vor checking Bayesian models. It is recommended to read this AFTER the general DHARMa vignette, as all comments made there (in pacticular regarding the interpretation of the residuals) also apply to Bayesian models.

Basic workflow

In principle, DHARMa residuals can be calculated and interpreted for Bayesian models in very much the same way as for frequentist models. Therefore, all comments regarding tests, residual interpretation etc. from the main vignette are equally valid for Bayesian model checks. There are some minor differences regarding the expected null distribution of the residuals, in particular in the low data limit, but I believe that for most people, these are of less concern.

The main difference for a Bayesian user is that, unlike for users of directly supported regression packages such as lme4 or glmmTMB, most Bayesian users will have to create the simulations for the fitted model themselves and then feed them into DHARMa by hand. The basic workflow for Bayesians that work with BUGS, JAGS, STAN or similar is:

  1. Create posterior predictive simulations for your model
  2. Read these in with the createDHARMa function
  3. Interpret those as described in the main vignette

This is more easy as it sounds. For the major Bayesian samplers (e.g.Ā BUGS, JAGS, STAN), it amounts to adding a block with data simulations to the model, and observing those during the MCMC sampling. Then, feed the simulations into DHARMa via createDHARMa, and all else will work pretty much the same as in the main vignette.

Example in Jags

Here is an example, with JAGS

library(rjags)
library(BayesianTools)

set.seed(123)

dat <- DHARMa::createData(200, overdispersion = 0.2)

Data = as.list(dat)
Data$nobs = nrow(dat)
Data$nGroups = length(unique(dat$group))

modelCode = "model{

  for(i in 1:nobs){
    observedResponse[i] ~ dpois(lambda[i])  # poisson error distribution
    lambda[i] <- exp(eta[i]) # inverse link function
    eta[i] <- intercept + env*Environment1[i]  # linear predictor
  }
  
  intercept ~ dnorm(0,0.0001)
  env ~ dnorm(0,0.0001)

  # Posterior predictive simulations 
  for (i in 1:nobs) {
    observedResponseSim[i]~dpois(lambda[i])
  }

}"

jagsModel <- jags.model(file= textConnection(modelCode), data=Data, n.chains = 3)
para.names <- c("intercept","env", "lambda", "observedResponseSim")
Samples <- coda.samples(jagsModel, variable.names = para.names, n.iter = 5000)

x = BayesianTools::getSample(Samples)

colnames(x) # problem: all the variables are in one array - this is better in STAN, where this is a list - have to extract the right columns by hand
posteriorPredDistr = x[,3:202] # this is the uncertainty of the mean prediction (lambda)
posteriorPredSim = x[,203:402] # these are the simulations 

sim = createDHARMa(simulatedResponse = t(posteriorPredSim), observedResponse = dat$observedResponse, fittedPredictedResponse = apply(posteriorPredDistr, 2, median), integerResponse = T)
plot(sim)

In the created plots, you will see overdispersion, which is completely expected, as the simulated data has overdispersion and a RE, which is not accounted for by the Jags model.

Exercise

As an exercise, you could now:

  • Add a RE
  • Account for overdispersion, e.g.Ā via an OLRE or a negative Binomial

And check how the residuals improve.

Conditional vs.Ā unconditional simulations in hierarchical models

The most important consideration in using DHARMa with Bayesian models is how to create the simulations. You can see in my jags code that the block

  # Posterior predictive simulations 
  for (i in 1:nobs) {
    observedResponseSim[i]~dpois(lambda[i])
  }

performs the posterior predictive simulations. Here, we just take the predicted lambda (mean perdictions) during the MCMC simulations and sample from the assumed distribution. This will works for any non-hierarchical model.

When we move to hierarchical or multi-level models, including GLMMs, the issue of simulation becomes a bit more complicated. In a hierarchical model, there are several random processes that sit on top of each other. In the same way as explained in the main vignette at the point conditional / unconditional simulations, we will have to decide which of these random processes should be included in the posterior predictive simulations.

As an example, imagine we add a RE in the likelihood of the previous model, to account for the group structure in the data.

  for(i in 1:nobs){
    observedResponse[i] ~ dpois(lambda[i])  # poisson error distribution
    lambda[i] <- exp(eta[i]) # inverse link function
    eta[i] <- intercept + env*Environment1[i] + RE[group[i]] # linear predictor
  }
  
  for(j in 1:nGroups){
   RE[j] ~ dnorm(0,tauRE)  
  }

The predictions lambda[i] now depend on a lower-level stochastic effect, which is described by RE[j] ~ dnorm(0,tauRE). We can now decide to create posterior predictive simulations conditional on posterior estimates RE[j] (conditional simulations), in which case we would have to change nothing in the block for the posterior predictive simulations. Alternatively, we can decide that we want to re-simulate the RE (unconditional simulations), in which case we have to copy the entire structure of the likelihood in the predictions

  for(j in 1:nGroups){
   RESim[j] ~ dnorm(0,tauRE)  
  }

  for (i in 1:nobs) {
    observedResponseSim[i] ~ dpois(lambdaSim[i]) 
    lambdaSim[i] <- exp(etaSim[i]) 
    etaSim[i] <- intercept + env*Environment1[i] + RESim[group[i]] 
  }

Essentially, you can remember that if you want full (uncoditional) simulations, you basically have to copy the entire likelihood of the hierarchical model, minus the priors, and sample along the hierarchical model structure. If you want to condition on a part of this structure, just cut the DAG at the point on which you want to condition on.

Statistical differences between Bayesian vs.Ā MLE quantile residuals

A common question is if there are differences between Bayesian and MLE quantile residuals.

First of all, note that MLE and Bayesian quantile residuals are not exactly identical. The main difference is in how the simulation of the data under the fitted model are performed:

  • For models fitted by MLE, simulations in DHARMa are with the MLE (point estimate)

  • For models fitted with Bayes, simulations are practically always performed while also drawing from the posterior parameter uncertainty (as a point estimate is not available).

Thus, Bayesian posterior predictive simulations include the parametric uncertainty of the model, additionally to the sampling uncertainty. From this we can directly conclude that Bayesian and MLE quantile residuals are asymptotically identical (and via the usual arguments uniformly distributed), but become more different the smaller n becomes.

To examine what those differences are, letā€™s imagine that we start with a situation of infinite data. In this case, we have a ā€œsharpā€ posterior that can be viewed as identical to the MLE.

If we reduce the number of data, there are two things happening

  1. The posterior gets wider, with the likelihood component being normally distributed, at least initially

  2. The influence of the prior increases, the faster the stronger the prior is.

Thus, if we reduce the data, for weak / uninformative priors, we will simulate data while sampling parameters from a normal distribution around the MLE, while for strong priors, we will effectively sample data while drawing parameters of the model from the prior.

In particular in the latter case (prior dominates, which can be checked via prior sensitivity analysis), you may see residual patterns that are caused by the prior, even though the model structure is correct. In some sense, you could say that the residuals check if the combination of prior + structure is compatible with the data. Itā€™s a philosophical debate how to react on such a deviation, as the prior is not really negotiable in a Bayesian analysis.

Of course, also the MLE distribution might get problems in low data situations, but I would argue that MLE is usually only used anyway if the MLE is reasonably sharp. In practice, I have self experienced problems with MLE estimates. Itā€™s a bit different in the Bayesian case, where it is possible and often done to fit very complex models with limited data. In this case, many of the general issues in defining null distributions for Bayesian p-values (as, e.g., reviewed in Conn et al., 2018) apply.

I would add though that while I find it important that users are aware of those differences, I have found that in practice these issues are small, and usually overruled by the much stronger effects of model error.

DHARMa/inst/doc/DHARMa.html0000644000176200001440001777524214704246642014714 0ustar liggesusers DHARMa: residual diagnostics for hierarchical (multi-level/mixed) regression models

DHARMa: residual diagnostics for hierarchical (multi-level/mixed) regression models

Florian Hartig, Theoretical Ecology, University of Regensburg website

2024-10-17

Abstract

The ā€˜DHARMaā€™ package uses a simulation-based approach to create readily interpretable scaled (quantile) residuals for fitted generalized linear (mixed) models. Currently supported are linear and generalized linear (mixed) models from ā€˜lme4ā€™ (classes ā€˜lmerModā€™, ā€˜glmerModā€™), ā€˜glmmTMBā€™, ā€˜GLMMadaptiveā€™ and ā€˜spaMMā€™; phylogenetic linear models from ā€˜phylolmā€™ (classes ā€˜phylolmā€™ and ā€˜phyloglmā€™); generalized additive models (ā€˜gamā€™ from ā€˜mgcvā€™); ā€˜glmā€™ (including ā€˜negbinā€™ from ā€˜MASSā€™, but excluding quasi-distributions) and ā€˜lmā€™ model classes. Moreover, externally created simulations, e.g.Ā posterior predictive simulations from Bayesian software such as ā€˜JAGSā€™, ā€˜STANā€™, or ā€˜BUGSā€™ can be processed as well. The resulting residuals are standardized to values between 0 and 1 and can be interpreted as intuitively as residuals from a linear regression. The package also provides a number of plot and test functions for typical model misspecification problems, such as over/underdispersion, zero-inflation, and residual spatial, temporal and phylogenetic autocorrelation.

Motivation

The interpretation of conventional residuals for generalized linear (mixed) and other hierarchical statistical models is often problematic. As an example, here the result of conventional Deviance, Pearson and raw residuals for two Poisson GLMMs, one that is lacking a quadratic effect, and one that fits the data perfectly. Could you tell which is the correct model?

Just for completeness - it was the second one. But donā€™t get too excited if you got it right. Probably you were just lucky - I canā€™t really tell a difference. But even so, would you have added a quadratic effect, instead of adding an overdispersion correction? The point here is that misspecifications in GL(M)Ms cannot reliably be diagnosed with standard residual plots, and thus GLMMs are often not as thoroughly checked as they should.

One reason why GL(M)Ms residuals are harder to interpret is that the expected distribution of the data (aka predictive distribution) changes with the fitted values. Reweighting with the expected dispersion, as done in Pearson residuals, or using deviance residuals, helps to some extent, but it does not lead to visually homogenous residuals, even if the model is correctly specified. As a result, standard residual plots, when interpreted in the same way as for linear models, seem to show all kind of problems, such as non-normality, heteroscedasticity, even if the model is correctly specified. Questions on the R mailing lists and forums show that practitioners are regularly confused about whether such patterns in GL(M)M residuals are a problem or not.

But even experienced statistical analysts currently have few options to diagnose misspecification problems in GLMMs. In my experience, the current standard practice is to eyeball the residual plots for major misspecifications, potentially have a look at the random effect distribution, and then run a test for overdispersion, which is usually positive, after which the model is modified towards an overdispersed / zero-inflated distribution. This approach, however, has a number of drawbacks, notably:

  • Overdispersion is often the result of missing predictors or a misspecified model structure. Standard residual plots make it difficult to identify these problems by examining residual correlations or patterns of residuals against predictors.

  • Not all overdispersion is the same. For count data, the negative binomial creates a different distribution than adding observation-level random effects to the Poisson. Once overdispersion is corrected for, such violations of distributional assumptions are not detectable with standard overdispersion tests (because the tests only looks at total dispersion), and nearly impossible to see visually from standard residual plots.

  • Dispersion frequently varies with predictors (heteroscedasticity). This can have a significant effect on the inference. While it is standard to tests for heteroscedasticity in linear regressions, heteroscedasticity is currently hardly ever tested for in GLMMs, although it is likely as frequent and influential.

  • Moreover, if residuals are checked, they are usually checked conditional on the fitted random effect estimates. Thus, standard checks only check the final level of the random structure in a GLMM. One can perform extra checks on the random effects, but it is somewhat unsatisfactory that there is no check on the entire model structure.

DHARMa aims at solving these problems by creating readily interpretable residuals for generalized linear (mixed) models that are standardized to values between 0 and 1, and that can be interpreted as intuitively as residuals for the linear model. This is achieved by a simulation-based approach, similar to the Bayesian p-value or the parametric bootstrap, that transforms the residuals to a standardized scale. The basic steps are:

  1. Simulate new response data from the fitted model for each observation.

  2. For each observation, calculate the empirical cumulative density function for the simulated observations, which describes the possible values (and their probability) at the predictor combination of the observed value, assuming the fitted model is correct.

  3. The residual is then defined as the value of the empirical density function at the value of the observed data, so a residual of 0 means that all simulated values are larger than the observed value, and a residual of 0.5 means half of the simulated values are larger than the observed value.

These steps are visualized in the following figure

The key advantage of this definition is that the so-defined residuals always have the same, known distribution, independent of the model that is fit, if the model is correctly specified. To see this, note that, if the observed data was created from the same data-generating process that we simulate from, all values of the cumulative distribution should appear with equal probability. That means we expect the distribution of the residuals to be flat, regardless of the model structure (Poisson, binomial, random effects and so on).

I currently prepare a more exact statistical justification for the approach in an accompanying paper, but if you must provide a reference in the meantime, I would suggest citing

  • Dunn, K. P., and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics 5, 1-10.

  • Gelman, A. & Hill, J. Data analysis using regression and multilevel/hierarchical models Cambridge University Press, 2006

p.s.: DHARMa stands for ā€œDiagnostics for HierArchical Regression Modelsā€ - which, strictly speaking, would make DHARM. But in German, Darm means intestines; plus, the meaning of DHARMa in Hinduism makes the current abbreviation so much more suitable for a package that tests whether your model is in harmony with your data:

From Wikipedia, 28/08/16: In Hinduism, dharma signifies behaviours that are considered to be in accord with rta, the order that makes life and universe possible, and includes duties, rights, laws, conduct, virtues and ā€˜right way of livingā€™.

Workflow in DHARMa

Installing, loading and citing the package

If you havenā€™t installed the package yet, either run

install.packages("DHARMa")

Or follow the instructions on https://github.com/florianhartig/DHARMa to install a development version.

Loading and citation

library(DHARMa)
citation("DHARMa")
## Para citar o pacote 'DHARMa' em publicaƧƵes use:
## 
##   Hartig F (2024). _DHARMa: Residual Diagnostics for Hierarchical
##   (Multi-Level / Mixed) Regression Models_. R package version 0.4.7,
##   <http://florianhartig.github.io/DHARMa/>.
## 
## Uma entrada BibTeX para usuƔrios(as) de LaTeX Ʃ
## 
##   @Manual{,
##     title = {DHARMa: Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models},
##     author = {Florian Hartig},
##     year = {2024},
##     note = {R package version 0.4.7},
##     url = {http://florianhartig.github.io/DHARMa/},
##   }

Calculating scaled residuals

Letā€™s assume we have a fitted model that is supported by DHARMa.

testData = createData(sampleSize = 250)
fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , 
                     family = "poisson", data = testData)

Most functions in DHARMa can be calculated directly on the fitted model object. For example, if you are only interested in testing for dispersion problems, you could run

testDispersion(fittedModel)

In this case, the randomized quantile residuals are calculated on the fly inside the function call. If you work in this way, however, residual calculation will be repeated by every test / plot you call, and this can take a while. It is therefore highly recommended to first calculate the residuals once, using the simulateResiduals() function

simulationOutput <- simulateResiduals(fittedModel = fittedModel, plot = F)

which calculates randomized quantile residuals according to the algorithm discussed above. The function returns an object of class DHARMa, containing the simulations and the scaled residuals, which can later be passed on to all other plots and test functions. When specifying the optional argument plot = T, the standard DHARMa residual plot is displayed directly. The interpretation of the plot will be discussed below. Using the simulateResiduals function has the added benefit that you can modify the way in which residuals are calculated. For example, you may want to change the number of simulations, or the REs to condition on. See ?simulateResiduals and section ā€œsimulation optionsā€ below for details.

The calculated (scaled) residuals can be plotted and tested via a number of DHARMa functions (see below), or accessed directly via

residuals(simulationOutput)

To interpret the residuals, remember that a scaled residual value of 0.5 means that half of the simulated data are higher than the observed value, and half of them lower. A value of 0.99 would mean that nearly all simulated data are lower than the observed value. The minimum/maximum values for the residuals are 0 and 1. For a correctly specified model we would expect asymptotically

  • a uniform (flat) distribution of the scaled residuals

  • uniformity in y direction if we plot against any predictor.

Note: the uniform distribution is the only differences to ā€œconventionalā€ residuals as calculated for a linear regression. If you cannot get used to this, you can transform the uniform distribution to another distribution, for example normal, via

residuals(simulationOutput, quantileFunction = qnorm, outlierValues = c(-7,7))

These normal residuals will behave exactly like the residuals of a linear regression. However, for reasons of a) numeric stability with low number of simulations, which makes it neccessary to descide on which value outliers are to be transformed and b) my conviction that it is much easier to visually detect deviations from uniformity than normality, DHARMa checks all residuals in the uniform space, and I would personally advice against using the transformation.

Plotting the scaled residuals

The main plot function for the calculated DHARMa object produced by simulateResiduals() is the plot.DHARMa() function

plot(simulationOutput)

The function creates two plots, which can also be called separately, and provide extended explanations / examples in the help

plotQQunif(simulationOutput) # left plot in plot.DHARMa()
plotResiduals(simulationOutput) # right plot in plot.DHARMa()

  • plotQQunif (left panel) creates a qq-plot to detect overall deviations from the expected distribution, by default with added tests for correct distribution (KS test), dispersion and outliers. Note that outliers in DHARMa are values that are by default defined as values outside the simulation envelope, not in terms of a particular quantile. Thus, which values will appear as outliers will depend on the number of simulations. If you want outliers in terms of a particuar quantile, you can use the outliers() function.

  • plotResiduals (right panel) produces a plot of the residuals against the predicted value (or alternatively, other variable). Simulation outliers (data points that are outside the range of simulated values) are highlighted as red stars. These points should be carefully interpreted, because we actually donā€™t know ā€œhow muchā€ these values deviate from the model expectation. Note also that the probability of an outlier depends on the number of simulations, so whether the existence of outliers is a reason for concern depends also on the number of simulations.

To provide a visual aid in detecting deviations from uniformity in y-direction, the plot function calculates an (optional default) quantile regression, which compares the empirical 0.25, 0.5 and 0.75 quantiles in y direction (red solid lines) with the theoretical 0.25, 0.5 and 0.75 quantiles (dashed black line), and provides a p-value for the deviation from the expected quantile. The significance of the deviation to the expected quantiles is tested and displayed visually, and can be additionally extracted with the testQuantiles function.

By default, plotResiduals plots against predicted values. However, you can also use it to plot residuals against a specific other predictors (highly recommend).

plotResiduals(simulationOutput, form = YOURPREDICTOR)

If the predictor is a factor, or if there is just a small number of observations on the x axis, plotResiduals will plot a box plot with additional tests instead of a scatter plot.

plotResiduals(simulationOutput, form = testData$group)

See ?plotResiduas for details, but very shortly: under H0 (perfect model), we would expect those boxes to range homogeneously from 0.25-0.75. To see whether there are deviations from this expecation, the plot calculates a test for uniformity per box, and a test for homogeneity of variances between boxes. A positive test will be highlighted in red.

Goodness-of-fit tests on the scaled residuals

To support the visual inspection of the residuals, the DHARMa package provides a number of specialized goodness-of-fit tests on the simulated residuals:

  • testUniformity() - tests if the overall distribution conforms to expectations.
  • testOutliers() - tests if there are more simulation outliers than expected.
  • testDispersion() - tests if the simulated dispersion is equal to the observed dispersion.
  • testQuantiles() - fits a quantile regression or residuals against a predictor (default predicted value), and tests of this conforms to the expected quantile.
  • testCategorical(simulationOutput, catPred = testData$group) tests residuals against a categorical predictor.
  • testZeroinflation() - tests if there are more zeros in the data than expected from the simulations.
  • testGeneric() - test if a generic summary statistics (user-defined) deviates from model expectations.
  • testTemporalAutocorrelation() - tests for temporal autocorrelation in the residuals.
  • testSpatialAutocorrelation() - tests for spatial autocorrelation in the residuals. Can also be used with a generic distance function.
  • testPhylogeneticAutocorrelation() - tests for phylogenetic signal in the residuals.

See the help of the functions and further comments below for a more detailed description.

Simulation options

There are a few important technical details regarding how the simulations are performed, in particular regarding the treatments of random effects and integer responses. It is strongly recommended to read the help of

?simulateResiduals

Refit

simulationOutput <- simulateResiduals(fittedModel = fittedModel, refit = T)

  • if refit = F (default), new datasets are simulated from the fitted model, and residuals are calculated by comparing the observed data to the new data

  • if refit = T, a parametric bootstrap is performed, meaning that the model is refit to all new datasets, and residuals are created by comparing observed residuals against refitted residuals

The second option is much much slower, and also seemed to have lower power in some tests I ran. It is therefore not recommended for standard residual diagnostics! I only recommend using it if you know what you are doing, and have particular reasons, for example if you estimate that the tested model is biased. A bias could, for example, arise in small data situations, or when estimating models with shrinkage estimators that include a purposeful bias, such as ridge/lasso, random effects or the splines in GAMs. My idea was then that simulated data would not fit to the observations, but that residuals for model fits on simulated data would have the same patterns/bias than model fits on the observed data.

Note also that refit = T can sometimes run into numerical problems, if the fitted model does not converge on the newly simulated data.

Conditinal vs.Ā unconditinal simulations

The second option is the treatment of the stochastic hierarchy. In a hierarchical model, several layers of stochasticity are placed on top of each other. Specifically, in a GLMM, we have a lower level stochastic process (random effect), whose result enters into a higher level (e.g.Ā Poisson distribution). For other hierarchical models, such as state-space models, similar considerations apply, but the hierarchy can be more complex. When simulating, we have to decide if we want to re-simulate all stochastic levels, or only a subset of those. For example, in a GLMM, it is common to only simulate the last stochastic level (e.g.Ā Poisson) conditional on the fitted random effects, meaning that the random effects are set on the fitted values.

For controlling how many levels should be re-simulated, the simulateResidual function allows to pass on parameters to the simulate function of the fitted model object. Please refer to the help of the different simulate functions (e.g.Ā ?simulate.merMod) for details. For merMod (lme4) model objects, the relevant parameters are ā€œuse.uā€, and ā€œre.formā€, as, e.g., in

simulationOutput <- simulateResiduals(fittedModel = fittedModel, n = 250, use.u = T)

If the model is correctly specified and the fitting procedure is unbiased (disclaimer: GLMM estimators are not always unbiased), the simulated residuals should be flat regardless how many hierarchical levels we re-simulate. The most thorough procedure would be therefore to test all possible options. If testing only one option, I would recommend to re-simulate all levels, because this essentially tests the model structure as a whole. This is the default setting in the DHARMa package. A potential drawback is that re-simulating the random effects creates more variability, which may reduce power for detecting problems in the upper-level stochastic processes, in particular overdispersion (see section on dispersion tests below).

Note: Although unconditional residuals implicitly also test the normal distribution of the REs, it is probably not a bad idea to look addditionally check for normality of the RE distribution. As this is not based on quantile residuals, there is no special DHARMa function for this, so you should just extract the REs, and then run e.g.Ā a Shapiro test.

Integer treatment / randomization

A third option is the treatment of integer responses. The background of this option is that, for integer-valued variables, some additional steps are necessary to make sure that the residual distribution becomes flat (essentially, we have to smoothen away the integer nature of the data). The idea is explained in

  • Dunn, K. P., and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics 5, 1-10.

DHARMa currently implements two procedures for randomization. The default procedure will randomize automatically. The second option requires knowledge about whether the model is integer-valued, which is usually implemented automatically. See ?simulateResiduals for details. Usually, these options should simply be kept at their defaults.

Calculating residuals for groups or subsets

In many situations, it can be useful to look at residuals per group, e.g.Ā to see how much the model over / underpredicts per plot, year or subject. To do this, use the recalculateResiduals() function, together with a grouping variable (group) or a subsetting variable (sel), which can also be used in combination.

simulationOutput = recalculateResiduals(simulationOutput, group = testData$group)

Note, however, that you will have to change the selection of variables that you provide to plots and tests (e.g.Ā in plotResiduals or testSpatialAutocorrelation) accordingly when you group or subset residuals.

Reproducibility notes, random seed and random state

As DHARMa uses simulations to calculate the residuals, a naive implementation of the algorithm would mean that residuals would look slightly different each time a DHARMa calculation is executed. This might both be confusing and bear the danger that a user would run the simulation several times and take the result that looks better (which would amount to multiple testing / p-hacking). By default, DHARMa therefore fixes the random seed to the same value every time a simulation is run, and afterwards restores the random state to the old value. This means that you will get exactly the same residual plot each time. If you want to avoid this behavior, for example for simulation experiments on DHARMa, use seed = NULL -> no seed set, but random state will be restored, or seed = F -> no seed set, and random state will not be restored. Whether or not you fix the seed, the setting for the random seed and the random state are stored in

simulationOutput$randomState

If you want to reproduce simulations for such a run, set the variable .Random.seed by hand, and simulate with seed = NULL.

Moreover (general advice), to ensure reproducibility, itā€™s advisable to add a set.seed() at the beginning, and a session.info() at the end of your script. The latter will list the version number of R and all loaded packages.

Interpreting residuals and recognizing misspecification problems

General remarks on interperting residual patterns and tests

So far, all shown DHARMa results were calculated for a correctly specified model, resulting in ā€œperfectā€ residual plots and diagnostics. In this section, we discuss how to recognize and interpret diagnostics that indicate a misspecified model. Before going into the details, note, however, that

  1. No residual pattern does not ā€œproveā€ that the model is correct: The fact that none of the DHARMa tests indicate a problem does not ā€œproveā€ that the model is correctly specified. For any model, there are likely a large number of structural problems that do not create a pattern in the DHARMa diagnostics. In good old Popper fashion, you should interpret no residual problems as your working hypothesis not being rejected in that particular test, which increases confidence in the model, but does not constitute a conclusive proof. So, keep your skepticism alive, and if you find the results fishy, keep searching and testing.

  2. Once a residual effect is statistically significant, look at the magnitude to decide if there is a problem: It is crucial to note that significance is NOT a measure of the strength of the residual pattern, it is a measure of the signal/noise ratio, i.e.Ā whether you are sure there is a pattern at all. Significance in hypothesis tests depends on at least 2 ingredients: the strength of the signal and the number of data points. If you have a lot of data points, residual diagnostics will nearly inevitably become significant, because having a perfectly fitting model is very unlikely. That, however, doesnā€™t necessarily mean that you need to change your model. The p-values confirm that there is a deviation from your null hypothesis. It is, however, in your discretion to decide whether this deviation is worth worrying about. For example, if you see a dispersion parameter of 1.01, I would not worry, even if the dispersion test is significant. A significant value of 5, however, is clearly a reason to move to a model that accounts for overdispersion.

  3. A residual pattern does not indicate that the model is unusable: While a significant pattern in the residuals indicates with good reliability that the observed data did likely not originate from the fitted model, this doesnā€™t necessarily imply that the inferential results from this wrong model are not usable. There are many situations in statistics where it is common practice to work with ā€œwrong modelsā€. For example, many statistical models use shrinkage estimators, which purposefully bias parameter estimates to certain values. Random effects are a special case of this. If DHARMa residuals for these estimators are calculated, they will often show a slight pattern in the residuals even if the model is correctly specified, and tests for this can get significant for large sample sizes. For this reason, DHARMa is excluding RE estimates in the predictions when plotting res ~ pred. Another example is data that is missing at random (MAR). Since it is known that this phenomenon does not create a bias on the fixed effects estimates, it is common practice to fit these data with standard mixed models. Nevertheless, DHARMa recognizes that the observed data looks different from what would be expected from the model assumptions, and flags the model as problematic (see here).

Important conclusion: DHARMa only flags a difference between the observed and expected data - the user has to decide whether this difference is actually a problem for the analysis!

Recognizing over/underdispersion

GL(M)Ms often display over/underdispersion, which means that residual variance is larger/smaller than expected under the fitted model. This phenomenon is most common for GLM families with constant (fixed) dispersion, in particular for Poisson and binomial models, but it can also occur in GLM families that adjust the variance (such as the beta or negative binomial) when distribution assumptions are violated. A few general rules of thumb about dealing with dispersion problems:

  • Dispersion is a property of the residuals, i.e.Ā you can detect dispersion problems only AFTER fitting the model. It doesnā€™t make sense to look at the dispersion of your response variable
  • Overdispersion is more common than underdispersion
  • If overdispersion is present, the main effect is that confidence intervals tend to be too narrow, and p-values to small, leading to inflated type I error. The opposite is true for underdispersion, i.e.Ā the main issue of underdispersion is that you loose power.
  • A common reason for overdispersion is a misspecified model. When overdispersion is detected, one should therefore first search for problems in the model specification (e.g.Ā by plotting residuals against predictors with DHARMa), and only if this doesnā€™t lead to success, overdispersion corrections such as individual-level random effects or changes in the distribution should be applied

Residual patterns of over/underdispersion

This this is how overdispersion looks like in the DHARMa residuals. Note that we get more residuals around 0 and 1, which means that more residuals are in the tail of distribution than would be expected under the fitted model.

testData = createData(sampleSize = 200, overdispersion = 1.5, family = poisson())
fittedModel <- glm(observedResponse ~  Environment1 , family = "poisson", 
                   data = testData)

simulationOutput <- simulateResiduals(fittedModel = fittedModel)
plot(simulationOutput)

If you see this pattern, note that overdispersion is often caused by model misfit. Thus, before moving to a GLM with variable dispersion (for count data this would typically be a negative binomial), you should check your model for misfit, e.g.Ā by plotting residuals against all predictors using plotResiduals().

Next, this is an example of underdispersion. Here, we get too many residuals around 0.5, which means that we are not getting as many residuals as we would expect in the tail of the distribution than expected from the fitted model.

testData = createData(sampleSize = 500, intercept=0, fixedEffects = 2,
                      overdispersion = 0, family = poisson(),
                      roundPoissonVariance = 0.001, randomEffectVariance = 0)
fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , 
                     family = "poisson", data = testData)

simulationOutput <- simulateResiduals(fittedModel = fittedModel)
plot(simulationOutput)

If you see this pattern, note that a common reason for underdispersion is overfitting, i.e.Ā your model is too complex. Other possible explanations to check for include zero-inflation (best to check by comparing to a ZIP model, but see also DHARMa::testZeroInflation), non-independence of the data (e.g.Ā temporal autocorrelation, check via DHARMa:: testTemporalAutocorrelation) that your predictors can use to overfit, or that your data-generating process is simply not a Poisson process.

From a technical side, underdispersion is not as concerning as over dispersion, as it will usually bias p-values to the conservative side, but if your goal is to get a good power, you may want to consider a simpler model. If that is not helping, you can move to a distribution for underdispersed count data (e.g.Ā Conway-Maxwell-Poisson, generalized Poisson).

Formal tests for over/underdispersion

Although, as discussed above, over/underdispersion will show up in the residuals, and itā€™s possible to detect it with the testUniformity function, simulations show that this test is less powerful than more targeted tests. DHARMa contains several overdispersion tests that compare the dispersion of simulated residuals to the observed residuals.

  1. default: a non-parametric test that compares the variance of the simulated residuals to the observed residuals (default), which has some analogy to the variance test implemented in aer::dispersiontest
  2. PearsonChisq: alternatively, DHARMa implements the Pearson-chi2 test that is popular in the literature, suggested in the glmm Wiki, and implemented in some other R packages such as performance::check_overdispersion
  3. refit if residual simulations are done via refit, DHARMa will compare the the Pearson residuals of the re-fitted simulations to the original Pearson residuals. This is essentially a nonparametric version of test 2.

All of these tests are included in the testDispersion function, see ?testDispersion for details.

testDispersion(simulationOutput)

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 0.067211, p-value < 2.2e-16
## alternative hypothesis: two.sided

IMPORTANT INFO: we have made extensive simulations, which have shown that the various tests have certain advantages and disadvantages. The basic results are that:

  • The most powerful and reliable test is option 3, but this costs a lot of time and is not available for all regression packages, as it requires that Pearson residuals are available
  • Option 2, the parametric Pearson-chi2 is fast if Pearson residuals are available, but based on a naive expectation of df (counts RE as 1 df) and the test statistic is thus biased towards underdispersion for mixed models. Similar to the df approximation, Bias increasing with the number of RE levels. When testing only for overdispersion (alternative = ā€œgreaterā€), this makes the test more conservative, but it also costs power.
  • The DHARMa default option 1 is fast, nearly unbiased (i.e.Ā you can test under and overdispersion), and only slightly less powerful as test 3, PROVIDED that simulations are made conditional on the fitted REs. Note that the latter is not the DHARMa default, so you have to actively request conditional simulations, e.g.Ā for lme4 by specifying re.form = NULL. Power compared to the parametric Pearson-chi2 test depends on the number of RE levels, it will be more powerful for typical number of RE levels.

As support for these statements, here results of the simulation, which compares the uniform (KS) test with the standard simuation-based test (conditional and unconditional) and the Pearson-chi2 test (two-sided and greater) for an n=200 Poisson GLMM with 30 RE levels.

Thus, my current recommendation is: for most users, use the default DHARMa test, but create simulations conditionally.

Zero-inflation / k-inflation or deficits

A common special case of overdispersion is zero-inflation, which is the situation when more zeros appear in the observation than expected under the fitted model. Zero-inflation requires special correction steps. More generally, we can also have too few zeros, or too much or too few of any other values. Weā€™ll discuss that at the end of this section.

Residual patterns

Here an example of a typical zero-inflated count dataset, plotted against the environmental predictor

testData = createData(sampleSize = 500, intercept = 2, fixedEffects = c(1),
                      overdispersion = 0, family = poisson(), 
                      quadraticFixedEffects = c(-3), randomEffectVariance = 0,
                      pZeroInflation = 0.6)

par(mfrow = c(1,2))
plot(testData$Environment1, testData$observedResponse, xlab = "Envrionmental Predictor", 
     ylab = "Response")
hist(testData$observedResponse, xlab = "Response", main = "")

We see a hump-shaped dependence of the environment, but with too many zeros. In the normal DHARMa residual plots, zero-inflation will look pretty much like overdispersion

fittedModel <- glmer(observedResponse ~ Environment1 + I(Environment1^2) + (1|group) , 
                     family = "poisson", data = testData)

simulationOutput <- simulateResiduals(fittedModel = fittedModel)
plot(simulationOutput)

The reason is that the model will usually try to find a compromise between the zeros, and the other values, which will lead to excess variance in the residuals.

Formal tests for zero-inflation

DHARMa also has a special test for zero-inflation, which compares the distribution of expected zeros in the data against the observed zeros

testZeroInflation(simulationOutput)

## 
##  DHARMa zero-inflation test via comparison to expected zeros with
##  simulation under H0 = fitted model
## 
## data:  simulationOutput
## ratioObsSim = 1.9533, p-value < 2.2e-16
## alternative hypothesis: two.sided

This test is likely better suited for detecting zero-inflation than the standard plot, but note that also overdispersion will lead to excess zeros, so only seeing too many zeros is not a reliable diagnostics for moving towards a zero-inflated model. A reliable differentiation between overdispersion and zero-inflation will usually only be possible when directly comparing alternative models, e.g.Ā through residual comparison / model selection of a model with / without zero-inflation, or by simply fitting a model with zero-inflation and looking at the parameter estimate for the zero-inflation. A good option is the R package glmmTMB, which is also supported by DHARMa. We can use this to fit

# requires glmmTMB
fittedModel <- glmmTMB(observedResponse ~ Environment1 + I(Environment1^2) + (1|group), ziformula = ~1 , family = "poisson", data = testData)
summary(fittedModel)

simulationOutput <- simulateResiduals(fittedModel = fittedModel)
plot(simulationOutput)

Testing generic summary statistics, e.g.Ā for k-inflation or deficits

To test for generic excess / deficits of particular values, we have the function testGeneric, which compares the values of a generic, user-provided summary statistics

Choose one of alternative = c(ā€œgreaterā€, ā€œtwo.sidedā€, ā€œlessā€) to test for inflation / deficit or both. Default is ā€œgreaterā€ = inflation.

countOnes <- function(x) sum(x == 1)  # testing for number of 1s
testGeneric(simulationOutput, summary = countOnes, alternative = "greater") # 1-inflation

## 
##  DHARMa generic simulation test
## 
## data:  simulationOutput
## ratioObsSim = 0.19944, p-value = 1
## alternative hypothesis: greater

Heteroscedasticity

So far, most of the things that we have tested could also have been detected with parametric tests. Here, we come to the first issue that is difficult to detect with current tests, and that is usually neglected.

Heteroscedasticity means that there is a systematic dependency of the dispersion / variance on another variable in the model. It is not sufficiently appreciated that also binomial or Poisson models can show heteroscedasticity. Basically, it means that the level of over/underdispersion depends on another parameter. Here an example where we create such data

testData = createData(sampleSize = 500, intercept = -1.5,  
                      overdispersion = function(x){return(rnorm(length(x), sd = 1 * abs(x)))}, 
                      family = poisson(), randomEffectVariance = 0)
fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData)

simulationOutput <- simulateResiduals(fittedModel = fittedModel)
plot(simulationOutput)

The exact p-values for the quantile lines in the plot can be displayed via

testQuantiles(simulationOutput)

As mentioned above, the equivalent test for categorical predictors (plot function will switch automatically) would be

testCategorical(simulationOutput, catPred = testData$group)

Adding a simple overdispersion correction will try to find a compromise between the different levels of dispersion in the model. The qq plot looks better now, but there is still a pattern in the residuals

testData = createData(sampleSize = 500, intercept = 0, overdispersion = function(x){return(rnorm(length(x), sd = 2*abs(x)))}, 
                      family = poisson(), randomEffectVariance = 0)
fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) + (1|ID), 
                     family = "poisson", data = testData)

# plotConventionalResiduals(fittedModel)

simulationOutput <- simulateResiduals(fittedModel = fittedModel)
plot(simulationOutput)

To remove this pattern, you would need to make the dispersion parameter dependent on a predictor (e.g.Ā in JAGS), or apply a transformation on the data.

Detecting missing predictors or wrong functional assumptions

A second test that is typically run for LMs, but not for GL(M)Ms is to plot residuals against the predictors in the model (or potentially predictors that were not in the model) to detect possible misspecifications. Doing this is highly recommended. For that purpose, you can retrieve the residuals via

simulationOutput$scaledResiduals

Note again that the residual values are scaled between 0 and 1. If you plot the residuals against predictors, space or time, the resulting plots should not only show no systematic dependency of those residuals on the covariates, but they should also again be flat for each fixed situation. That means that if you have, for example, a categorical predictor: treatment / control, the distribution of residuals for each predictor alone should be flat as well.

Here an example with a missing quadratic effect in the model and 2 predictors

testData = createData(sampleSize = 200, intercept = 1, fixedEffects = c(1,2),
                      overdispersion = 0, family = poisson(), 
                      quadraticFixedEffects = c(-3,0))
fittedModel <- glmer(observedResponse ~ Environment1 + Environment2 + (1|group),
                     family = "poisson", data = testData)
simulationOutput <- simulateResiduals(fittedModel = fittedModel)
# plotConventionalResiduals(fittedModel)
plot(simulationOutput, quantreg = T)

# testUniformity(simulationOutput = simulationOutput)

It is difficult to see that there is a problem at all in the general plot, but it becomes clear if we plot against the environment

par(mfrow = c(1,2))
plotResiduals(simulationOutput, testData$Environment1)
plotResiduals(simulationOutput, testData$Environment2)

Residual correlation structures (temporal, spatial, phylogenetic)

If a distance between residuals can be defined (temporal, spatial, phylogenetic), you should check if there is a distance-dependence in the residuals, which would suggest to move to a GLS (generalized least squares) structure for analysis.

The three functions to test for this in DHARMa are:

  • testTemporalAutocrrelation based on the Durbin-Watson test.
  • testSpatialAutocorrelation, based on Moranā€™s I, can also be used for generic distance functions.
  • testPhylogeneticAutocorrelation, based on Moranā€™s I test from Moran.I function on package ape.

Here a short example for the spatial case, see help of the functions for extended examples.

testData = createData(sampleSize = 100, family = poisson(), 
                      spatialAutocorrelation = 3, numGroups = 1,
                       randomEffectVariance = 0)
fittedModel <- glm(observedResponse ~ Environment1 , data = testData, 
                   family = poisson() )
simulationOutput <- simulateResiduals(fittedModel = fittedModel)
testSpatialAutocorrelation(simulationOutput = simulationOutput, x = testData$x,
                           y= testData$y)

## 
##  DHARMa Moran's I test for distance-based autocorrelation
## 
## data:  simulationOutput
## observed = 0.123622, expected = -0.010101, sd = 0.015421, p-value <
## 2.2e-16
## alternative hypothesis: Distance-based autocorrelation
# plot(simulationOutput)

Note that all these tests are most sensitive against homogeneous residual structure, and might miss local and heterogeneous (non-stationary) residual structures. Additional visual checks can be useful.

However, standard DHARMa simulations from models with temporal / spatial / phylogenetic conditional autoregressive terms will still have the respective correlation in the DHARMa residuals, unless the package you are using is modelling the autoregressive terms as explicit REs and is able to simulate conditional on the fitted REs. It means that the residuals will still show significant autocorrelation, even if the model fully accounts for this strucuture, and other tests, such as dispersion, uniformity, may have inflated type I error. See the example below with a glmmTMB model with a spatial autocorrelation structure:

library(glmmTMB)
testData$pos <- numFactor(testData$x, testData$y)
fittedModel2 <- glmmTMB(observedResponse ~ Environment1 + exp(pos + 0|group), 
                        data = testData, family = poisson())
simulationOutput2 <- simulateResiduals(fittedModel = fittedModel2)
testSpatialAutocorrelation(simulationOutput = simulationOutput2, x = testData$x, 
                           y= testData$y)

## 
##  DHARMa Moran's I test for distance-based autocorrelation
## 
## data:  simulationOutput2
## observed = 0.138255, expected = -0.010101, sd = 0.015421, p-value <
## 2.2e-16
## alternative hypothesis: Distance-based autocorrelation
# plot(simulationOutput2)

One of the options to solve it and get correct tests and no residual pattern (if the model is correct) is to rotate the residual space according to the coariance structure of the fitted model, such that the rotated residuals are conditionally independent. The argument rotation in simulateResiduals does it (see also ?getQuantile for details about the rotation options):

# rotation of the residuals 
simulationOutput3 <- simulateResiduals(fittedModel = fittedModel2,
                                       rotation = "estimated")
testSpatialAutocorrelation(simulationOutput = simulationOutput3, x = testData$x, 
                           y= testData$y)

## 
##  DHARMa Moran's I test for distance-based autocorrelation
## 
## data:  simulationOutput3
## observed = 0.035283, expected = -0.010101, sd = 0.015451, p-value =
## 0.003311
## alternative hypothesis: Distance-based autocorrelation
# plot(simulationOutput3)

Case studies and examples

Note: More real-world examples can be found on the DHARMa GitHub repository.

Budworm example (count-proportion n/k binomial)

This example comes from Jochen Fruend. Measured are the number of parasitized observations, with population density as a covariate:

plot(N_parasitized / (N_adult + N_parasitized ) ~ logDensity, 
     xlab = "Density", ylab = "Proportion infected", data = data)

Letā€™s fit the data with a regular binomial n/k glm

mod1 <- glm(cbind(N_parasitized, N_adult) ~ logDensity, data = data, family=binomial)
simulationOutput <- simulateResiduals(fittedModel = mod1)
plot(simulationOutput)

We see various signals of overdispersion

  • QQ: s-shaped QQ plot, distribution test (KS) signficant
  • QQ: Dispersion test is significant
  • QQ: Outlier test significant
  • Res ~ predicted: Quantile fits are spread out too far

OK, so letā€™s add overdispersion through an individual-level random effect

mod2 <- glmer(cbind(N_parasitized, N_adult) ~ logDensity + (1|ID), data = data, family=binomial)
simulationOutput <- simulateResiduals(fittedModel = mod2)
plot(simulationOutput)

The overdispersion looks better, but you can see that the residuals still look a bit irregular (although tests are n.s.). The raw data looks a bit humped-shaped, so we might be tempted to add a quadratic effect.

mod3 <- glmer(cbind(N_parasitized, N_adult) ~ logDensity + I(logDensity^2) + (1|ID), data = data, family=binomial)
simulationOutput <- simulateResiduals(fittedModel = mod3)
plot(simulationOutput)

The residuals look perfect now. That being said, we dontā€™ have a lot of data, and we have to be sure weā€™re not overfitting. A likelihood ratio test tells us that the quadratic effect is not significantly supported.

anova(mod2, mod3)
## Data: data
## Models:
## mod2: cbind(N_parasitized, N_adult) ~ logDensity + (1 | ID)
## mod3: cbind(N_parasitized, N_adult) ~ logDensity + I(logDensity^2) + (1 | ID)
##      npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)  
## mod2    3 214.68 217.95 -104.34   208.68                       
## mod3    4 213.54 217.90 -102.77   205.54 3.1401  1    0.07639 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Also AIC differences are small, although slightly in favor of model 3

AIC(mod2) 
## [1] 214.6776
AIC(mod3)
## [1] 213.5375

I guess you could use either Model 2 or 3 - the broader point is: increasing model complexity will nearly always improve the residuals, but according to standard statistical arguments (power, bias-variance trade-off) itā€™s not always advisable to get them perfect, just good enough!

Owl example (count data)

The next examples uses the fairly well known Owl dataset which is provided in glmmTMB (see ?Owls for more info about the data). The following shows a sequence of models, all checked with DHARMa. The example is discussed in a talk at ISEC 2018, see slides here.

library(glmmTMB)
m1 <- glm(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)), data=Owls , family = poisson)
res <- simulateResiduals(m1)
plot(res)

OK, this is highly overdispersed. Letā€™s add a RE on nest:

m2 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), data=Owls , family = poisson)
res <- simulateResiduals(m2)
plot(res)

Somewhat better, but not good. Move to neg binom, to adjust dispersion, and checking dispersion and residuals against FoodTreatment predictor:

m3 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), data=Owls , family = nbinom1)

res <- simulateResiduals(m3, plot = T)

par(mfrow = c(1,2))
testDispersion(res)
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 0.63438, p-value < 2.2e-16
## alternative hypothesis: two.sided
plotResiduals(res, Owls$FoodTreatment)

We see underdispersion now. In a model with variable dispersion, this is often the signal that some other distributional assumptions are violated. Letā€™s check for zero-inflation:

testZeroInflation(res)

## 
##  DHARMa zero-inflation test via comparison to expected zeros with
##  simulation under H0 = fitted model
## 
## data:  simulationOutput
## ratioObsSim = 1.2488, p-value = 0.064
## alternative hypothesis: two.sided

It looks as if there is some zero-inflation, although non-significant. Fitting a zero-inflated model:

m4 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) +
                (1|Nest), 
              ziformula = ~ FoodTreatment + SexParent,  data=Owls , family = nbinom1)

res <- simulateResiduals(m4, plot = T)

par(mfrow = c(1,3))
plotResiduals(res, Owls$FoodTreatment)
testDispersion(res)
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 0.81335, p-value = 0.168
## alternative hypothesis: two.sided
testZeroInflation(res)

## 
##  DHARMa zero-inflation test via comparison to expected zeros with
##  simulation under H0 = fitted model
## 
## data:  simulationOutput
## ratioObsSim = 1.0389, p-value = 0.616
## alternative hypothesis: two.sided

This looks a lot better. Trying a slightly different model specification, adding a dispersion model as well:

m5 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) +
                (1|Nest), 
              dispformula = ~ FoodTreatment + SexParent , 
              ziformula = ~ FoodTreatment + SexParent,  data=Owls , family = nbinom1)

res <- simulateResiduals(m5, plot = T)

par(mfrow = c(1,3))
plotResiduals(res, Owls$FoodTreatment)
testDispersion(res)
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 0.78311, p-value = 0.104
## alternative hypothesis: two.sided
testZeroInflation(res)

## 
##  DHARMa zero-inflation test via comparison to expected zeros with
##  simulation under H0 = fitted model
## 
## data:  simulationOutput
## ratioObsSim = 1.0465, p-value = 0.608
## alternative hypothesis: two.sided

but that does not seem to make things better.

Both models would be acceptable in terms of their fit to the data. Which one should you prefer? This is not a question for residual checks. Residual checks tell you which models can be rejected with the data. Which of the typically many acceptable models you should fit must be decided by your scientific question, and/or possibly by model selection methods. In doubt, I would tend towards the simpler model though.

Notes on particular data types

Poisson data

The main concern in Poisson data is dispersion. See comments in the section on the dispersion test, in particular regarding the advantage of conditional simulations in this case. To address overdispersion, I would recommend to prefer the negative binomial model over observation-level random effects, because this mode will be easier to test in DHARMa and its dispersion can be easier modeled, e.g.Ā with glmmTMB. The third option would be quasi models, but there are few advantages, except runtime. Note also that quasi models cannot be tested with DHARMa.

Once dispersion is adjusted, you should check for heteroscedasticity (via standard plot, also against all predictors), and for zero-inflation. As noted, zero-inflation tests are often negative, and rather show up as underdispersion. Work through the owl example below.

Proportional data

Proportional data expressed as percentage or fractions of a whole, i.e.Ā non-count-based data, is often modeled with beta regressions. Those can be tested with DHARMa. Note that beta regressions are often 0 or 1 inflated. Both should be tested with testZeroInflation or testGeneric.

techniques for analysing continuous (also called non-count-based or non-binomial) proportions (e.g.Ā percent cover, fraction time spent on an activity)

Note: discrete proportions, i.e.Ā count-based proportions, of the type k/n should NOT be modeled with the beta regression. Use the binomial (see below).

Binomial data

Binomial data behave slightly different depending on whether we have a 0/1 response (Bernoulli) or a k/n response (true binomial).

A k/n response, in particular when n is large, will behave similar to the Poisson, in that it approaches a normal distribution with fixed dispersion for large n and becomes more assymetric at its borders (for k = 0 or n). You should check for dispersion and consider a beta-binomial in cases of overdispersion.

Things are a bit different for the 0/1 response. Letā€™s look at the residuals of a clearly misspecified binomial model (missing predictor) with 0/1 response data.

testData = createData(sampleSize = 500, overdispersion = 0, fixedEffects = 5, 
                      family = binomial(), randomEffectVariance = 3, 
                      numGroups = 25)

fittedModel <- glm(observedResponse ~ 1, family = "binomial", data = testData)

simulationOutput <- simulateResiduals(fittedModel = fittedModel)

If you would do the same with a binomial k/n response or count data, such a misspecification would produce overdispersion (try it out). For the 0/1 response we see neither dispersion problems nor a misfit in the general res ~ predicted plot.

plot(simulationOutput, asFactor = T)

Even though the misfit is clearly visible if we plot the residuals against the missing predictor.

plotResiduals(simulationOutput, testData$Environment1, quantreg = T)

However, we can see the overdispersion arising from the misfit if we group our residuals, which basically transforms the 0/1 response in a k/n response.

To show this, letā€™s look at the dispersion test for the same model, once ungrouped (left), and grouped according to the variable group which was in the data (right).

par(mfrow = c(1,2))
testDispersion(simulationOutput)
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0023, p-value = 0.824
## alternative hypothesis: two.sided
simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group)
testDispersion(simulationOutput2)

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 3.0805, p-value < 2.2e-16
## alternative hypothesis: two.sided

In general, you can group according to any variable that you like, including continous variables or space. However, some variables make more sense than others. To understand this, consider a simulation where we create binonial data with true probabilities p, drawn from a uniform distribution:

n = 1000
p = runif(n, 0.1, 0.9) # true probabilities
obs = rbinom(n, 1, p)

The important thing to note here is that rbinom(n, 1, p) will generate an identical overall distribution as rbinom(1, n, mean(p)). What that means: a misfit of the prediction will not show up unless they are wrong in the overall mean. Consequenly, if we fit:

fit <- glm(obs ~ 1, family = "binomial") # wrong model, assumes equal probabilities
library(DHARMa)
res <- simulateResiduals(fit, plot = T) # nothing to see

We see no misfit, and neither do we see a misfit when we group the data points randomly, as the mean of a random group is still fit well by the overall mean.

res2 <- recalculateResiduals(res, group = rep(1:20, each = 10))
plot(res2)

However, we see thes misfit / overdispersion if we aggregate according to something that is correlated to the misfit. For our example, letā€™s just group according to the true means:

grouping = cut(p, breaks = quantile(p, seq(0,1,0.02)))
res3 <- recalculateResiduals(res, group = grouping)
plot(res3)

In this case, the groups have a different mean than the fitted grand mean, and the misfit shows up in the residuals. Thus, what we are looking for in the grouping is variables that may correlate with the misfit.

If you donā€™t have a natural grouping variable, you can introduce arbitrary grouping variables, e.g.Ā via discretising a predictor or the response (usually preferable), and grouping according to that, or via discretising space (e.g.Ā group observation in spatial blocks). The pattern appears only, however, if the grouping variable correlates with the model error. Consider the following example:

We create data and fit a model with a missing predictor (Environment2):

set.seed(123)

testData = createData(sampleSize = 500, overdispersion = 0, fixedEffects = c(0,3), family = binomial(), randomEffectVariance = 3, numGroups = 50)

Apparently, no problem with the residuals for the misfitted model:

res <- simulateResiduals(fittedModel = fittedModel)
fittedModel <- glm(observedResponse ~ Environment1, family = "binomial", 
                   data = testData)
plot(res)

  1. Grouping according to the RE produces overdispersion because RE is missing in the first model:
res2 = recalculateResiduals(res , group = testData$group)
plot(res2)

  1. Grouping according to a random factor does not produce an effect. In this respect, the model has correct dispersion:
grouping = as.factor(sample.int(50, 500, replace = T))

res2 = recalculateResiduals(res , group = grouping)
plot(res2)

  1. Grouping according to the response doesnā€™t create a pattern:
x = predict(fittedModel)
grouping = cut(x, breaks = quantile(x, seq(0,1,0.02)))
res2 = recalculateResiduals(res , group = grouping)
plot(res2)

  1. Grouping according to the missing variable creates pattern, because in relation to this variable, the model is overdispersed:
x = testData$Environment2
grouping = cut(x, breaks = quantile(x, seq(0,1,0.02)))
res2 = recalculateResiduals(res , group = grouping)
plot(res2)

  1. Grouping according to space does not create a pattern, because there is no missing spatial predictor:
x = testData$x
grouping = cut(x, breaks = quantile(x, seq(0,1,0.02)))
res3 = recalculateResiduals(res , group = grouping)
plot(res3)

Conclusions: if you see overdispersion or a pattern after grouping, it highlights a model error that is structured by group. As the pattern usually highlights a model misfit, rather than a dispersion problem akin to what happens in an overdispersed binomial (which has major impacts on p-values and CIs), I view this binomial grouping pattern as less critical. Likely, most conclusions will not change if you ignore the problem. Nevertheless, you should try to understand the reason for it. When the group is spatial, it could be the sign of residual spatial autocorrelation which could be addressed by a spatial RE or a spatial model. When grouped by a continuous variable, it could be the sign of a nonlinear effect.

Supported packages and frameworks

lm and glm

lm and glm and MASS::glm.nb are fully supported.

lme4

lme4 model classes are fully supported.

Possible to condition on REs via re.form, see help of predict.merMod

mgcv

When using mgcv with DHARMa, it is highly recommended to also install mgcViz. Since version 0.4.5, this will allow DHARMa to fall back on the simulate.gam function in mgcViz, which is more general than the default simulate function. For example, without mgcViz, it will not be possible to simulate from mgcv::gam objects fitted with extended families.

If you absolutely want to use DHARMa without mgcViz, you should make sure that simulate(model) works correctly for the model object for which you want to calculate DHARMa residuals.

gamm4

Models fitted with gamm4 return a list that contains a lme4 object under the name ā€œmerā€. You can test this object like an lme4 model, so e.g.Ā simulateResiduals(myGamm4Model$mer). All remarks regarding lme4 objects apply.

glmmTMB

glmmTMB is nearly fully supported since DHARMa 0.2.7 and glmmTMB 1.0.0. A remaining limitation is that you canā€™t adjust whether simulation are conditional or not, so simulateResiduals(model, re.form = NULL) will have no effect, simulations will always be done from the full model.

spaMM

spaMM is supported by DHARMa since 0.2.1

GLMMadaptive

GLMMadaptive is supported by DHARMa since 0.3.4.

phylolm

phylom (version >= 2.6.5) is supported by DHARMa since 0.4.7 for both model classes phylolm and phyloglm.

phyr

DHARMa residuals work with phyr, but the correct implementation is not fully tested as of DHARMa 0.4.2. See also https://github.com/florianhartig/DHARMa/issues/235

brms

brms can be made to work together with DHARMa, see https://github.com/florianhartig/DHARMa/issues/33

Unsupported packages

If confronted with an unsupported package, DHARMa will try to use standard S3 functions such as coef(), simulate() etc. to perform simulations. If no error occurs, a residual object will be calculated, and a warning will be provided that this package has not been checked for full functionality. In many cases, the results can be used though (but no guarantee, maybe check with null simulations if the results are OK). Other than that, see my general comments about adding new R packages to DHARMa

Importing external simulations (e.g.Ā from Bayesian software or unsupported packages)

DHARMa can also import external simulations from a fitted model via createDHARMa(), which will be interesting for unsupported packages and for Bayesians.

Bayesians should note the extra Vignette on ā€œDHARMa for Bayesiansā€ regarding the interpretation of these residuals.

Here, an example for how to create simulations for a Poisson glm. Of course, it doesnā€™t make sense to do this as glm is a supported model class, but you could do the same in case you want to check a model class that is currently not supported by DHARMa.

testData = createData(sampleSize = 200, overdispersion = 0.5, family = poisson())
fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData)

simulatePoissonGLM <- function(fittedModel, n){
  pred = predict(fittedModel, type = "response")
  nObs = length(pred)
  sim = matrix(nrow = nObs, ncol = n)
  for(i in 1:n) sim[,i] = rpois(nObs, pred)
  return(sim)
}

sim = simulatePoissonGLM(fittedModel, 100)

DHARMaRes = createDHARMa(simulatedResponse = sim, observedResponse = testData$observedResponse, 
             fittedPredictedResponse = predict(fittedModel), integerResponse = T)
plot(DHARMaRes, quantreg = F)

DHARMa/inst/doc/DHARMaForBayesians.Rmd0000644000176200001440000002276214665273541016764 0ustar liggesusers--- title: "DHARMa for Bayesians" author: "Florian Hartig, Theoretical Ecology, University of Regensburg [website](https://www.uni-regensburg.de/biologie-vorklinische-medizin/theoretische-oekologie/mitarbeiter/hartig/)" date: "`r Sys.Date()`" output: rmarkdown::html_vignette: toc: true vignette: > %\VignetteIndexEntry{DHARMa for Bayesians} \usepackage[utf8]{inputenc} %\VignetteEngine{knitr::rmarkdown} abstract: "The 'DHARMa' package uses a simulation-based approach to create readily interpretable scaled (quantile) residuals for fitted (generalized) linear mixed models. This Vignette describes how to user DHARMa vor checking Bayesian models. It is recommended to read this AFTER the general DHARMa vignette, as all comments made there (in pacticular regarding the interpretation of the residuals) also apply to Bayesian models. \n \n \n" editor_options: chunk_output_type: console --- ```{r global_options, include=FALSE} knitr::opts_chunk$set(fig.width=8.5, fig.height=5.5, fig.align='center', warning=FALSE, message=FALSE) ``` ```{r, echo = F, message = F} library(DHARMa) set.seed(123) ``` # Basic workflow In principle, DHARMa residuals can be calculated and interpreted for Bayesian models in very much the same way as for frequentist models. Therefore, all comments regarding tests, residual interpretation etc. from the main vignette are equally valid for Bayesian model checks. There are some minor differences regarding the expected null distribution of the residuals, in particular in the low data limit, but I believe that for most people, these are of less concern. The main difference for a Bayesian user is that, unlike for users of directly supported regression packages such as lme4 or glmmTMB, most Bayesian users will have to create the simulations for the fitted model themselves and then feed them into DHARMa by hand. The basic workflow for Bayesians that work with BUGS, JAGS, STAN or similar is: 1. Create posterior predictive simulations for your model 2. Read these in with the createDHARMa function 3. Interpret those as described in the main vignette This is more easy as it sounds. For the major Bayesian samplers (e.g. BUGS, JAGS, STAN), it amounts to adding a block with data simulations to the model, and observing those during the MCMC sampling. Then, feed the simulations into DHARMa via createDHARMa, and all else will work pretty much the same as in the main vignette. ## Example in Jags Here is an example, with JAGS ```{r, eval = F} library(rjags) library(BayesianTools) set.seed(123) dat <- DHARMa::createData(200, overdispersion = 0.2) Data = as.list(dat) Data$nobs = nrow(dat) Data$nGroups = length(unique(dat$group)) modelCode = "model{ for(i in 1:nobs){ observedResponse[i] ~ dpois(lambda[i]) # poisson error distribution lambda[i] <- exp(eta[i]) # inverse link function eta[i] <- intercept + env*Environment1[i] # linear predictor } intercept ~ dnorm(0,0.0001) env ~ dnorm(0,0.0001) # Posterior predictive simulations for (i in 1:nobs) { observedResponseSim[i]~dpois(lambda[i]) } }" jagsModel <- jags.model(file= textConnection(modelCode), data=Data, n.chains = 3) para.names <- c("intercept","env", "lambda", "observedResponseSim") Samples <- coda.samples(jagsModel, variable.names = para.names, n.iter = 5000) x = BayesianTools::getSample(Samples) colnames(x) # problem: all the variables are in one array - this is better in STAN, where this is a list - have to extract the right columns by hand posteriorPredDistr = x[,3:202] # this is the uncertainty of the mean prediction (lambda) posteriorPredSim = x[,203:402] # these are the simulations sim = createDHARMa(simulatedResponse = t(posteriorPredSim), observedResponse = dat$observedResponse, fittedPredictedResponse = apply(posteriorPredDistr, 2, median), integerResponse = T) plot(sim) ``` In the created plots, you will see overdispersion, which is completely expected, as the simulated data has overdispersion and a RE, which is not accounted for by the Jags model. ## Exercise As an exercise, you could now: * Add a RE * Account for overdispersion, e.g. via an OLRE or a negative Binomial And check how the residuals improve. # Conditional vs. unconditional simulations in hierarchical models The most important consideration in using DHARMa with Bayesian models is how to create the simulations. You can see in my jags code that the block ```{r, eval=F} # Posterior predictive simulations for (i in 1:nobs) { observedResponseSim[i]~dpois(lambda[i]) } ``` performs the posterior predictive simulations. Here, we just take the predicted lambda (mean perdictions) during the MCMC simulations and sample from the assumed distribution. This will works for any non-hierarchical model. When we move to hierarchical or multi-level models, including GLMMs, the issue of simulation becomes a bit more complicated. In a hierarchical model, there are several random processes that sit on top of each other. In the same way as explained in the main vignette at the point conditional / unconditional simulations, we will have to decide which of these random processes should be included in the posterior predictive simulations. As an example, imagine we add a RE in the likelihood of the previous model, to account for the group structure in the data. ```{r, eval = F} for(i in 1:nobs){ observedResponse[i] ~ dpois(lambda[i]) # poisson error distribution lambda[i] <- exp(eta[i]) # inverse link function eta[i] <- intercept + env*Environment1[i] + RE[group[i]] # linear predictor } for(j in 1:nGroups){ RE[j] ~ dnorm(0,tauRE) } ``` The predictions lambda[i] now depend on a lower-level stochastic effect, which is described by RE[j] ~ dnorm(0,tauRE). We can now decide to create posterior predictive simulations conditional on posterior estimates RE[j] (conditional simulations), in which case we would have to change nothing in the block for the posterior predictive simulations. Alternatively, we can decide that we want to re-simulate the RE (unconditional simulations), in which case we have to copy the entire structure of the likelihood in the predictions ```{r, eval=F} for(j in 1:nGroups){ RESim[j] ~ dnorm(0,tauRE) } for (i in 1:nobs) { observedResponseSim[i] ~ dpois(lambdaSim[i]) lambdaSim[i] <- exp(etaSim[i]) etaSim[i] <- intercept + env*Environment1[i] + RESim[group[i]] } ``` Essentially, you can remember that if you want full (uncoditional) simulations, you basically have to copy the entire likelihood of the hierarchical model, minus the priors, and sample along the hierarchical model structure. If you want to condition on a part of this structure, just cut the DAG at the point on which you want to condition on. # Statistical differences between Bayesian vs. MLE quantile residuals A common question is if there are differences between Bayesian and MLE quantile residuals. First of all, note that MLE and Bayesian quantile residuals are not exactly identical. The main difference is in how the simulation of the data under the fitted model are performed: * For models fitted by MLE, simulations in DHARMa are with the MLE (point estimate) * For models fitted with Bayes, simulations are practically always performed while also drawing from the posterior parameter uncertainty (as a point estimate is not available). Thus, Bayesian posterior predictive simulations include the parametric uncertainty of the model, additionally to the sampling uncertainty. From this we can directly conclude that Bayesian and MLE quantile residuals are asymptotically identical (and via the usual arguments uniformly distributed), but become more different the smaller n becomes. To examine what those differences are, let's imagine that we start with a situation of infinite data. In this case, we have a "sharp" posterior that can be viewed as identical to the MLE. If we reduce the number of data, there are two things happening 1. The posterior gets wider, with the likelihood component being normally distributed, at least initially 2. The influence of the prior increases, the faster the stronger the prior is. Thus, if we reduce the data, for weak / uninformative priors, we will simulate data while sampling parameters from a normal distribution around the MLE, while for strong priors, we will effectively sample data while drawing parameters of the model from the prior. In particular in the latter case (prior dominates, which can be checked via prior sensitivity analysis), you may see residual patterns that are caused by the prior, even though the model structure is correct. In some sense, you could say that the residuals check if the combination of prior + structure is compatible with the data. It's a philosophical debate how to react on such a deviation, as the prior is not really negotiable in a Bayesian analysis. Of course, also the MLE distribution might get problems in low data situations, but I would argue that MLE is usually only used anyway if the MLE is reasonably sharp. In practice, I have self experienced problems with MLE estimates. It's a bit different in the Bayesian case, where it is possible and often done to fit very complex models with limited data. In this case, many of the general issues in defining null distributions for Bayesian p-values (as, e.g., reviewed in [Conn et al., 2018](https://esajournals.onlinelibrary.wiley.com/doi/10.1002/ecm.1314)) apply. I would add though that while I find it important that users are aware of those differences, I have found that in practice these issues are small, and usually overruled by the much stronger effects of model error. DHARMa/inst/doc/DHARMa.Rmd0000644000176200001440000017254014704245735014454 0ustar liggesusers--- title: "DHARMa: residual diagnostics for hierarchical (multi-level/mixed) regression models" author: "Florian Hartig, Theoretical Ecology, University of Regensburg [website](https://www.uni-regensburg.de/biologie-vorklinische-medizin/theoretische-oekologie/mitarbeiter/hartig/)" date: "`r Sys.Date()`" output: rmarkdown::html_vignette: toc: true pdf_document: toc: true vignette: > %\VignetteIndexEntry{The import package} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} abstract: "The 'DHARMa' package uses a simulation-based approach to create readily interpretable scaled (quantile) residuals for fitted generalized linear (mixed) models. Currently supported are linear and generalized linear (mixed) models from 'lme4' (classes 'lmerMod', 'glmerMod'), 'glmmTMB', 'GLMMadaptive' and 'spaMM'; phylogenetic linear models from 'phylolm' (classes 'phylolm' and 'phyloglm'); generalized additive models ('gam' from 'mgcv'); 'glm' (including 'negbin' from 'MASS', but excluding quasi-distributions) and 'lm' model classes. Moreover, externally created simulations, e.g. posterior predictive simulations from Bayesian software such as 'JAGS', 'STAN', or 'BUGS' can be processed as well. The resulting residuals are standardized to values between 0 and 1 and can be interpreted as intuitively as residuals from a linear regression. The package also provides a number of plot and test functions for typical model misspecification problems, such as over/underdispersion, zero-inflation, and residual spatial, temporal and phylogenetic autocorrelation. \n \n \n" editor_options: chunk_output_type: console --- ```{r global_options, include=FALSE} knitr::opts_chunk$set(fig.width=6.5, fig.height=4.5, fig.align='center', warning=FALSE, message=FALSE, cache = T) ``` ```{r, echo = F, message = F} library(DHARMa) set.seed(123) ``` # Motivation The interpretation of conventional residuals for generalized linear (mixed) and other hierarchical statistical models is often problematic. As an example, here the result of conventional Deviance, Pearson and raw residuals for two Poisson GLMMs, one that is lacking a quadratic effect, and one that fits the data perfectly. Could you tell which is the correct model? ```{r, echo = F, fig.width=6, fig.height=3} library(lme4) overdispersedData = createData(sampleSize = 250, overdispersion = 0, quadraticFixedEffects = -2, family = poisson()) fittedModelOverdispersed <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = overdispersedData) plotConventionalResiduals(fittedModelOverdispersed) testData = createData(sampleSize = 250, intercept = 0, overdispersion = 0, family = poisson(), randomEffectVariance = 0) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = testData) plotConventionalResiduals(fittedModel) ``` Just for completeness - it was the second one. But don't get too excited if you got it right. Probably you were just lucky - I can't really tell a difference. But even so, would you have added a quadratic effect, instead of adding an overdispersion correction? The point here is that misspecifications in GL(M)Ms cannot reliably be diagnosed with standard residual plots, and thus GLMMs are often not as thoroughly checked as they should. One reason why GL(M)Ms residuals are harder to interpret is that the expected distribution of the data (aka predictive distribution) changes with the fitted values. Reweighting with the expected dispersion, as done in Pearson residuals, or using deviance residuals, helps to some extent, but it does not lead to visually homogenous residuals, even if the model is correctly specified. As a result, standard residual plots, when interpreted in the same way as for linear models, seem to show all kind of problems, such as non-normality, heteroscedasticity, even if the model is correctly specified. Questions on the R mailing lists and forums show that practitioners are regularly confused about whether such patterns in GL(M)M residuals are a problem or not. But even experienced statistical analysts currently have few options to diagnose misspecification problems in GLMMs. In my experience, the current standard practice is to eyeball the residual plots for major misspecifications, potentially have a look at the random effect distribution, and then run a test for overdispersion, which is usually positive, after which the model is modified towards an overdispersed / zero-inflated distribution. This approach, however, has a number of drawbacks, notably: - Overdispersion is often the result of missing predictors or a misspecified model structure. Standard residual plots make it difficult to identify these problems by examining residual correlations or patterns of residuals against predictors. - Not all overdispersion is the same. For count data, the negative binomial creates a different distribution than adding observation-level random effects to the Poisson. Once overdispersion is corrected for, such violations of distributional assumptions are not detectable with standard overdispersion tests (because the tests only looks at total dispersion), and nearly impossible to see visually from standard residual plots. - Dispersion frequently varies with predictors (heteroscedasticity). This can have a significant effect on the inference. While it is standard to tests for heteroscedasticity in linear regressions, heteroscedasticity is currently hardly ever tested for in GLMMs, although it is likely as frequent and influential. - Moreover, if residuals are checked, they are usually checked conditional on the fitted random effect estimates. Thus, standard checks only check the final level of the random structure in a GLMM. One can perform extra checks on the random effects, but it is somewhat unsatisfactory that there is no check on the entire model structure. DHARMa aims at solving these problems by creating readily interpretable residuals for generalized linear (mixed) models that are standardized to values between 0 and 1, and that can be interpreted as intuitively as residuals for the linear model. This is achieved by a simulation-based approach, similar to the Bayesian p-value or the parametric bootstrap, that transforms the residuals to a standardized scale. The basic steps are: 1. Simulate new response data from the fitted model for each observation. 2. For each observation, calculate the empirical cumulative density function for the simulated observations, which describes the possible values (and their probability) at the predictor combination of the observed value, assuming the fitted model is correct. 3. The residual is then defined as the value of the empirical density function at the value of the observed data, so a residual of 0 means that all simulated values are larger than the observed value, and a residual of 0.5 means half of the simulated values are larger than the observed value. These steps are visualized in the following figure The key advantage of this definition is that the so-defined residuals always have the same, known distribution, independent of the model that is fit, if the model is correctly specified. To see this, note that, if the observed data was created from the same data-generating process that we simulate from, all values of the cumulative distribution should appear with equal probability. That means we expect the distribution of the residuals to be flat, regardless of the model structure (Poisson, binomial, random effects and so on). I currently prepare a more exact statistical justification for the approach in an accompanying paper, but if you must provide a reference in the meantime, I would suggest citing - Dunn, K. P., and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics 5, 1-10. - Gelman, A. & Hill, J. Data analysis using regression and multilevel/hierarchical models Cambridge University Press, 2006 p.s.: DHARMa stands for "Diagnostics for HierArchical Regression Models" - which, strictly speaking, would make DHARM. But in German, Darm means intestines; plus, the meaning of DHARMa in Hinduism makes the current abbreviation so much more suitable for a package that tests whether your model is in harmony with your data: > From Wikipedia, 28/08/16: In Hinduism, dharma signifies behaviours that are considered to be in accord with rta, the order that makes life and universe possible, and includes duties, rights, laws, conduct, virtues and 'right way of living'. # Workflow in DHARMa ## Installing, loading and citing the package If you haven't installed the package yet, either run ```{r, eval = F} install.packages("DHARMa") ``` Or follow the instructions on to install a development version. Loading and citation ```{r} library(DHARMa) citation("DHARMa") ``` ## Calculating scaled residuals Let's assume we have a fitted model that is supported by DHARMa. ```{r} testData = createData(sampleSize = 250) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = testData) ``` Most functions in DHARMa can be calculated directly on the fitted model object. For example, if you are only interested in testing for dispersion problems, you could run ```{r, results = "hide", fig.show='hide'} testDispersion(fittedModel) ``` In this case, the randomized quantile residuals are calculated on the fly inside the function call. If you work in this way, however, residual calculation will be repeated by every test / plot you call, and this can take a while. It is therefore highly recommended to first calculate the residuals once, using the simulateResiduals() function ```{r} simulationOutput <- simulateResiduals(fittedModel = fittedModel, plot = F) ``` which calculates randomized quantile residuals according to the algorithm discussed above. The function returns an object of class DHARMa, containing the simulations and the scaled residuals, which can later be passed on to all other plots and test functions. When specifying the optional argument plot = T, the standard DHARMa residual plot is displayed directly. The interpretation of the plot will be discussed below. Using the simulateResiduals function has the added benefit that you can modify the way in which residuals are calculated. For example, you may want to change the number of simulations, or the REs to condition on. See ?simulateResiduals and section "simulation options" below for details. The calculated (scaled) residuals can be plotted and tested via a number of DHARMa functions (see below), or accessed directly via ```{r, results = "hide"} residuals(simulationOutput) ``` To interpret the residuals, remember that a scaled residual value of 0.5 means that half of the simulated data are higher than the observed value, and half of them lower. A value of 0.99 would mean that nearly all simulated data are lower than the observed value. The minimum/maximum values for the residuals are 0 and 1. For a correctly specified model we would expect asymptotically - a uniform (flat) distribution of the scaled residuals - uniformity in y direction if we plot against any predictor. Note: the uniform distribution is the only differences to "conventional" residuals as calculated for a linear regression. If you cannot get used to this, you can transform the uniform distribution to another distribution, for example normal, via ```{r, eval = F} residuals(simulationOutput, quantileFunction = qnorm, outlierValues = c(-7,7)) ``` These normal residuals will behave exactly like the residuals of a linear regression. However, for reasons of a) numeric stability with low number of simulations, which makes it neccessary to descide on which value outliers are to be transformed and b) my conviction that it is much easier to visually detect deviations from uniformity than normality, DHARMa checks all residuals in the uniform space, and I would personally advice against using the transformation. ## Plotting the scaled residuals The main plot function for the calculated DHARMa object produced by simulateResiduals() is the plot.DHARMa() function ```{r} plot(simulationOutput) ``` The function creates two plots, which can also be called separately, and provide extended explanations / examples in the help ```{r, eval = F} plotQQunif(simulationOutput) # left plot in plot.DHARMa() plotResiduals(simulationOutput) # right plot in plot.DHARMa() ``` - plotQQunif (left panel) creates a qq-plot to detect overall deviations from the expected distribution, by default with added tests for correct distribution (KS test), dispersion and outliers. Note that outliers in DHARMa are values that are by default defined as values outside the simulation envelope, not in terms of a particular quantile. Thus, which values will appear as outliers will depend on the number of simulations. If you want outliers in terms of a particuar quantile, you can use the outliers() function. - plotResiduals (right panel) produces a plot of the residuals against the predicted value (or alternatively, other variable). Simulation outliers (data points that are outside the range of simulated values) are highlighted as red stars. These points should be carefully interpreted, because we actually don't know "how much" these values deviate from the model expectation. Note also that the probability of an outlier depends on the number of simulations, so whether the existence of outliers is a reason for concern depends also on the number of simulations. To provide a visual aid in detecting deviations from uniformity in y-direction, the plot function calculates an (optional default) quantile regression, which compares the empirical 0.25, 0.5 and 0.75 quantiles in y direction (red solid lines) with the theoretical 0.25, 0.5 and 0.75 quantiles (dashed black line), and provides a p-value for the deviation from the expected quantile. The significance of the deviation to the expected quantiles is tested and displayed visually, and can be additionally extracted with the testQuantiles function. By default, plotResiduals plots against predicted values. However, you can also use it to plot residuals against a specific other predictors (highly recommend). ```{r, eval = F} plotResiduals(simulationOutput, form = YOURPREDICTOR) ``` If the predictor is a factor, or if there is just a small number of observations on the x axis, plotResiduals will plot a box plot with additional tests instead of a scatter plot. ```{r, eval = F} plotResiduals(simulationOutput, form = testData$group) ``` See ?plotResiduas for details, but very shortly: under H0 (perfect model), we would expect those boxes to range homogeneously from 0.25-0.75. To see whether there are deviations from this expecation, the plot calculates a test for uniformity per box, and a test for homogeneity of variances between boxes. A positive test will be highlighted in red. ## Goodness-of-fit tests on the scaled residuals To support the visual inspection of the residuals, the DHARMa package provides a number of specialized goodness-of-fit tests on the simulated residuals: - testUniformity() - tests if the overall distribution conforms to expectations. - testOutliers() - tests if there are more simulation outliers than expected. - testDispersion() - tests if the simulated dispersion is equal to the observed dispersion. - testQuantiles() - fits a quantile regression or residuals against a predictor (default predicted value), and tests of this conforms to the expected quantile. - testCategorical(simulationOutput, catPred = testData\$group) tests residuals against a categorical predictor. - testZeroinflation() - tests if there are more zeros in the data than expected from the simulations. - testGeneric() - test if a generic summary statistics (user-defined) deviates from model expectations. - testTemporalAutocorrelation() - tests for temporal autocorrelation in the residuals. - testSpatialAutocorrelation() - tests for spatial autocorrelation in the residuals. Can also be used with a generic distance function. - testPhylogeneticAutocorrelation() - tests for phylogenetic signal in the residuals. See the help of the functions and further comments below for a more detailed description. ## Simulation options There are a few important technical details regarding how the simulations are performed, in particular regarding the treatments of random effects and integer responses. It is strongly recommended to read the help of ```{r, eval = F} ?simulateResiduals ``` #### Refit ```{r, eval= F} simulationOutput <- simulateResiduals(fittedModel = fittedModel, refit = T) ``` - if refit = F (default), new datasets are simulated from the fitted model, and residuals are calculated by comparing the observed data to the new data - if refit = T, a parametric bootstrap is performed, meaning that the model is refit to all new datasets, and residuals are created by comparing observed residuals against refitted residuals The second option is much much slower, and also seemed to have lower power in some tests I ran. **It is therefore not recommended for standard residual diagnostics!** I only recommend using it if you know what you are doing, and have particular reasons, for example if you estimate that the tested model is biased. A bias could, for example, arise in small data situations, or when estimating models with shrinkage estimators that include a purposeful bias, such as ridge/lasso, random effects or the splines in GAMs. My idea was then that simulated data would not fit to the observations, but that residuals for model fits on simulated data would have the same patterns/bias than model fits on the observed data. Note also that refit = T can sometimes run into numerical problems, if the fitted model does not converge on the newly simulated data. #### Conditinal vs. unconditinal simulations The second option is the treatment of the stochastic hierarchy. In a hierarchical model, several layers of stochasticity are placed on top of each other. Specifically, in a GLMM, we have a lower level stochastic process (random effect), whose result enters into a higher level (e.g. Poisson distribution). For other hierarchical models, such as state-space models, similar considerations apply, but the hierarchy can be more complex. When simulating, we have to decide if we want to re-simulate all stochastic levels, or only a subset of those. For example, in a GLMM, it is common to only simulate the last stochastic level (e.g. Poisson) conditional on the fitted random effects, meaning that the random effects are set on the fitted values. For controlling how many levels should be re-simulated, the simulateResidual function allows to pass on parameters to the simulate function of the fitted model object. Please refer to the help of the different simulate functions (e.g. ?simulate.merMod) for details. For merMod (lme4) model objects, the relevant parameters are "use.u", and "re.form", as, e.g., in ```{r, eval= F} simulationOutput <- simulateResiduals(fittedModel = fittedModel, n = 250, use.u = T) ``` If the model is correctly specified and the fitting procedure is unbiased (disclaimer: GLMM estimators are not always unbiased), the simulated residuals should be flat regardless how many hierarchical levels we re-simulate. The most thorough procedure would be therefore to test all possible options. If testing only one option, I would recommend to re-simulate all levels, because this essentially tests the model structure as a whole. This is the default setting in the DHARMa package. A potential drawback is that re-simulating the random effects creates more variability, which may reduce power for detecting problems in the upper-level stochastic processes, in particular overdispersion (see section on dispersion tests below). *Note:* Although unconditional residuals implicitly also test the normal distribution of the REs, it is probably not a bad idea to look addditionally check for normality of the RE distribution. As this is not based on quantile residuals, there is no special DHARMa function for this, so you should just extract the REs, and then run e.g. a Shapiro test. #### Integer treatment / randomization A third option is the treatment of integer responses. The background of this option is that, for integer-valued variables, some additional steps are necessary to make sure that the residual distribution becomes flat (essentially, we have to smoothen away the integer nature of the data). The idea is explained in - Dunn, K. P., and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics 5, 1-10. DHARMa currently implements two procedures for randomization. The default procedure will randomize automatically. The second option requires knowledge about whether the model is integer-valued, which is usually implemented automatically. See ?simulateResiduals for details. Usually, these options should simply be kept at their defaults. #### Calculating residuals for groups or subsets In many situations, it can be useful to look at residuals per group, e.g. to see how much the model over / underpredicts per plot, year or subject. To do this, use the recalculateResiduals() function, together with a grouping variable (group) or a subsetting variable (sel), which can also be used in combination. ```{r, eval= F} simulationOutput = recalculateResiduals(simulationOutput, group = testData$group) ``` Note, however, that you will have to change the selection of variables that you provide to plots and tests (e.g. in plotResiduals or testSpatialAutocorrelation) accordingly when you group or subset residuals. #### Reproducibility notes, random seed and random state As DHARMa uses simulations to calculate the residuals, a naive implementation of the algorithm would mean that residuals would look slightly different each time a DHARMa calculation is executed. This might both be confusing and bear the danger that a user would run the simulation several times and take the result that looks better (which would amount to multiple testing / p-hacking). By default, DHARMa therefore fixes the random seed to the same value every time a simulation is run, and afterwards restores the random state to the old value. This means that you will get exactly the same residual plot each time. If you want to avoid this behavior, for example for simulation experiments on DHARMa, use seed = NULL -\> no seed set, but random state will be restored, or seed = F -\> no seed set, and random state will not be restored. Whether or not you fix the seed, the setting for the random seed and the random state are stored in ```{r, eval = F} simulationOutput$randomState ``` If you want to reproduce simulations for such a run, set the variable .Random.seed by hand, and simulate with seed = NULL. Moreover (general advice), to ensure reproducibility, it's advisable to add a set.seed() at the beginning, and a session.info() at the end of your script. The latter will list the version number of R and all loaded packages. # Interpreting residuals and recognizing misspecification problems ## General remarks on interperting residual patterns and tests So far, all shown DHARMa results were calculated for a correctly specified model, resulting in "perfect" residual plots and diagnostics. In this section, we discuss how to recognize and interpret diagnostics that indicate a misspecified model. Before going into the details, note, however, that 1. **No residual pattern does not "prove" that the model is correct**: The fact that none of the DHARMa tests indicate a problem does not "prove" that the model is correctly specified. For any model, there are likely a large number of structural problems that do not create a pattern in the DHARMa diagnostics. In good old Popper fashion, you should interpret no residual problems as your working hypothesis not being rejected in that particular test, which increases confidence in the model, but does not constitute a conclusive proof. So, keep your skepticism alive, and if you find the results fishy, keep searching and testing. 2. **Once a residual effect is statistically significant, look at the magnitude to decide if there is a problem**: It is crucial to note that significance is NOT a measure of the strength of the residual pattern, it is a measure of the signal/noise ratio, i.e. whether you are sure there is a pattern at all. Significance in hypothesis tests depends on at least 2 ingredients: the strength of the signal and the number of data points. If you have a lot of data points, residual diagnostics will nearly inevitably become significant, because having a perfectly fitting model is very unlikely. That, however, doesn't necessarily mean that you need to change your model. The p-values confirm that there is a deviation from your null hypothesis. It is, however, in your discretion to decide whether this deviation is worth worrying about. For example, if you see a dispersion parameter of 1.01, I would not worry, even if the dispersion test is significant. A significant value of 5, however, is clearly a reason to move to a model that accounts for overdispersion. 3. **A residual pattern does not indicate that the model is unusable**: While a significant pattern in the residuals indicates with good reliability that the observed data did likely not originate from the fitted model, this doesn't necessarily imply that the inferential results from this wrong model are not usable. There are many situations in statistics where it is common practice to work with "wrong models". For example, many statistical models use shrinkage estimators, which purposefully bias parameter estimates to certain values. Random effects are a special case of this. If DHARMa residuals for these estimators are calculated, they will often show a slight pattern in the residuals even if the model is correctly specified, and tests for this can get significant for large sample sizes. For this reason, DHARMa is excluding RE estimates in the predictions when plotting res \~ pred. Another example is data that is missing at random (MAR). Since it is known that this phenomenon does not create a bias on the fixed effects estimates, it is common practice to fit these data with standard mixed models. Nevertheless, DHARMa recognizes that the observed data looks different from what would be expected from the model assumptions, and flags the model as problematic (see [here](https://github.com/florianhartig/DHARMa/issues/101)). **Important conclusion: DHARMa only flags a difference between the observed and expected data - the user has to decide whether this difference is actually a problem for the analysis!** ## Recognizing over/underdispersion GL(M)Ms often display over/underdispersion, which means that residual variance is larger/smaller than expected under the fitted model. This phenomenon is most common for GLM families with constant (fixed) dispersion, in particular for Poisson and binomial models, but it can also occur in GLM families that adjust the variance (such as the beta or negative binomial) when distribution assumptions are violated. A few general rules of thumb about dealing with dispersion problems: - Dispersion is a property of the residuals, i.e. you can detect dispersion problems only AFTER fitting the model. It doesn't make sense to look at the dispersion of your response variable - Overdispersion is more common than underdispersion - If overdispersion is present, the main effect is that confidence intervals tend to be too narrow, and p-values to small, leading to inflated type I error. The opposite is true for underdispersion, i.e. the main issue of underdispersion is that you loose power. - A common reason for overdispersion is a misspecified model. When overdispersion is detected, one should therefore first search for problems in the model specification (e.g. by plotting residuals against predictors with DHARMa), and only if this doesn't lead to success, overdispersion corrections such as individual-level random effects or changes in the distribution should be applied ### Residual patterns of over/underdispersion This this is how **overdispersion** looks like in the DHARMa residuals. Note that we get more residuals around 0 and 1, which means that more residuals are in the tail of distribution than would be expected under the fitted model. ```{r} testData = createData(sampleSize = 200, overdispersion = 1.5, family = poisson()) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` If you see this pattern, note that overdispersion is often caused by model misfit. Thus, before moving to a GLM with variable dispersion (for count data this would typically be a negative binomial), you should check your model for misfit, e.g. by plotting residuals against all predictors using plotResiduals(). Next, this is an example of underdispersion. Here, we get too many residuals around 0.5, which means that we are not getting as many residuals as we would expect in the tail of the distribution than expected from the fitted model. ```{r} testData = createData(sampleSize = 500, intercept=0, fixedEffects = 2, overdispersion = 0, family = poisson(), roundPoissonVariance = 0.001, randomEffectVariance = 0) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` If you see this pattern, note that a common reason for underdispersion is overfitting, i.e. your model is too complex. Other possible explanations to check for include zero-inflation (best to check by comparing to a ZIP model, but see also DHARMa::testZeroInflation), non-independence of the data (e.g. temporal autocorrelation, check via DHARMa:: testTemporalAutocorrelation) that your predictors can use to overfit, or that your data-generating process is simply not a Poisson process. From a technical side, underdispersion is not as concerning as over dispersion, as it will usually bias p-values to the conservative side, but if your goal is to get a good power, you may want to consider a simpler model. If that is not helping, you can move to a distribution for underdispersed count data (e.g. Conway-Maxwell-Poisson, generalized Poisson). ### Formal tests for over/underdispersion Although, as discussed above, over/underdispersion will show up in the residuals, and it's possible to detect it with the testUniformity function, simulations show that this test is less powerful than more targeted tests. DHARMa contains several overdispersion tests that compare the dispersion of simulated residuals to the observed residuals. 1. *default:* a non-parametric test that compares the variance of the simulated residuals to the observed residuals (default), which has some analogy to the variance test implemented in aer::dispersiontest 2. *PearsonChisq:* alternatively, DHARMa implements the Pearson-chi2 test that is popular in the literature, suggested in the glmm Wiki, and implemented in some other R packages such as performance::check_overdispersion 3. *refit* if residual simulations are done via refit, DHARMa will compare the the Pearson residuals of the re-fitted simulations to the original Pearson residuals. This is essentially a nonparametric version of test 2. All of these tests are included in the testDispersion function, see ?testDispersion for details. ```{r overDispersionTest, echo = T, fig.width=4, fig.height=4} testDispersion(simulationOutput) ``` IMPORTANT INFO: we have made extensive simulations, which have shown that the various tests have certain advantages and disadvantages. The basic results are that: - The most powerful and reliable test is option 3, but this costs a lot of time and is not available for all regression packages, as it requires that Pearson residuals are available - Option 2, the parametric Pearson-chi2 is fast if Pearson residuals are available, but based on a naive expectation of df (counts RE as 1 df) and the test statistic is thus biased towards underdispersion for mixed models. Similar to the df approximation, Bias increasing with the number of RE levels. When testing only for overdispersion (alternative = "greater"), this makes the test more conservative, but it also costs power. - The DHARMa default option 1 is fast, nearly unbiased (i.e. you can test under and overdispersion), and only slightly less powerful as test 3, PROVIDED that simulations are made conditional on the fitted REs. Note that the latter is not the DHARMa default, so you have to actively request conditional simulations, e.g. for lme4 by specifying re.form = NULL. Power compared to the parametric Pearson-chi2 test depends on the number of RE levels, it will be more powerful for typical number of RE levels. As support for these statements, here results of the simulation, which compares the uniform (KS) test with the standard simuation-based test (conditional and unconditional) and the Pearson-chi2 test (two-sided and greater) for an n=200 Poisson GLMM with 30 RE levels. Thus, my current recommendation is: for most users, use the default DHARMa test, but create simulations conditionally. ## Zero-inflation / k-inflation or deficits A common special case of overdispersion is zero-inflation, which is the situation when more zeros appear in the observation than expected under the fitted model. Zero-inflation requires special correction steps. More generally, we can also have too few zeros, or too much or too few of any other values. We'll discuss that at the end of this section. ### Residual patterns Here an example of a typical zero-inflated count dataset, plotted against the environmental predictor ```{r} testData = createData(sampleSize = 500, intercept = 2, fixedEffects = c(1), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3), randomEffectVariance = 0, pZeroInflation = 0.6) par(mfrow = c(1,2)) plot(testData$Environment1, testData$observedResponse, xlab = "Envrionmental Predictor", ylab = "Response") hist(testData$observedResponse, xlab = "Response", main = "") ``` We see a hump-shaped dependence of the environment, but with too many zeros. In the normal DHARMa residual plots, zero-inflation will look pretty much like overdispersion ```{r, fig.height=5.5} fittedModel <- glmer(observedResponse ~ Environment1 + I(Environment1^2) + (1|group) , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` The reason is that the model will usually try to find a compromise between the zeros, and the other values, which will lead to excess variance in the residuals. ### Formal tests for zero-inflation DHARMa also has a special test for zero-inflation, which compares the distribution of expected zeros in the data against the observed zeros ```{r, fig.width=4, fig.height=4} testZeroInflation(simulationOutput) ``` This test is likely better suited for detecting zero-inflation than the standard plot, but note that also overdispersion will lead to excess zeros, so only seeing too many zeros is not a reliable diagnostics for moving towards a zero-inflated model. A reliable differentiation between overdispersion and zero-inflation will usually only be possible when directly comparing alternative models, e.g. through residual comparison / model selection of a model with / without zero-inflation, or by simply fitting a model with zero-inflation and looking at the parameter estimate for the zero-inflation. A good option is the R package glmmTMB, which is also supported by DHARMa. We can use this to fit ```{r, eval= F} # requires glmmTMB fittedModel <- glmmTMB(observedResponse ~ Environment1 + I(Environment1^2) + (1|group), ziformula = ~1 , family = "poisson", data = testData) summary(fittedModel) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` ### Testing generic summary statistics, e.g. for k-inflation or deficits To test for generic excess / deficits of particular values, we have the function testGeneric, which compares the values of a generic, user-provided summary statistics Choose one of alternative = c("greater", "two.sided", "less") to test for inflation / deficit or both. Default is "greater" = inflation. ```{r, fig.width=4.5, fig.height=4.5} countOnes <- function(x) sum(x == 1) # testing for number of 1s testGeneric(simulationOutput, summary = countOnes, alternative = "greater") # 1-inflation ``` ## Heteroscedasticity So far, most of the things that we have tested could also have been detected with parametric tests. Here, we come to the first issue that is difficult to detect with current tests, and that is usually neglected. Heteroscedasticity means that there is a systematic dependency of the dispersion / variance on another variable in the model. It is not sufficiently appreciated that also binomial or Poisson models can show heteroscedasticity. Basically, it means that the level of over/underdispersion depends on another parameter. Here an example where we create such data ```{r} testData = createData(sampleSize = 500, intercept = -1.5, overdispersion = function(x){return(rnorm(length(x), sd = 1 * abs(x)))}, family = poisson(), randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` The exact p-values for the quantile lines in the plot can be displayed via ```{r, eval = F} testQuantiles(simulationOutput) ``` As mentioned above, the equivalent test for categorical predictors (plot function will switch automatically) would be ```{r, eval = F} testCategorical(simulationOutput, catPred = testData$group) ``` Adding a simple overdispersion correction will try to find a compromise between the different levels of dispersion in the model. The qq plot looks better now, but there is still a pattern in the residuals ```{r} testData = createData(sampleSize = 500, intercept = 0, overdispersion = function(x){return(rnorm(length(x), sd = 2*abs(x)))}, family = poisson(), randomEffectVariance = 0) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) + (1|ID), family = "poisson", data = testData) # plotConventionalResiduals(fittedModel) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ``` To remove this pattern, you would need to make the dispersion parameter dependent on a predictor (e.g. in JAGS), or apply a transformation on the data. ## Detecting missing predictors or wrong functional assumptions A second test that is typically run for LMs, but not for GL(M)Ms is to plot residuals against the predictors in the model (or potentially predictors that were not in the model) to detect possible misspecifications. Doing this is *highly recommended*. For that purpose, you can retrieve the residuals via ```{r, eval = F} simulationOutput$scaledResiduals ``` Note again that the residual values are scaled between 0 and 1. If you plot the residuals against predictors, space or time, the resulting plots should not only show no systematic dependency of those residuals on the covariates, but they should also again be flat for each fixed situation. That means that if you have, for example, a categorical predictor: treatment / control, the distribution of residuals for each predictor alone should be flat as well. Here an example with a missing quadratic effect in the model and 2 predictors ```{r} testData = createData(sampleSize = 200, intercept = 1, fixedEffects = c(1,2), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3,0)) fittedModel <- glmer(observedResponse ~ Environment1 + Environment2 + (1|group), family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # plotConventionalResiduals(fittedModel) plot(simulationOutput, quantreg = T) # testUniformity(simulationOutput = simulationOutput) ``` It is difficult to see that there is a problem at all in the general plot, but it becomes clear if we plot against the environment ```{r} par(mfrow = c(1,2)) plotResiduals(simulationOutput, testData$Environment1) plotResiduals(simulationOutput, testData$Environment2) ``` ## Residual correlation structures (temporal, spatial, phylogenetic) If a distance between residuals can be defined (temporal, spatial, phylogenetic), you should check if there is a distance-dependence in the residuals, which would suggest to move to a GLS (generalized least squares) structure for analysis. The three functions to test for this in DHARMa are: - testTemporalAutocrrelation based on the Durbin-Watson test. - testSpatialAutocorrelation, based on Moran's I, can also be used for generic distance functions. - testPhylogeneticAutocorrelation, based on Moran's I test from `Moran.I` function on package `ape`. Here a short example for the spatial case, see help of the functions for extended examples. ```{r, fig.width=4, fig.height=4} testData = createData(sampleSize = 100, family = poisson(), spatialAutocorrelation = 3, numGroups = 1, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , data = testData, family = poisson() ) simulationOutput <- simulateResiduals(fittedModel = fittedModel) testSpatialAutocorrelation(simulationOutput = simulationOutput, x = testData$x, y= testData$y) # plot(simulationOutput) ``` Note that all these tests are most sensitive against homogeneous residual structure, and might miss local and heterogeneous (non-stationary) residual structures. Additional visual checks can be useful. However, standard DHARMa simulations from models with temporal / spatial / phylogenetic conditional autoregressive terms will still have the respective correlation in the DHARMa residuals, unless the package you are using is modelling the autoregressive terms as explicit REs and is able to simulate conditional on the fitted REs. It means that the residuals will still show significant autocorrelation, even if the model fully accounts for this strucuture, and other tests, such as dispersion, uniformity, may have inflated type I error. See the example below with a `glmmTMB` model with a spatial autocorrelation structure: ```{r, fig.width=4, fig.height=4} library(glmmTMB) testData$pos <- numFactor(testData$x, testData$y) fittedModel2 <- glmmTMB(observedResponse ~ Environment1 + exp(pos + 0|group), data = testData, family = poisson()) simulationOutput2 <- simulateResiduals(fittedModel = fittedModel2) testSpatialAutocorrelation(simulationOutput = simulationOutput2, x = testData$x, y= testData$y) # plot(simulationOutput2) ``` One of the options to solve it and get correct tests and no residual pattern (if the model is correct) is to rotate the residual space according to the coariance structure of the fitted model, such that the rotated residuals are conditionally independent. The argument rotation in `simulateResiduals` does it (see also `?getQuantile` for details about the rotation options): ```{r, fig.width=4, fig.height=4} # rotation of the residuals simulationOutput3 <- simulateResiduals(fittedModel = fittedModel2, rotation = "estimated") testSpatialAutocorrelation(simulationOutput = simulationOutput3, x = testData$x, y= testData$y) # plot(simulationOutput3) ``` # Case studies and examples **Note:** More real-world examples can be found on the DHARMa GitHub repository. ## Budworm example (count-proportion n/k binomial) This example comes from [Jochen Fruend](https://jochenfruend.wordpress.com/). Measured are the number of parasitized observations, with population density as a covariate: ```{r, echo = F} data = structure(list(N_parasitized = c(226, 689, 481, 960, 1177, 266, 46, 4, 884, 310, 19, 4, 7, 1, 3, 0, 365, 388, 369, 829, 532, 5), N_adult = c(1415, 2227, 2854, 3699, 2094, 376, 8, 1, 1379, 323, 2, 2, 11, 2, 0, 1, 1394, 1392, 1138, 719, 685, 3), density.attack = c(216.461273226486, 214.662143448767, 251.881252132684, 400.993643475831, 207.897856251888, 57.0335141562012, 6.1642552100285, 0.503930659141302, 124.673812637575, 27.3764667492035, 0.923453215863429, 0.399890030241684, 0.829818131526174, 0.146640466903247, 0.216795117773948, 0.215498663908284, 110.635445098884, 91.3766566822467, 126.157080458047, 82.9699108890686, 61.0476207779938, 0.574539291305784), Plot = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L ), .Label = c("1", "2", "3", "4"), class = "factor"), PY = c("p1y82", "p1y83", "p1y84", "p1y85", "p1y86", "p1y87", "p1y88", "p1y89", "p2y86", "p2y87", "p2y88", "p2y89", "p2y90", "p2y91", "p2y92", "p2y93", "p3y88", "p3y89", "p3y90", "p3y91", "p3y92", "p3y93" ), Year = c(82, 83, 84, 85, 86, 87, 88, 89, 86, 87, 88, 89, 90, 91, 92, 93, 88, 89, 90, 91, 92, 93), ID = 1:22), .Names = c("N_parasitized", "N_adult", "density.attack", "Plot", "PY", "Year", "ID"), row.names = c("p1y82", "p1y83", "p1y84", "p1y85", "p1y86", "p1y87", "p1y88", "p1y89", "p2y86", "p2y87", "p2y88", "p2y89", "p2y90", "p2y91", "p2y92", "p2y93", "p3y88", "p3y89", "p3y90", "p3y91", "p3y92", "p3y93" ), class = "data.frame") data$logDensity = log10(data$density.attack+1) ``` ```{r, fig.height=4, fig.width=4} plot(N_parasitized / (N_adult + N_parasitized ) ~ logDensity, xlab = "Density", ylab = "Proportion infected", data = data) ``` Let's fit the data with a regular binomial n/k glm ```{r} mod1 <- glm(cbind(N_parasitized, N_adult) ~ logDensity, data = data, family=binomial) simulationOutput <- simulateResiduals(fittedModel = mod1) plot(simulationOutput) ``` We see various signals of overdispersion - QQ: s-shaped QQ plot, distribution test (KS) signficant - QQ: Dispersion test is significant - QQ: Outlier test significant - Res \~ predicted: Quantile fits are spread out too far OK, so let's add overdispersion through an individual-level random effect ```{r} mod2 <- glmer(cbind(N_parasitized, N_adult) ~ logDensity + (1|ID), data = data, family=binomial) simulationOutput <- simulateResiduals(fittedModel = mod2) plot(simulationOutput) ``` The overdispersion looks better, but you can see that the residuals still look a bit irregular (although tests are n.s.). The raw data looks a bit humped-shaped, so we might be tempted to add a quadratic effect. ```{r} mod3 <- glmer(cbind(N_parasitized, N_adult) ~ logDensity + I(logDensity^2) + (1|ID), data = data, family=binomial) simulationOutput <- simulateResiduals(fittedModel = mod3) plot(simulationOutput) ``` The residuals look perfect now. That being said, we dont' have a lot of data, and we have to be sure we're not overfitting. A likelihood ratio test tells us that the quadratic effect is not significantly supported. ```{r} anova(mod2, mod3) ``` Also AIC differences are small, although slightly in favor of model 3 ```{r} AIC(mod2) AIC(mod3) ``` I guess you could use either Model 2 or 3 - the broader point is: increasing model complexity will nearly always improve the residuals, but according to standard statistical arguments (power, bias-variance trade-off) it's not always advisable to get them perfect, just good enough! ## Owl example (count data) The next examples uses the fairly well known Owl dataset which is provided in glmmTMB (see ?Owls for more info about the data). The following shows a sequence of models, all checked with DHARMa. The example is discussed in a talk at ISEC 2018, see slides [here](https://www.slideshare.net/florianhartig/mon-c5hartig2493). ```{r, error=TRUE} library(glmmTMB) m1 <- glm(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)), data=Owls , family = poisson) res <- simulateResiduals(m1) plot(res) ``` OK, this is highly overdispersed. Let's add a RE on nest: ```{r, error=TRUE} m2 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), data=Owls , family = poisson) res <- simulateResiduals(m2) plot(res) ``` Somewhat better, but not good. Move to neg binom, to adjust dispersion, and checking dispersion and residuals against FoodTreatment predictor: ```{r, error=TRUE} m3 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), data=Owls , family = nbinom1) res <- simulateResiduals(m3, plot = T) par(mfrow = c(1,2)) testDispersion(res) plotResiduals(res, Owls$FoodTreatment) ``` We see underdispersion now. In a model with variable dispersion, this is often the signal that some other distributional assumptions are violated. Let's check for zero-inflation: ```{r, fig.height=4, fig.width=4} testZeroInflation(res) ``` It looks as if there is some zero-inflation, although non-significant. Fitting a zero-inflated model: ```{r, error=TRUE} m4 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), ziformula = ~ FoodTreatment + SexParent, data=Owls , family = nbinom1) res <- simulateResiduals(m4, plot = T) ``` ```{r, error=TRUE, fig.width=7} par(mfrow = c(1,3)) plotResiduals(res, Owls$FoodTreatment) testDispersion(res) testZeroInflation(res) ``` This looks a lot better. Trying a slightly different model specification, adding a dispersion model as well: ```{r, error=TRUE} m5 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), dispformula = ~ FoodTreatment + SexParent , ziformula = ~ FoodTreatment + SexParent, data=Owls , family = nbinom1) res <- simulateResiduals(m5, plot = T) ``` ```{r, error=TRUE, fig.width=7} par(mfrow = c(1,3)) plotResiduals(res, Owls$FoodTreatment) testDispersion(res) testZeroInflation(res) ``` but that does not seem to make things better. Both models would be acceptable in terms of their fit to the data. Which one should you prefer? This is not a question for residual checks. Residual checks tell you which models can be rejected with the data. Which of the typically many acceptable models you should fit must be decided by your scientific question, and/or possibly by model selection methods. In doubt, I would tend towards the simpler model though. # Notes on particular data types ## Poisson data The main concern in Poisson data is dispersion. See comments in the section on the dispersion test, in particular regarding the advantage of conditional simulations in this case. To address overdispersion, I would recommend to prefer the negative binomial model over observation-level random effects, because this mode will be easier to test in DHARMa and its dispersion can be easier modeled, e.g. with glmmTMB. The third option would be quasi models, but there are few advantages, except runtime. Note also that quasi models cannot be tested with DHARMa. Once dispersion is adjusted, you should check for heteroscedasticity (via standard plot, also against all predictors), and for zero-inflation. As noted, zero-inflation tests are often negative, and rather show up as underdispersion. Work through the owl example below. ## Proportional data Proportional data expressed as percentage or fractions of a whole, i.e. non-count-based data, is often modeled with beta regressions. Those can be tested with DHARMa. Note that beta regressions are often 0 or 1 inflated. Both should be tested with testZeroInflation or testGeneric. techniques for analysing continuous (also called non-count-based or non-binomial) proportions (e.g. percent cover, fraction time spent on an activity) Note: discrete proportions, i.e. count-based proportions, of the type k/n should NOT be modeled with the beta regression. Use the binomial (see below). ## Binomial data Binomial data behave slightly different depending on whether we have a 0/1 response (Bernoulli) or a k/n response (true binomial). A k/n response, in particular when n is large, will behave similar to the Poisson, in that it approaches a normal distribution with fixed dispersion for large n and becomes more assymetric at its borders (for k = 0 or n). You should check for dispersion and consider a beta-binomial in cases of overdispersion. Things are a bit different for the 0/1 response. Let's look at the residuals of a clearly misspecified binomial model (missing predictor) with 0/1 response data. ```{r} testData = createData(sampleSize = 500, overdispersion = 0, fixedEffects = 5, family = binomial(), randomEffectVariance = 3, numGroups = 25) fittedModel <- glm(observedResponse ~ 1, family = "binomial", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) ``` If you would do the same with a binomial k/n response or count data, such a misspecification would produce overdispersion (try it out). For the 0/1 response we see neither dispersion problems nor a misfit in the general res \~ predicted plot. ```{r} plot(simulationOutput, asFactor = T) ``` Even though the misfit is clearly visible if we plot the residuals against the missing predictor. ```{r, fig.width=4, fig.height=4} plotResiduals(simulationOutput, testData$Environment1, quantreg = T) ``` However, we can see the overdispersion arising from the misfit if we group our residuals, which basically transforms the 0/1 response in a k/n response. To show this, let's look at the dispersion test for the same model, once ungrouped (left), and grouped according to the variable group which was in the data (right). ```{r} par(mfrow = c(1,2)) testDispersion(simulationOutput) simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group) testDispersion(simulationOutput2) ``` In general, you can group according to any variable that you like, including continous variables or space. However, some variables make more sense than others. To understand this, consider a simulation where we create binonial data with true probabilities p, drawn from a uniform distribution: ```{r} n = 1000 p = runif(n, 0.1, 0.9) # true probabilities obs = rbinom(n, 1, p) ``` The important thing to note here is that `rbinom(n, 1, p)` will generate an identical overall distribution as `rbinom(1, n, mean(p))`. What that means: a misfit of the prediction will not show up unless they are wrong in the overall mean. Consequenly, if we fit: ```{r} fit <- glm(obs ~ 1, family = "binomial") # wrong model, assumes equal probabilities library(DHARMa) res <- simulateResiduals(fit, plot = T) # nothing to see ``` We see no misfit, and neither do we see a misfit when we group the data points randomly, as the mean of a random group is still fit well by the overall mean. ```{r} res2 <- recalculateResiduals(res, group = rep(1:20, each = 10)) plot(res2) ``` However, we see thes misfit / overdispersion if we aggregate according to something that is correlated to the misfit. For our example, let's just group according to the true means: ```{r} grouping = cut(p, breaks = quantile(p, seq(0,1,0.02))) res3 <- recalculateResiduals(res, group = grouping) plot(res3) ``` In this case, the groups have a different mean than the fitted grand mean, and the misfit shows up in the residuals. Thus, what we are looking for in the grouping is variables that may correlate with the misfit. If you don't have a natural grouping variable, you can introduce arbitrary grouping variables, e.g. via discretising a predictor or the response (usually preferable), and grouping according to that, or via discretising space (e.g. group observation in spatial blocks). The pattern appears only, however, if the grouping variable correlates with the model error. Consider the following example: We create data and fit a model with a missing predictor (Environment2): ```{r} set.seed(123) testData = createData(sampleSize = 500, overdispersion = 0, fixedEffects = c(0,3), family = binomial(), randomEffectVariance = 3, numGroups = 50) ``` Apparently, no problem with the residuals for the misfitted model: ```{r} res <- simulateResiduals(fittedModel = fittedModel) fittedModel <- glm(observedResponse ~ Environment1, family = "binomial", data = testData) plot(res) ``` 1. Grouping according to the RE produces overdispersion because RE is missing in the first model: ```{r} res2 = recalculateResiduals(res , group = testData$group) plot(res2) ``` 2. Grouping according to a random factor does not produce an effect. In this respect, the model has correct dispersion: ```{r} grouping = as.factor(sample.int(50, 500, replace = T)) res2 = recalculateResiduals(res , group = grouping) plot(res2) ``` 3. Grouping according to the response doesn't create a pattern: ```{r} x = predict(fittedModel) grouping = cut(x, breaks = quantile(x, seq(0,1,0.02))) res2 = recalculateResiduals(res , group = grouping) plot(res2) ``` 4. Grouping according to the missing variable creates pattern, because in relation to this variable, the model is overdispersed: ```{r} x = testData$Environment2 grouping = cut(x, breaks = quantile(x, seq(0,1,0.02))) res2 = recalculateResiduals(res , group = grouping) plot(res2) ``` 5. Grouping according to space does not create a pattern, because there is no missing spatial predictor: ```{r} x = testData$x grouping = cut(x, breaks = quantile(x, seq(0,1,0.02))) res3 = recalculateResiduals(res , group = grouping) plot(res3) ``` **Conclusions:** if you see overdispersion or a pattern after grouping, it highlights a model error that is structured by group. As the pattern usually highlights a model misfit, rather than a dispersion problem akin to what happens in an overdispersed binomial (which has major impacts on p-values and CIs), I view this binomial grouping pattern as less critical. Likely, most conclusions will not change if you ignore the problem. Nevertheless, you should try to understand the reason for it. When the group is spatial, it could be the sign of residual spatial autocorrelation which could be addressed by a spatial RE or a spatial model. When grouped by a continuous variable, it could be the sign of a nonlinear effect. # Supported packages and frameworks ## lm and glm lm and glm and MASS::glm.nb are fully supported. ## lme4 lme4 model classes are fully supported. Possible to condition on REs via re.form, see help of predict.merMod ## mgcv When using mgcv with DHARMa, it is highly recommended to also install mgcViz. Since version 0.4.5, this will allow DHARMa to fall back on the simulate.gam function in mgcViz, which is more general than the default simulate function. For example, without mgcViz, it will not be possible to simulate from mgcv::gam objects fitted with extended families. If you absolutely want to use DHARMa without mgcViz, you should make sure that simulate(model) works correctly for the model object for which you want to calculate DHARMa residuals. ## gamm4 Models fitted with gamm4 return a list that contains a lme4 object under the name "mer". You can test this object like an lme4 model, so e.g. simulateResiduals(myGamm4Model\$mer). All remarks regarding lme4 objects apply. ## glmmTMB glmmTMB is nearly fully supported since DHARMa 0.2.7 and glmmTMB 1.0.0. A remaining limitation is that you can't adjust whether simulation are conditional or not, so simulateResiduals(model, re.form = NULL) will have no effect, simulations will always be done from the full model. ## spaMM spaMM is supported by DHARMa since 0.2.1 ## GLMMadaptive GLMMadaptive is supported by DHARMa since 0.3.4. ## phylolm phylom (version \>= 2.6.5) is supported by DHARMa since 0.4.7 for both model classes phylolm and phyloglm. ## phyr DHARMa residuals work with phyr, but the correct implementation is not fully tested as of DHARMa 0.4.2. See also ## brms brms can be made to work together with DHARMa, see ## Unsupported packages If confronted with an unsupported package, DHARMa will try to use standard S3 functions such as coef(), simulate() etc. to perform simulations. If no error occurs, a residual object will be calculated, and a warning will be provided that this package has not been checked for full functionality. In many cases, the results can be used though (but no guarantee, maybe check with null simulations if the results are OK). Other than that, see my general comments about [adding new R packages to DHARMa](https://github.com/florianhartig/DHARMa/wiki/Adding-new-R-packages-to-DHARMA) ## Importing external simulations (e.g. from Bayesian software or unsupported packages) DHARMa can also import external simulations from a fitted model via createDHARMa(), which will be interesting for unsupported packages and for Bayesians. **Bayesians should note the extra Vignette on "DHARMa for Bayesians" regarding the interpretation of these residuals.** Here, an example for how to create simulations for a Poisson glm. Of course, it doesn't make sense to do this as glm is a supported model class, but you could do the same in case you want to check a model class that is currently not supported by DHARMa. ```{r, eval = T} testData = createData(sampleSize = 200, overdispersion = 0.5, family = poisson()) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulatePoissonGLM <- function(fittedModel, n){ pred = predict(fittedModel, type = "response") nObs = length(pred) sim = matrix(nrow = nObs, ncol = n) for(i in 1:n) sim[,i] = rpois(nObs, pred) return(sim) } sim = simulatePoissonGLM(fittedModel, 100) DHARMaRes = createDHARMa(simulatedResponse = sim, observedResponse = testData$observedResponse, fittedPredictedResponse = predict(fittedModel), integerResponse = T) plot(DHARMaRes, quantreg = F) ``` DHARMa/inst/doc/DHARMa.R0000644000176200001440000004362514704246641014131 0ustar liggesusers## ----global_options, include=FALSE-------------------------------------------- knitr::opts_chunk$set(fig.width=6.5, fig.height=4.5, fig.align='center', warning=FALSE, message=FALSE, cache = T) ## ----echo = F, message = F---------------------------------------------------- library(DHARMa) set.seed(123) ## ----echo = F, fig.width=6, fig.height=3-------------------------------------- library(lme4) overdispersedData = createData(sampleSize = 250, overdispersion = 0, quadraticFixedEffects = -2, family = poisson()) fittedModelOverdispersed <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = overdispersedData) plotConventionalResiduals(fittedModelOverdispersed) testData = createData(sampleSize = 250, intercept = 0, overdispersion = 0, family = poisson(), randomEffectVariance = 0) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = testData) plotConventionalResiduals(fittedModel) ## ----eval = F----------------------------------------------------------------- # install.packages("DHARMa") ## ----------------------------------------------------------------------------- library(DHARMa) citation("DHARMa") ## ----------------------------------------------------------------------------- testData = createData(sampleSize = 250) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = testData) ## ----results = "hide", fig.show='hide'---------------------------------------- testDispersion(fittedModel) ## ----------------------------------------------------------------------------- simulationOutput <- simulateResiduals(fittedModel = fittedModel, plot = F) ## ----results = "hide"--------------------------------------------------------- residuals(simulationOutput) ## ----eval = F----------------------------------------------------------------- # residuals(simulationOutput, quantileFunction = qnorm, outlierValues = c(-7,7)) ## ----------------------------------------------------------------------------- plot(simulationOutput) ## ----eval = F----------------------------------------------------------------- # plotQQunif(simulationOutput) # left plot in plot.DHARMa() # plotResiduals(simulationOutput) # right plot in plot.DHARMa() ## ----eval = F----------------------------------------------------------------- # plotResiduals(simulationOutput, form = YOURPREDICTOR) ## ----eval = F----------------------------------------------------------------- # plotResiduals(simulationOutput, form = testData$group) ## ----eval = F----------------------------------------------------------------- # ?simulateResiduals ## ----eval= F------------------------------------------------------------------ # simulationOutput <- simulateResiduals(fittedModel = fittedModel, refit = T) ## ----eval= F------------------------------------------------------------------ # simulationOutput <- simulateResiduals(fittedModel = fittedModel, n = 250, use.u = T) ## ----eval= F------------------------------------------------------------------ # simulationOutput = recalculateResiduals(simulationOutput, group = testData$group) ## ----eval = F----------------------------------------------------------------- # simulationOutput$randomState ## ----------------------------------------------------------------------------- testData = createData(sampleSize = 200, overdispersion = 1.5, family = poisson()) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ## ----------------------------------------------------------------------------- testData = createData(sampleSize = 500, intercept=0, fixedEffects = 2, overdispersion = 0, family = poisson(), roundPoissonVariance = 0.001, randomEffectVariance = 0) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ## ----overDispersionTest, echo = T, fig.width=4, fig.height=4------------------ testDispersion(simulationOutput) ## ----------------------------------------------------------------------------- testData = createData(sampleSize = 500, intercept = 2, fixedEffects = c(1), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3), randomEffectVariance = 0, pZeroInflation = 0.6) par(mfrow = c(1,2)) plot(testData$Environment1, testData$observedResponse, xlab = "Envrionmental Predictor", ylab = "Response") hist(testData$observedResponse, xlab = "Response", main = "") ## ----fig.height=5.5----------------------------------------------------------- fittedModel <- glmer(observedResponse ~ Environment1 + I(Environment1^2) + (1|group) , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ## ----fig.width=4, fig.height=4------------------------------------------------ testZeroInflation(simulationOutput) ## ----eval= F------------------------------------------------------------------ # # requires glmmTMB # fittedModel <- glmmTMB(observedResponse ~ Environment1 + I(Environment1^2) + (1|group), ziformula = ~1 , family = "poisson", data = testData) # summary(fittedModel) # # simulationOutput <- simulateResiduals(fittedModel = fittedModel) # plot(simulationOutput) ## ----fig.width=4.5, fig.height=4.5-------------------------------------------- countOnes <- function(x) sum(x == 1) # testing for number of 1s testGeneric(simulationOutput, summary = countOnes, alternative = "greater") # 1-inflation ## ----------------------------------------------------------------------------- testData = createData(sampleSize = 500, intercept = -1.5, overdispersion = function(x){return(rnorm(length(x), sd = 1 * abs(x)))}, family = poisson(), randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ## ----eval = F----------------------------------------------------------------- # testQuantiles(simulationOutput) ## ----eval = F----------------------------------------------------------------- # testCategorical(simulationOutput, catPred = testData$group) ## ----------------------------------------------------------------------------- testData = createData(sampleSize = 500, intercept = 0, overdispersion = function(x){return(rnorm(length(x), sd = 2*abs(x)))}, family = poisson(), randomEffectVariance = 0) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group) + (1|ID), family = "poisson", data = testData) # plotConventionalResiduals(fittedModel) simulationOutput <- simulateResiduals(fittedModel = fittedModel) plot(simulationOutput) ## ----eval = F----------------------------------------------------------------- # simulationOutput$scaledResiduals ## ----------------------------------------------------------------------------- testData = createData(sampleSize = 200, intercept = 1, fixedEffects = c(1,2), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3,0)) fittedModel <- glmer(observedResponse ~ Environment1 + Environment2 + (1|group), family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # plotConventionalResiduals(fittedModel) plot(simulationOutput, quantreg = T) # testUniformity(simulationOutput = simulationOutput) ## ----------------------------------------------------------------------------- par(mfrow = c(1,2)) plotResiduals(simulationOutput, testData$Environment1) plotResiduals(simulationOutput, testData$Environment2) ## ----fig.width=4, fig.height=4------------------------------------------------ testData = createData(sampleSize = 100, family = poisson(), spatialAutocorrelation = 3, numGroups = 1, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , data = testData, family = poisson() ) simulationOutput <- simulateResiduals(fittedModel = fittedModel) testSpatialAutocorrelation(simulationOutput = simulationOutput, x = testData$x, y= testData$y) # plot(simulationOutput) ## ----fig.width=4, fig.height=4------------------------------------------------ library(glmmTMB) testData$pos <- numFactor(testData$x, testData$y) fittedModel2 <- glmmTMB(observedResponse ~ Environment1 + exp(pos + 0|group), data = testData, family = poisson()) simulationOutput2 <- simulateResiduals(fittedModel = fittedModel2) testSpatialAutocorrelation(simulationOutput = simulationOutput2, x = testData$x, y= testData$y) # plot(simulationOutput2) ## ----fig.width=4, fig.height=4------------------------------------------------ # rotation of the residuals simulationOutput3 <- simulateResiduals(fittedModel = fittedModel2, rotation = "estimated") testSpatialAutocorrelation(simulationOutput = simulationOutput3, x = testData$x, y= testData$y) # plot(simulationOutput3) ## ----echo = F----------------------------------------------------------------- data = structure(list(N_parasitized = c(226, 689, 481, 960, 1177, 266, 46, 4, 884, 310, 19, 4, 7, 1, 3, 0, 365, 388, 369, 829, 532, 5), N_adult = c(1415, 2227, 2854, 3699, 2094, 376, 8, 1, 1379, 323, 2, 2, 11, 2, 0, 1, 1394, 1392, 1138, 719, 685, 3), density.attack = c(216.461273226486, 214.662143448767, 251.881252132684, 400.993643475831, 207.897856251888, 57.0335141562012, 6.1642552100285, 0.503930659141302, 124.673812637575, 27.3764667492035, 0.923453215863429, 0.399890030241684, 0.829818131526174, 0.146640466903247, 0.216795117773948, 0.215498663908284, 110.635445098884, 91.3766566822467, 126.157080458047, 82.9699108890686, 61.0476207779938, 0.574539291305784), Plot = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L ), .Label = c("1", "2", "3", "4"), class = "factor"), PY = c("p1y82", "p1y83", "p1y84", "p1y85", "p1y86", "p1y87", "p1y88", "p1y89", "p2y86", "p2y87", "p2y88", "p2y89", "p2y90", "p2y91", "p2y92", "p2y93", "p3y88", "p3y89", "p3y90", "p3y91", "p3y92", "p3y93" ), Year = c(82, 83, 84, 85, 86, 87, 88, 89, 86, 87, 88, 89, 90, 91, 92, 93, 88, 89, 90, 91, 92, 93), ID = 1:22), .Names = c("N_parasitized", "N_adult", "density.attack", "Plot", "PY", "Year", "ID"), row.names = c("p1y82", "p1y83", "p1y84", "p1y85", "p1y86", "p1y87", "p1y88", "p1y89", "p2y86", "p2y87", "p2y88", "p2y89", "p2y90", "p2y91", "p2y92", "p2y93", "p3y88", "p3y89", "p3y90", "p3y91", "p3y92", "p3y93" ), class = "data.frame") data$logDensity = log10(data$density.attack+1) ## ----fig.height=4, fig.width=4------------------------------------------------ plot(N_parasitized / (N_adult + N_parasitized ) ~ logDensity, xlab = "Density", ylab = "Proportion infected", data = data) ## ----------------------------------------------------------------------------- mod1 <- glm(cbind(N_parasitized, N_adult) ~ logDensity, data = data, family=binomial) simulationOutput <- simulateResiduals(fittedModel = mod1) plot(simulationOutput) ## ----------------------------------------------------------------------------- mod2 <- glmer(cbind(N_parasitized, N_adult) ~ logDensity + (1|ID), data = data, family=binomial) simulationOutput <- simulateResiduals(fittedModel = mod2) plot(simulationOutput) ## ----------------------------------------------------------------------------- mod3 <- glmer(cbind(N_parasitized, N_adult) ~ logDensity + I(logDensity^2) + (1|ID), data = data, family=binomial) simulationOutput <- simulateResiduals(fittedModel = mod3) plot(simulationOutput) ## ----------------------------------------------------------------------------- anova(mod2, mod3) ## ----------------------------------------------------------------------------- AIC(mod2) AIC(mod3) ## ----error=TRUE--------------------------------------------------------------- library(glmmTMB) m1 <- glm(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)), data=Owls , family = poisson) res <- simulateResiduals(m1) plot(res) ## ----error=TRUE--------------------------------------------------------------- m2 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), data=Owls , family = poisson) res <- simulateResiduals(m2) plot(res) ## ----error=TRUE--------------------------------------------------------------- m3 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), data=Owls , family = nbinom1) res <- simulateResiduals(m3, plot = T) par(mfrow = c(1,2)) testDispersion(res) plotResiduals(res, Owls$FoodTreatment) ## ----fig.height=4, fig.width=4------------------------------------------------ testZeroInflation(res) ## ----error=TRUE--------------------------------------------------------------- m4 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), ziformula = ~ FoodTreatment + SexParent, data=Owls , family = nbinom1) res <- simulateResiduals(m4, plot = T) ## ----error=TRUE, fig.width=7-------------------------------------------------- par(mfrow = c(1,3)) plotResiduals(res, Owls$FoodTreatment) testDispersion(res) testZeroInflation(res) ## ----error=TRUE--------------------------------------------------------------- m5 <- glmmTMB(SiblingNegotiation ~ FoodTreatment*SexParent + offset(log(BroodSize)) + (1|Nest), dispformula = ~ FoodTreatment + SexParent , ziformula = ~ FoodTreatment + SexParent, data=Owls , family = nbinom1) res <- simulateResiduals(m5, plot = T) ## ----error=TRUE, fig.width=7-------------------------------------------------- par(mfrow = c(1,3)) plotResiduals(res, Owls$FoodTreatment) testDispersion(res) testZeroInflation(res) ## ----------------------------------------------------------------------------- testData = createData(sampleSize = 500, overdispersion = 0, fixedEffects = 5, family = binomial(), randomEffectVariance = 3, numGroups = 25) fittedModel <- glm(observedResponse ~ 1, family = "binomial", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) ## ----------------------------------------------------------------------------- plot(simulationOutput, asFactor = T) ## ----fig.width=4, fig.height=4------------------------------------------------ plotResiduals(simulationOutput, testData$Environment1, quantreg = T) ## ----------------------------------------------------------------------------- par(mfrow = c(1,2)) testDispersion(simulationOutput) simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group) testDispersion(simulationOutput2) ## ----------------------------------------------------------------------------- n = 1000 p = runif(n, 0.1, 0.9) # true probabilities obs = rbinom(n, 1, p) ## ----------------------------------------------------------------------------- fit <- glm(obs ~ 1, family = "binomial") # wrong model, assumes equal probabilities library(DHARMa) res <- simulateResiduals(fit, plot = T) # nothing to see ## ----------------------------------------------------------------------------- res2 <- recalculateResiduals(res, group = rep(1:20, each = 10)) plot(res2) ## ----------------------------------------------------------------------------- grouping = cut(p, breaks = quantile(p, seq(0,1,0.02))) res3 <- recalculateResiduals(res, group = grouping) plot(res3) ## ----------------------------------------------------------------------------- set.seed(123) testData = createData(sampleSize = 500, overdispersion = 0, fixedEffects = c(0,3), family = binomial(), randomEffectVariance = 3, numGroups = 50) ## ----------------------------------------------------------------------------- res <- simulateResiduals(fittedModel = fittedModel) fittedModel <- glm(observedResponse ~ Environment1, family = "binomial", data = testData) plot(res) ## ----------------------------------------------------------------------------- res2 = recalculateResiduals(res , group = testData$group) plot(res2) ## ----------------------------------------------------------------------------- grouping = as.factor(sample.int(50, 500, replace = T)) res2 = recalculateResiduals(res , group = grouping) plot(res2) ## ----------------------------------------------------------------------------- x = predict(fittedModel) grouping = cut(x, breaks = quantile(x, seq(0,1,0.02))) res2 = recalculateResiduals(res , group = grouping) plot(res2) ## ----------------------------------------------------------------------------- x = testData$Environment2 grouping = cut(x, breaks = quantile(x, seq(0,1,0.02))) res2 = recalculateResiduals(res , group = grouping) plot(res2) ## ----------------------------------------------------------------------------- x = testData$x grouping = cut(x, breaks = quantile(x, seq(0,1,0.02))) res3 = recalculateResiduals(res , group = grouping) plot(res3) ## ----eval = T----------------------------------------------------------------- testData = createData(sampleSize = 200, overdispersion = 0.5, family = poisson()) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulatePoissonGLM <- function(fittedModel, n){ pred = predict(fittedModel, type = "response") nObs = length(pred) sim = matrix(nrow = nObs, ncol = n) for(i in 1:n) sim[,i] = rpois(nObs, pred) return(sim) } sim = simulatePoissonGLM(fittedModel, 100) DHARMaRes = createDHARMa(simulatedResponse = sim, observedResponse = testData$observedResponse, fittedPredictedResponse = predict(fittedModel), integerResponse = T) plot(DHARMaRes, quantreg = F) DHARMa/inst/doc/DHARMaForBayesians.R0000644000176200001440000000535714704246643016441 0ustar liggesusers## ----global_options, include=FALSE-------------------------------------------- knitr::opts_chunk$set(fig.width=8.5, fig.height=5.5, fig.align='center', warning=FALSE, message=FALSE) ## ----echo = F, message = F---------------------------------------------------- library(DHARMa) set.seed(123) ## ----eval = F----------------------------------------------------------------- # library(rjags) # library(BayesianTools) # # set.seed(123) # # dat <- DHARMa::createData(200, overdispersion = 0.2) # # Data = as.list(dat) # Data$nobs = nrow(dat) # Data$nGroups = length(unique(dat$group)) # # modelCode = "model{ # # for(i in 1:nobs){ # observedResponse[i] ~ dpois(lambda[i]) # poisson error distribution # lambda[i] <- exp(eta[i]) # inverse link function # eta[i] <- intercept + env*Environment1[i] # linear predictor # } # # intercept ~ dnorm(0,0.0001) # env ~ dnorm(0,0.0001) # # # Posterior predictive simulations # for (i in 1:nobs) { # observedResponseSim[i]~dpois(lambda[i]) # } # # }" # # jagsModel <- jags.model(file= textConnection(modelCode), data=Data, n.chains = 3) # para.names <- c("intercept","env", "lambda", "observedResponseSim") # Samples <- coda.samples(jagsModel, variable.names = para.names, n.iter = 5000) # # x = BayesianTools::getSample(Samples) # # colnames(x) # problem: all the variables are in one array - this is better in STAN, where this is a list - have to extract the right columns by hand # posteriorPredDistr = x[,3:202] # this is the uncertainty of the mean prediction (lambda) # posteriorPredSim = x[,203:402] # these are the simulations # # sim = createDHARMa(simulatedResponse = t(posteriorPredSim), observedResponse = dat$observedResponse, fittedPredictedResponse = apply(posteriorPredDistr, 2, median), integerResponse = T) # plot(sim) ## ----eval=F------------------------------------------------------------------- # # Posterior predictive simulations # for (i in 1:nobs) { # observedResponseSim[i]~dpois(lambda[i]) # } ## ----eval = F----------------------------------------------------------------- # for(i in 1:nobs){ # observedResponse[i] ~ dpois(lambda[i]) # poisson error distribution # lambda[i] <- exp(eta[i]) # inverse link function # eta[i] <- intercept + env*Environment1[i] + RE[group[i]] # linear predictor # } # # for(j in 1:nGroups){ # RE[j] ~ dnorm(0,tauRE) # } ## ----eval=F------------------------------------------------------------------- # for(j in 1:nGroups){ # RESim[j] ~ dnorm(0,tauRE) # } # # for (i in 1:nobs) { # observedResponseSim[i] ~ dpois(lambdaSim[i]) # lambdaSim[i] <- exp(etaSim[i]) # etaSim[i] <- intercept + env*Environment1[i] + RESim[group[i]] # } DHARMa/README.md0000644000176200001440000000161014704245735012536 0ustar liggesusers# DHARMa - Residual Diagnostics for HierARchical Models The DHARMa package creates readily interpretable residuals for generalized linear (mixed) models that are standardized to values between 0 and 1. This is achieved by a simulation-based approach, similar to the Bayesian p-value or the parametric bootstrap: 1) simulate new data from the fitted model 2) from this simulated data, calculate the cummulative density function 3) residual is the value of the empirical density function at the value of the observed data. The package includes various functions that deal with issues such as * Misfit * Heteroscedasticity * Under/Overdispersion * Zero-inflation * Residual temporal autocorrelation * Residual spatial autocorrelation * Residual phylogenetic autocorrelation To get more information, install the package and run ```{r} library(DHARMa) ?DHARMa vignette("DHARMa", package="DHARMa") ``` DHARMa/build/0000755000176200001440000000000014704246643012357 5ustar liggesusersDHARMa/build/vignette.rds0000644000176200001440000000036014704246643014715 0ustar liggesusers‹uŻ ‚@…ן, *źÖ'š ‘ ‚ˆ.ŗt+I]Yń®'Ļ&ŻVźbgv¾įģ9{v!:1Mč^9 Ļ“ćÄĘīųŪõqŽ1Yv$`|5-bȊv«źf§uć4g¼tsļp„b³čōī…q÷óBO=®·2MZż°m×Ŗr$óŖnjZäóVÓiÉW’ĆĶ7Óěƒ R*#[šAœČ/NqłŒƒˆ«&S }šÓ,*dč­+ĘqVlĪ*OšMŽÉXš¦yö… 2‘„N%xŽzœž/£ē«ĀļDHARMa/man/0000755000176200001440000000000014704245735012034 5ustar liggesusersDHARMa/man/createDHARMa.Rd0000644000176200001440000000706014677165224014511 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/DHARMa.R \name{createDHARMa} \alias{createDHARMa} \title{Create a DHARMa object from hand-coded simulations or Bayesian posterior predictive simulations.} \usage{ createDHARMa(simulatedResponse, observedResponse, fittedPredictedResponse = NULL, integerResponse = FALSE, seed = 123, method = c("PIT", "traditional"), rotation = NULL) } \arguments{ \item{simulatedResponse}{matrix of observations simulated from the fitted model - row index for observations and colum index for simulations.} \item{observedResponse}{true observations.} \item{fittedPredictedResponse}{optional fitted predicted response. For Bayesian posterior predictive simulations, using the median posterior prediction as fittedPredictedResponse is recommended. If not provided, the mean simulatedResponse will be used.} \item{integerResponse}{if T, noise will be added at to the residuals to maintain a uniform expectations for integer responses (such as Poisson or Binomial). Unlike in \link{simulateResiduals}, the nature of the data is not automatically detected, so this MUST be set by the user appropriately.} \item{seed}{the random seed to be used within DHARMa. The default setting, recommended for most users, is keep the random seed on a fixed value 123. This means that you will always get the same randomization and thus teh same result when running the same code. NULL = no new seed is set, but previous random state will be restored after simulation. FALSE = no seed is set, and random state will not be restored. The latter two options are only recommended for simulation experiments. See vignette for details.} \item{method}{the quantile randomization method used. The two options implemented at the moment are probability integral transform (PIT-) residuals (current default), and the "traditional" randomization procedure, that was used in DHARMa until version 0.3.0. For details, see \link{getQuantile}.} \item{rotation}{optional rotation of the residual space to remove residual autocorrelation. See details in \link{simulateResiduals}, section \emph{residual auto-correlation} for an extended explanation, and \link{getQuantile} for syntax.} } \description{ Create a DHARMa object from hand-coded simulations or Bayesian posterior predictive simulations. } \details{ The use of this function is to convert simulated residuals (e.g. from a point estimate, or Bayesian p-values) to a DHARMa object, to make use of the plotting / test functions in DHARMa. } \note{ Either scaled residuals or (simulatedResponse AND observed response) have to be provided. } \examples{ ## READING IN HAND-CODED SIMULATIONS testData = createData(sampleSize = 50, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1, data = testData, family = "poisson") # in DHARMA, using the simulate.glm function of glm sims = simulateResiduals(fittedModel) plot(sims, quantreg = FALSE) # Doing the same with a handcoded simulate function. # of course this code will only work with a 1-par glm model simulateMyfit <- function(n=10, fittedModel){ int = coef(fittedModel)[1] slo = coef(fittedModel)[2] pred = exp(int + slo * testData$Environment1) predSim = replicate(n, rpois(length(pred), pred)) return(predSim) } sims = simulateMyfit(250, fittedModel) dharmaRes <- createDHARMa(simulatedResponse = sims, observedResponse = testData$observedResponse, fittedPredictedResponse = predict(fittedModel, type = "response"), integer = TRUE) plot(dharmaRes, quantreg = FALSE) } DHARMa/man/getSimulations.Rd0000644000176200001440000000765714704245735015351 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{getSimulations} \alias{getSimulations} \alias{getSimulations.default} \alias{getSimulations.negbin} \alias{getSimulations.gam} \alias{getSimulations.lmerMod} \alias{getSimulations.glmmTMB} \alias{getSimulations.HLfit} \alias{getSimulations.MixMod} \alias{getSimulations.phylolm} \alias{getSimulations.phyloglm} \title{Get model simulations} \usage{ getSimulations(object, nsim = 1, type = c("normal", "refit"), ...) \method{getSimulations}{default}(object, nsim = 1, type = c("normal", "refit"), ...) \method{getSimulations}{negbin}(object, nsim = 1, type = c("normal", "refit"), ...) \method{getSimulations}{gam}(object, nsim = 1, type = c("normal", "refit"), mgcViz = TRUE, ...) \method{getSimulations}{lmerMod}(object, nsim = 1, type = c("normal", "refit"), ...) \method{getSimulations}{glmmTMB}(object, nsim = 1, type = c("normal", "refit"), ...) \method{getSimulations}{HLfit}(object, nsim = 1, type = c("normal", "refit"), ...) \method{getSimulations}{MixMod}(object, nsim = 1, type = c("normal", "refit"), ...) \method{getSimulations}{phylolm}(object, nsim = 1, type = c("normal", "refit"), ...) \method{getSimulations}{phyloglm}(object, nsim = 1, type = c("normal", "refit"), ...) } \arguments{ \item{object}{a fitted model.} \item{nsim}{number of simulations.} \item{type}{if simulations should be prepared for getQuantile or for refit.} \item{...}{additional parameters to be passed on, usually to the simulate function of the respective model class.} \item{mgcViz}{whether simulations should be created with mgcViz (if mgcViz is available)} } \value{ A matrix with simulations. } \description{ Wrapper to simulate from a fitted model. } \details{ The purpose of this function is to wrap or implement the simulate function of different model classes and thus return simulations from fitted models in a standardized way. Note: GLMM and other regression packages often differ in how simulations are produced, and which parameters can be used to modify this behavior. One important difference is how to modifiy which hierarchical levels are held constant, and which are re-simulated. In lme4, this is controlled by the re.form argument (see \link[lme4:simulate.merMod]{lme4::simulate.merMod}). In glmmTMB, the package version 1.1.10 has a temporary solution to simulate conditional to all random effects (see \link[glmmTMB:set_simcodes]{glmmTMB::set_simcodes} val = "fix", and issue \href{https://github.com/glmmTMB/glmmTMB/issues/888}{#888} in glmmTMB GitHub repository. For other packages, please consult the help. If the model was fit with weights and the respective model class does not include the weights in the simulations, getSimulations will throw a warning. The background is if weights are used on the likelihood directly, then what is fitted is effectively a pseudo likelihood, and there is no way to directly simulate from the specified likelihood. Whether or not residuals can be used in this case depends very much on what is tested and how weights are used. I'm sorry to say that it is hard to give a general recommendation, you have to consult someone that understands how weights are processed in the respective model class. } \examples{ testData = createData(sampleSize = 400, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) # response that was used to fit the model getObservedResponse(fittedModel) # predictions of the model for these points getFitted(fittedModel) # extract simulations from the model as matrix getSimulations(fittedModel, nsim = 2) # extract simulations from the model for refit (often requires different structure) x = getSimulations(fittedModel, nsim = 2, type = "refit") getRefit(fittedModel, x[[1]]) getRefit(fittedModel, getObservedResponse(fittedModel)) } \seealso{ \link{getObservedResponse}, \link{getRefit}, \link{getFixedEffects}, \link{getFitted} } \author{ Florian Hartig } DHARMa/man/getRefit.Rd0000644000176200001440000000404714703461527014077 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{getRefit} \alias{getRefit} \alias{getRefit.default} \alias{getRefit.lm} \alias{getRefit.glmmTMB} \alias{getRefit.HLfit} \alias{getRefit.MixMod} \alias{getRefit.phylolm} \alias{getRefit.phyloglm} \title{Get model refit} \usage{ getRefit(object, newresp, ...) \method{getRefit}{default}(object, newresp, ...) \method{getRefit}{lm}(object, newresp, ...) \method{getRefit}{glmmTMB}(object, newresp, ...) \method{getRefit}{HLfit}(object, newresp, ...) \method{getRefit}{MixMod}(object, newresp, ...) \method{getRefit}{phylolm}(object, newresp, ...) \method{getRefit}{phyloglm}(object, newresp, ...) } \arguments{ \item{object}{a fitted model.} \item{newresp}{the new response that should be used to refit the model.} \item{...}{additional parameters to be passed on to the refit or update class that is used to refit the model.} } \description{ Wrapper to refit a fitted model. } \details{ The purpose of this wrapper is to standardize the refit of a model. The behavior of this function depends on the supplied model. When available, it uses the refit method, otherwise it will use update. For glmmTMB: since version 1.0, glmmTMB has a refit function, but this didn't work, so I switched back to this implementation, which is a hack based on the update function. } \examples{ testData = createData(sampleSize = 400, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) # response that was used to fit the model getObservedResponse(fittedModel) # predictions of the model for these points getFitted(fittedModel) # extract simulations from the model as matrix getSimulations(fittedModel, nsim = 2) # extract simulations from the model for refit (often requires different structure) x = getSimulations(fittedModel, nsim = 2, type = "refit") getRefit(fittedModel, x[[1]]) getRefit(fittedModel, getObservedResponse(fittedModel)) } \seealso{ \link{getObservedResponse}, \link{getSimulations}, \link{getFixedEffects} } \author{ Florian Hartig } DHARMa/man/checkDots.Rd0000644000176200001440000000057414665273541014242 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/helper.R \name{checkDots} \alias{checkDots} \title{Check dot operator} \usage{ checkDots(name, default, ...) } \arguments{ \item{name}{variable name} \item{default}{variable default} } \description{ Check dot operator } \details{ modified from https://github.com/lcolladotor/dots } \keyword{internal} DHARMa/man/DHARMa.ecdf.Rd0000644000176200001440000000060714703461527014220 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/helper.R \name{DHARMa.ecdf} \alias{DHARMa.ecdf} \title{Modified ECDF function.} \usage{ DHARMa.ecdf(x) } \description{ Modified ECDF function. } \details{ Ensures symmetric ECDF (standard ECDF is <), and that 0 / 1 values are only produced if the data is strictly < > than the observed data. } \keyword{internal} DHARMa/man/getFitted.Rd0000644000176200001440000000414714677165224014253 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{getFitted} \alias{getFitted} \alias{getFitted.default} \alias{getFitted.gam} \alias{getFitted.HLfit} \alias{getFitted.MixMod} \alias{getFitted.phylolm} \alias{getFitted.phyloglm} \title{Get fitted/predicted values} \usage{ getFitted(object, ...) \method{getFitted}{default}(object, ...) \method{getFitted}{gam}(object, ...) \method{getFitted}{HLfit}(object, ...) \method{getFitted}{MixMod}(object, ...) \method{getFitted}{phylolm}(object, ...) \method{getFitted}{phyloglm}(object, ...) } \arguments{ \item{object}{A fitted model.} \item{...}{Additional parameters to be passed on, usually to the simulate function of the respective model class.} } \description{ Wrapper to get the fitted/predicted response of model at the response scale. } \details{ The purpose of this wrapper is to standardize extract the fitted values, which is implemented via predict(model, type = "response") for most model classes. If you implement this function for a new model class, you should include an option to modifying which random effects (REs) are included in the predictions. If this option is not available, it is essential that predictions are provided marginally/unconditionally, i.e. without the RE estimates (because of https://github.com/florianhartig/DHARMa/issues/43), which corresponds to re-form = ~0 in lme4. } \examples{ testData = createData(sampleSize = 400, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) # response that was used to fit the model getObservedResponse(fittedModel) # predictions of the model for these points getFitted(fittedModel) # extract simulations from the model as matrix getSimulations(fittedModel, nsim = 2) # extract simulations from the model for refit (often requires different structure) x = getSimulations(fittedModel, nsim = 2, type = "refit") getRefit(fittedModel, x[[1]]) getRefit(fittedModel, getObservedResponse(fittedModel)) } \seealso{ \link{getObservedResponse}, \link{getSimulations}, \link{getRefit}, \link{getFixedEffects} } \author{ Florian Hartig } DHARMa/man/hurricanes.Rd0000644000176200001440000000524214703461527014467 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/data.R \docType{data} \name{hurricanes} \alias{hurricanes} \title{Hurricanes} \format{ A 'data.frame': 92 obs. of 14 variables \describe{ \item{Year}{Year of the hurricane (1950-2012) } \item{Name}{Name of the hurricane } \item{MasFem}{Masculinity-femininity rating of the hurricane's name in the range 1 = very masculine, 11 = very feminine.} \item{MinPressure_before}{Minimum air pressure (909-1002).} \item{Minpressure_Updated_2014}{Updated minimum air pressure (909-1003).} \item{Gender_MF}{Binary gender categorization based on MasFem (male = 0, female = 1).} \item{Category}{Strength of the hurricane in categories (1:7). (1 = not at all, 7 = very intense).} \item{alldeaths}{Human deaths occured (1:256).} \item{NDAM}{Normalized damage in millions (1:75.000). The raw (dollar) amounts of property damage caused by hurricanes were obtained, and the unadjusted dollar amounts were normalized to 2013 monetary values by adjusting them to inflation, wealth and population density.} \item{Elapsed_Yrs}{Elapsed years since the occurrence of hurricanes (1:63).} \item{Source}{MWR/wikipedia ()} \item{ZMasFem}{Scaled (MasFem)} \item{ZMinPressure_A}{Scaled (Minpressure_Updated_2014)} \item{ZNDAM}{Scaled (NDAM)} ... } } \description{ A data set on hurricane strength and fatalities in the US between 1950 and 2012. The data originates from the study by Jung et al., PNAS, 2014, who claim that the masculinity / femininity of a hurricane name has a causal effect on fatalities, presumably through a different perception of danger caused by the names. } \examples{ \dontrun{ # Loading hurricanes dataset library(DHARMa) data(hurricanes) str(hurricanes) # this is the model fit by Jung et al. library(glmmTMB) originalModelGAM = glmmTMB(alldeaths ~ scale(MasFem) * (scale(Minpressure_Updated_2014) + scale(NDAM)), data = hurricanes, family = nbinom2) # no significant deviation in the general DHARMa plot res <- simulateResiduals(originalModelGAM) plot(res) # but residuals ~ NDAM looks funny, which was pointed # out by Bob O'Hara in a blog post after publication of the paper plotResiduals(res, hurricanes$NDAM) # we also find temporal autocorrelation res2 = recalculateResiduals(res, group = hurricanes$Year) testTemporalAutocorrelation(res2, time = unique(hurricanes$Year)) # task: try to address these issues - in many instances, this will # make the MasFem predictor n.s. } } \references{ Jung, K., Shavitt, S., Viswanathan, M., & Hilbe, J. M. (2014). Female hurricanes are deadlier than male hurricanes. Proceedings of the National Academy of Sciences, 111(24), 8782-8787. } DHARMa/man/getRandomState.Rd0000644000176200001440000000323514677165224015252 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/random.R \name{getRandomState} \alias{getRandomState} \title{Record and restore a random state} \usage{ getRandomState(seed = NULL) } \arguments{ \item{seed}{seed argument to set.seed(), typically a number. Additional options: NULL = no seed is set, but return includes function for restoring random seed. F = function does nothing, i.e. neither seed is changed, nor does the returned function do anything.} } \value{ A list with various infos about the random state that after function execution, as well as a function to restore the previous state before the function execution. } \description{ The aim of this function is to record, manipulate and restore a random state. } \details{ This function is intended for two (not mutually exclusive tasks): a) record the current random state. b) change the current random state in a way that the previous state can be restored. } \examples{ set.seed(13) runif(1) # testing the function in standard settings currentSeed = .Random.seed x = getRandomState(123) runif(1) x$restoreCurrent() all(.Random.seed == currentSeed) # if no seed was set in env, this will also be restored rm(.Random.seed) # now, there is no random seed x = getRandomState(123) exists(".Random.seed") # TRUE runif(1) x$restoreCurrent() exists(".Random.seed") # False runif(1) # re-create a seed # with seed = false currentSeed = .Random.seed x = getRandomState(FALSE) runif(1) x$restoreCurrent() all(.Random.seed == currentSeed) # with seed = NULL currentSeed = .Random.seed x = getRandomState(NULL) runif(1) x$restoreCurrent() all(.Random.seed == currentSeed) } \author{ Florian Hartig } DHARMa/man/getPossibleModels.Rd0000644000176200001440000000043014665273541015746 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{getPossibleModels} \alias{getPossibleModels} \title{get possible models} \usage{ getPossibleModels() } \description{ returns a list of supported model classes } \keyword{internal} DHARMa/man/simulateLRT.Rd0000644000176200001440000001040414677165224014532 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/simulateLRT.R \name{simulateLRT} \alias{simulateLRT} \title{Simulated likelihood ratio tests for (generalized) linear mixed models} \usage{ simulateLRT(m0, m1, n = 250, seed = 123, plot = TRUE, suppressWarnings = TRUE, saveModels = FALSE, ...) } \arguments{ \item{m0}{null Model.} \item{m1}{alternative Model.} \item{n}{number of simulations.} \item{seed}{random seed.} \item{plot}{whether null distribution should be plotted.} \item{suppressWarnings}{whether to suppress warnings that occur during refitting the models to simulated data. See details for explanations.} \item{saveModels}{Whether to save refitted models.} \item{...}{additional parameters to pass on to the simulate function of the model object. See \link{getSimulations} for details.} } \description{ This function uses the DHARMa model wrappers to generate simulated likelihood ratio tests (LRTs) for (generalized) linear mixed models based on a parametric bootstrap. The motivation for using a simulated LRT rather than a standard ANOVA or AIC for model selection in mixed models is that df for mixed models are not clearly defined, thus standard ANOVA based on Chi2 statistics or AIC are unreliable, in particular for models with large contributions of REs to the likelihood. Interpretation of the results as in a normal LRT: the null hypothesis is that m0 is correct, the tests checks if the increase in likelihood of m1 is higher than expected, using data simulated from m0. } \details{ The function performs a simulated LRT, which works as follows: \enumerate{ \item H0: Model 1 is correct. \item Our test statistic is the log LRT of M1/M2. Empirical value will always be > 1 because in a nested setting, the more complex model cannot have a worse likelihood. \item To generate an expected distribution of the test statistic under H0, we simulate new response data under M0, refit M0 and M1 on this data, and calculate the LRs. \item Based on this, calculate p-values etc. in the usual way. } About warnings: warnings such as "boundary (singular) fit: see ?isSingular" will likely occur in this function and are not necessarily the sign of a problem. lme4 warns if RE variances are fit to zero. This is desired / likely in this case, however, because we are simulating data with zero RE variances. Therefore, warnings are turned off per default. For diagnostic reasons, you can turn warnings on, and possibly also inspect fitted models via the parameter saveModels to see if there are any other problems in the re-fitted models. Data simulations are performed by \link{getSimulations}, which is a wrapper for the respective model functions. The default for all packages, wherever possible, is to generate marginal simulations (meaning that REs are re-simulated as well). I see no sensible reason to change this, but if you want to and if supported by the respective regression package, you could do so by supplying the necessary arguments via ... } \note{ The logic of an LRT assumes that m0 is nested in m1, which guarantees that the L(M1) > L(M0). The function does not explicitly check if models are nested and will work as long as data can be simulated from M0 that can be refit with M) and M1; however, I would strongly advice against using this for non-nested models unless you have a good statistical reason for doing so. Also, note that LRTs may be unreliable when fit with REML or some other kind of penalized / restricted ML. Therefore, you should fit model with ML for use in this function. } \examples{ library(DHARMa) library(lme4) # create test data set.seed(123) dat <- createData(sampleSize = 200, randomEffectVariance = 1) # define Null and alternative model (should be nested) m1 = glmer(observedResponse ~ Environment1 + (1|group), data = dat, family = "poisson") m0 = glm(observedResponse ~ Environment1 , data = dat, family = "poisson") \dontrun{ # run LRT - n should be increased to at least 250 for a real study out = simulateLRT(m0, m1, n = 10) # To inspect warnings thrown during the refits: out = simulateLRT(m0, m1, saveModels = TRUE, suppressWarnings = FALSE, n = 10) summary(out$saveModels[[2]]$refittedM1) # RE SD = 0, no problem # If there are warnings that seem problematic, # could try changing the optimizer or iterations } } \author{ Florian Hartig } DHARMa/man/testPDistribution.Rd0000644000176200001440000000101414677165224016021 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/runBenchmarks.R \name{testPDistribution} \alias{testPDistribution} \title{Plot distribution of p-values.} \usage{ testPDistribution(x, plot = TRUE, main = "p distribution \\n expected is flat at 1", ...) } \arguments{ \item{x}{vector of p values.} \item{plot}{should the values be plotted.} \item{main}{title for the plot.} \item{...}{additional arguments to hist.} } \description{ Plot distribution of p-values. } \author{ Florian Hartig } DHARMa/man/testOverdispersion.Rd0000644000176200001440000000117014677165224016240 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testOverdispersion} \alias{testOverdispersion} \title{Simulated overdisperstion tests} \usage{ testOverdispersion(simulationOutput, ...) } \arguments{ \item{simulationOutput}{an object of class DHARMa with simulated quantile residuals, either created via \link{simulateResiduals} or by \link{createDHARMa} for simulations created outside DHARMa} \item{...}{additional arguments to \link{testDispersion}} } \description{ Simulated overdisperstion tests } \details{ Deprecated, switch your code to using the \link{testDispersion} function } DHARMa/man/testQuantiles.Rd0000644000176200001440000000523114677165224015174 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testQuantiles} \alias{testQuantiles} \title{Test for quantiles} \usage{ testQuantiles(simulationOutput, predictor = NULL, quantiles = c(0.25, 0.5, 0.75), plot = TRUE) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{predictor}{an optional predictor variable to be used, instead of the predicted response (default)} \item{quantiles}{the quantiles to be tested} \item{plot}{if TRUE, the function will create an additional plot} } \description{ This function tests } \details{ The function fits quantile regressions (via package qgam) on the residuals, and compares their location to the expected location (because of the uniform distributionm, the expected location is 0.5 for the 0.5 quantile). A significant p-value for the splines means the fitted spline deviates from a flat line at the expected location (p-values of intercept and spline are combined via Benjamini & Hochberg adjustment to control the FDR) The p-values of the splines are combined into a total p-value via Benjamini & Hochberg adjustment to control the FDR. } \examples{ testData = createData(sampleSize = 200, overdispersion = 0.0, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # run the quantile test x = testQuantiles(simulationOutput) x # the test shows a combined p-value, corrected for multiple testing \dontrun{ # accessing results of the test x$pvals # pvalues for the individual quantiles x$qgamFits # access the fitted quantile regression summary(x$qgamFits[[1]]) # summary of the first fitted quantile # possible to test user-defined quantiles testQuantiles(simulationOutput, quantiles = c(0.7)) # example with missing environmental predictor fittedModel <- glm(observedResponse ~ 1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) testQuantiles(simulationOutput, predictor = testData$Environment1) plot(simulationOutput) plotResiduals(simulationOutput) } } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/print.DHARMa.Rd0000644000176200001440000000067314677165224014463 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/DHARMa.R \name{print.DHARMa} \alias{print.DHARMa} \title{Print simulated residuals} \usage{ \method{print}{DHARMa}(x, ...) } \arguments{ \item{x}{an object with simulated residuals created by \link{simulateResiduals}.} \item{...}{optional arguments for compatibility with the generic function, no function implemented.} } \description{ Print simulated residuals } DHARMa/man/testDispersion.Rd0000644000176200001440000001521014677165224015344 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testDispersion} \alias{testDispersion} \title{DHARMa dispersion tests} \usage{ testDispersion(simulationOutput, alternative = c("two.sided", "greater", "less"), plot = T, type = c("DHARMa", "PearsonChisq"), ...) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{alternative}{a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis. Greater corresponds to testing only for overdispersion. It is recommended to keep the default setting (testing for both over and underdispersion)} \item{plot}{whether to provide a plot for the results} \item{type}{which test to run. Default is DHARMa, other options are PearsonChisq (see details)} \item{...}{arguments to pass on to \link{testGeneric}} } \description{ This function performs simulation-based tests for over/underdispersion. If type = "DHARMa" (default and recommended), simulation-based dispersion tests are performed. Their behavior differs depending on whether simulations are done with refit = F, or refit = T, and whether data is simulated conditional (e.g. re.form ~0 in lme4) (see below). If type = "PearsonChisq", a chi2 test on Pearson residuals is performed. } \details{ Over / underdispersion means that the observed data is more / less dispersed than expected under the fitted model. There is no unique way to test for dispersion problems, and there are a number of different dispersion tests implemented in various R packages. The testDispersion function implements several dispersion tests: \strong{Simulation-based dispersion tests (type == "DHARMa")} If type = "DHARMa" (default and recommended), simulation-based dispersion tests are performed. Their behavior differs depending on whether simulations are done with refit = F, or refit = T #' \strong{Important:} for either refit = T or F, the results of type = "DHARMa" dispersion test will differ depending on whether simulations are done conditional (= conditional on fitted random effects) or unconditional (= REs are re-simulated). How to change between conditional or unconditional simulations is discussed in \link{simulateResiduals}. The general default in DHARMa is to use unconditional simulations, because this has advantages in other situations, but dispersion tests for models with strong REs specifically may increase substantially in power / sensitivity when switching to conditional simulations. I therefore recommend checking dispersion with conditional simulations if supported by the used regression package. If refit = F, the function uses \link{testGeneric} to compare the variance of the observed raw residuals (i.e. var(observed - predicted), displayed as a red line) against the variance of the simulated residuals (i.e. var(simulated - predicted), histogram). The variances are scaled to the mean simulated variance. A significant ratio > 1 indicates overdispersion, a significant ratio < 1 underdispersion. If refit = T, the function compares the approximate deviance (via squared pearson residuals) with the same quantity from the models refitted with simulated data. Applying this is much slower than the previous alternative. Given the computational cost, I would suggest that most users will be satisfied with the standard dispersion test. ** Analytical dispersion tests (type == "PearsonChisq")** This is the test described in https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#overdispersion, identical to performance::check_overdispersion. Works only if the fitted model provides df.residual and Pearson residuals. The test statistics is biased to lower values under quite general conditions, and will therefore tend to test significant for underdispersion. It is recommended to use this test only for overdispersion, i.e. use alternative == "greater". Also, obviously, it requires that Pearson residuals are available for the chosen model, which will not be the case for all models / packages. } \note{ For particular model classes / situations, there may be more powerful and thus preferable over the DHARMa test. The advantage of the DHARMa test is that it directly targets the spread of the data (unless other tests such as dispersion/df, which essentially measure fit and may thus be triggered by problems other than dispersion as well), and it makes practically no assumptions about the fitted model, other than the availability of simulations. } \examples{ library(lme4) set.seed(123) testData = createData(sampleSize = 100, overdispersion = 0.5, randomEffectVariance = 1) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # default DHARMa dispersion test - simulation-based testDispersion(simulationOutput) testDispersion(simulationOutput, alternative = "less", plot = FALSE) # only underdispersion testDispersion(simulationOutput, alternative = "greater", plot = FALSE) # only oversispersion # for mixed models, the test is usually more powerful if residuals are calculated # conditional on fitted REs simulationOutput <- simulateResiduals(fittedModel = fittedModel, re.form = NULL) testDispersion(simulationOutput) # DHARMa also implements the popular Pearson-chisq test that is also on the glmmWiki by Ben Bolker # The issue with this test is that it requires the df of the model, which are not well defined # for GLMMs. It is biased towards underdispersion, with bias getting larger with the number # of RE groups. In doubt, only test for overdispersion testDispersion(simulationOutput, type = "PearsonChisq", alternative = "greater") # if refit = TRUE, a different test on simulated Pearson residuals will calculated (see help) simulationOutput2 <- simulateResiduals(fittedModel = fittedModel, refit = TRUE, seed = 12, n = 20) testDispersion(simulationOutput2) # often useful to test dispersion per group (in particular for binomial data, see vignette) simulationOutputAggregated = recalculateResiduals(simulationOutput2, group = testData$group) testDispersion(simulationOutputAggregated) } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/plotConventionalResiduals.Rd0000644000176200001440000000055614665273541017545 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plots.R \name{plotConventionalResiduals} \alias{plotConventionalResiduals} \title{Conventional residual plot} \usage{ plotConventionalResiduals(fittedModel) } \arguments{ \item{fittedModel}{a fitted model object} } \description{ Convenience function to draw conventional residual plots } DHARMa/man/testTemporalAutocorrelation.Rd0000644000176200001440000002313014677165224020103 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testTemporalAutocorrelation} \alias{testTemporalAutocorrelation} \title{Test for temporal autocorrelation} \usage{ testTemporalAutocorrelation(simulationOutput, time, alternative = c("two.sided", "greater", "less"), plot = TRUE) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{time}{the time, in the same order as the data points.} \item{alternative}{a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis} \item{plot}{whether to plot output} } \description{ This function performs a standard test for temporal autocorrelation on the simulated residuals } \details{ The function performs a Durbin-Watson test on the uniformly scaled residuals, and plots the residuals against time. The DB test was originally be designed for normal residuals. In simulations, I didn't see a problem with this setting though. The alternative is to transform the uniform residuals to normal residuals and perform the DB test on those. Testing for temporal autocorrelation requires unique time values - if you have several observations per time value, either use \link{recalculateResiduals} function to aggregate residuals per time step, or extract the residuals from the fitted object, and plot / test each of them independently for temporally repeated subgroups (typical choices would be location / subject etc.). Note that the latter must be done by hand, outside testTemporalAutocorrelation. } \note{ Standard DHARMa simulations from models with (temporal / spatial / phylogenetic) conditional autoregressive terms will still have the respective temporal / spatial / phylogenetic correlation in the DHARMa residuals, unless the package you are using is modelling the autoregressive terms as explicit REs and is able to simulate conditional on the fitted REs. This has two consequences \enumerate{ \item If you check the residuals for such a model, they will still show significant autocorrelation, even if the model fully accounts for this structure. \item Because the DHARMa residuals for such a model are not statistically independent any more, other tests (e.g. dispersion, uniformity) may have inflated type I error, i.e. you will have a higher likelihood of spurious residual problems. } There are three (non-exclusive) routes to address these issues when working with spatial / temporal / other autoregressive models: \enumerate{ \item Simulate conditional on the fitted CAR structures (see conditional simulations in the help of \link{simulateResiduals}) \item Rotate simulations prior to residual calculations (see parameter rotation in \link{simulateResiduals}) \item Use custom tests / plots that explicitly compare the correlation structure in the simulated data to the correlation structure in the observed data. } } \examples{ testData = createData(sampleSize = 40, family = gaussian(), randomEffectVariance = 0) fittedModel <- lm(observedResponse ~ Environment1, data = testData) res = simulateResiduals(fittedModel) # Standard use testTemporalAutocorrelation(res, time = testData$time) # If you have several observations per time step, e.g. # because you have several locations, you will have to # aggregate timeSeries1 = createData(sampleSize = 40, family = gaussian(), randomEffectVariance = 0) timeSeries1$location = 1 timeSeries2 = createData(sampleSize = 40, family = gaussian(), randomEffectVariance = 0) timeSeries2$location = 2 testData = rbind(timeSeries1, timeSeries2) fittedModel <- lm(observedResponse ~ Environment1, data = testData) res = simulateResiduals(fittedModel) # Will not work because several residuals per time # testTemporalAutocorrelation(res, time = testData$time) # aggregating residuals by time res = recalculateResiduals(res, group = testData$time) testTemporalAutocorrelation(res, time = unique(testData$time)) # testing only subgroup location 1, could do same with loc 2 res = recalculateResiduals(res, sel = testData$location == 1) testTemporalAutocorrelation(res, time = unique(testData$time)) # example to demonstrate problems with strong temporal correlations and # how to possibly remove them by rotating residuals # note that if your model allows to condition on estimated REs, this may # be preferable! \dontrun{ set.seed(123) # Gaussian error # Create AR data with 5 observations per time point n <- 100 x <- MASS::mvrnorm(mu = rep(0,n), Sigma = .9 ^ as.matrix(dist(1:n)) ) y <- rep(x, each = 5) + 0.2 * rnorm(5*n) times <- factor(rep(1:n, each = 5), levels=1:n) levels(times) group <- factor(rep(1,n*5)) dat0 <- data.frame(y,times,group) # fit model / would be similar for nlme::gls and similar models model = glmmTMB(y ~ ar1(times + 0 | group), data=dat0) # Note that standard residuals still show problems because of autocorrelation res <- simulateResiduals(model) plot(res) # The reason is that most (if not all) autoregressive models treat the # autocorrelated error as random, i.e. the autocorrelated error structure # is not used for making predictions. If you then make predictions based # on the fixed effects and calculate residuals, the autocorrelation in the # residuals remains. We can see this if we again calculate the auto- # correlation test res2 <- recalculateResiduals(res, group=dat0$times) testTemporalAutocorrelation(res2, time = 1:length(res2$scaledResiduals)) # so, how can we check then if the current model correctly removed the # autocorrelation? # Option 1: rotate the residuals in the direction of the autocorrelation # to make the independent. Note that this only works perfectly for gls # type models as nonlinear link function make the residuals covariance # different from a multivariate normal distribution # this can be either done by extracting estimated AR1 covariance cov <- VarCorr(model) cov <- cov$cond$group # extract covariance matrix of REs # grouped according to times, rotated with estimated Cov - how all fine! res3 <- recalculateResiduals(res, group=dat0$times, rotation=cov) plot(res3) testTemporalAutocorrelation(res3, time = 1:length(res2$scaledResiduals)) # alternatively, you can let DHARMa estimate the covariance from the # simulations res4 <- recalculateResiduals(res, group=dat0$times, rotation="estimated") plot(res4) testTemporalAutocorrelation(res3, time = 1:length(res2$scaledResiduals)) # Alternatively, in glmmTMB, we can condition on the estimated correlated # residuals. Unfortunately, in this case, we will have to do simulations by # hand as glmmTMB does not allow to simulate conditional on a fitted # correlation structure # re.form = NULL creates predictions conditional on the fitted temporally # autocorreated REs pred = predict(model, re.form = NULL) # now we simulate data, conditional on the autocorrelation part, with the # uncorrelated residual error simulations = sapply(1:250, function(i) rnorm(length(pred), pred, summary(model)$sigma)) res5 = createDHARMa(simulations, dat0$y, pred) plot(res5) res5b <- recalculateResiduals(res5, group=dat0$times) testTemporalAutocorrelation(res5b, time = 1:length(res5b$scaledResiduals)) # Poisson error # note that for GLMMs, covariances will be estimated at the scale of the # linear predictor, while residual covariance will be at the responses scale # and thus further distorted by the link. Thus, for GLMMs with a nonlinear # link, there will be no exact rotation for a given covariance structure set.seed(123) # Create AR data with 5 observations per time point n <- 100 x <- MASS::mvrnorm(mu = rep(0,n), Sigma = .9 ^ as.matrix(dist(1:n)) ) y <- rpois(n = n*5, lambda = exp(rep(x, each = 5))) times <- factor(rep(1:n, each = 5), levels=1:n) levels(times) group <- factor(rep(1,n*5)) dat0 <- data.frame(y,times,group) # fit model model = glmmTMB(y ~ ar1(times + 0 | group), data=dat0, family = poisson) res <- simulateResiduals(model) # grouped according to times, unrotated res2 <- recalculateResiduals(res, group=dat0$times) testTemporalAutocorrelation(res2, time = 1:length(res2$scaledResiduals)) # grouped according to times, rotated with estimated Cov - problems remain cov <- VarCorr(model) cov <- cov$cond$group # extract covariance matrix of REs res3 <- recalculateResiduals(res, group=dat0$times, rotation=cov) testTemporalAutocorrelation(res3, time = 1:length(res2$scaledResiduals)) # grouped according to times, rotated with covariance estimated from residual # simulations at the response scale res4 <- recalculateResiduals(res, group=dat0$times, rotation="estimated") testTemporalAutocorrelation(res4, time = 1:length(res2$scaledResiduals)) } } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/residuals.DHARMa.Rd0000644000176200001440000000517114677165224015320 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/DHARMa.R \name{residuals.DHARMa} \alias{residuals.DHARMa} \title{Return residuals of a DHARMa simulation} \usage{ \method{residuals}{DHARMa}(object, quantileFunction = NULL, outlierValues = NULL, ...) } \arguments{ \item{object}{an object with simulated residuals created by \link{simulateResiduals}} \item{quantileFunction}{optional - a quantile function to transform the uniform 0/1 scaling of DHARMa to another distribution} \item{outlierValues}{if a quantile function with infinite support (such as dnorm) is used, residuals that are 0/1 are mapped to -Inf / Inf. outlierValues allows to convert -Inf / Inf values to an optional min / max value.} \item{...}{optional arguments for compatibility with the generic function, no function implemented} } \description{ Return residuals of a DHARMa simulation } \details{ the function accesses the slot $scaledResiduals in a fitted DHARMa object, and optionally transforms the standard DHARMa quantile residuals (which have a uniform distribution) to a particular pdf. } \note{ some of the papers on simulated quantile residuals transforming the residuals (which are natively uniform) back to a normal distribution. I presume this is because of the larger familiarity of most users with normal residuals. Personally, I never considered this desirable, for the reasons explained in https://github.com/florianhartig/DHARMa/issues/39, but with this function, I wanted to give users the option to plot normal residuals if they so wish. } \examples{ library(lme4) testData = createData(sampleSize = 100, overdispersion = 0.5, family = poisson()) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # standard plot plot(simulationOutput) # one of the possible test, for other options see ?testResiduals / vignette testDispersion(simulationOutput) # the calculated residuals can be accessed via residuals(simulationOutput) # transform residuals to other pdf, see ?residuals.DHARMa for details residuals(simulationOutput, quantileFunction = qnorm, outlierValues = c(-7,7)) # get residuals that are outside the simulation envelope outliers(simulationOutput) # calculating aggregated residuals per group simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group) plot(simulationOutput2, quantreg = FALSE) # calculating residuals only for subset of the data simulationOutput3 = recalculateResiduals(simulationOutput, sel = testData$group == 1 ) plot(simulationOutput3, quantreg = FALSE) } DHARMa/man/testZeroInflation.Rd0000644000176200001440000001112014703461527015777 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testZeroInflation} \alias{testZeroInflation} \title{Tests for zero-inflation} \usage{ testZeroInflation(simulationOutput, ...) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{...}{further arguments to \link{testGeneric}} } \description{ This function compares the observed number of zeros with the zeros expected from simulations. } \details{ Zero-inflation means that the observed data contain more zeros than would be expected under the fitted model. Zero-inflation must always be accessed with respect to a particular model, so the mere fact that there are many zeros in the observed data is not an indication of zero-inflation, see Warton, D. I. (2005). Many zeros does not mean zero inflation: comparing the goodness-of-fit of parametric models to multivariate abundance data. Environmetrics 16(3), 275-289. The testZeroInflation function simulates new datasets from the fitted model and compares this null distribution (gray histogram in the plot) with the observed values (red line in the plot). Technically, it is a wrapper for \link{testGeneric}, with the summary argument set to function(x) sum(x == 0). The test statistic is the ratio of observed to simulated zeros. A value < 1 means that the observed data have fewer zeros than expected, a value > 1 means that they have more zeros than expected (aka zero inflation). By default, the function tests both sides, so it would also test for fewer zeros than expected. } \note{ Zero-inflation can occur for a number of reasons other than an underlying data generating process corresponding to a ZIP model. Vice versa, it is very well possible that no zero-inflation will be observed when fitting models to data derived from a ZIP process. The latter is due to the fact that excess zeros can often be explained by other model parameters, such as the theta parameter in the negative binomial. For this reason, results of the zero-inflation test should be interpreted as a residual pattern that can have many reasons, not as a decision criterion for whether or not to fit a ZIP model. To decide whether to add a ZIP term, I would advise relying on appropriate model selection techniques such as AIC, BIC, WAIC, Bayes factor, or LRT. Note that these tests are often not reliable in GLMMs because it is difficult to determine the df spent by the different models. The \link{simulateLRT} function in DHARMa provides a nonparametric alternative to obtain p-values for LRT is nested models with unknown df. } \examples{ testData = createData(sampleSize = 100, overdispersion = 0.5, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # the plot function shows 2 plots and runs 4 tests # i) KS test i) Dispersion test iii) Outlier test iv) quantile test plot(simulationOutput, quantreg = TRUE) # testResiduals tests distribution, dispersion and outliers testResiduals(simulationOutput) ####### Individual tests ####### # KS test for correct distribution of residuals testUniformity(simulationOutput) # KS test for correct distribution within and between groups testCategorical(simulationOutput, testData$group) # Dispersion test - for details see ?testDispersion testDispersion(simulationOutput) # tests under and overdispersion # Outlier test (number of observations outside simulation envelope) # Use type = "boostrap" for exact values, see ?testOutliers testOutliers(simulationOutput, type = "binomial") # testing zero inflation testZeroInflation(simulationOutput) # testing generic summaries countOnes <- function(x) sum(x == 1) # testing for number of 1s testGeneric(simulationOutput, summary = countOnes) # 1-inflation testGeneric(simulationOutput, summary = countOnes, alternative = "less") # 1-deficit means <- function(x) mean(x) # testing if mean prediction fits testGeneric(simulationOutput, summary = means) spread <- function(x) sd(x) # testing if mean sd fits testGeneric(simulationOutput, summary = spread) } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/runBenchmarks.Rd0000644000176200001440000000765314677165224015143 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/runBenchmarks.R \name{runBenchmarks} \alias{runBenchmarks} \title{Benchmark calculations} \usage{ runBenchmarks(calculateStatistics, controlValues = NULL, nRep = 10, alpha = 0.05, parallel = FALSE, exportGlobal = FALSE, ...) } \arguments{ \item{calculateStatistics}{the statistics to be benchmarked. Should return one value, or a vector of values. If controlValues are given, must accept a parameter control} \item{controlValues}{optionally, a vector with a control parameter (e.g. to vary the strength of a problem the test should be specific to). See help for an example} \item{nRep}{number of replicates per level of the controlValues} \item{alpha}{significance level} \item{parallel}{whether to use parallel computations. Possible values are F, T (sets the cores automatically to number of available cores -1), or an integer number for the number of cores that should be used for the cluster} \item{exportGlobal}{whether the global environment should be exported to the parallel nodes. This will use more memory. Set to true only if you function calculate statistics depends on other functions or global variables.} \item{...}{additional parameters to calculateStatistics} } \value{ A object with list structure of class DHARMaBenchmark. Contains an entry simulations with a matrix of simulations, and an entry summaries with an list of summaries (significant (T/F), mean, p-value for KS-test uniformity). Can be plotted with \link{plot.DHARMaBenchmark} } \description{ This function runs statistical benchmarks, including Power / Type I error simulations for an arbitrary test with a control parameter } \note{ The benchmark function in DHARMa are intended for development purposes, and for users that want to test / confirm the properties of functions in DHARMa. If you are running an applied data analysis, they are probably of little use. } \examples{ # define a function that will run a simulation and return a number of statistics, typically p-values returnStatistics <- function(control = 0){ testData = createData(sampleSize = 20, family = poisson(), overdispersion = control, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1, data = testData, family = poisson()) res <- simulateResiduals(fittedModel = fittedModel, n = 250) out <- c(testUniformity(res, plot = FALSE)$p.value, testDispersion(res, plot = FALSE)$p.value) return(out) } # testing a single return returnStatistics() # running benchmark for a fixed simulation, increase nRep for sensible results out = runBenchmarks(returnStatistics, nRep = 5) # plotting results depend on whether a vector or a single value is provided for control plot(out) \dontrun{ # running benchmark with varying control values out = runBenchmarks(returnStatistics, controlValues = c(0,0.5,1), nRep = 100) plot(out) # running benchmark can be done using parallel cores out = runBenchmarks(returnStatistics, nRep = 100, parallel = TRUE) out = runBenchmarks(returnStatistics, controlValues = c(0,0.5,1), nRep = 10, parallel = TRUE) # Alternative plot function using vioplot, provides nicer pictures plot.DHARMaBenchmark <- function(x, ...){ if(length(x$controlValues)== 1){ vioplot::vioplot(x$simulations[,x$nSummaries:1], las = 2, horizontal = TRUE, side = "right", areaEqual = FALSE, main = "p distribution under H0", ylim = c(-0.15,1), ...) abline(v = 1, lty = 2) abline(v = c(0.05, 0), lty = 2, col = "red") text(-0.1, x$nSummaries:1, labels = x$summaries$propSignificant[-1]) }else{ res = x$summaries$propSignificant matplot(res$controlValues, res[,-1], type = "l", main = "Power analysis", ylab = "Power", ...) legend("bottomright", colnames(res[,-1]), col = 1:x$nSummaries, lty = 1:x$nSummaries, lwd = 2) } } } } \seealso{ \link{plot.DHARMaBenchmark} } \author{ Florian Hartig } DHARMa/man/getQuantile.Rd0000644000176200001440000001017214703461527014604 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/helper.R \name{getQuantile} \alias{getQuantile} \title{Calculate Residual Quantiles} \usage{ getQuantile(simulations, observed, integerResponse, method = c("PIT", "traditional"), rotation = NULL) } \arguments{ \item{simulations}{A matrix with simulations from a fitted model. Rows = observations, columns = replicate simulations.} \item{observed}{A vector with the observed data.} \item{integerResponse}{Is the response integer-valued? Only has an effect for method = "traditional".} \item{method}{The quantile randomization method used. See details.} \item{rotation}{Optional rotation of the residuals. You can either provide as a known or estimated covariance matrix (e.g. when fitting an AR1 model), or use the argument "estimated", in which case the residual covariance will be approximated by simulations. See comments in details.} } \description{ Calculates residual quantiles from a given simulation. } \details{ The function calculates residual quantiles from the simulated data. For continuous distributions, this will simply be the value of the ecdf. \strong{Randomization procedure for discrete data} For discrete data, there are two options implemented. The current default (available since DHARMa 0.3.1) are probability integral transform (PIT-) residuals (Smith, 1985; Dunn & Smyth, 1996; see also Warton, et al., 2017). Before DHARMa 0.3.1, a different randomization procedure was used, in which the a U(-0.5, 0.5) distribution was added on observations and simulations for discrete distributions. For a completely discrete distribution, the two procedures should deliver equivalent results, but the second method has the disadvantage that (a) one has to know if the distribution is discrete (DHARMa tries to recognize this automatically), and (b) that it leads to inefficiencies for some distributions such as the Tweedie, which are partly continuous, partly discrete (see e.g. \href{https://github.com/florianhartig/DHARMa/issues/168}{issue #168} on DHARMa GitHub page). \strong{Rotation (optional)} The getQuantile function includes an additional option to rotate residuals prior to calculating the quantile residuals. This option should ONLY be used when the fitted model includes a particular residuals covariance structure, such as an AR1 or a spatial or phylogenetic CAR model. For these models, residuals calculated from unconditional simulations will include the specified covariance structure, which will trigger e.g. temporal autocorrelation tests and can inflate type I errors of other tests. The idea of the rotation is to rotate the residual space according to the covariance structure of the fitted model, such that the rotated residuals are conditional independent (provided the fitted model is correct). If the residual covariance of the fitted model at the response scale can be extracted (e.g. when fitting gls type models), it would be best to extract it and provide this covariance matrix to the rotation option. If that is not the case, providing the argument "estimated" to rotation will estimate the covariance from the data simulated by the model. This is probably without alternative for GLMMs, where the covariance at the response scale is likely not known / provided, but note, that this approximation will tend to have considerable error and may be slow to compute for high-dimensional data. If you try to estimate the rotation from simulations, you should set n as high as possible! See \link{testTemporalAutocorrelation} for a practical example. The rotation of residuals implemented here is similar to the Variogram.lme() and Variongram.gls() functions in nlme package using the argument resType = "normalized". } \references{ Smith, J. Q. "Diagnostic checks of non-standard time series models." Journal of Forecasting 4.3 (1985): 283-291. Dunn, P.K., & Smyth, G.K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics 5, 236-244. Warton, David I., LoĆÆc Thibaut, and Yi Alice Wang. "The PIT-trapā€”A ā€œmodel-freeā€ bootstrap procedure for inference about regression models with discrete, multivariate responses." PloS one 12.7 (2017). } DHARMa/man/plot.DHARMa.Rd0000644000176200001440000000776714701671620014306 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plots.R \name{plot.DHARMa} \alias{plot.DHARMa} \title{DHARMa standard residual plots} \usage{ \method{plot}{DHARMa}(x, title = "DHARMa residual", ...) } \arguments{ \item{x}{An object of class DHARMa with simulated residuals created by \link{simulateResiduals}.} \item{title}{The title for both panels (plotted via mtext, outer = TRUE).} \item{...}{Further options for \link{plotResiduals}. Consider in particular parameters quantreg, rank and asFactor. xlab, ylab and main cannot be changed when using plot.DHARMa, but can be changed when using \link{plotResiduals}.} } \description{ This S3 function creates standard plots for the simulated residuals contained in an object of class DHARMa, using \link{plotQQunif} (left panel) and \link{plotResiduals} (right panel) } \details{ The function creates a plot with two panels. The left panel is a uniform qq plot (calling \link{plotQQunif}), and the right panel shows residuals against predicted values (calling \link{plotResiduals}), with outliers highlighted in red (default color but see Note). Very briefly, we would expect that a correctly specified model shows: a) a straight 1-1 line, as well as non-significance of the displayed tests in the qq-plot (left) -> evidence for an the correct overall residual distribution (for more details on the interpretation of this plot, see \link{plotQQunif}) b) visual homogeneity of residuals in both vertical and horizontal direction, as well as n.s. of quantile tests in the res ~ predictor plot (for more details on the interpretation of this plot, see \link{plotResiduals}) Deviations from these expectations can be interpreted similar to a linear regression. See the vignette for detailed examples. Note that, unlike \link{plotResiduals}, plot.DHARMa command uses the default rank = T. } \note{ The color for highlighting outliers and significant tests can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. This is convenient for a color-blind friendly display, since red and black are difficult for some people to separate. } \examples{ testData = createData(sampleSize = 200, family = poisson(), randomEffectVariance = 1, numGroups = 10) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) ######### main plotting function ############# # for all functions, quantreg = T will be more # informative, but slower plot(simulationOutput, quantreg = FALSE) ############# Distribution ###################### plotQQunif(simulationOutput = simulationOutput, testDispersion = FALSE, testUniformity = FALSE, testOutliers = FALSE) hist(simulationOutput ) ############# residual plots ############### # rank transformation, using a simulationOutput plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE) # smooth scatter plot - usually used for large datasets, default for n > 10000 plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE, smoothScatter = TRUE) # residual vs predictors, using explicit values for pred, residual plotResiduals(simulationOutput, form = testData$Environment1, quantreg = FALSE) # if pred is a factor, or if asFactor = TRUE, will produce a boxplot plotResiduals(simulationOutput, form = testData$group) # to diagnose overdispersion and heteroskedasticity it can be useful to # display residuals as absolute deviation from the expected mean 0.5 plotResiduals(simulationOutput, absoluteDeviation = TRUE, quantreg = FALSE) # All these options can also be provided to the main plotting function # If you want to plot summaries per group, use simulationOutput = recalculateResiduals(simulationOutput, group = testData$group) plot(simulationOutput, quantreg = FALSE) # we see one residual point per RE } \seealso{ \link{plotResiduals}, \link{plotQQunif} } DHARMa/man/transformQuantiles.Rd0000644000176200001440000000175714677165224016241 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/transformQuantiles.R \name{transformQuantiles} \alias{transformQuantiles} \title{Transform quantiles to pdf (deprecated)} \usage{ transformQuantiles(res, quantileFunction = qnorm, outlierValue = 7) } \arguments{ \item{res}{an object with simulated residuals created by \link{simulateResiduals}} \item{quantileFunction}{optional - a quantile function to transform the uniform 0/1 scaling of DHARMa to another distribution} \item{outlierValue}{if a quantile function with infinite support (such as dnorm) is used, residuals that are 0/1 are mapped to -Inf / Inf. outlierValues allows to convert -Inf / Inf values to an optional min / max value.} } \description{ The purpose of this function was to transform the DHARMa quantile residuals (which have a uniform distribution) to a particular pdf. Since DHARMa 0.3.0, this functionality is integrated in the \link{residuals.DHARMa} function. Please switch to using this function. } DHARMa/man/testCategorical.Rd0000644000176200001440000000667414677165224015460 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testCategorical} \alias{testCategorical} \title{Test for categorical dependencies} \usage{ testCategorical(simulationOutput, catPred, quantiles = c(0.25, 0.5, 0.75), plot = TRUE) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{catPred}{a categorical predictor with the same dimensions as the residuals in simulationOutput} \item{quantiles}{whether to draw the quantile lines.} \item{plot}{if TRUE, the function will create an additional plot} } \description{ This function tests if there are probles in a res ~ group structure. It performs two tests: test for within-group uniformity, and test for between-group homogeneity of variances } \details{ The function tests for two common problems: are residuals within each group distributed according to model assumptions, and is the variance between group heterogeneous. The test for within-group uniformity is performed via multipe KS-tests, with adjustment of p-values for multiple testing. If the plot is drawn, problematic groups are highlighted in red, and a corresponding message is displayed in the plot. The test for homogeneity of variances is done with a Levene test. A significant p-value means that group variances are not constant. In this case, you should consider modelling variances, e.g. via ~dispformula in glmmTMB. } \examples{ testData = createData(sampleSize = 100, overdispersion = 0.5, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # the plot function shows 2 plots and runs 4 tests # i) KS test i) Dispersion test iii) Outlier test iv) quantile test plot(simulationOutput, quantreg = TRUE) # testResiduals tests distribution, dispersion and outliers testResiduals(simulationOutput) ####### Individual tests ####### # KS test for correct distribution of residuals testUniformity(simulationOutput) # KS test for correct distribution within and between groups testCategorical(simulationOutput, testData$group) # Dispersion test - for details see ?testDispersion testDispersion(simulationOutput) # tests under and overdispersion # Outlier test (number of observations outside simulation envelope) # Use type = "boostrap" for exact values, see ?testOutliers testOutliers(simulationOutput, type = "binomial") # testing zero inflation testZeroInflation(simulationOutput) # testing generic summaries countOnes <- function(x) sum(x == 1) # testing for number of 1s testGeneric(simulationOutput, summary = countOnes) # 1-inflation testGeneric(simulationOutput, summary = countOnes, alternative = "less") # 1-deficit means <- function(x) mean(x) # testing if mean prediction fits testGeneric(simulationOutput, summary = means) spread <- function(x) sd(x) # testing if mean sd fits testGeneric(simulationOutput, summary = spread) } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/benchmarkRuntime.Rd0000644000176200001440000000251014677165224015622 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/runBenchmarks.R \name{benchmarkRuntime} \alias{benchmarkRuntime} \title{Benchmark runtimes of several functions} \usage{ benchmarkRuntime(createModel, evaluationFunctions, n) } \arguments{ \item{createModel}{a function that creates and returns a fitted model.} \item{evaluationFunctions}{a list of functions that are to be evaluated on the fitted models.} \item{n}{number of replicates.} } \description{ Benchmark runtimes of several functions } \details{ This is a small helper function designed to benchmark runtimes of several operations that are to be performed on a list of fitted models. In the example, this is used to benchmark the runtimes of several DHARMa tests. } \examples{ createModel = function(){ testData = createData(family = poisson(), overdispersion = 1, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1, data = testData, family = poisson()) return(fittedModel) } a = function(m){ testUniformity(m, plot = FALSE)$p.value } b = function(m){ testDispersion(m, plot = FALSE)$p.value } c = function(m){ testDispersion(m, plot = FALSE, type = "PearsonChisq")$p.value } evaluationFunctions = list(a,b, c) benchmarkRuntime(createModel, evaluationFunctions, 2) } \author{ Florian Hartig } DHARMa/man/getResiduals.Rd0000644000176200001440000000302014677165224014754 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{getResiduals} \alias{getResiduals} \alias{getResiduals.default} \alias{getResiduals.MixMod} \title{Get model residuals} \usage{ getResiduals(object, ...) \method{getResiduals}{default}(object, ...) \method{getResiduals}{MixMod}(object, ...) } \arguments{ \item{object}{a fitted model.} \item{...}{additional parameters to be passed on, usually to the residual function of the respective model class.} } \description{ Wrapper to get the residuals of a fitted model. } \details{ The purpose of this wrapper is to standardize the extraction of model residuals. Similar to some other functions, a key question is whether to calculate those conditional or unconditional on the fitted Random Effects. } \examples{ testData = createData(sampleSize = 400, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) # response that was used to fit the model getObservedResponse(fittedModel) # predictions of the model for these points getFitted(fittedModel) # extract simulations from the model as matrix getSimulations(fittedModel, nsim = 2) # extract simulations from the model for refit (often requires different structure) x = getSimulations(fittedModel, nsim = 2, type = "refit") getRefit(fittedModel, x[[1]]) getRefit(fittedModel, getObservedResponse(fittedModel)) } \seealso{ \link{getObservedResponse}, \link{getSimulations}, \link{getRefit}, \link{getFixedEffects}, \link{getFitted} } \author{ Florian Hartig } DHARMa/man/testGeneric.Rd0000644000176200001440000000760014677165224014605 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testGeneric} \alias{testGeneric} \title{Test for a generic summary statistic based on simulated data} \usage{ testGeneric(simulationOutput, summary, alternative = c("two.sided", "greater", "less"), plot = T, methodName = "DHARMa generic simulation test") } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{summary}{a function that can be applied to simulated / observed data. See examples below} \item{alternative}{a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis} \item{plot}{whether to plot the simulated summary} \item{methodName}{name of the test (will be used in plot)} } \description{ This function tests if a user-defined summary differs when applied to simulated / observed data. } \details{ This function applies a user-defined summary to the simulated/observed data of a DHARMa object and then performs a hypothesis test using the ratio Obs / Sim as the test statistic. The summary is applied directly to the data and not to the residuals, but it can easily be remodeled to apply summaries to the residuals by simply defining something like f = function(x) summary (x - predictions), as done in \link{testDispersion} } \note{ The summary function you specify will be applied to the data as it appears in your fitted model, which may not always be what you want. As an example, consider the case where we want to test for n-inflation in k/n data. If you provide your data via cbind (k, n-k), you have to test for n-inflation, but if you provide your data via k/n and weights = n, you should test for 1-inflation. When in doubt, check how the data is represented internally in model.frame(model) or via simulate(model). } \examples{ testData = createData(sampleSize = 100, overdispersion = 0.5, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # the plot function shows 2 plots and runs 4 tests # i) KS test i) Dispersion test iii) Outlier test iv) quantile test plot(simulationOutput, quantreg = TRUE) # testResiduals tests distribution, dispersion and outliers testResiduals(simulationOutput) ####### Individual tests ####### # KS test for correct distribution of residuals testUniformity(simulationOutput) # KS test for correct distribution within and between groups testCategorical(simulationOutput, testData$group) # Dispersion test - for details see ?testDispersion testDispersion(simulationOutput) # tests under and overdispersion # Outlier test (number of observations outside simulation envelope) # Use type = "boostrap" for exact values, see ?testOutliers testOutliers(simulationOutput, type = "binomial") # testing zero inflation testZeroInflation(simulationOutput) # testing generic summaries countOnes <- function(x) sum(x == 1) # testing for number of 1s testGeneric(simulationOutput, summary = countOnes) # 1-inflation testGeneric(simulationOutput, summary = countOnes, alternative = "less") # 1-deficit means <- function(x) mean(x) # testing if mean prediction fits testGeneric(simulationOutput, summary = means) spread <- function(x) sd(x) # testing if mean sd fits testGeneric(simulationOutput, summary = spread) } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/outliers.Rd0000644000176200001440000000426014677165224014176 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/DHARMa.R \name{outliers} \alias{outliers} \title{Return outliers} \usage{ outliers(object, lowerQuantile = 0, upperQuantile = 1, return = c("index", "logical")) } \arguments{ \item{object}{an object with simulated residuals created by \link{simulateResiduals}.} \item{lowerQuantile}{lower threshold for outliers. Default is zero = outside simulation envelope.} \item{upperQuantile}{upper threshold for outliers. Default is 1 = outside simulation envelope.} \item{return}{wheter to return an indices of outliers or a logical vector.} } \description{ Returns the outliers of a DHARMa object. } \details{ First of all, note that the standard definition of outlier in the DHARMa plots and outlier tests is an observation that is outside the simulation envelope. How far outside that is depends a lot on how many simulations you do. If you have 100 data points and to 100 simulations, you would expect to have one "outlier" on average, even with a perfectly fitting model. This is in fact what the outlier test tests. Thus, keep in mind that for a small number of simulations, outliers are mostly a technical term: these are points that are outside our simulations, but we don't know how far away they are. If you are seriously interested in HOW FAR outside the expected distribution a data point is, you should increase the number of simulations in \link{simulateResiduals} to be sure to get the tail of the data distribution correctly. In this case, it may make sense to adjust lowerQuantile and upperQuantile, e.g. to 0.025, 0.975, which would define outliers as values outside the central 95\% of the distribution. Also, note that outliers are particularly concerning if they have a strong influence on the model fit. One could test the influence, for example, by removing them from the data, or by some meausures of leverage, e.g. generalisations for Cook's distance as in Pinho, L. G. B., Nobre, J. S., & Singer, J. M. (2015). Cookā€™s distance for generalized linear mixed models. Computational Statistics & Data Analysis, 82, 126ā€“136. doi:10.1016/j.csda.2014.08.008. At the moment, however, no such function is provided in DHARMa. } DHARMa/man/testSpatialAutocorrelation.Rd0000644000176200001440000001671714703461527017725 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testSpatialAutocorrelation} \alias{testSpatialAutocorrelation} \title{Test for distance-based spatial (or similar type) autocorrelation} \usage{ testSpatialAutocorrelation(simulationOutput, x = NULL, y = NULL, distMat = NULL, alternative = c("two.sided", "greater", "less"), plot = TRUE) } \arguments{ \item{simulationOutput}{An object of class DHARMa, either created via \link{simulateResiduals} for supported models or via \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{x}{The x coordinate, in the same order as the data points. Must be specified unless distMat is provided.} \item{y}{The y coordinate, in the same order as the data points. Must be specified unless distMat is provided.} \item{distMat}{Optional distance matrix. If not provided, euclidean distances based on x and y will be calculated. See details for explanation.} \item{alternative}{A character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis.} \item{plot}{If T, and if x and y is provided, plot the output (see Details).} } \description{ This function performs a Moran's I test for distance-based spatial (or similar type) autocorrelation on the calculated quantile residuals. } \details{ The function performs Moran.I test from the package ape on the DHARMa residuals. If a distance matrix (distMat) is provided, calculations will be based on this distance matrix, and x,y coordinates will only used for the plotting (if provided). If distMat is not provided, the function will calculate the euclidean distances between x,y coordinates, and test Moran.I based on these distances. If plot = T, a plot will be produced showing each residual with at its x,y position, colored according to the residual value. Residuals with 0.5 are colored white, everything below 0.5 is colored increasinly red, everything above 0.5 is colored increasingly blue. Testing for spatial autocorrelation requires unique x,y values - if you have several observations per location, either use the \link{recalculateResiduals} function to aggregate residuals per location, or extract the residuals from the fitted object, and plot / test each of them independently for spatially repeated subgroups (a typical scenario would repeated spatial observation, in which case one could plot / test each time step separately for temporal autocorrelation). Note that the latter must be done by hand, outside \link{testSpatialAutocorrelation}. } \note{ Standard DHARMa simulations from models with (temporal / spatial / phylogenetic) conditional autoregressive terms will still have the respective temporal / spatial / phylogenetic correlation in the DHARMa residuals, unless the package you are using is modelling the autoregressive terms as explicit REs and is able to simulate conditional on the fitted REs. This has two consequences: \enumerate{ \item If you check the residuals for such a model, they will still show significant autocorrelation, even if the model fully accounts for this structure. \item Because the DHARMa residuals for such a model are not statistically independent any more, other tests (e.g. dispersion, uniformity) may have inflated type I error, i.e. you will have a higher likelihood of spurious residual problems. } There are three (non-exclusive) routes to address these issues when working with spatial / temporal / phylogenetic / other autoregressive models: \enumerate{ \item Simulate conditional on the fitted CAR structures (see conditional simulations in the help of \link{simulateResiduals}). \item Rotate simulations prior to residual calculations (see parameter rotation in \link{simulateResiduals}). \item Use custom tests / plots that explicitly compare the correlation structure in the simulated data to the correlation structure in the observed data. } } \examples{ testData = createData(sampleSize = 40, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1, data = testData) res = simulateResiduals(fittedModel) # Standard use testSpatialAutocorrelation(res, x = testData$x, y = testData$y) # Alternatively, one can provide a distance matrix dM = as.matrix(dist(cbind(testData$x, testData$y))) testSpatialAutocorrelation(res, distMat = dM) # You could add a spatial variogram via # library(gstat) # dat = data.frame(res = residuals(res), x = testData$x, y = testData$y) # coordinates(dat) = ~x+y # vario = variogram(res~1, data = dat, alpha=c(0,45,90,135)) # plot(vario, ylim = c(-1,1)) # if there are multiple observations with the same x values, # create first ar group with unique values for each location # then aggregate the residuals per location, and calculate # spatial autocorrelation on the new group # modifying x, y, so that we have the same location per group # just for completeness testData$x = as.numeric(testData$group) testData$y = as.numeric(testData$group) # calculating x, y positions per group groupLocations = aggregate(testData[, 6:7], list(testData$group), mean) # calculating residuals per group res2 = recalculateResiduals(res, group = testData$group) # running the spatial test on grouped residuals testSpatialAutocorrelation(res2, groupLocations$x, groupLocations$y) # careful when using REs to account for spatially clustered (but not grouped) # data. this originates from https://github.com/florianhartig/DHARMa/issues/81 # Assume our data is divided into clusters, where observations are close together # but not at the same point, and we suspect that observations in clusters are # autocorrelated clusters = 100 subsamples = 10 size = clusters * subsamples testData = createData(sampleSize = size, family = gaussian(), numGroups = clusters ) testData$x = rnorm(clusters)[testData$group] + rnorm(size, sd = 0.01) testData$y = rnorm(clusters)[testData$group] + rnorm(size, sd = 0.01) # It's a good idea to use a RE to take out the cluster effects. This accounts # for the autocorrelation within clusters library(lme4) fittedModel <- lmer(observedResponse ~ Environment1 + (1|group), data = testData) # DHARMa default is to re-simulate REs - this means spatial pattern remains # because residuals are still clustered res = simulateResiduals(fittedModel) testSpatialAutocorrelation(res, x = testData$x, y = testData$y) # However, it should disappear if you just calculate an aggregate residuals per cluster # Because at least how the data are simulated, cluster are spatially independent res2 = recalculateResiduals(res, group = testData$group) testSpatialAutocorrelation(res2, x = aggregate(testData$x, list(testData$group), mean)$x, y = aggregate(testData$y, list(testData$group), mean)$x) # For lme4, it's also possible to simulated residuals conditional on fitted # REs (re.form). Conditional on the fitted REs (i.e. accounting for the clusters) # the residuals should now be indepdendent. The remaining RSA we see here is # probably due to the RE shrinkage res = simulateResiduals(fittedModel, re.form = NULL) testSpatialAutocorrelation(res, x = testData$x, y = testData$y) } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/testResiduals.Rd0000644000176200001440000000535314703461527015162 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testResiduals} \alias{testResiduals} \title{DHARMa general residual test} \usage{ testResiduals(simulationOutput, plot = TRUE) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{plot}{if TRUE, plots functions of the tests are called.} } \description{ Calls uniformity, dispersion and outliers tests. } \details{ This function is a wrapper for the various test functions implemented in DHARMa. Currently, this function calls the functions \link{testUniformity}, \link{testDispersion}, and \link{testOutliers}. All other tests (see list below) have to be called by hand. } \examples{ testData = createData(sampleSize = 100, overdispersion = 0.5, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # the plot function shows 2 plots and runs 4 tests # i) KS test i) Dispersion test iii) Outlier test iv) quantile test plot(simulationOutput, quantreg = TRUE) # testResiduals tests distribution, dispersion and outliers testResiduals(simulationOutput) ####### Individual tests ####### # KS test for correct distribution of residuals testUniformity(simulationOutput) # KS test for correct distribution within and between groups testCategorical(simulationOutput, testData$group) # Dispersion test - for details see ?testDispersion testDispersion(simulationOutput) # tests under and overdispersion # Outlier test (number of observations outside simulation envelope) # Use type = "boostrap" for exact values, see ?testOutliers testOutliers(simulationOutput, type = "binomial") # testing zero inflation testZeroInflation(simulationOutput) # testing generic summaries countOnes <- function(x) sum(x == 1) # testing for number of 1s testGeneric(simulationOutput, summary = countOnes) # 1-inflation testGeneric(simulationOutput, summary = countOnes, alternative = "less") # 1-deficit means <- function(x) mean(x) # testing if mean prediction fits testGeneric(simulationOutput, summary = means) spread <- function(x) sd(x) # testing if mean sd fits testGeneric(simulationOutput, summary = spread) } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/checkSimulations.Rd0000644000176200001440000000071314677165224015634 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/simulateResiduals.R \name{checkSimulations} \alias{checkSimulations} \title{Check simulated data} \usage{ checkSimulations(simulatedResponse, nObs, nSim) } \arguments{ \item{simulatedResponse}{the simulated response} \item{nObs}{number of observations} \item{nSim}{number of simulations} } \description{ The function checks if the simulated data seems fine. } \keyword{internal} DHARMa/man/getPearsonResiduals.Rd0000644000176200001440000000314514677165224016314 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{getPearsonResiduals} \alias{getPearsonResiduals} \alias{getPearsonResiduals.default} \alias{getPearsonResiduals.gam} \title{Get Pearson residuals} \usage{ getPearsonResiduals(object, ...) \method{getPearsonResiduals}{default}(object, ...) \method{getPearsonResiduals}{gam}(object, ...) } \arguments{ \item{object}{a fitted model.} \item{...}{additional parameters to be passed on, usually to the residual function of the respective model class.} } \description{ Wrapper to get the Pearson residuals of a fitted model. } \details{ The purpose of this wrapper is to extract the Pearson residuals of a fitted model. This needed to be adopted because for some reason, mgcv uses the argument "scaled.pearson" for what most packags define as "pearson". See comments in ?residuals.gam. } \examples{ testData = createData(sampleSize = 400, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) # response that was used to fit the model getObservedResponse(fittedModel) # predictions of the model for these points getFitted(fittedModel) # extract simulations from the model as matrix getSimulations(fittedModel, nsim = 2) # extract simulations from the model for refit (often requires different structure) x = getSimulations(fittedModel, nsim = 2, type = "refit") getRefit(fittedModel, x[[1]]) getRefit(fittedModel, getObservedResponse(fittedModel)) } \seealso{ \link{getObservedResponse}, \link{getSimulations}, \link{getRefit}, \link{getFixedEffects}, \link{getFitted} } \author{ Florian Hartig } DHARMa/man/plotSimulatedResiduals.Rd0000644000176200001440000000135414677165224017033 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plots.R \name{plotSimulatedResiduals} \alias{plotSimulatedResiduals} \title{DHARMa standard residual plots} \usage{ plotSimulatedResiduals(simulationOutput, ...) } \arguments{ \item{simulationOutput}{an object with simulated residuals created by \link{simulateResiduals}} \item{...}{further options for \link{plotResiduals}. Consider in particular parameters quantreg, rank and asFactor. xlab, ylab and main cannot be changed when using plotSimulatedResiduals, but can be changed when using plotResiduals.} } \description{ DEPRECATED, use plot() instead } \note{ This function is deprecated. Use \link{plot.DHARMa} } \seealso{ \link{plotResiduals}, \link{plotQQunif} } DHARMa/man/testOverdispersionParametric.Rd0000644000176200001440000000073414677165224020255 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testOverdispersionParametric} \alias{testOverdispersionParametric} \title{Parametric overdisperstion tests} \usage{ testOverdispersionParametric(...) } \arguments{ \item{...}{arguments will be ignored, the parametric tests is no longer recommend} } \description{ Parametric overdisperstion tests } \details{ Deprecated, switch your code to using the \link{testDispersion} function. } DHARMa/man/testUniformity.Rd0000644000176200001440000000562014703461527015371 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testUniformity} \alias{testUniformity} \title{Test for overall uniformity} \usage{ testUniformity(simulationOutput, alternative = c("two.sided", "less", "greater"), plot = TRUE) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{alternative}{a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis. See \link[stats:ks.test]{stats::ks.test} for details} \item{plot}{if TRUE, plots calls \link{plotQQunif} as well} } \description{ This function tests the overall uniformity of the simulated residuals in a DHARMa object } \details{ The function applies a \link[stats:ks.test]{stats::ks.test} for uniformity on the simulated residuals. } \examples{ testData = createData(sampleSize = 100, overdispersion = 0.5, randomEffectVariance = 0) fittedModel <- glm(observedResponse ~ Environment1 , family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # the plot function shows 2 plots and runs 4 tests # i) KS test i) Dispersion test iii) Outlier test iv) quantile test plot(simulationOutput, quantreg = TRUE) # testResiduals tests distribution, dispersion and outliers testResiduals(simulationOutput) ####### Individual tests ####### # KS test for correct distribution of residuals testUniformity(simulationOutput) # KS test for correct distribution within and between groups testCategorical(simulationOutput, testData$group) # Dispersion test - for details see ?testDispersion testDispersion(simulationOutput) # tests under and overdispersion # Outlier test (number of observations outside simulation envelope) # Use type = "boostrap" for exact values, see ?testOutliers testOutliers(simulationOutput, type = "binomial") # testing zero inflation testZeroInflation(simulationOutput) # testing generic summaries countOnes <- function(x) sum(x == 1) # testing for number of 1s testGeneric(simulationOutput, summary = countOnes) # 1-inflation testGeneric(simulationOutput, summary = countOnes, alternative = "less") # 1-deficit means <- function(x) mean(x) # testing if mean prediction fits testGeneric(simulationOutput, summary = means) spread <- function(x) sd(x) # testing if mean sd fits testGeneric(simulationOutput, summary = spread) } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/hist.DHARMa.Rd0000644000176200001440000000565714701671620014273 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plots.R \name{hist.DHARMa} \alias{hist.DHARMa} \title{Histogram of DHARMa residuals} \usage{ \method{hist}{DHARMa}(x, breaks = seq(-0.02, 1.02, len = 53), col = c(.Options$DHARMaSignalColor, rep("lightgrey", 50), .Options$DHARMaSignalColor), main = "Hist of DHARMa residuals", xlab = "Residuals (outliers are marked red)", cex.main = 1, ...) } \arguments{ \item{x}{A DHARMa simulation output (class DHARMa)} \item{breaks}{Breaks for hist() function.} \item{col}{Color for histogram bars.} \item{main}{Plot title.} \item{xlab}{Plot x-axis label.} \item{cex.main}{Plot cex.main.} \item{...}{Other arguments to be passed on to hist().} } \description{ The function produces a histogram from a DHARMa output. Outliers are marked red. } \details{ The function calls hist() to create a histogram of the scaled residuals. Outliers are marked red as default but it can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. } \examples{ testData = createData(sampleSize = 200, family = poisson(), randomEffectVariance = 1, numGroups = 10) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) ######### main plotting function ############# # for all functions, quantreg = T will be more # informative, but slower plot(simulationOutput, quantreg = FALSE) ############# Distribution ###################### plotQQunif(simulationOutput = simulationOutput, testDispersion = FALSE, testUniformity = FALSE, testOutliers = FALSE) hist(simulationOutput ) ############# residual plots ############### # rank transformation, using a simulationOutput plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE) # smooth scatter plot - usually used for large datasets, default for n > 10000 plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE, smoothScatter = TRUE) # residual vs predictors, using explicit values for pred, residual plotResiduals(simulationOutput, form = testData$Environment1, quantreg = FALSE) # if pred is a factor, or if asFactor = TRUE, will produce a boxplot plotResiduals(simulationOutput, form = testData$group) # to diagnose overdispersion and heteroskedasticity it can be useful to # display residuals as absolute deviation from the expected mean 0.5 plotResiduals(simulationOutput, absoluteDeviation = TRUE, quantreg = FALSE) # All these options can also be provided to the main plotting function # If you want to plot summaries per group, use simulationOutput = recalculateResiduals(simulationOutput, group = testData$group) plot(simulationOutput, quantreg = FALSE) # we see one residual point per RE } \seealso{ \link{plotSimulatedResiduals}, \link{plotResiduals} } DHARMa/man/recalculateResiduals.Rd0000644000176200001440000000751414677165224016475 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/simulateResiduals.R \name{recalculateResiduals} \alias{recalculateResiduals} \title{Recalculate residuals with grouping} \usage{ recalculateResiduals(simulationOutput, group = NULL, aggregateBy = sum, sel = NULL, seed = 123, method = c("PIT", "traditional"), rotation = NULL) } \arguments{ \item{simulationOutput}{an object with simulated residuals created by \link{simulateResiduals}.} \item{group}{group of each data point.} \item{aggregateBy}{function for the aggregation. Default is sum. This should only be changed if you know what you are doing. Note in particular that the expected residual distribution might not be flat any more if you choose general functions, such as sd etc.} \item{sel}{an optional vector for selecting the data to be aggregated.} \item{seed}{the random seed to be used within DHARMa. The default setting, recommended for most users, is keep the random seed on a fixed value 123. This means that you will always get the same randomization and thus teh same result when running the same code. NULL = no new seed is set, but previous random state will be restored after simulation. FALSE = no seed is set, and random state will not be restored. The latter two options are only recommended for simulation experiments. See vignette for details.} \item{method}{the quantile randomization method used. The two options implemented at the moment are probability integral transform (PIT-) residuals (current default), and the "traditional" randomization procedure, that was used in DHARMa until version 0.3.0. For details, see \link{getQuantile}.} \item{rotation}{optional rotation of the residual space to remove residual autocorrelation. See details in \link{simulateResiduals}, section \emph{residual auto-correlation} for an extended explanation, and \link{getQuantile} for syntax.} } \value{ an object of class DHARMa, similar to what is returned by \link{simulateResiduals}, but with additional outputs for the new grouped calculations. Note that the relevant outputs are 2x in the object, the first is the grouped calculations (which is returned by $name access), and later another time, under identical name, the original output. Moreover, there is a function 'aggregateByGroup', which can be used to aggregate predictor variables in the same way as the variables calculated here. } \description{ The purpose of this function is to recalculate scaled residuals per group, based on the simulations done by \link{simulateResiduals}. } \details{ The function aggregates the observed and simulated data per group according to the function provided by the aggregateBy option. DHARMa residuals are then calculated exactly as for a single data point (see \link{getQuantile} for details). } \examples{ library(lme4) testData = createData(sampleSize = 100, overdispersion = 0.5, family = poisson()) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # standard plot plot(simulationOutput) # one of the possible test, for other options see ?testResiduals / vignette testDispersion(simulationOutput) # the calculated residuals can be accessed via residuals(simulationOutput) # transform residuals to other pdf, see ?residuals.DHARMa for details residuals(simulationOutput, quantileFunction = qnorm, outlierValues = c(-7,7)) # get residuals that are outside the simulation envelope outliers(simulationOutput) # calculating aggregated residuals per group simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group) plot(simulationOutput2, quantreg = FALSE) # calculating residuals only for subset of the data simulationOutput3 = recalculateResiduals(simulationOutput, sel = testData$group == 1 ) plot(simulationOutput3, quantreg = FALSE) } DHARMa/man/plotQQunif.Rd0000644000176200001440000000636214701671620014425 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plots.R \name{plotQQunif} \alias{plotQQunif} \title{Quantile-quantile plot for a uniform distribution} \usage{ plotQQunif(simulationOutput, testUniformity = TRUE, testOutliers = TRUE, testDispersion = TRUE, ...) } \arguments{ \item{simulationOutput}{A DHARMa simulation output (class DHARMa).} \item{testUniformity}{If T, the function \link{testUniformity} will be called and the result will be added to the plot.} \item{testOutliers}{If T, the function \link{testOutliers} will be called and the result will be added to the plot.} \item{testDispersion}{If T, the function \link{testDispersion} will be called and the result will be added to the plot.} \item{...}{Arguments to be passed on to \link[gap:qqunif]{gap::qqunif}.} } \description{ The function produces a uniform quantile-quantile plot from a DHARMa output. Optionally, tests for uniformity, outliers and dispersion can be added. } \details{ The function calls qqunif() from the R package gap to create a quantile-quantile plot for a uniform distribution, and overlays tests for particular distributional problems as specified. When tests are displayed, significant p-values are highlighted in the color red by default. This can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. } \examples{ testData = createData(sampleSize = 200, family = poisson(), randomEffectVariance = 1, numGroups = 10) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) ######### main plotting function ############# # for all functions, quantreg = T will be more # informative, but slower plot(simulationOutput, quantreg = FALSE) ############# Distribution ###################### plotQQunif(simulationOutput = simulationOutput, testDispersion = FALSE, testUniformity = FALSE, testOutliers = FALSE) hist(simulationOutput ) ############# residual plots ############### # rank transformation, using a simulationOutput plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE) # smooth scatter plot - usually used for large datasets, default for n > 10000 plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE, smoothScatter = TRUE) # residual vs predictors, using explicit values for pred, residual plotResiduals(simulationOutput, form = testData$Environment1, quantreg = FALSE) # if pred is a factor, or if asFactor = TRUE, will produce a boxplot plotResiduals(simulationOutput, form = testData$group) # to diagnose overdispersion and heteroskedasticity it can be useful to # display residuals as absolute deviation from the expected mean 0.5 plotResiduals(simulationOutput, absoluteDeviation = TRUE, quantreg = FALSE) # All these options can also be provided to the main plotting function # If you want to plot summaries per group, use simulationOutput = recalculateResiduals(simulationOutput, group = testData$group) plot(simulationOutput, quantreg = FALSE) # we see one residual point per RE } \seealso{ \link{plotSimulatedResiduals}, \link{plotResiduals} } DHARMa/man/DHARMa-package.Rd0000644000176200001440000000363314704245735014715 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/DHARMa.R \docType{package} \name{DHARMa-package} \alias{DHARMa} \alias{DHARMa-package} \title{DHARMa: Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models} \description{ The 'DHARMa' package uses a simulation-based approach to create readily interpretable scaled (quantile) residuals for fitted (generalized) linear mixed models. Currently supported are linear and generalized linear (mixed) models from 'lme4' (classes 'lmerMod', 'glmerMod'), 'glmmTMB', 'GLMMadaptive', and 'spaMM'; phylogenetic linear models from 'phylolm' (classes 'phylolm' and 'phyloglm'); generalized additive models ('gam' from 'mgcv'); 'glm' (including 'negbin' from 'MASS', but excluding quasi-distributions) and 'lm' model classes. Moreover, externally created simulations, e.g. posterior predictive simulations from Bayesian software such as 'JAGS', 'STAN', or 'BUGS' can be processed as well. The resulting residuals are standardized to values between 0 and 1 and can be interpreted as intuitively as residuals from a linear regression. The package also provides a number of plot and test functions for typical model misspecification problems, such as over/underdispersion, zero-inflation, and residual spatial, phylogenetic and temporal autocorrelation. } \details{ To get started with the package, look at the vignette and start with \link{simulateResiduals} } \references{ vignette("DHARMa", package="DHARMa") } \seealso{ Useful links: \itemize{ \item \url{http://florianhartig.github.io/DHARMa/} \item Report bugs at \url{https://github.com/florianhartig/DHARMa/issues} } } \author{ \strong{Maintainer}: Florian Hartig \email{florian.hartig@biologie.uni-regensburg.de} (\href{https://orcid.org/0000-0002-6255-9059}{ORCID}) Other contributors: \itemize{ \item Lukas Lohse [contributor] \item Melina de Souza leite [contributor] } } \keyword{internal} DHARMa/man/plotResiduals.Rd0000644000176200001440000001576114701671620015160 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plots.R \name{plotResiduals} \alias{plotResiduals} \title{Generic res ~ pred scatter plot with spline or quantile regression on top} \usage{ plotResiduals(simulationOutput, form = NULL, quantreg = NULL, rank = TRUE, asFactor = NULL, smoothScatter = NULL, quantiles = c(0.25, 0.5, 0.75), absoluteDeviation = FALSE, ...) } \arguments{ \item{simulationOutput}{An object, usually a DHARMa object, from which residual values can be extracted. Alternatively, a vector with residuals or a fitted model can be provided, which will then be transformed into a DHARMa object.} \item{form}{Optional predictor against which the residuals should be plotted. Default is to used the predicted(simulationOutput).} \item{quantreg}{Whether to perform a quantile regression based on \link{testQuantiles} or a smooth spline around the mean. Default NULL chooses T for nObs < 2000, and F otherwise.} \item{rank}{If T, the values provided in form will be rank transformed. This will usually make patterns easier to spot visually, especially if the distribution of the predictor is skewed. If form is a factor, this has no effect.} \item{asFactor}{Should a numeric predictor provided in form be treated as a factor. Default is to choose this for < 10 unique values, as long as enough predictions are available to draw a boxplot.} \item{smoothScatter}{if T, a smooth scatter plot will plotted instead of a normal scatter plot. This makes sense when the number of residuals is very large. Default NULL chooses T for nObs > 10000, and F otherwise.} \item{quantiles}{For a quantile regression, which quantiles should be plotted. Default is 0.25, 0.5, 0.75.} \item{absoluteDeviation}{If T, switch from displaying normal quantile residuals to absolute deviation from the mean expectation of 0.5 (calculated as 2 * abs(res - 0.5)). The purpose of this is to test explicitly for heteroskedasticity, see details.} \item{...}{Additional arguments to plot / boxplot.} } \value{ If quantile tests are performed, the function returns them invisibly. } \description{ The function creates a generic residual plot with either spline or quantile regression to highlight patterns in the residuals. Outliers are highlighted in red by default (but see Details). } \details{ The function plots residuals against a predictor (by default against the fitted value, extracted from the DHARMa object, or any other predictor). Outliers are highlighted in red as default (for information on definition and interpretation of outliers, see \link{testOutliers}). This can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. To provide a visual aid for detecting deviations from uniformity in the y-direction, the plot function calculates an (optional) quantile regression of the residuals, by default for the 0.25, 0.5 and 0.75 quantiles. Since the residuals should be uniformly distributed for a correctly specified model, the theoretical expectations for these regressions are straight lines at 0.25, 0.5 and 0.75, shown as dashed black lines on the plot. However, even for a perfect model, some deviation from these expectations is to be expected by chance, especially if the sample size is small. The function therefore tests whether the deviation of the fitted quantile regression from the expectation is significant, using \link{testQuantiles}. If so, the significant quantile regression is highlighted in red (as default) and a warning is displayed in the plot. Overdispersion typically manifests itself as Q1 (0.25) deviating towards 0 and Q3 (0.75) deviating towards 1. Heteroskedasticity manifests itself as non-parallel quantile lines. To diagnose heteroskedasticity and overdispersion, it can be helpful to additionally plot the absolute deviation of the residuals from the mean expectation of 0.5, using the option absoluteDeviation = T. In this case, we would again expect Q1-Q3 quantile lines at 0.25, 0.5, 0.75, but greater dispersion (also locally in the case of heteroskedasticity) always manifests itself in deviations towards 1. The quantile regression can take some time to calculate, especially for larger data sets. For this reason, quantreg = F can be set to generate a smooth spline instead. This is the default for n > 2000. If form is a factor, a boxplot will be plotted instead of a scatter plot. The distribution for each factor level should be uniformly distributed, so the box should go from 0.25 to 0.75, with the median line at 0.5 (within-group). To test if deviations from those expecations are significant, KS-tests per group and a Levene test for homogeneity of variances is performed. See \link{testCategorical} for details. } \note{ If nObs > 10000, the scatter plot is replaced by graphics::smoothScatter #' @note The color for highlighting outliers and quantile lines/splines with significant tests can be changed by setting \code{options(DHARMaSignalColor = "red")} to a different color. See \code{getOption("DHARMaSignalColor")} for the current setting. This is convenient for a color-blind friendly display, since red and black are difficult for some people to separate. } \examples{ testData = createData(sampleSize = 200, family = poisson(), randomEffectVariance = 1, numGroups = 10) fittedModel <- glm(observedResponse ~ Environment1, family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) ######### main plotting function ############# # for all functions, quantreg = T will be more # informative, but slower plot(simulationOutput, quantreg = FALSE) ############# Distribution ###################### plotQQunif(simulationOutput = simulationOutput, testDispersion = FALSE, testUniformity = FALSE, testOutliers = FALSE) hist(simulationOutput ) ############# residual plots ############### # rank transformation, using a simulationOutput plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE) # smooth scatter plot - usually used for large datasets, default for n > 10000 plotResiduals(simulationOutput, rank = TRUE, quantreg = FALSE, smoothScatter = TRUE) # residual vs predictors, using explicit values for pred, residual plotResiduals(simulationOutput, form = testData$Environment1, quantreg = FALSE) # if pred is a factor, or if asFactor = TRUE, will produce a boxplot plotResiduals(simulationOutput, form = testData$group) # to diagnose overdispersion and heteroskedasticity it can be useful to # display residuals as absolute deviation from the expected mean 0.5 plotResiduals(simulationOutput, absoluteDeviation = TRUE, quantreg = FALSE) # All these options can also be provided to the main plotting function # If you want to plot summaries per group, use simulationOutput = recalculateResiduals(simulationOutput, group = testData$group) plot(simulationOutput, quantreg = FALSE) # we see one residual point per RE } \seealso{ \link{plotQQunif}, \link{testQuantiles}, \link{testOutliers} } DHARMa/man/testOutliers.Rd0000644000176200001440000001132614701671620015025 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testOutliers} \alias{testOutliers} \title{Test for outliers} \usage{ testOutliers(simulationOutput, alternative = c("two.sided", "greater", "less"), margin = c("both", "upper", "lower"), type = c("default", "bootstrap", "binomial"), nBoot = 100, plot = TRUE, plotBoostrap = FALSE) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{alternative}{a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" (default) compared to the simulated null hypothesis} \item{margin}{whether to test for outliers only at the lower, only at the upper, or both sides (default) of the simulated data distribution} \item{type}{either default, bootstrap or binomial. See details} \item{nBoot}{number of boostrap replicates. Only used ot type = "bootstrap"} \item{plot}{if TRUE, the function will create an additional plot} \item{plotBoostrap}{if plot should be produced of outlier frequencies calculated under the bootstrap} } \description{ This function tests if the number of observations outside the simulatio envelope are larger or smaller than expected } \details{ DHARMa residuals are created by simulating from the fitted model, and comparing the simulated values to the observed data. It can occur that all simulated values are higher or smaller than the observed data, in which case they get the residual value of 0 and 1, respectively. I refer to these values as simulation outliers, or simply outliers. Because no data was simulated in the range of the observed value, we don't know "how strongly" these values deviate from the model expectation, so the term "outlier" should be used with a grain of salt. It is not a judgment about the magnitude of the residual deviation, but simply a dichotomous sign that we are outside the simulated range. Moreover, the number of outliers will decrease as we increase the number of simulations. To test if the outliers are a concern, testOutliers implements 2 options (bootstrap, binomial), which can be chosen via the parameter "type". The third option (default) chooses bootstrap for integer-valued distribubtions with nObs < 500, and else binomial. The binomial test considers that under the null hypothesis that the model is correct, and for continuous distributions (i.e. data and the model distribution are identical and continous), the probability that a given observation is higher than all simulations is 1/(nSim +1), and binomial distributed. The testOutlier function can test this null hypothesis via type = "binomial". In principle, it would be nice if we could extend this idea to integer-valued distributions, which are randomized via the PIT procedure (see \link{simulateResiduals}), the rate of "true" outliers is more difficult to calculate, and in general not 1/(nSim +1). The testOutlier function implements a small tweak that calculates the rate of residuals that are closer than 1/(nSim+1) to the 0/1 border, which roughly occur at a rate of nData /(nSim +1). This approximate value, however, is generally not exact, and may be particularly off non-bounded integer-valued distributions (such as Poisson or Negative Binomial). For this reason, the testOutlier function implements an alternative procedure that uses the bootstrap to generate a simulation-based expectation for the outliers. It is recommended to use the bootstrap for integer-valued distributions (and integer-valued only, because it has no advantage for continuous distributions, ideally with reasonably high values of nSim and nBoot (I recommend at least 1000 for both). Because of the high runtime, however, this option is switched off for type = default when nObs > 500. Both binomial or bootstrap generate a null expectation, and then test for an excess or lack of outliers. Per default, testOutliers() looks for both, so if you get a significant p-value, you have to check if you have to many or too few outliers. An excess of outliers is to be interpreted as too many values outside the simulation envelope. This could be caused by overdispersion, or by what we classically call outliers. A lack of outliers would be caused, for example, by underdispersion. } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/ensurePredictor.Rd0000644000176200001440000000115314701671620015471 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/plots.R \name{ensurePredictor} \alias{ensurePredictor} \title{Ensures the existence of a valid predictor to plot residuals against} \usage{ ensurePredictor(simulationOutput, predictor = NULL) } \arguments{ \item{simulationOutput}{A DHARMa simulation output or an object that can be converted into a DHARMa simulation output.} \item{predictor}{An optional predictor. If no predictor is provided, will try to extract the fitted value.} } \description{ Ensures the existence of a valid predictor to plot residuals against } \keyword{internal} DHARMa/man/createData.Rd0000644000176200001440000000652114677165224014367 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/createData.R \name{createData} \alias{createData} \title{Simulate test data} \usage{ createData(sampleSize = 100, intercept = 0, fixedEffects = 1, quadraticFixedEffects = NULL, numGroups = 10, randomEffectVariance = 1, overdispersion = 0, family = poisson(), scale = 1, cor = 0, roundPoissonVariance = NULL, pZeroInflation = 0, binomialTrials = 1, temporalAutocorrelation = 0, spatialAutocorrelation = 0, factorResponse = FALSE, replicates = 1, hasNA = FALSE) } \arguments{ \item{sampleSize}{sample size of the dataset.} \item{intercept}{intercept (linear scale).} \item{fixedEffects}{vector of fixed effects (linear scale).} \item{quadraticFixedEffects}{vector of quadratic fixed effects (linear scale).} \item{numGroups}{number of groups for the random effect.} \item{randomEffectVariance}{variance of the random effect (intercept).} \item{overdispersion}{if this is a numeric value, it will be used as the sd of a random normal variate that is added to the linear predictor. Alternatively, a random function can be provided that takes as input the linear predictor.} \item{family}{family.} \item{scale}{scale if the distribution has a scale (e.g. sd for the Gaussian)} \item{cor}{correlation between predictors.} \item{roundPoissonVariance}{if set, this creates a uniform noise on the possion response. The aim of this is to create heteroscedasticity.} \item{pZeroInflation}{probability to set any data point to zero.} \item{binomialTrials}{Number of trials for the binomial. Only active if family == binomial.} \item{temporalAutocorrelation}{strength of temporalAutocorrelation.} \item{spatialAutocorrelation}{strength of spatial Autocorrelation.} \item{factorResponse}{should the response be transformed to a factor (inteded to be used for 0/1 data).} \item{replicates}{number of datasets to create.} \item{hasNA}{should an NA be added to the environmental predictor (for test purposes).} } \description{ This function creates synthetic dataset with various problems such as overdispersion, zero-inflation, etc. } \examples{ testData = createData(sampleSize = 500, intercept = 2, fixedEffects = c(1), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3), randomEffectVariance = 0) par(mfrow = c(1,2)) plot(testData$Environment1, testData$observedResponse) hist(testData$observedResponse) # with zero-inflation testData = createData(sampleSize = 500, intercept = 2, fixedEffects = c(1), overdispersion = 0, family = poisson(), quadraticFixedEffects = c(-3), randomEffectVariance = 0, pZeroInflation = 0.6) par(mfrow = c(1,2)) plot(testData$Environment1, testData$observedResponse) hist(testData$observedResponse) # binomial with multiple trials testData = createData(sampleSize = 40, intercept = 2, fixedEffects = c(1), overdispersion = 0, family = binomial(), quadraticFixedEffects = c(-3), randomEffectVariance = 0, binomialTrials = 20) plot(observedResponse1 / observedResponse0 ~ Environment1, data = testData, ylab = "Proportion 1") # spatial / temporal correlation testData = createData(sampleSize = 100, family = poisson(), spatialAutocorrelation = 3, temporalAutocorrelation = 3) plot(log(observedResponse) ~ time, data = testData) plot(log(observedResponse) ~ x, data = testData) } DHARMa/man/checkModel.Rd0000644000176200001440000000142314677165224014364 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{checkModel} \alias{checkModel} \title{Check if the fitted model is supported by DHARMa} \usage{ checkModel(fittedModel, stop = F) } \arguments{ \item{fittedModel}{a fitted model.} \item{stop}{whether to throw an error if the model is not supported by DHARMa.} } \description{ The function checks if the fitted model is supported by DHARMa, and if there are other issues that could create problems. } \details{ The main purpose of this function os to check if the fitted model class is supported by DHARMa. The function additionally checks for properties of the fitted model that could create problems for calculating residuals or working with the resuls in DHARMa. } \keyword{internal} DHARMa/man/testSimulatedResiduals.Rd0000644000176200001440000000126614677165224017036 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testSimulatedResiduals} \alias{testSimulatedResiduals} \title{Residual tests} \usage{ testSimulatedResiduals(simulationOutput) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or by \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} } \description{ Residual tests } \details{ Deprecated, switch your code to using the \link{testResiduals} function } \author{ Florian Hartig } DHARMa/man/ensureDHARMa.Rd0000644000176200001440000000116014665273541014541 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/DHARMa.R \name{ensureDHARMa} \alias{ensureDHARMa} \title{Ensures that an object is of class DHARMa} \usage{ ensureDHARMa(simulationOutput, convert = FALSE) } \arguments{ \item{simulationOutput}{a DHARMa simulation output or an object that can be converted into a DHARMa simulation output} \item{convert}{if TRUE, attempts to convert model + numeric to DHARMa, if "Model", converts only supported models to DHARMa} } \value{ an object of class DHARMa } \description{ Ensures that an object is of class DHARMa } \details{ The } \keyword{internal} DHARMa/man/getFamily.Rd0000644000176200001440000000127214703461527014244 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{getFamily} \alias{getFamily} \alias{getFamily.default} \alias{getFamily.phylolm} \alias{getFamily.phyloglm} \title{Get model family} \usage{ getFamily(object, ...) \method{getFamily}{default}(object, ...) \method{getFamily}{phylolm}(object, ...) \method{getFamily}{phyloglm}(object, ...) } \arguments{ \item{object}{a fitted model.} \item{...}{additional parameters to be passed on.} } \description{ Wrapper to get the family of a fitted model. } \seealso{ \link{getObservedResponse}, \link{getSimulations}, \link{getRefit}, \link{getFixedEffects}, \link{getFitted} } \author{ Florian Hartig } DHARMa/man/simulateResiduals.Rd0000644000176200001440000002302014704245735016017 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/simulateResiduals.R \name{simulateResiduals} \alias{simulateResiduals} \title{Create simulated residuals} \usage{ simulateResiduals(fittedModel, n = 250, refit = FALSE, integerResponse = NULL, plot = FALSE, seed = 123, method = c("PIT", "traditional"), rotation = NULL, ...) } \arguments{ \item{fittedModel}{A fitted model of a class supported by DHARMa.} \item{n}{Number of simulations. The smaller the number, the higher the stochastic error on the residuals. Also, for very small n, discretization artefacts can influence the tests. Default is 250, which is a relatively safe value. You can consider increasing to 1000 to stabilize the simulated values.} \item{refit}{If FALSE, new data will be simulated and scaled residuals will be created by comparing observed data with new data. If TRUE, the model will be refitted on the simulated data (parametric bootstrap), and scaled residuals will be created by comparing observed with refitted residuals.} \item{integerResponse}{If TRUE, noise will be added at to the residuals to maintain a uniform expectations for integer responses (such as Poisson or Binomial). Usually, the model will automatically detect the appropriate setting, so there is no need to adjust this setting.} \item{plot}{If TRUE, \link{plotResiduals} will be directly run after the residuals have been calculated.} \item{seed}{The random seed to be used within DHARMa. The default setting, recommended for most users, is keep the random seed on a fixed value 123. This means that you will always get the same randomization and thus the same result when running the same code. If NULL, no new seed is set, but previous random state will be restored after simulation. If FALSE, no seed is set, and random state will not be restored. The latter two options are only recommended for simulation experiments. See vignette for details.} \item{method}{For refit = FALSE, the quantile randomization method is used. The two options implemented at the moment are probability integral transform (PIT-) residuals (current default), and the "traditional" randomization procedure, that was used in DHARMa until version 0.3.0. refit = T will always use "traditional", respectively of the value of method. For details, see \link{getQuantile}.} \item{rotation}{Optional rotation of the residual space prior to calculating the quantile residuals. The main purpose of this is to account for residual covariance as created by temporal, spatial or phylogenetic autocorrelation. See details below, section \emph{residual autocorrelation} as well as the help of \link{getQuantile} and, for a practical example, \link{testTemporalAutocorrelation}.} \item{...}{Further parameters to pass on to the simulate function of the model object. An important use of this is to specify whether simulations should be conditional on the current random effect estimates, e.g. via re.form. Note that not all models support syntax to specify conditional or unconditional simulations. See details and \link{getSimulations}.} } \value{ An S3 class of type "DHARMa". Implemented S3 functions include \link{plot.DHARMa}, \link{print.DHARMa} and \link{residuals.DHARMa}. For other functions that can be used on a DHARMa object, see section "See Also" below. } \description{ The function creates scaled residuals by simulating from the fitted model. Residuals can be extracted with \link{residuals.DHARMa}. See \link{testResiduals} for an overview of residual tests, \link{plot.DHARMa} for an overview of available plots. } \details{ There are a number of important considerations when simulating from a more complex (hierarchical) model: \strong{Re-simulating random effects / hierarchical structure}: in a hierarchical model, we have several stochastic processes aligned on top of each other. Specifically, in a GLMM, we have a lower level stochastic process (random effect), whose result enters into a higher level (e.g. Poisson distribution). For other hierarchical models such as state-space models, similar considerations apply. In such a situation, we have to decide if we want to re-simulate all stochastic levels, or only a subset of those. For example, in a GLMM, it is common to only simulate the last stochastic level (e.g. Poisson) conditional on the fitted random effects. This is often referred to as a conditional simulation. For controlling how many levels should be re-simulated, the simulateResidual function allows to pass on parameters to the simulate function of the fitted model object. Please refer to the help of the different simulate functions (e.g. ?simulate.merMod) for details. For merMod (lme4) model objects, the relevant parameters are parameters are use.u and re.form. For glmmTMB model objects, the package version 1.1.10 has a temporary solution to simulate conditional to all random effects (see \link[glmmTMB:set_simcodes]{glmmTMB::set_simcodes} val = "fix", and issue \href{https://github.com/glmmTMB/glmmTMB/issues/888}{#888} in glmmTMB GitHub repository. If the model is correctly specified, the simulated residuals should be flat regardless how many hierarchical levels we re-simulate. The most thorough procedure would therefore be to test all possible options. If testing only one option, I would recommend to re-simulate all levels, because this essentially tests the model structure as a whole. This is the default setting in the DHARMa package. A potential drawback is that re-simulating the lower-level random effects creates more variability, which may reduce power for detecting problems in the upper-level stochastic processes. In particular dispersion tests may produce different results when switching from conditional to unconditional simulations, and often the conditional simulation is more sensitive. \strong{Refitting or not}: a third issue is how residuals are calculated. simulateResiduals has two options that are controlled by the refit parameter: \enumerate{ \item if refit = FALSE (default), new data is simulated from the fitted model, and residuals are calculated by comparing the observed data to the new data. \item if refit = TRUE, a parametric bootstrap is performed, meaning that the model is refit on the new data, and residuals are created by comparing observed residuals against refitted residuals. I advise against using this method per default (see more comments in the vignette), unless you are really sure that you need it. } \strong{Residuals per group}: In many situations, it can be useful to look at residuals per group, e.g. to see how much the model over / underpredicts per plot, year or subject. To do this, use \link{recalculateResiduals}, together with a grouping variable (see also help). \strong{Transformation to other distributions}: DHARMa calculates residuals for which the theoretical expectation (assuming a correctly specified model) is uniform. To transform this residuals to another distribution (e.g. so that a correctly specified model will have normal residuals) see \link{residuals.DHARMa}. \strong{Integer responses}: this is only relevant if method = "traditional", in which case it activates the randomization of the residuals. Usually, this does not need to be changed, as DHARMa will try to automatically check if the fitted model has an integer or discrete distribution via the family argument. However, in some cases the family does not allow to uniquely identify the distribution type. For example, a tweedie distribution can be interger or continuous. Therefore, DHARMa will additionally check the simulation results for repeated values, and will change the distribution type if repeated values are found (a message is displayed in this case). \strong{Residual autocorrelation}: a common problem is residual autocorrelation. Spatial, temporal and phylogenetic autocorrelation can be tested with \link{testSpatialAutocorrelation}, \link{testTemporalAutocorrelation} and \link{testPhylogeneticAutocorrelation}. If simulations are unconditional, residual correlations will be maintained, even if the autocorrelation is addressed by an appropriate CAR structure. This may be a problem, because autocorrelation may create apparently systematic patterns in plots or tests such as \link{testUniformity}. To reduce this problem, either simulate conditional on fitted correlated REs, or rotate residuals via the rotation parameter (the latter will likely only work in approximately linear models). See \link{getQuantile} for details on the rotation. } \examples{ library(lme4) testData = createData(sampleSize = 100, overdispersion = 0.5, family = poisson()) fittedModel <- glmer(observedResponse ~ Environment1 + (1|group), family = "poisson", data = testData) simulationOutput <- simulateResiduals(fittedModel = fittedModel) # standard plot plot(simulationOutput) # one of the possible test, for other options see ?testResiduals / vignette testDispersion(simulationOutput) # the calculated residuals can be accessed via residuals(simulationOutput) # transform residuals to other pdf, see ?residuals.DHARMa for details residuals(simulationOutput, quantileFunction = qnorm, outlierValues = c(-7,7)) # get residuals that are outside the simulation envelope outliers(simulationOutput) # calculating aggregated residuals per group simulationOutput2 = recalculateResiduals(simulationOutput, group = testData$group) plot(simulationOutput2, quantreg = FALSE) # calculating residuals only for subset of the data simulationOutput3 = recalculateResiduals(simulationOutput, sel = testData$group == 1 ) plot(simulationOutput3, quantreg = FALSE) } \seealso{ \link{testResiduals}, \link{plotResiduals}, \link{recalculateResiduals}, \link{outliers} } DHARMa/man/getObservedResponse.Rd0000644000176200001440000000303414677165224016316 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{getObservedResponse} \alias{getObservedResponse} \alias{getObservedResponse.default} \alias{getObservedResponse.HLfit} \alias{getObservedResponse.phylolm} \alias{getObservedResponse.phyloglm} \title{Get model response} \usage{ getObservedResponse(object, ...) \method{getObservedResponse}{default}(object, ...) \method{getObservedResponse}{HLfit}(object, ...) \method{getObservedResponse}{phylolm}(object, ...) \method{getObservedResponse}{phyloglm}(object, ...) } \arguments{ \item{object}{a fitted model.} \item{...}{additional parameters.} } \description{ Extract the response of a fitted model. } \details{ The purpose of this function is to safely extract the observed response (dependent variable) of the fitted model classes. } \examples{ testData = createData(sampleSize = 400, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) # response that was used to fit the model getObservedResponse(fittedModel) # predictions of the model for these points getFitted(fittedModel) # extract simulations from the model as matrix getSimulations(fittedModel, nsim = 2) # extract simulations from the model for refit (often requires different structure) x = getSimulations(fittedModel, nsim = 2, type = "refit") getRefit(fittedModel, x[[1]]) getRefit(fittedModel, getObservedResponse(fittedModel)) } \seealso{ \link{getRefit}, \link{getSimulations}, \link{getFixedEffects}, \link{getFitted} } \author{ Florian Hartig } DHARMa/man/testPhylogeneticAutocorrelation.Rd0000644000176200001440000000720114703461527020746 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/tests.R \name{testPhylogeneticAutocorrelation} \alias{testPhylogeneticAutocorrelation} \title{Test for phylogenetic autocorrelation} \usage{ testPhylogeneticAutocorrelation(simulationOutput, tree, alternative = c("two.sided", "greater", "less")) } \arguments{ \item{simulationOutput}{an object of class DHARMa, either created via \link{simulateResiduals} for supported models or via \link{createDHARMa} for simulations created outside DHARMa, or a supported model. Providing a supported model directly is discouraged, because simulation settings cannot be changed in this case.} \item{tree}{A phylogenetic tree object.} \item{alternative}{A character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis of no phylogenetic correlation.} } \description{ This function performs a Moran's I test for phylogenetic autocorrelation on the calculated quantile residuals. } \details{ The function performs Moran.I test from the package ape on the DHARMa residuals, based on the phylogenetic distance matrix internally created from the provided tree. For custom distance matrices, you can use \link{testSpatialAutocorrelation}. } \note{ Standard DHARMa simulations from models with (temporal / spatial / phylogenetic) conditional autoregressive terms will still have the respective temporal / spatial / phylogenetic correlation in the DHARMa residuals, unless the package you are using is modelling the autoregressive terms as explicit REs and is able to simulate conditional on the fitted REs. This has two consequences: \enumerate{ \item If you check the residuals for such a model, they will still show significant autocorrelation, even if the model fully accounts for this structure. \item Because the DHARMa residuals for such a model are not statistically independent any more, other tests (e.g. dispersion, uniformity) may have inflated type I error, i.e. you will have a higher likelihood of spurious residual problems. } There are three (non-exclusive) routes to address these issues when working with spatial / temporal / phylogenetic autoregressive models: \enumerate{ \item Simulate conditional on the fitted CAR structures (see conditional simulations in the help of \link{simulateResiduals}). \item Rotate simulations prior to residual calculations (see parameter rotation in \link{simulateResiduals}). \item Use custom tests / plots that explicitly compare the correlation structure in the simulated data to the correlation structure in the observed data. } } \examples{ \dontrun{ library(DHARMa) library(phylolm) set.seed(123) tre = rcoal(60) b0 = 0; b1 = 1; x <- runif(length(tre$tip.label), 0, 1) y <- b0 + b1*x + rTrait(n = 1, phy = tre,model="BM", parameters = list(ancestral.state = 0, sigma2 = 10)) dat = data.frame(trait = y, pred = x) fit = lm(trait ~ pred, data = dat) res = simulateResiduals(fit, plot = T) testPhylogeneticAutocorrelation(res, tree = tre) fit = phylolm(trait ~ pred, data = dat, phy = tre, model = "BM") summary(fit) # phylogenetic autocorrelation still present in residuals res = simulateResiduals(fit, plot = T) # with "rotation" the residual autcorrelation is gone, see ?simulateResiduals. res = simulateResiduals(fit, plot = T, rotation = "estimated") } } \seealso{ \link{testResiduals}, \link{testUniformity}, \link{testOutliers}, \link{testDispersion}, \link{testZeroInflation}, \link{testGeneric}, \link{testTemporalAutocorrelation}, \link{testSpatialAutocorrelation}, \link{testQuantiles}, \link{testCategorical} } \author{ Florian Hartig } DHARMa/man/plot.DHARMaBenchmark.Rd0000644000176200001440000000215614677165224016116 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/runBenchmarks.R \name{plot.DHARMaBenchmark} \alias{plot.DHARMaBenchmark} \title{Plots DHARMa benchmarks} \usage{ \method{plot}{DHARMaBenchmark}(x, ...) } \arguments{ \item{x}{object of class DHARMaBenchmark, created by \link{runBenchmarks}.} \item{...}{parameters to pass to the plot function.} } \description{ The function plots the result of an object of class DHARMaBenchmark, created by \link{runBenchmarks}. } \details{ The function will create two types of plots, depending on whether the run contains only a single value (or no value) of the control parameter, or whether a vector of control values is provided: If a single or no value of the control parameter is provided, the function will create box plots of the estimated p-values, with the number of significant p-values plotted to the left. If a control parameter is provided, the function will plot the proportion of significant p-values against the control parameter, with 95\% CIs based based on the performed replicates displayed as confidence bands. } \seealso{ \link{runBenchmarks} } DHARMa/man/getFixedEffects.Rd0000644000176200001440000000233514677165224015370 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/compatibility.R \name{getFixedEffects} \alias{getFixedEffects} \alias{getFixedEffects.default} \alias{getFixedEffects.MixMod} \title{Extract fixed effects of a supported model} \usage{ getFixedEffects(object, ...) \method{getFixedEffects}{default}(object, ...) \method{getFixedEffects}{MixMod}(object, ...) } \arguments{ \item{object}{a fitted model.} \item{...}{additional parameters.} } \description{ A wrapper to extract fixed effects of a supported model. } \examples{ testData = createData(sampleSize = 400, family = gaussian()) fittedModel <- lm(observedResponse ~ Environment1 , data = testData) # response that was used to fit the model getObservedResponse(fittedModel) # predictions of the model for these points getFitted(fittedModel) # extract simulations from the model as matrix getSimulations(fittedModel, nsim = 2) # extract simulations from the model for refit (often requires different structure) x = getSimulations(fittedModel, nsim = 2, type = "refit") getRefit(fittedModel, x[[1]]) getRefit(fittedModel, getObservedResponse(fittedModel)) } \seealso{ \link{getObservedResponse}, \link{getSimulations}, \link{getRefit}, \link{getFitted} } DHARMa/DESCRIPTION0000644000176200001440000000457414704441036012771 0ustar liggesusersPackage: DHARMa Title: Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models Version: 0.4.7 Date: 2024-10-16 Authors@R: c(person("Florian", "Hartig", email = "florian.hartig@biologie.uni-regensburg.de", role = c("aut", "cre"), comment=c(ORCID="0000-0002-6255-9059")), person("Lukas", "Lohse", role = "ctb"), person("Melina", "de Souza leite", role = "ctb")) Description: The 'DHARMa' package uses a simulation-based approach to create readily interpretable scaled (quantile) residuals for fitted (generalized) linear mixed models. Currently supported are linear and generalized linear (mixed) models from 'lme4' (classes 'lmerMod', 'glmerMod'), 'glmmTMB', 'GLMMadaptive', and 'spaMM'; phylogenetic linear models from 'phylolm' (classes 'phylolm' and 'phyloglm'); generalized additive models ('gam' from 'mgcv'); 'glm' (including 'negbin' from 'MASS', but excluding quasi-distributions) and 'lm' model classes. Moreover, externally created simulations, e.g. posterior predictive simulations from Bayesian software such as 'JAGS', 'STAN', or 'BUGS' can be processed as well. The resulting residuals are standardized to values between 0 and 1 and can be interpreted as intuitively as residuals from a linear regression. The package also provides a number of plot and test functions for typical model misspecification problems, such as over/underdispersion, zero-inflation, and residual spatial, phylogenetic and temporal autocorrelation. Depends: R (>= 3.0.2) Imports: stats, graphics, utils, grDevices, Matrix, parallel, gap, lmtest, ape, qgam (>= 1.3.2), lme4 Suggests: knitr, testthat (>= 3.0.0), rmarkdown, KernSmooth, sfsmisc, MASS, mgcv, mgcViz (>= 0.1.9), spaMM (>= 3.2.0), GLMMadaptive, glmmTMB (>= 1.1.2.3), phylolm (>= 2.6.5) Enhances: phyr, rstan, rjags, BayesianTools License: GPL (>= 3) URL: http://florianhartig.github.io/DHARMa/ LazyData: TRUE BugReports: https://github.com/florianhartig/DHARMa/issues RoxygenNote: 7.3.2 VignetteBuilder: knitr Encoding: UTF-8 Config/testthat/edition: 3 NeedsCompilation: no Packaged: 2024-10-17 17:47:16 UTC; melinaleite Author: Florian Hartig [aut, cre] (), Lukas Lohse [ctb], Melina de Souza leite [ctb] Maintainer: Florian Hartig Repository: CRAN Date/Publication: 2024-10-18 11:10:22 UTC