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flexmix/R/0000755000176200001440000000000014757625373012152 5ustar liggesusersflexmix/R/z.R0000644000176200001440000000063114404637304012530 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: z.R 5079 2016-01-31 12:21:12Z gruen $ # ###********************************************************** ## Backward compatibility ## component model driver FLXglm <- FLXMRglm FLXglmFix <- FLXMRglmfix FLXmclust <- FLXMCmvnorm FLXbclust <- FLXMCmvbinary ## concomitant model driver FLXmultinom <- FLXPmultinom FLXconstant <- FLXPconstant flexmix/R/plot.R0000644000176200001440000000656514404637304013251 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: plot.R 5079 2016-01-31 12:21:12Z gruen $ # ###********************************************************** plotEll <- function(object, data, which=1:2, model = 1, project=NULL, points=TRUE, eqscale=TRUE, col=NULL, number = TRUE, cex=1.5, numcol="black", pch=NULL, ...) { if(is.null(col)) col <- rep(FullColors, length.out = object@k) if (!is.list(data)) { response <- data data <- list() data[[deparse(object@model[[model]]@fullformula[[2]])]] <- response } else { mf <- model.frame(object@model[[model]]@fullformula, data=data, na.action = NULL) response <- as.matrix(model.response(mf)) response <- object@model[[model]]@preproc.y(response) } clustering <- clusters(object, newdata = data) if(!is.null(project)) response <- predict(project, response) type=ifelse(points, "p", "n") if(is.null(pch)){ pch <- (clustering %% 10) pch[pch==0] <- 10 } else if(length(pch)!=nrow(response)){ pch <- rep(pch, length.out = object@k) pch <- pch[clustering] } if(eqscale) plot(response[,which], asp = 1, col=col[clustering], pch=pch, type=type, ...) else plot(response[,which], col=col[clustering], pch=pch, type=type, ...) for(k in seq_along(object@components)){ p = parameters(object, k, model, simplify=FALSE) if(!is.null(project)){ p <- projCentCov(project, p) } lines(ellipse::ellipse(p$cov[which,which], centre=p$center[which], level=0.5), col=col[k], lwd=2) lines(ellipse::ellipse(p$cov[which,which], centre=p$center[which], level=0.95), col=col[k], lty=2) } ## und nochmal fuer die zentren und nummern (damit die immer oben sind) for(k in seq_along(object@components)){ p = parameters(object, k, model, simplify=FALSE) if(!is.null(project)){ p <- projCentCov(project, p) } if(number){ rad <- ceiling(log10(object@k)) + 1.5 points(p$center[which[1]], p$center[which[2]], col=col[k], pch=21, cex=rad*cex, lwd=cex, bg="white") text(p$center[which[1]], p$center[which[2]], k, cex=cex, col=numcol) } else{ points(p$center[which[1]], p$center[which[2]], pch=16, cex=cex, col=col[k]) } } } projCentCov <- function(object, p) UseMethod("projCentCov") projCentCov.default <- function(object, p) stop(paste("Cannot handle projection objects of class", sQuote(class(object)))) projCentCov.prcomp <- function(object, p) { cent <- matrix(p$center, ncol=length(p$center)) cent <- scale(cent, object$center, object$scale) %*% object$rotation cov <- p$cov if(length(object$scale)>1) cov <- cov/outer(object$scale, object$scale, "*") cov <- t(object$rotation) %*% cov %*% object$rotation list(center=cent, cov=cov) } flexmix/R/condlogit.R0000644000176200001440000000553214404637304014246 0ustar liggesuserssetClass("FLXMRcondlogit", representation(strata="ANY", strata_formula="ANY"), contains = "FLXMRglm") FLXMRcondlogit <- function(formula=.~., strata) { z <- new("FLXMRcondlogit", weighted=TRUE, formula=formula, strata_formula=strata, family="multinomial", name=paste("FLXMRcondlogit")) z@defineComponent <- function(para) { predict <- function(x, ...) tcrossprod(x, t(para$coef)) logLik <- function(x, y, strata) { llh_all <- vector("numeric", length = length(y)) eta <- predict(x) llh_all[as.logical(y)] <- eta[as.logical(y)] ((tapply(llh_all, strata, sum) - tapply(exp(eta), strata, function(z) log(sum(z))))/tabulate(strata))[strata] } new("FLXcomponent", parameters=list(coef=para$coef), logLik=logLik, predict=predict, df=para$df) } z@fit <- function(x, y, w, strata){ index <- w > 0 fit <- survival::coxph.fit(x[index,,drop=FALSE], survival::Surv(1-y, y)[index], strata[index], weights=w[index], control = survival::coxph.control(), method = "exact", rownames = seq_len(nrow(y))[index]) coef <- coef(fit) df <- length(coef) z@defineComponent(list(coef = coef, df = df)) } z } setMethod("FLXgetModelmatrix", signature(model="FLXMRcondlogit"), function(model, data, formula, lhs=TRUE, ...) { formula <- RemoveGrouping(formula) if(is.null(model@formula)) model@formula = formula model@fullformula = update(terms(formula, data=data), model@formula) ## Ensure that an intercept is included model@fullformula <- update(model@fullformula, ~ . + 1) if (lhs) { mf <- model.frame(model@fullformula, data=data, na.action = NULL) model@x <- model.matrix(attr(mf, "terms"), data=mf) response <- as.matrix(model.response(mf)) model@y <- model@preproc.y(response) } else { mt1 <- terms(model@fullformula, data=data) mf <- model.frame(delete.response(mt1), data=data, na.action = NULL) mt <- attr(mf, "terms") model@x <- model.matrix(mt, data=mf) } strata <- update(model@strata_formula, ~ . + 0) mf <- model.frame(strata, data=data, na.action=NULL) model@strata <- as.integer(model.matrix(attr(mf, "terms"), data=mf)) ## Omit the intercept for identifiability model@x <- model@x[,attr(model@x, "assign") != 0, drop=FALSE] model@x <- model@preproc.x(model@x) model }) setMethod("FLXmstep", signature(model = "FLXMRcondlogit"), function(model, weights, ...) { apply(weights, 2, function(w) model@fit(model@x, model@y, w, model@strata)) }) setMethod("FLXdeterminePostunscaled", signature(model = "FLXMRcondlogit"), function(model, components, ...) { sapply(components, function(x) x@logLik(model@x, model@y, model@strata)) }) setMethod("existGradient", signature(object = "FLXMRcondlogit"), function(object) FALSE) flexmix/R/lmm.R0000644000176200001440000002413214404637304013046 0ustar liggesuserssetClass("FLXcomponentlmm", representation(random="list"), contains = "FLXcomponent") setClass("FLXMRlmm", representation(family = "character", random = "formula", group = "factor", z = "matrix", which = "ANY"), contains = "FLXMR") setClass("FLXMRlmmfix", contains = "FLXMRlmm") setMethod("allweighted", signature(model = "FLXMRlmm", control = "ANY", weights = "ANY"), function(model, control, weights) { if (!control@classify %in% c("auto", "weighted")) stop("Model class only supports weighted ML estimation.") model@weighted }) FLXMRlmm <- function(formula = . ~ ., random, lm.fit = c("lm.wfit", "smooth.spline"), varFix = c(Random = FALSE, Residual = FALSE), ...) { family <- "gaussian" lm.fit <- match.arg(lm.fit) if (length(varFix) != 2 || is.null(names(varFix)) || any(is.na(pmatch(names(varFix), c("Random", "Residual"))))) stop("varFix has to be a named vector of length two") else names(varFix) <- c("Random", "Residual")[pmatch(names(varFix), c("Random", "Residual"))] random <- if (length(random) == 3) random else formula(paste(".", paste(deparse(random), collapse = ""))) object <- new("FLXMRlmm", formula = formula, random = random, weighted = TRUE, family = family, name = "FLXMRlmm:gaussian") if (any(varFix)) object <- new("FLXMRlmmfix", object) object@preproc.y <- function(x){ if (ncol(x) > 1) stop(paste("y must be univariate")) x } if (lm.fit == "smooth.spline") { object@preproc.x <- function(x){ if (ncol(x) > 1) stop(paste("x must be univariate")) x } } add <- function(x) Reduce("+", x) lmm.wfit <- function(x, y, w, z, which, random) { effect <- lapply(seq_along(which), function(i) z[[which[i]]] %*% random$beta[[i]]) W <- rep(w, sapply(x, nrow)) X <- do.call("rbind", x) Y <- do.call("rbind", y) Effect <- do.call("rbind", effect) fit <- get(lm.fit)(X, Y - Effect, W, ...) XSigmaX <- sapply(seq_along(z), function(i) sum(diag(crossprod(z[[i]]) %*% random$Sigma[[i]]))) wSum <- tapply(w, which, sum) sigma2 <- (sum(W*residuals(fit)^2) + sum(wSum*XSigmaX))/sum(W) wSigma <- add(lapply(seq_along(z), function(i) wSum[i]*random$Sigma[[i]])) bb <- add(lapply(seq_along(which), function(i) tcrossprod(random$beta[[i]])*w[i])) psi <- (wSigma + bb)/sum(w) list(coefficients = if (is(fit, "smooth.spline")) fit$fit else coef(fit), sigma2 = list(Random = psi, Residual = sigma2), df = if (is(fit, "smooth.spline")) fit$df else ncol(x[[1]])) } object@defineComponent <- function(para) { predict <- function(x, ...) { if (is(para$coef, "smooth.spline.fit")) lapply(x, function(X) getS3method("predict", "smooth.spline.fit")(para$coef, X)$y) else lapply(x, function(X) X %*% para$coef) } logLik <- function(x, y, z, which, group, ...) { V <- lapply(z, function(Z) tcrossprod(tcrossprod(Z, para$sigma2$Random), Z) + diag(nrow(Z)) * para$sigma2$Residual) mu <- predict(x, ...) llh <- sapply(seq_along(x), function(i) mvtnorm::dmvnorm(t(y[[i]]), mean = mu[[i]], sigma = V[[which[i]]], log=TRUE)/nrow(V[[which[i]]])) as.vector(ungroupPriors(matrix(llh), group, !duplicated(group))) } new("FLXcomponentlmm", parameters = list(coef = para$coef, sigma2 = para$sigma2), random = list(), logLik = logLik, predict = predict, df = para$df) } determineRandom <- function(mu, y, z, which, sigma2) { Sigma <- lapply(z, function(Z) solve(crossprod(Z) / sigma2$Residual + solve(sigma2$Random))) Sigma_tilde <- lapply(seq_along(z), function(i) (tcrossprod(Sigma[[i]], z[[i]])/sigma2$Residual)) beta <- lapply(seq_along(which), function(i) Sigma_tilde[[which[i]]] %*% (y[[i]] - mu[[i]])) list(beta = beta, Sigma = Sigma) } object@fit <- if (any(varFix)) { function(x, y, w, z, which, random) { fit <- lapply(seq_len(ncol(w)), function(k) lmm.wfit(x, y, w[,k], z, which, random[[k]])) if (varFix["Random"]) { prior_w <- apply(w, 2, weighted.mean, w = sapply(x, length)) Random <- add(lapply(seq_along(fit), function(i) fit[[i]]$sigma2$Random * prior_w[i])) for (i in seq_along(fit)) fit[[i]]$sigma2$Random <- Random } if (varFix["Residual"]) { prior <- colMeans(w) Residual <- sum(sapply(fit, function(x) x$sigma2$Residual) * prior) for (i in seq_along(fit)) fit[[i]]$sigma2$Residual <- Residual } n <- nrow(fit[[1]]$sigma2$Random) lapply(fit, function(Z) { comp <- object@defineComponent(list(coef = coef(Z), sigma2 = Z$sigma2, df = Z$df + n*(n+1)/(2*ifelse(varFix["Random"], ncol(w), 1)) + ifelse(varFix["Residual"], 1/ncol(w), 1))) comp@random <- determineRandom(comp@predict(x), y, z, which, comp@parameters$sigma2) comp }) } } else { function(x, y, w, z, which, random){ fit <- lmm.wfit(x, y, w, z, which, random) n <- nrow(fit$sigma2$Random) comp <- object@defineComponent( list(coef = coef(fit), df = fit$df + n*(n+1)/2 + 1, sigma2 = fit$sigma2)) comp@random <- determineRandom(comp@predict(x), y, z, which, comp@parameters$sigma2) comp } } object } setMethod("FLXmstep", signature(model = "FLXMRlmm"), function(model, weights, components) { weights <- weights[!duplicated(model@group),,drop=FALSE] if (!is(components[[1]], "FLXcomponentlmm")) { random <- list(beta = lapply(model@which, function(i) rep(0, ncol(model@z[[i]]))), Sigma = lapply(model@z, function(x) diag(ncol(x)))) return(sapply(seq_len(ncol(weights)), function(k) model@fit(model@x, model@y, weights[,k], model@z, model@which, random))) }else { return(sapply(seq_len(ncol(weights)), function(k) model@fit(model@x, model@y, weights[,k], model@z, model@which, components[[k]]@random))) } }) setMethod("FLXmstep", signature(model = "FLXMRlmmfix"), function(model, weights, components) { weights <- weights[!duplicated(model@group),,drop=FALSE] if (!is(components[[1]], "FLXcomponentlmm")) { random <- rep(list(list(beta = lapply(model@which, function(i) rep(0, ncol(model@z[[i]]))), Sigma = lapply(model@z, function(x) diag(ncol(x))))), ncol(weights)) return(model@fit(model@x, model@y, weights, model@z, model@which, random)) }else return(model@fit(model@x, model@y, weights, model@z, model@which, lapply(components, function(x) x@random))) }) setMethod("FLXgetModelmatrix", signature(model="FLXMRlmm"), function(model, data, formula, lhs=TRUE, ...) { formula_nogrouping <- RemoveGrouping(formula) if (identical(paste(deparse(formula_nogrouping), collapse = ""), paste(deparse(formula), collapse = ""))) stop("please specify a grouping variable") model <- callNextMethod(model, data, formula, lhs) model@fullformula <- update(model@fullformula, paste(".~. |", .FLXgetGroupingVar(formula))) mt1 <- terms(model@random, data=data) mf <- model.frame(delete.response(mt1), data=data, na.action = NULL) model@z <- model.matrix(attr(mf, "terms"), data) model@group <- grouping <- .FLXgetGrouping(formula, data)$group rownames(model@z) <- rownames(model@x) <- rownames(model@y) <- NULL model@x <- matrix(lapply(unique(grouping), function(g) model@x[grouping == g, , drop = FALSE]), ncol = 1) if (lhs) model@y <- matrix(lapply(unique(grouping), function(g) model@y[grouping == g, , drop = FALSE]), ncol = 1) z <- lapply(unique(grouping), function(g) model@z[grouping == g, , drop = FALSE]) z1 <- unique(z) if (length(z) == length(z1)) { model@which <- seq_along(z) } else { model@which <- sapply(z, function(y) which(sapply(z1, function(x) isTRUE(all.equal(x, y))))) } model@z <- matrix(z1, ncol = 1) model }) setMethod("FLXgetObs", "FLXMRlmm", function(model) sum(sapply(model@x, nrow))) setMethod("FLXdeterminePostunscaled", signature(model = "FLXMRlmm"), function(model, components, ...) { sapply(components, function(x) x@logLik(model@x, model@y, model@z, model@which, model@group)) }) setMethod("predict", signature(object="FLXMRlmm"), function(object, newdata, components, ...) { object <- FLXgetModelmatrix(object, newdata, formula = object@fullformula, lhs = FALSE) lapply(components, function(comp) unlist(comp@predict(object@x, ...))) }) setMethod("rFLXM", signature(model="FLXMRlmm", components="list"), function(model, components, class, group, ...) { class <- class[!duplicated(group)] y <- NULL for (l in seq_along(components)) { yl <- as.matrix(rFLXM(model, components[[l]], ...)) if (is.null(y)) y <- matrix(NA, nrow = length(class), ncol = ncol(yl)) y[class == l,] <- yl[class==l,,drop=FALSE] y <- matrix(y, ncol = ncol(yl)) } y }) setMethod("rFLXM", signature(model = "FLXMRlmm", components = "FLXcomponent"), function(model, components, ...) { sigma2 <- components@parameters$sigma2 V <- lapply(model@z, function(Z) tcrossprod(tcrossprod(Z, sigma2$Random), Z) + diag(nrow(Z)) * sigma2$Residual) mu <- components@predict(model@x) matrix(lapply(seq_along(model@x), function(i) t(mvtnorm::rmvnorm(1, mean = mu[[i]], sigma = V[[model@which[i]]]))), ncol = 1) }) setMethod("FLXgetNewModelmatrix", "FLXMRlmm", function(object, model, indices, groups) { object@y <- model@y[indices,,drop=FALSE] object@x <- model@x[indices,,drop=FALSE] object@which <- model@which[indices] if (length(unique(object@which)) < length(object@z)) { object@z <- model@z[sort(unique(object@which)),,drop=FALSE] object@which <- match(object@which, sort(unique(object@which))) } object }) flexmix/R/mgcv.R0000644000176200001440000001373114404637304013220 0ustar liggesuserssetOldClass("gam.prefit") setClassUnion("listOrgam.prefit", c("list", "gam.prefit")) setClass("FLXMRmgcv", representation(G = "listOrgam.prefit", control = "list"), contains="FLXMRglm") FLXMRmgcv <- function(formula = .~., family = c("gaussian", "binomial", "poisson"), offset = NULL, control = NULL, optimizer = c("outer", "newton"), in.out = NULL, eps = .Machine$double.eps, ...) { if (is.null(control)) control <- mgcv::gam.control() family <- match.arg(family) am <- if (family == "gaussian" && get(family)()$link == "identity") TRUE else FALSE z <- new("FLXMRmgcv", FLXMRglm(formula = formula, family = family, offset = offset), name=paste("FLXMRmgcv", family, sep=":"), control = control) scale <- if (family %in% c("binomial", "poisson")) 1 else -1 gam_fit <- function(G, w) { G$family <- get(family)() G$am <- am G$w <- w G$conv.tol <- control$mgcv.tol G$max.half <- control$mgcv.half zero_weights <- any(w < eps) if (zero_weights) { ok <- w >= eps w <- w[ok] G$X <- G$X[ok,,drop=FALSE] if (is.matrix(G$y)) G$y <- G$y[ok,,drop=FALSE] else G$y <- G$y[ok] G$mf <- G$mf[ok,,drop=FALSE] G$w <- G$w[ok] G$offset <- G$offset[ok] if (G$n.paraPen > 0) { OMIT <- which(colSums(abs(G$X)) == 0) if (length(OMIT) > 0) { Ncol <- ncol(G$X) Assign <- unique(G$assign[OMIT]) G$assign <- G$assign[-OMIT] G$nsdf <- G$nsdf - length(OMIT) G$X <- G$X[,-OMIT,drop=FALSE] G$mf$Grouping <- G$mf$Grouping[,-which(colSums(abs(G$mf$Grouping))==0),drop=FALSE] if (length(G$off) > 1) G$off[2] <- G$off[2] - length(OMIT) for (i in seq_along(G$smooth)) { G$smooth[[i]]$first.para <- G$smooth[[i]]$first.para - length(OMIT) G$smooth[[i]]$last.para <- G$smooth[[i]]$last.para - length(OMIT) } G$S[[1]] <- G$S[[1]][-c(OMIT-sum(G$assign != Assign)), -c(OMIT-sum(G$assign != Assign))] } } } z <- mgcv::gam(G = G, method = "ML", optimizer = optimizer, control = control, scale = scale, in.out = in.out, ...) if (zero_weights) { residuals <- z$residuals z$residuals <- rep(0, length(ok)) z$residuals[ok] <- residuals if (G$n.paraPen > 0 && length(OMIT) > 0) { coefficients <- z$coefficients z$coefficients <- rep(0, Ncol) z$coefficients[-OMIT] <- coefficients } } z } if (family=="gaussian"){ z@fit <- function(x, y, w, G){ gam.fit <- gam_fit(G, w) z@defineComponent(list(coef = gam.fit$coefficients, df = sum(gam.fit$edf)+1, sigma = sqrt(sum(w * gam.fit$residuals^2 / mean(w))/ (nrow(x)-sum(gam.fit$edf))))) } } else if(family %in% c("binomial", "poisson")){ z@fit <- function(x, y, w, G){ gam.fit <- gam_fit(G, w) z@defineComponent( list(coef = gam.fit$coefficients, df = sum(gam.fit$edf))) } } else stop(paste("Unknown family", family)) z } setMethod("FLXmstep", signature(model = "FLXMRmgcv"), function(model, weights, ...) { apply(weights, 2, function(w) model@fit(model@x, model@y, w, model@G)) }) setMethod("FLXgetModelmatrix", signature(model="FLXMRmgcv"), function(model, data, formula, lhs=TRUE, paraPen = list(), ...) { formula <- RemoveGrouping(formula) if (length(grep("\\|", deparse(model@formula)))) stop("no grouping variable allowed in the model") if(is.null(model@formula)) model@formula <- formula model@fullformula <- update(terms(formula, data=data), model@formula) gp <- mgcv::interpret.gam(model@fullformula) if (lhs) { model@terms <- terms(gp$fake.formula, data = data) mf <- model.frame(model@terms, data=data, na.action = NULL, drop.unused.levels = TRUE) response <- as.matrix(model.response(mf, "numeric")) model@y <- model@preproc.y(response) } else { model@terms <- terms(gp$fake.formula, data = data) mf <- model.frame(delete.response(model@terms), data=data, na.action = NULL, drop.unused.levels = TRUE) } model@G <- mgcv::gam(model@fullformula, data = data, fit = FALSE) model@x <- model@G$X model@contrasts <- attr(model@x, "contrasts") model@x <- model@preproc.x(model@x) model@xlevels <- .getXlevels(delete.response(model@terms), mf) model }) setMethod("predict", signature(object="FLXMRmgcv"), function(object, newdata, components, ...) { predict_gam <- function (object, newdata, ...) { nn <- names(newdata) mn <- colnames(object$model) for (i in 1:length(newdata)) if (nn[i] %in% mn && is.factor(object$model[, nn[i]])) { newdata[[i]] <- factor(newdata[[i]], levels = levels(object$model[, nn[i]])) } if (length(newdata) == 1) newdata[[2]] <- newdata[[1]] n.smooth <- length(object$smooth) Terms <- delete.response(object$pterms) X <- matrix(0, nrow(newdata), length(object$coefficients)) Xoff <- matrix(0, nrow(newdata), n.smooth) mf <- model.frame(Terms, newdata, xlev = object$xlevels) if (!is.null(cl <- attr(object$pterms, "dataClasses"))) .checkMFClasses(cl, mf) Xp <- model.matrix(Terms, mf, contrasts = object$contrasts) if (object$nsdf) X[, 1:object$nsdf] <- Xp if (n.smooth) for (k in 1:n.smooth) { Xfrag <- mgcv::PredictMat(object$smooth[[k]], newdata) X[, object$smooth[[k]]$first.para:object$smooth[[k]]$last.para] <- Xfrag Xfrag.off <- attr(Xfrag, "offset") if (!is.null(Xfrag.off)) { Xoff[, k] <- Xfrag.off } } X } object@G$model <- object@G$mf z <- list() for(k in seq_along(components)) { object@G$coefficients <- components[[k]]@parameters$coef X <- predict_gam(object@G, newdata) z[[k]] <- components[[k]]@predict(X, ...) } z }) flexmix/R/initFlexmix.R0000644000176200001440000000355614404637304014570 0ustar liggesuserssetClass("initMethod", representation(step1 = "FLXcontrol", step2 = "FLXcontrol")) initMethod <- function(name = c("tol.em", "cem.em", "sem.em"), step1 = list(tolerance = 10^-2), step2 = list(), control = list(), nrep = 3L) { name <- match.arg(name) z <- new("initMethod", step1 = as(c(step1, control), "FLXcontrol"), step2 = as(c(step2, control), "FLXcontrol")) z@step1@nrep <- as.integer(nrep) z@step2@nrep <- 1L z@step1@classify <- switch(name, cem.em = "CEM", sem.em = "SEM", tol.em = "weighted") z } initFlexmix <- function(..., k, init = list(), control = list(), nrep = 3L, verbose = TRUE, drop = TRUE, unique = FALSE) { MYCALL <- match.call() if (missing(k)) stop("'k' is missing.") if (!missing(control) & is(init, "initMethod")) warning("'control' argument ignored.") init <- do.call("initMethod", c(init, list(control = control, nrep = nrep))) MYCALL1 <- lapply(k, function(K) { MYCALL[["k"]] <- as.numeric(K) MYCALL }) names(MYCALL1) <- paste(k) STEP1 <- stepFlexmix(..., k = k, verbose = verbose, drop = FALSE, unique = FALSE, nrep = init@step1@nrep, control = init@step1) models <- lapply(k, function(K) { if (length(k) > 1 && verbose) cat("* ") new("flexmix", flexmix(..., control = init@step2, cluster = posterior(getModel(STEP1, paste(K)))), k0 = as.integer(K), call = MYCALL1[[paste(K)]]) }) if (length(k) > 1 && verbose) cat("\n") names(models) <- paste(k) if (drop & length(models) == 1) { return(models[[1]]) } else { z <- new("stepFlexmix", models = models, k = as.integer(k), logLiks = STEP1@logLiks, nrep = STEP1@nrep, call = MYCALL) if (unique) z <- unique(z) return(z) } } flexmix/R/factanal.R0000644000176200001440000000345214404637304014034 0ustar liggesuserssetClass("FLXMCfactanal", contains = "FLXMC") ###********************************************************** FLXMCfactanal <- function(formula=.~., factors = 1, ...) { z <- new("FLXMCfactanal", weighted=TRUE, formula=formula, dist = "mvnorm", name="mixtures of factor analyzers") z@fit <- function(x, y, w, ...){ cov.weighted <- cov.wt(y, wt = w)[c("center","cov")] cov <- cov.weighted$cov; center <- cov.weighted$center fa <- factanal(covmat = cov, factors = factors, ...) Sigma <- fa$loadings %*% t(fa$loadings) + diag(fa$uniquenesses) df <- (factors + 2) * ncol(y) predict <- function(x) matrix(center, nrow=nrow(x), ncol=length(center), byrow=TRUE) logLik <- function(x, y){ sds <- sqrt(diag(cov)) mvtnorm::dmvnorm(y, mean = center, sigma = Sigma * (sds %o% sds), log = TRUE) } new("FLXcomponent", parameters=list(mu = center, variance = diag(cov), loadings = fa$loadings, uniquenesses = fa$uniquenesses), df=df, logLik=logLik, predict=predict) } z } ###********************************************************** setMethod("rFLXM", signature(model = "FLXMCfactanal", components = "FLXcomponent"), function(model, components, class, ...) { FUN <- paste("r", model@dist, sep = "") Sigma <- components@parameters$loadings %*% t(components@parameters$loadings) + diag(components@parameters$uniquenesses) sds <- sqrt(components@parameters$variance) args <- list(n = nrow(model@x), mean = components@parameters$mu, sigma = Sigma * (sds %o% sds)) return(do.call(FUN, args)) }) flexmix/R/robust.R0000644000176200001440000000421714404637304013601 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: robust.R 5079 2016-01-31 12:21:12Z gruen $ # ###********************************************************* setClass("FLXMRrobglm", representation(bgw="logical"), prototype(bgw=FALSE), contains = "FLXMRglm") FLXMRrobglm <- function(formula = . ~ ., family=c("gaussian", "poisson"), bgw=FALSE, ...) { family <- match.arg(family) new("FLXMRrobglm", FLXMRglm(formula, family, ...), name = paste("FLXMRrobglm", family, sep=":"), bgw = bgw) } setMethod("FLXgetModelmatrix", signature(model="FLXMRrobglm"), function(model, data, formula, lhs=TRUE, ...) { model <- callNextMethod(model, data, formula, lhs) if (attr(terms(model@fullformula), "intercept")==0) stop("please include an intercept") new("FLXMRrobglm", model) }) setMethod("FLXremoveComponent", signature(model = "FLXMRrobglm"), function(model, nok, ...) { if (1 %in% nok) model <- as(model, "FLXMRglm") model }) setMethod("FLXmstep", signature(model = "FLXMRrobglm"), function(model, weights, ...) { if(model@bgw){ w <- weights[,1] } else{ w <- rep(1, nrow(weights)) } if(model@family=="gaussian") { cwt <- cov.wt(model@y, w) coef <- c(cwt$center, rep(0, ncol(model@x)-1)) names(coef) <- colnames(model@x) comp.1 <- model@defineComponent(list(coef = coef, df = 0, offset = NULL, sigma=sqrt(cwt$cov), family = model@family)) } else if(model@family=="poisson") { cwt <- cov.wt(model@y, w) coef <- c(log(3*cwt$center), rep(0, ncol(model@x)-1)) names(coef) <- colnames(model@x) comp.1 <- model@defineComponent(list(coef = coef, df = 0, offset = NULL, family = model@family)) } else{ stop("Other families not implemented yet!") } c(list(comp.1), FLXmstep(as(model, "FLXMRglm"), weights[, -1, drop=FALSE], ...)) }) flexmix/R/glmnet.R0000644000176200001440000000724114404637304013551 0ustar liggesusers#' @title flexmix model driver for adaptive lasso (elastic-net) with GLMs #' @author F. Mortier (fmortier@cirad.fr) and N. Picard (nicolas.picard@cirad.fr) #' @param formula A symbolic description of the model to be fit. #' The general form is y~x|g where y is the response, x the set of predictors and g an #' optional grouping factor for repeated measurements. #' @param family a description of the error distribution and link function to be used in the model. #' "gausian", "poisson" and "binomial" are allowed. #' @param adaptive boolean indicating if algorithm should perform adaptive lasso or not #' @param select boolean vector indicating which covariates will be included in the selection process. #' Others will be included in the model. #' @details Some care is needed to ensure convergence of the #' algorithm, which is computationally more challenging than a standard EM. #' In the proposed method, not only are cluster allocations identified #' and component parameters estimated as commonly done in mixture models, #' but there is also variable selection via penalized regression using #' $k$-fold cross-validation to choose the penalty parameter. #' For the algorithm to converge, it is necessary that the same cross-validation #' partitioning be used across the EM iterations, i.e., #' the subsamples for cross-validation must be defined at the beginning #' This is accomplished using the {\tt foldid} option #' as an additional parameter to be passed to \code{\link{cv.glmnet}} (see \link{glmnet} package documentation). FLXMRglmnet <- function(formula = .~., family = c("gaussian", "binomial", "poisson"), adaptive = TRUE, select = TRUE, offset = NULL, ...) { family <- match.arg(family) z <- FLXMRglm(formula = formula, family = family) z@preproc.x <- function(x) { if (!isTRUE(all.equal(x[, 1], rep(1, nrow(x)), check.attributes = FALSE))) stop("The model needs to include an intercept in the first column.") x } z@fit <- function(x, y, w) { if (all(!select)) { coef <- if (family == "gaussian") lm.wfit(x, y, w = w)$coef else if (family == "binomial") glm.fit(x, y, family = binomial(), weights = w)$coef else if (family == "poisson") glm.fit(x, y, family=poisson(), weights = w)$coef } else { if (adaptive) { coef <- if (family == "gaussian") lm.wfit(x, y, w = w)$coef[-1] else if(family == "binomial") glm.fit(x, y, family = binomial(), weights = w)$coef[-1] else if (family == "poisson") glm.fit(x, y, family = poisson(), weights = w)$coef[-1] penalty <- mean(w) / abs(coef) } else penalty <- rep(1, ncol(x) - 1) if (any(!select)){ select <- which(!select) penalty[select] <- 0 } m <- glmnet::cv.glmnet(x[, -1, drop = FALSE], y, family = family, weights = w, penalty.factor = penalty, ...) coef <- as.vector(coef(m, s = "lambda.min")) } df <- sum(coef != 0) sigma <- if (family == "gaussian") sqrt(sum(w * (y - x %*% coef)^2/mean(w))/(nrow(x) - df)) else NULL z@defineComponent( list(coef = coef, sigma = sigma, df = df + ifelse(family == "gaussian", 1, 0))) } z } flexmix/R/flxmcmvpois.R0000644000176200001440000000153714404637304014634 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: flxmcmvpois.R 5079 2016-01-31 12:21:12Z gruen $ # FLXMCmvpois <- function(formula=.~.) { z <- new("FLXMC", weighted=TRUE, formula=formula, dist="mvpois", name="model-based Poisson clustering") z@preproc.y <- function(x){ storage.mode(x) <- "integer" x } z@defineComponent <- function(para) { logLik <- function(x, y){ colSums(dpois(t(y), para$lambda, log=TRUE)) } predict <- function(x, ...){ matrix(para$lambda, nrow = nrow(x), ncol=length(para$lambda), byrow=TRUE) } new("FLXcomponent", parameters=list(lambda=para$lambda), df=para$df, logLik=logLik, predict=predict) } z@fit <- function(x, y, w, ...){ z@defineComponent(list(lambda = colSums(w*y)/sum(w), df = ncol(y))) } z } flexmix/R/models.R0000644000176200001440000002641214404637304013547 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: models.R 5079 2016-01-31 12:21:12Z gruen $ # FLXMRglm <- function(formula=.~., family=c("gaussian", "binomial", "poisson", "Gamma"), offset=NULL) { family <- match.arg(family) glmrefit <- function(x, y, w) { fit <- c(glm.fit(x, y, weights=w, offset=offset, family=get(family, mode="function")()), list(call = sys.call(), offset = offset, control = eval(formals(glm.fit)$control), method = "weighted.glm.fit")) fit$df.null <- sum(w) + fit$df.null - fit$df.residual - fit$rank fit$df.residual <- sum(w) - fit$rank fit$x <- x fit } z <- new("FLXMRglm", weighted=TRUE, formula=formula, name=paste("FLXMRglm", family, sep=":"), offset = offset, family=family, refit=glmrefit) z@preproc.y <- function(x){ if (ncol(x) > 1) stop(paste("for the", family, "family y must be univariate")) x } if(family=="gaussian"){ z@defineComponent <- function(para) { predict <- function(x, ...) { dotarg = list(...) if("offset" %in% names(dotarg)) offset <- dotarg$offset p <- x %*% para$coef if (!is.null(offset)) p <- p + offset p } logLik <- function(x, y, ...) dnorm(y, mean=predict(x, ...), sd=para$sigma, log=TRUE) new("FLXcomponent", parameters=list(coef=para$coef, sigma=para$sigma), logLik=logLik, predict=predict, df=para$df) } z@fit <- function(x, y, w, component){ fit <- lm.wfit(x, y, w=w, offset=offset) z@defineComponent(para = list(coef = coef(fit), df = ncol(x)+1, sigma = sqrt(sum(fit$weights * fit$residuals^2 / mean(fit$weights))/ (nrow(x)-fit$rank)))) } } else if(family=="binomial"){ z@preproc.y <- function(x){ if (ncol(x) != 2) stop("for the binomial family, y must be a 2 column matrix\n", "where col 1 is no. successes and col 2 is no. failures") if (any(x < 0)) stop("negative values are not allowed for the binomial family") x } z@defineComponent <- function(para) { predict <- function(x, ...) { dotarg = list(...) if("offset" %in% names(dotarg)) offset <- dotarg$offset p <- x %*% para$coef if (!is.null(offset)) p <- p + offset get(family, mode = "function")()$linkinv(p) } logLik <- function(x, y, ...) dbinom(y[,1], size=rowSums(y), prob=predict(x, ...), log=TRUE) new("FLXcomponent", parameters=list(coef=para$coef), logLik=logLik, predict=predict, df=para$df) } z@fit <- function(x, y, w, component){ fit <- glm.fit(x, y, weights=w, family=binomial(), offset=offset, start=component$coef) z@defineComponent(para = list(coef = coef(fit), df = ncol(x))) } } else if(family=="poisson"){ z@defineComponent <- function(para) { predict <- function(x, ...) { dotarg = list(...) if("offset" %in% names(dotarg)) offset <- dotarg$offset p <- x %*% para$coef if (!is.null(offset)) p <- p + offset get(family, mode = "function")()$linkinv(p) } logLik <- function(x, y, ...) dpois(y, lambda=predict(x, ...), log=TRUE) new("FLXcomponent", parameters=list(coef=para$coef), logLik=logLik, predict=predict, df=para$df) } z@fit <- function(x, y, w, component){ fit <- glm.fit(x, y, weights=w, family=poisson(), offset=offset, start=component$coef) z@defineComponent(para = list(coef = coef(fit), df = ncol(x))) } } else if(family=="Gamma"){ z@defineComponent <- function(para) { predict <- function(x, ...) { dotarg = list(...) if("offset" %in% names(dotarg)) offset <- dotarg$offset p <- x %*% para$coef if (!is.null(offset)) p <- p + offset get(family, mode = "function")()$linkinv(p) } logLik <- function(x, y, ...) dgamma(y, shape = para$shape, scale=predict(x, ...)/para$shape, log=TRUE) new("FLXcomponent", parameters = list(coef = para$coef, shape = para$shape), predict = predict, logLik = logLik, df = para$df) } z@fit <- function(x, y, w, component){ fit <- glm.fit(x, y, weights=w, family=Gamma(), offset=offset, start=component$coef) z@defineComponent(para = list(coef = coef(fit), df = ncol(x)+1, shape = sum(fit$prior.weights)/fit$deviance)) } } else stop(paste("Unknown family", family)) z } ###********************************************************** FLXMCmvnorm <- function(formula=.~., diagonal=TRUE) { z <- new("FLXMC", weighted=TRUE, formula=formula, dist = "mvnorm", name="model-based Gaussian clustering") z@defineComponent <- function(para) { logLik <- function(x, y) mvtnorm::dmvnorm(y, mean=para$center, sigma=para$cov, log=TRUE) predict <- function(x, ...) matrix(para$center, nrow=nrow(x), ncol=length(para$center), byrow=TRUE) new("FLXcomponent", parameters=list(center = para$center, cov = para$cov), df=para$df, logLik=logLik, predict=predict) } z@fit <- function(x, y, w, ...){ para <- cov.wt(y, wt=w)[c("center","cov")] para$df <- (3*ncol(y) + ncol(y)^2)/2 if(diagonal){ para$cov <- diag(diag(para$cov)) para$df <- 2*ncol(y) } z@defineComponent(para) } z } FLXMCnorm1 <- function(formula=.~.) { z <- new("FLXMC", weighted=TRUE, formula=formula, dist = "mvnorm", name="model-based univariate Gaussian clustering") z@defineComponent <- function(para) { logLik <- function(x, y) dnorm(y, mean=para$center, sd=sqrt(para$cov), log=TRUE) predict <- function(x, ...) matrix(para$center, nrow=nrow(x), ncol=1, byrow=TRUE) new("FLXcomponent", parameters=list(mean = as.vector(para$center), sd = as.vector(sqrt(para$cov))), df=para$df, logLik=logLik, predict=predict) } z@fit <- function(x, y, w, ...){ para <- cov.wt(as.matrix(y), wt=w)[c("center","cov")] z@defineComponent(c(para, list(df = 2))) } z } ###********************************************************** FLXMCmvbinary <- function(formula=.~., truncated = FALSE) { if (truncated) return(MCmvbinary_truncated(formula)) else return(MCmvbinary(formula)) } MCmvbinary <- function(formula=.~.) { z <- new("FLXMC", weighted=TRUE, formula=formula, dist = "mvbinary", name="model-based binary clustering") ## make sure that y is binary z@preproc.y <- function(x){ storage.mode(x) <- "logical" storage.mode(x) <- "integer" x } z@defineComponent <- function(para) { predict <- function(x, ...){ matrix(para$center, nrow=nrow(x), ncol=length(para$center), byrow=TRUE) } logLik <- function(x, y){ p <- matrix(para$center, nrow=nrow(x), ncol=length(para$center), byrow=TRUE) rowSums(log(y*p+(1-y)*(1-p))) } new("FLXcomponent", parameters=list(center=para$center), df=para$df, logLik=logLik, predict=predict) } z@fit <- function(x, y, w, ...) z@defineComponent(list(center = colSums(w*y)/sum(w), df = ncol(y))) z } ###********************************************************** binary_truncated <- function(y, w, maxit = 200, epsilon = .Machine$double.eps) { r_k <- colSums(y*w)/sum(w) r_0 <- 0 llh.old <- -Inf for (i in seq_len(maxit)) { p <- r_k/(1+r_0) llh <- sum((r_k*log(p))[r_k > 0])+ sum(((1 - r_k + r_0) * log(1-p))[(1-r_k+r_0) > 0]) if (abs(llh - llh.old)/(abs(llh) + 0.1) < epsilon) break llh.old <- llh prod_p <- prod(1-p) r_0 <- prod_p/(1-prod_p) } p } MCmvbinary_truncated <- function(formula=.~.) { z <- MCmvbinary(formula=formula) z@defineComponent <- function(para) { predict <- function(x, ...) { matrix(para$center, nrow = nrow(x), ncol = length(para$center), byrow = TRUE) } logLik <- function(x, y) { p <- matrix(para$center, nrow = nrow(x), ncol = length(para$center), byrow = TRUE) rowSums(log(y * p + (1 - y) * (1 - p))) - log(1 - prod(1-para$center)) } new("FLXcomponent", parameters = list(center = para$center), df = para$df, logLik = logLik, predict = predict) } z@fit <- function(x, y, w, ...){ z@defineComponent(list(center = binary_truncated(y, w), df = ncol(y))) } z } ###********************************************************** setClass("FLXMCmvcombi", representation(binary = "vector"), contains = "FLXMC") FLXMCmvcombi <- function(formula=.~.) { z <- new("FLXMCmvcombi", weighted=TRUE, formula=formula, dist = "mvcombi", name="model-based binary-Gaussian clustering") z@defineComponent <- function(para) { predict <- function(x, ...){ matrix(para$center, nrow=nrow(x), ncol=length(para$center), byrow=TRUE) } logLik <- function(x, y){ if(any(para$binary)){ p <- matrix(para$center[para$binary], nrow=nrow(x), ncol=sum(para$binary), byrow=TRUE) z <- rowSums(log(y[,para$binary,drop=FALSE]*p + (1-y[,para$binary,drop=FALSE])*(1-p))) } else z <- rep(0, nrow(x)) if(!all(para$binary)){ if(sum(!para$binary)==1) z <- z + dnorm(y[,!para$binary], mean=para$center[!para$binary], sd=sqrt(para$var), log=TRUE) else z <- z + mvtnorm::dmvnorm(y[,!para$binary,drop=FALSE], mean=para$center[!para$binary], sigma=diag(para$var), log=TRUE) } z } new("FLXcomponent", parameters=list(center=para$center, var=para$var), df=para$df, logLik=logLik, predict=predict) } z@fit <- function(x, y, w, binary, ...){ para <- cov.wt(y, wt=w)[c("center","cov")] para <- list(center = para$center, var = diag(para$cov)[!binary], df = ncol(y) + sum(!binary), binary = binary) z@defineComponent(para) } z } setMethod("FLXgetModelmatrix", signature(model="FLXMCmvcombi"), function(model, data, formula, lhs=TRUE, ...) { model <- callNextMethod(model, data, formula, lhs) model@binary <- apply(model@y, 2, function(z) all(unique(z) %in% c(0,1))) model }) setMethod("FLXmstep", signature(model = "FLXMCmvcombi"), function(model, weights, components) { return(sapply(seq_len(ncol(weights)), function(k) model@fit(model@x, model@y, weights[,k], model@binary))) }) flexmix/R/boot.R0000644000176200001440000003401314404637304013223 0ustar liggesuserssetGeneric("boot", function(object, ...) standardGeneric("boot")) setGeneric("LR_test", function(object, ...) standardGeneric("LR_test")) setClass("FLXboot", representation(call="call", object="flexmix", parameters="list", concomitant="list", priors="list", logLik="matrix", k="matrix", converged="matrix", models="list", weights="list")) setMethod("show", "FLXboot", function(object) { cat("\nCall:", deparse(object@call,0.75*getOption("width")), sep="\n") }) generate_weights <- function(object) { if(is.null(object@weights) & is(object@model, "FLXMC")) { X <- do.call("cbind", lapply(object@model, function(z) z@y)) x <- apply(X, 1, paste, collapse = "") x <- as.integer(factor(x, unique(x))) object@weights <- as.vector(table(x)) indices_unique <- !duplicated(x) for (i in seq_along(object@model)) { object@model[[i]]@x <- object@model[[i]]@x[indices_unique,,drop=FALSE] object@model[[i]]@y <- object@model[[i]]@y[indices_unique,,drop=FALSE] } object@concomitant@x <- object@concomitant@x[indices_unique,,drop=FALSE] } object } setGeneric("FLXgetNewModelmatrix", function(object, ...) standardGeneric("FLXgetNewModelmatrix")) setMethod("FLXgetNewModelmatrix", "FLXM", function(object, model, indices, groups) { if (length(groups$group) > 0) { obs_groups <- lapply(groups$group[groups$groupfirst][indices], function(x) which(x == groups$group)) indices_grouped <- unlist(obs_groups) } else { indices_grouped <- indices } object@y <- model@y[indices_grouped,,drop=FALSE] object@x <- model@x[indices_grouped,,drop=FALSE] object }) setMethod("FLXgetNewModelmatrix", "FLXMRglmfix", function(object, model, indices, groups) { if (length(groups$group) > 0) { obs_groups <- lapply(groups$group[groups$groupfirst][indices], function(x) which(x == groups$group)) indices_grouped <- unlist(obs_groups) } else { indices_grouped <- indices } object@y <- do.call("rbind", rep(list(model@y[indices_grouped,,drop=FALSE]), sum(model@nestedformula@k))) object@x <- do.call("rbind", lapply(seq_len(sum(model@nestedformula@k)), function(K) model@x[model@segment[,K],,drop=FALSE][indices_grouped,,drop=FALSE])) N <- nrow(object@x)/sum(model@nestedformula@k) object@segment <- matrix(FALSE, ncol = sum(model@nestedformula@k), nrow = nrow(object@x)) for (m in seq_len(sum(model@nestedformula@k))) object@segment[(m - 1) * N + seq_len(N), m] <- TRUE object }) boot_flexmix <- function(object, R, sim = c("ordinary", "empirical", "parametric"), initialize_solution = FALSE, keep_weights = FALSE, keep_groups = TRUE, verbose = 0, control, k, model = FALSE, ...) { sim <- match.arg(sim) if (missing(R)) stop("R needs to be specified") if (!missing(control)) object@control <- do.call("new", c(list(Class = "FLXcontrol", object@control), control)) if (missing(k)) k <- object@k m <- length(object@model) has_weights <- !keep_weights & !is.null(object@weights) if (has_weights) object <- undo_weights(object) if (!keep_groups & length(object@group)) { object@concomitant@x <- object@concomitant@x[as.integer(object@group),,drop = FALSE] object@group <- factor() } groups <- list() groups$group <- object@group groups$groupfirst <- if (length(groups$group) > 0) groupFirst(groups$group) else rep(TRUE, FLXgetObs(object@model[[1]])) concomitant <- parameters <- priors <- models <- weights <- vector("list", R) logLik <- ks <- converged <- matrix(nrow=R, ncol = length(k), dimnames = list(BS = seq_len(R), k = k)) for (iter in seq_len(R)) { new <- object newgroups <- groups if(verbose && !(iter%%verbose)) cat("* ") if (iter > 1) { if (sim == "parametric") { y <- rflexmix(object, ...)$y for (i in seq_len(m)) new@model[[i]]@y <- matrix(as.vector(t(y[[i]])), nrow = nrow(new@model[[i]]@x), ncol = ncol(y[[i]]), byrow = TRUE) } else { n <- sum(groups$groupfirst) indices <- sample(seq_len(n), n, replace = TRUE) if (length(groups$group) > 0) { obs_groups <- lapply(groups$group[groups$groupfirst][indices], function(x) which(x == groups$group)) newgroups$group <- factor(rep(seq_along(obs_groups), sapply(obs_groups, length))) newgroups$groupfirst <- !duplicated(newgroups$group) } for (i in seq_len(m)) { new@model[[i]] <- FLXgetNewModelmatrix(new@model[[i]], object@model[[i]], indices, groups) } new@concomitant@x <- new@concomitant@x[indices,,drop=FALSE] } } if (has_weights & !length(groups$group) > 0) { new <- generate_weights(new) newgroups$groupfirst <- rep(TRUE, FLXgetObs(new@model[[1]])) } parameters[[iter]] <- concomitant[[iter]] <- priors[[iter]] <- list() NREP <- rep(object@control@nrep, length(k)) if (initialize_solution & object@k %in% k) NREP[k == object@k] <- 1L for (K in seq_along(k)) { fit <- new("flexmix", logLik = -Inf) for (nrep in seq_len(NREP[K])) { if (k[K] != object@k | !initialize_solution) { postunscaled <- initPosteriors(k[K], NULL, FLXgetObs(new@model[[1]]), newgroups) } else { postunscaled <- matrix(0, nrow = FLXgetObs(new@model[[1]]), ncol = k[K]) for (i in seq_len(m)) postunscaled <- postunscaled + FLXdeterminePostunscaled(new@model[[i]], lapply(new@components, function(x) x[[i]])) if(length(newgroups$group)>0) postunscaled <- groupPosteriors(postunscaled, newgroups$group) prior <- evalPrior(new@prior, new@concomitant) postunscaled <- if (is(prior, "matrix")) postunscaled + log(prior) else sweep(postunscaled, 2, log(prior), "+") postunscaled <- exp(postunscaled - log_row_sums(postunscaled)) } x <- try(FLXfit(new@model, new@concomitant, new@control, postunscaled, newgroups, weights = new@weights)) if (!is(x, "try-error")) { if(logLik(x) > logLik(fit)) fit <- x } } if (is.finite(logLik(fit))) { parameters[[iter]][paste(k[K])] <- list(parameters(fit, simplify = FALSE, drop = FALSE)) concomitant[[iter]][paste(k[K])] <- list(parameters(fit, which = "concomitant")) priors[[iter]][[paste(k[K])]] <- prior(fit) logLik[iter, paste(k[K])] <- logLik(fit) ks[iter, paste(k[K])] <- fit@k converged[iter, paste(k[K])] <- fit@converged if (model) { models[[iter]] <- fit@model weights[[iter]] <- fit@weights } } else { parameters[[iter]][[paste(k[K])]] <- concomitant[[iter]][[paste(k[K])]] <- priors[[iter]][[paste(k[K])]] <- NULL } } } if(verbose) cat("\n") new("FLXboot", call = sys.call(-1), object = object, parameters = parameters, concomitant = concomitant, priors = priors, logLik = logLik, k = ks, converged = converged, models = models, weights = weights) } setMethod("boot", signature(object="flexmix"), boot_flexmix) setMethod("LR_test", signature(object="flexmix"), function(object, R, alternative = c("greater", "less"), control, ...) { alternative <- match.arg(alternative) if (missing(control)) control <- object@control if (object@k == 1 & alternative == "less") stop(paste("alternative", alternative, "only possible for a mixture\n", "with at least two components")) k <- object@k + switch(alternative, greater = 0:1, less = 0:-1) names(k) <- k boot <- boot(object, R, sim = "parametric", k = k, initialize_solution = TRUE, control = control, ...) ok <- apply(boot@k, 1, identical, k) lrts <- 2*apply(boot@logLik[ok,order(k)], 1, diff) STATISTIC <- lrts[1] names(STATISTIC) <- "LRTS" PARAMETER <- length(lrts) names(PARAMETER) <- "BS" RETURN <- list(parameter = PARAMETER, p.value = sum(lrts[1] <= lrts)/length(lrts), alternative = alternative, null.value = object@k, method = "Bootstrap likelihood ratio test", data.name = deparse(substitute(object)), bootstrap.results = boot) class(RETURN) <- "htest" RETURN }) setMethod("parameters", "FLXboot", function(object, k, ...) { if (missing(k)) k <- object@object@k Coefs <- lapply(seq_along(object@parameters), function(i) if (is.na(object@k[i])) NULL else do.call("cbind", c(lapply(seq_len(object@k[i]), function(j) unlist(sapply(seq_along(object@object@model), function(m) FLXgetParameters(as(object@object@model[[m]], "FLXMR"), if (is(object@object@model[[m]]@defineComponent, "expression")) list(eval(object@object@model[[m]]@defineComponent, c(object@parameters[[i]][[paste(k)]][[m]][[j]], list(df = object@object@components[[j]][[m]]@df)))) else { list(object@object@model[[m]]@defineComponent( c(object@parameters[[i]][[paste(k)]][[m]][[j]], list(df = object@object@components[[j]][[m]]@df)))) })))), as.list(rep(NA, k - object@k[i]))))) Coefs <- t(do.call("cbind", Coefs)) colnames(Coefs) <- gsub("Comp.1_", "", colnames(Coefs)) Prior <- t(do.call("cbind", lapply(object@concomitant, function(x) do.call("cbind", c(list(x[[paste(k)]]), as.list(rep(NA, k - ifelse(length(x), ncol(x[[paste(k)]]), k)))))))) cbind(Coefs, Prior) }) setMethod("clusters", signature(object = "FLXboot", newdata = "listOrdata.frame"), function(object, newdata, k, ...) { if (missing(k)) k <- object@object@k lapply(seq_len(length(object@priors)), function(i) { new <- object@object new@prior <- object@priors[[i]][[paste(k)]] new@k <- length(new@prior) new@components <- rep(list(vector("list", length(object@object@model))), length(new@prior)) for (m in seq_along(new@model)) { variables <- c("x", "y", "offset", "family") variables <- variables[variables %in% slotNames(new@model[[m]])] for (var in variables) assign(var, slot(new@model[[m]], var)) for (K in seq_len(object@k[i])) { new@components[[K]][[m]] <- if (is(object@object@model[[m]]@defineComponent, "expression")) eval(object@object@model[[m]]@defineComponent, c(object@parameters[[i]][[paste(k)]][[m]][[K]], list(df = object@object@components[[K]][[m]]@df))) else object@object@model[[m]]@defineComponent( c(object@parameters[[i]][[paste(k)]][[m]][[K]], list(df = object@object@components[[K]][[m]]@df))) } } clusters(new, newdata = newdata)}) }) setMethod("posterior", signature(object = "FLXboot", newdata = "listOrdata.frame"), function(object, newdata, k, ...) { if (missing(k)) k <- object@object@k lapply(seq_len(length(object@priors)), function(i) { new <- object@object new@prior <- object@priors[[i]][[paste(k)]] new@k <- length(new@prior) new@components <- rep(list(vector("list", length(object@object@model))), length(new@prior)) for (m in seq_along(new@model)) { variables <- c("x", "y", "offset", "family") variables <- variables[variables %in% slotNames(new@model[[m]])] for (var in variables) assign(var, slot(new@model[[m]], var)) for (K in seq_len(object@k[i])) { new@components[[K]][[m]] <- if (is(object@object@model[[m]]@defineComponent, "expression")) eval(object@object@model[[m]]@defineComponent, c(object@parameters[[i]][[paste(k)]][[m]][[K]], list(df = object@object@components[[K]][[m]]@df))) else object@object@model[[m]]@defineComponent( c(object@parameters[[i]][[paste(k)]][[m]][[K]], list(df = object@object@components[[K]][[m]]@df))) } } posterior(new, newdata = newdata)}) }) setMethod("predict", signature(object = "FLXboot"), function(object, newdata, k, ...) { if (missing(k)) k <- object@object@k lapply(seq_len(length(object@priors)), function(i) { new <- object@object new@components <- vector("list", object@k[i, paste(k)]) new@components <- lapply(new@components, function(x) vector("list", length(new@model))) for (m in seq_along(new@model)) { variables <- c("x", "y", "offset", "family") variables <- variables[variables %in% slotNames(new@model[[m]])] for (var in variables) assign(var, slot(new@model[[m]], var)) for (K in seq_len(object@k[i, paste(k)])) { new@components[[K]][[m]] <- if (is(object@object@model[[m]]@defineComponent, "expression")) eval(object@object@model[[m]]@defineComponent, c(object@parameters[[i]][[paste(k)]][[m]][[K]], list(df = object@object@components[[1]][[m]]@df))) else object@object@model[[m]]@defineComponent( c(object@parameters[[i]][[paste(k)]][[m]][[K]], list(df = object@object@components[[1]][[m]]@df))) } } predict(new, newdata = newdata, ...)}) }) flexmix/R/glmFix.R0000644000176200001440000001622614404637304013514 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: glmFix.R 5156 2019-02-12 08:11:16Z gruen $ # FLXMRglmfix <- function(formula=.~., fixed=~0, varFix = FALSE, nested = NULL, family=c("gaussian", "binomial", "poisson", "Gamma"), offset=NULL) { family <- match.arg(family) nested <- as(nested, "FLXnested") if (length(fixed) == 3) stop("no left hand side allowed for fixed") z <- new("FLXMRglmfix", FLXMRglm(formula, family, offset), fixed=fixed, name=paste("FLXMRglmfix", family, sep=":"), nestedformula=nested, variance = varFix) if(family=="gaussian"){ z@fit <- function(x, y, w, incidence, variance, ...){ fit <- lm.wfit(x, y, w=w, offset=offset) k <- nrow(incidence) n <- nrow(x)/k sigma <- vector(length=k) cumVar <- cumsum(c(0, variance)) for (i in seq_along(variance)) { ind <- cumVar[i]*n + seq_len(n*variance[i]) sigma[cumVar[i] + seq_len(variance[i])] <- sqrt(sum(fit$weights[ind] * fit$residuals[ind]^2 / mean(fit$weights[ind]))/ (length(ind) - sum(incidence[i,]))) } fit <- fit[c("coefficients")] coefs <- coef(fit) names(coefs) <- colnames(incidence) df <- rowSums(incidence/rep(colSums(incidence), each = nrow(incidence))) + rep(1/variance, variance) lapply(seq_len(k), function(K) z@defineComponent( list(coef = coefs[as.logical(incidence[K, ])], sigma = sigma[K], df = df[K]))) } } else if(family=="binomial"){ z@fit <- function(x, y, w, incidence, ...){ fit <- glm.fit(x, y, weights=w, family=binomial(), offset=offset) fit <- fit[c("coefficients","family")] k <- nrow(incidence) coefs <- coef(fit) names(coefs) <- colnames(incidence) df <- rowSums(incidence/rep(colSums(incidence), each = nrow(incidence))) lapply(seq_len(k), function(K) z@defineComponent( list(coef = coefs[as.logical(incidence[K, ])], df = df[K]))) } } else if(family=="poisson"){ z@fit <- function(x, y, w, incidence, ...){ fit <- glm.fit(x, y, weights=w, family=poisson(), offset=offset) fit <- fit[c("coefficients","family")] k <- nrow(incidence) coefs <- coef(fit) names(coefs) <- colnames(incidence) df <- rowSums(incidence/rep(colSums(incidence), each = nrow(incidence))) lapply(seq_len(k), function(K) z@defineComponent( list(coef = coefs[as.logical(incidence[K, ])], df = df[K]))) } } else if(family=="Gamma"){ z@fit <- function(x, y, w, incidence, ...){ fit <- glm.fit(x, y, weights=w, family=Gamma(), offset=offset) shape <- sum(fit$prior.weights)/fit$deviance fit <- fit[c("coefficients","family")] k <- nrow(incidence) coefs <- coef(fit) names(coefs) <- colnames(incidence) df <- rowSums(incidence/rep(colSums(incidence), each = nrow(incidence))) lapply(seq_len(k), function(K) z@defineComponent( list(coef = coefs[as.logical(incidence[K, ])], df = df[K], shape = shape))) } } else stop(paste("Unknown family", family)) z } ###********************************************************** setMethod("refit_mstep", signature(object="FLXMRglmfix", newdata="missing"), function(object, newdata, weights, ...) { warning("Separate regression models are fitted using posterior weights.") lapply(seq_len(ncol(weights)), function(k) { x <- object@x[object@segment[, k], as.logical(object@design[k,]), drop = FALSE] colnames(x) <- colnames(object@design)[as.logical(object@design[k,])] y <- object@y[object@segment[, k],, drop = FALSE] fit <- object@refit(x, y, weights[,k], ...) fit <- c(fit, list(formula = object@fullformula, terms = object@terms, contrasts = object@contrasts, xlevels = object@xlevels)) class(fit) <- c("glm", "lm") fit }) }) ###********************************************************** setMethod("fitted", signature(object="FLXMRglmfix"), function(object, components, ...) { N <- nrow(object@x)/length(components) z <- list() for(n in seq_along(components)){ x <- object@x[(n-1)*N + seq_len(N), as.logical(object@design[n,]), drop=FALSE] z[[n]] <- list(components[[n]]@predict(x)) } z }) ###********************************************************** setMethod("predict", signature(object="FLXMRglmfix"), function(object, newdata, components, ...) { model <- FLXgetModelmatrix(object, newdata, object@fullformula, lhs=FALSE) k <- sum(object@nestedformula@k) N <- nrow(model@x)/k z <- list() for (m in seq_len(k)) { z[[m]] <- components[[m]]@predict(model@x[model@segment[,m], as.logical(model@design[m,]), drop=FALSE], ...) } z }) ###********************************************************** setMethod("FLXgetModelmatrix", signature(model="FLXMRfix"), function(model, data, formula, lhs=TRUE, ...) { formula <- RemoveGrouping(formula) if (length(grep("\\|", deparse(model@formula)))) stop("no grouping variable allowed in the model") if(is.null(model@formula)) model@formula <- formula model@fullformula <- update.formula(formula, model@formula) k <- model@nestedformula mm.all <- modelMatrix(model@fullformula, model@fixed, k@formula, data, lhs, model@xlevels) model@design <- modelDesign(mm.all, k) desNested <- if (sum(sapply(mm.all$nested, ncol))) { rbind(ncol(mm.all$fixed) + seq_len(sum(sapply(mm.all$nested, ncol))), unlist(lapply(seq_along(mm.all$nested), function(i) rep(i, ncol(mm.all$nested[[i]]))))) }else matrix(ncol=0, nrow=2) model@x <- cbind(kronecker(rep(1, sum(k@k)), mm.all$fixed), do.call("cbind", lapply(unique(desNested[2,]), function(i) { kronecker(model@design[,desNested[1, desNested[2, ] == i][1]], mm.all$nested[[i]])})), kronecker(diag(sum(k@k)), mm.all$random)) N <- nrow(model@x)/sum(k@k) model@segment <- matrix(FALSE, ncol = sum(k@k), nrow = nrow(model@x)) for (m in seq_len(sum(k@k))) model@segment[(m - 1) * N + seq_len(N), m] <- TRUE if (lhs) { y <- mm.all$response rownames(y) <- NULL response <- as.matrix(apply(y, 2, rep, sum(k@k))) model@y <- model@preproc.y(response) } model@x <- model@preproc.x(model@x) model@xlevels <- mm.all$xlevels model }) flexmix/R/FLXMCdist1.R0000644000176200001440000002123114404637304014074 0ustar liggesusers## Note that the implementation of the weighted ML estimation is ## influenced and inspired by the function fitdistr from package MASS ## and function fitdist from package fitdistrplus. FLXMCdist1 <- function(formula=.~., dist, ...) { foo <- paste("FLXMC", dist, sep = "") if (!exists(foo)) stop("This distribution has not been implemented yet.") get(foo)(formula, ...) } prepoc.y.pos.1 <- function(x) { if (ncol(x) > 1) stop("for the inverse gaussian family y must be univariate") if (any(x < 0)) stop("values must be >= 0") x } FLXMClnorm <- function(formula=.~., ...) { z <- new("FLXMC", weighted=TRUE, formula=formula, dist = "lnorm", name="model-based log-normal clustering") z@preproc.y <- prepoc.y.pos.1 z@defineComponent <- function(para) { predict <- function(x, ...) matrix(para$meanlog, nrow = nrow(x), ncol = 1, byrow = TRUE) logLik <- function(x, y) dlnorm(y, meanlog = predict(x, ...), sdlog = para$sdlog, log = TRUE) new("FLXcomponent", parameters = list(meanlog = para$meanlog, sdlog = para$sdlog), predict = predict, logLik = logLik, df = para$df) } z@fit <- function(x, y, w, ...) { logy <- log(y); meanw <- mean(w) meanlog <- mean(w * logy) / meanw sdlog <- sqrt(mean(w * (logy - meanlog)^2) / meanw) z@defineComponent(list(meanlog = meanlog, sdlog = sdlog, df = 2)) } z } FLXMCinvGauss <- function(formula=.~., ...) { z <- new("FLXMC", weighted=TRUE, formula=formula, name = "model-based inverse Gaussian clustering", dist = "invGauss") z@preproc.y <- prepoc.y.pos.1 z@defineComponent <- function(para) { predict <- function(x, ...) matrix(para$nu, nrow = nrow(x), ncol = length(para$nu), byrow = TRUE) logLik <- function(x, y, ...) SuppDists::dinvGauss(y, nu = predict(x, ...), lambda = para$lambda, log = TRUE) new("FLXcomponent", parameters = list(nu = para$nu, lambda = para$lambda), predict = predict, logLik = logLik, df = para$df) } z@fit <- function(x, y, w, ...){ nu <- mean(w * y) / mean(w) lambda <- mean(w) / mean(w * (1 / y - 1 / nu)) z@defineComponent(list(nu = nu, lambda = lambda, df = 2)) } z } FLXMCgamma <- function(formula=.~., method = "Nelder-Mead", warn = -1, ...) { z <- new("FLXMC", weighted=TRUE, formula=formula, name = "model-based gamma clustering", dist = "gamma") z@preproc.y <- prepoc.y.pos.1 z@defineComponent <- function(para) { predict <- function(x, ...) matrix(para$shape, nrow = nrow(x), ncol = length(para$shape), byrow = TRUE) logLik <- function(x, y, ...) dgamma(y, shape = predict(x, ...), rate = para$rate, log = TRUE) new("FLXcomponent", parameters = list(shape = para$shape, rate = para$rate), predict = predict, logLik = logLik, df = para$df) } z@fit <- function(x, y, w, component){ if (!length(component)) { sw <- sum(w) mean <- sum(y * w) / sw var <- (sum(y^2 * w) / sw - mean^2) * sw / (sw - 1) start <- c(mean^2/var, mean/var) } else start <- unname(unlist(component)) control <- list(parscale = c(1, start[2])) f <- function(parms) -sum(dgamma(y, shape = parms[1], rate = parms[2], log = TRUE) * w) oop <- options(warn = warn) on.exit(oop) parms <- optim(start, f, method = method, control = control)$par z@defineComponent(list(shape = parms[1], rate = parms[2], df = 2)) } z } FLXMCexp <- function(formula=.~., ...) { z <- new("FLXMC", weighted=TRUE, formula=formula, name = "model-based exponential clustering", dist = "exp") z@preproc.y <- prepoc.y.pos.1 z@defineComponent <- function(para) { predict <- function(x, ...) matrix(para$rate, nrow = nrow(x), ncol = length(para$rate), byrow = TRUE) logLik <- function(x, y, ...) dexp(y, rate = predict(x, ...), log = TRUE) new("FLXcomponent", parameters = list(rate = para$rate), predict = predict, logLik = logLik, df = para$df) } z@fit <- function(x, y, w, component) z@defineComponent(list(rate = mean(w) / mean(w * y), df = 1)) z } FLXMCweibull <- function(formula=.~., method = "Nelder-Mead", warn = -1, ...) { z <- new("FLXMC", weighted=TRUE, formula=formula, name = "model-based Weibull clustering", dist = "weibull") z@preproc.y <- prepoc.y.pos.1 z@defineComponent <- function(para) { predict <- function(x, ...) matrix(para$shape, nrow = nrow(x), ncol = length(para$shape), byrow = TRUE) logLik <- function(x, y, ...) dweibull(y, shape = predict(x, ...), scale = para$scale, log = TRUE) new("FLXcomponent", parameters = list(shape = para$shape, scale = para$scale), predict = predict, logLik = logLik, df = para$df) } z@fit <- function(x, y, w, component){ if (!length(component)) { ly <- log(y) sw <- sum(w) mean <- sum(ly * w) / sw var <- (sum(ly^2 * w) / sw - mean^2) * sw / (sw - 1) shape <- 1.2/sqrt(var) scale <- exp(mean + 0.572/shape) start <- c(shape, scale) } else start <- unname(unlist(component)) f <- function(parms) -sum(dweibull(y, shape = parms[1], scale = parms[2], log = TRUE) * w) oop <- options(warn = warn) on.exit(oop) parms <- optim(start, f, method = method)$par z@defineComponent(list(shape = parms[1], scale = parms[2], df = 2)) } z } FLXMCburr <- function(formula=.~., start = NULL, method = "Nelder-Mead", warn = -1, ...) { z <- new("FLXMC", weighted=TRUE, formula=formula, name = "model-based Burr clustering", dist = "burr") z@preproc.y <- prepoc.y.pos.1 z@defineComponent <- function(para) { predict <- function(x, ...) matrix(para$shape1, nrow = nrow(x), ncol = length(para$shape1), byrow = TRUE) logLik <- function(x, y, ...) actuar::dburr(y, shape1 = predict(x, ...), shape2 = para$shape2, scale = para$scale, log = TRUE) new("FLXcomponent", parameters = list(shape1 = para$shape1, shape2 = para$shape2, scale = para$scale), predict = predict, logLik = logLik, df = para$df) } z@fit <- function(x, y, w, component){ if (!length(component)) { if (is.null(start)) start <- c(1, 1) } else start <- unname(unlist(component[2:3])) f <- function(parms) { shape1 <- sum(w) / sum(w * log(1 + (y/parms[2])^parms[1])) -sum(actuar::dburr(y, shape1 = shape1, shape2 = parms[1], scale = parms[2], log = TRUE) * w) } oop <- options(warn = warn) on.exit(oop) parms <- optim(start, f, method = method)$par z@defineComponent(list(shape1 = sum(w) / sum(w * log(1 + (y/parms[2])^parms[1])), shape2 = parms[1], scale = parms[2], df = 3)) } z } FLXMCinvburr <- function(formula=.~., start = NULL, warn = -1, ...) { z <- new("FLXMC", weighted=TRUE, formula=formula, name = "model-based Inverse Burr clustering", dist = "invburr") z@preproc.y <- prepoc.y.pos.1 z@defineComponent <- function(para) { predict <- function(x, ...) matrix(para$shape1, nrow = nrow(x), ncol = length(para$shape1), byrow = TRUE) logLik <- function(x, y, ...) actuar::dinvburr(y, shape1 = predict(x, ...), shape2 = para$shape2, scale = para$scale, log = TRUE) new("FLXcomponent", parameters = list(shape1 = para$shape1, shape2 = para$shape2, scale = para$scale), predict = predict, logLik = logLik, df = para$df) } z@fit <- function(x, y, w, component){ if (!length(component)) { if (is.null(start)) start <- c(1, 1) } else start <- unname(unlist(component[2:3])) f <- function(parms) { shape1 <- sum(w) / sum(w * log(1 + (parms[2]/y)^parms[1])) -sum(actuar::dinvburr(y, shape1 = shape1, shape2 = parms[1], scale = parms[2], log = TRUE) * w) } oop <- options(warn = warn) on.exit(oop) parms <- optim(start, f, method = "Nelder-Mead")$par z@defineComponent(list(shape1 = sum(w) / sum(w * log(1 + (parms[2]/y)^parms[1])), shape2 = parms[1], scale = parms[2], df = 3)) } z } flexmix/R/refit.R0000644000176200001440000005270514404637304013401 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: refit.R 5079 2016-01-31 12:21:12Z gruen $ # ###********************************************************* setMethod("FLXgetParameters", signature(object="FLXdist"), function(object, model) { if (missing(model)) model <- seq_along(object@model) coefficients <- unlist(lapply(model, function(m) { Model <- unlist(FLXgetParameters(object@model[[m]], lapply(object@components, "[[", m))) names(Model) <- paste("model.", m, "_", names(Model), sep = "") Model })) c(coefficients, FLXgetParameters(object@concomitant)) }) setMethod("FLXgetParameters", signature(object="FLXM"), function(object, components, ...) { lapply(components, function(x) unlist(slot(x, "parameters"))) }) setMethod("FLXgetParameters", signature(object="FLXMC"), function(object, components, ...) { if (object@dist == "mvnorm") { return(lapply(components, function(x) { pars <- x@parameters if (identical(pars$cov, diag(diag(pars$cov)))) return(c(pars$center, diag(pars$cov))) else return(c(pars$center, pars$cov[lower.tri(pars$cov, diag = TRUE)])) })) } else return(lapply(components, function(x) unlist(slot(x, "parameters")))) }) setMethod("FLXgetParameters", signature(object="FLXMRglm"), function(object, components, ...) { parms <- lapply(components, function(x) unlist(slot(x, "parameters"))) Design <- FLXgetDesign(object, components) if (object@family == "gaussian") { parms <- lapply(parms, function(x) { x["sigma"] <- log(x["sigma"]) x }) colnames(Design) <- gsub("sigma$", "log(sigma)", colnames(Design)) } parms_unique <- vector(length = ncol(Design)) names(parms_unique) <- colnames(Design) for (k in seq_along(parms)) parms_unique[as.logical(Design[k,])] <- parms[[k]] parms_unique }) setMethod("FLXgetParameters", signature(object="FLXP"), function(object, ...) { if (length(object@coef) == 1) return(NULL) alpha <- log(object@coef[-1]) - log(object@coef[1]) names(alpha) <- paste("concomitant", paste("Comp", seq_along(object@coef)[-1], "alpha", sep = "."), sep = "_") return(alpha) }) setMethod("FLXgetParameters", signature(object="FLXPmultinom"), function(object, ...) { coefficients <- object@coef[,-1,drop=FALSE] if (ncol(coefficients) > 0) { Names <- paste("Comp", rep(seq_len(ncol(coefficients)+1)[-1], each = nrow(coefficients)), rownames(coefficients), sep = ".") coefficients <- as.vector(coefficients) names(coefficients) <- paste("concomitant", Names, sep = "_") return(coefficients) }else return(NULL) }) setMethod("VarianceCovariance", signature(object="flexmix"), function(object, model = TRUE, gradient, optim_control = list(), ...) { if (object@control@classify != "weighted") stop("Only for weighted ML estimation possible.") if (length(FLXgetParameters(object)) != object@df) stop("not implemented yet for restricted parameters.") if (missing(gradient)) gradient <- FLXgradlogLikfun(object) optim_control$fnscale <- -1 fit <- optim(fn = FLXlogLikfun(object), par = FLXgetParameters(object), gr = gradient, hessian = TRUE, method = "BFGS", control = optim_control, ...) list(coef = fit$par, vcov = -solve(as.matrix(fit$hessian))) }) setMethod("logLikfun_comp", signature(object="flexmix"), function(object) { postunscaled <- matrix(0, nrow = FLXgetObs(object@model[[1]]), ncol = object@k) for (m in seq_along(object@model)) postunscaled <- postunscaled + FLXdeterminePostunscaled(object@model[[m]], lapply(object@components, "[[", m)) if(length(object@group)>0) postunscaled <- groupPosteriors(postunscaled, object@group) postunscaled }) setMethod("FLXlogLikfun", signature(object="flexmix"), function(object, ...) function(parms) { object <- FLXreplaceParameters(object, parms) groupfirst <- if (length(object@group) > 1) groupFirst(object@group) else rep(TRUE, FLXgetObs(object@model[[1]])) logpostunscaled <- logLikfun_comp(object) + log(getPriors(object@concomitant, object@group, groupfirst)) if (is.null(object@weights)) sum(log_row_sums(logpostunscaled[groupfirst,,drop=FALSE])) else sum(log_row_sums(logpostunscaled[groupfirst,,drop=FALSE])*object@weights[groupfirst]) }) setMethod("getPriors", signature(object="FLXP"), function(object, group, groupfirst) { priors <- matrix(apply(object@coef, 2, function(x) object@x %*% x), nrow = nrow(object@x)) ungroupPriors(priors/rowSums(priors), group, groupfirst) }) setMethod("getPriors", signature(object="FLXPmultinom"), function(object, group, groupfirst) { priors <- matrix(apply(object@coef, 2, function(x) exp(object@x %*% x)), nrow = nrow(object@x)) ungroupPriors(priors/rowSums(priors), group, groupfirst) }) setMethod("FLXreplaceParameters", signature(object="FLXdist"), function(object, parms) { comp_names <- names(object@components) components <- list() for (m in seq_along(object@model)) { indices <- grep(paste("^model.", m, sep = ""), names(parms)) components[[m]] <- FLXreplaceParameters(object@model[[m]], lapply(object@components, "[[", m), parms[indices]) } object@components <- lapply(seq_along(object@components), function(k) lapply(components, "[[", k)) names(object@components) <- comp_names if (object@k > 1) { indices <- grep("^concomitant_", names(parms)) object@concomitant <- FLXreplaceParameters(object@concomitant, parms[indices]) } object }) setMethod("FLXreplaceParameters", signature(object="FLXM"), function(object, components, parms) { Design <- FLXgetDesign(object, components) lapply(seq_along(components), function(k) { Parameters <- list() parms_k <- parms[as.logical(Design[k,])] for (i in seq_along(components[[k]]@parameters)) { Parameters[[i]] <- parms_k[seq_along(components[[k]]@parameters[[i]])] attributes(Parameters[[i]]) <- attributes(components[[k]]@parameters[[i]]) parms_k <- parms_k[-seq_along(components[[k]]@parameters[[i]])] } names(Parameters) <- names(components[[k]]@parameters) Parameters$df <- components[[k]]@df variables <- c("x", "y") for (var in variables) assign(var, slot(object, var)) if (is(object@defineComponent, "expression")) eval(object@defineComponent, Parameters) else object@defineComponent(Parameters) }) }) setMethod("FLXreplaceParameters", signature(object="FLXMC"), function(object, components, parms) { Design <- FLXgetDesign(object, components) if (object@dist == "mvnorm") { p <- sqrt(1/4+ncol(Design)/nrow(Design)) - 1/2 diagonal <- get("diagonal", environment(object@fit)) if (diagonal) { cov <- diag(seq_len(p)) parms_comp <- as.vector(sapply(seq_len(nrow(Design)), function(i) c(parms[(i-1) * 2 * p + seq_len(p)], as.vector(diag(diag(parms[(i-1) * 2 * p + p + seq_len(p)])))))) parms <- c(parms_comp, parms[(nrow(Design) * 2 * p + 1):length(parms)]) } else { cov <- matrix(NA, nrow = p, ncol = p) cov[lower.tri(cov, diag = TRUE)] <- seq_len(sum(lower.tri(cov, diag = TRUE))) cov[upper.tri(cov)] <- t(cov)[upper.tri(cov)] parms <- parms[c(as.vector(sapply(seq_len(nrow(Design)), function(i) (i-1)*(max(cov)+p) + c(seq_len(p), as.vector(cov) + p))), (nrow(Design) * (max(cov) + p)+1):length(parms))] } } callNextMethod(object = object, components = components, parms = parms) }) setMethod("FLXreplaceParameters", signature(object="FLXMRglm"), function(object, components, parms) { Design <- FLXgetDesign(object, components) lapply(seq_along(components), function(k) { Parameters <- list() parms_k <- parms[as.logical(Design[k,])] for (i in seq_along(components[[k]]@parameters)) { Parameters[[i]] <- parms_k[seq_along(components[[k]]@parameters[[i]])] attributes(Parameters[[i]]) <- attributes(components[[k]]@parameters[[i]]) parms_k <- parms_k[-seq_along(components[[k]]@parameters[[i]])] } names(Parameters) <- names(components[[k]]@parameters) if (object@family == "gaussian") { Parameters[["sigma"]] <- exp(Parameters[["sigma"]]) } Parameters$df <- components[[k]]@df variables <- c("x", "y", "offset", "family") for (var in variables) { assign(var, slot(object, var)) } if (is(object@defineComponent, "expression")) eval(object@defineComponent, Parameters) else object@defineComponent(Parameters) }) }) setMethod("FLXreplaceParameters", signature(object="FLXP"), function(object, parms) { parms <- exp(c(0, parms)) parms <- parms/sum(parms) attributes(parms) <- attributes(object@coef) object@coef <- parms object }) setMethod("FLXreplaceParameters", signature(object="FLXPmultinom"), function(object, parms) { parms <- cbind(0, matrix(parms, nrow = nrow(object@coef))) attributes(parms) <- attributes(object@coef) object@coef <- parms object }) setMethod("FLXgradlogLikfun", signature(object="flexmix"), function(object, ...) { existFunction <- all(sapply(object@model, existGradient)) if (object@k > 1) existFunction <- c(existFunction, existGradient(object@concomitant)) if (any(!existFunction)) return(NULL) function(parms) { object <- FLXreplaceParameters(object, parms) groupfirst <- if (length(object@group) > 1) groupFirst(object@group) else rep(TRUE, FLXgetObs(object@model[[1]])) logLik_comp <- logLikfun_comp(object) Priors <- getPriors(object@concomitant, object@group, groupfirst) Priors_Lik_comp <- logLik_comp + log(Priors) weights <- exp(Priors_Lik_comp - log_row_sums(Priors_Lik_comp)) if (object@k > 1) { ConcomitantScores <- FLXgradlogLikfun(object@concomitant, Priors[groupfirst,,drop=FALSE], weights[groupfirst,,drop=FALSE]) if (!is.null(object@weights)) ConcomitantScores <- lapply(ConcomitantScores, "*", object@weights[groupfirst]) } else ConcomitantScores <- list() ModelScores <- lapply(seq_along(object@model), function(m) FLXgradlogLikfun(object@model[[m]], lapply(object@components, "[[", m), weights)) ModelScores <- lapply(ModelScores, lapply, groupPosteriors, object@group) if (!is.null(object@weights)) ModelScores <- lapply(ModelScores, lapply, "*", object@weights) colSums(cbind(do.call("cbind", lapply(ModelScores, function(x) do.call("cbind", x)))[groupfirst,,drop=FALSE], do.call("cbind", ConcomitantScores))) } }) setMethod("existGradient", signature(object = "FLXM"), function(object) FALSE) setMethod("existGradient", signature(object = "FLXMRglm"), function(object) { if (object@family == "Gamma") return(FALSE) TRUE }) setMethod("existGradient", signature(object = "FLXMRglmfix"), function(object) FALSE) setMethod("existGradient", signature(object = "FLXP"), function(object) TRUE) setMethod("FLXgradlogLikfun", signature(object="FLXMRglm"), function(object, components, weights, ...) { lapply(seq_along(components), function(k) { res <- if (object@family == "binomial") as.vector(object@y[,1] - rowSums(object@y)*components[[k]]@predict(object@x)) else as.vector(object@y - components[[k]]@predict(object@x)) Scores <- weights[,k] * res * object@x if (object@family == "gaussian") { Scores <- cbind(Scores/components[[k]]@parameters$sigma^2, weights[,k] * (-1 + res^2/components[[k]]@parameters$sigma^2)) } Scores }) }) setMethod("FLXgradlogLikfun", signature(object="FLXP"), function(object, fitted, weights, ...) { Pi <- lapply(seq_len(ncol(fitted))[-1], function(i) - fitted[,i] + weights[,i]) lapply(Pi, function(p) apply(object@x, 2, "*", p)) }) setMethod("refit", signature(object = "flexmix"), function(object, newdata, method = c("optim", "mstep"), ...) { method <- match.arg(method) if (method == "optim") { VarCov <- VarianceCovariance(object, ...) z <- new("FLXRoptim", call=sys.call(-1), k = object@k, coef = VarCov$coef, vcov = VarCov$vcov) z@components <- lapply(seq_along(object@model), function(m) { begin_name <- paste("^model", m, sep = ".") indices <- grep(begin_name, names(z@coef)) refit_optim(object@model[[m]], components = lapply(object@components, "[[", m), coef = z@coef[indices], se = sqrt(diag(z@vcov)[indices])) }) z@concomitant <- if (object@k > 1) { indices <- grep("^concomitant_", names(z@coef)) refit_optim(object@concomitant, coef = z@coef[indices], se = sqrt(diag(z@vcov)[indices])) } else NULL } else { z <- new("FLXRmstep", call=sys.call(-1), k = object@k) z@components <- lapply(object@model, function(x) { x <- refit_mstep(x, weights=object@posterior$scaled) names(x) <- paste("Comp", seq_len(object@k), sep=".") x }) z@concomitant <- if (object@k > 1) refit_mstep(object@concomitant, posterior = object@posterior$scaled, group = object@group, w = object@weights) else NULL } z }) setMethod("refit_optim", signature(object = "FLXM"), function(object, components, coef, se) { Design <- FLXgetDesign(object, components) x <- lapply(seq_len(nrow(Design)), function(k) { rval <- cbind(Estimate = coef[as.logical(Design[k,])], "Std. Error" = se[as.logical(Design[k,])]) pars <- components[[k]]@parameters[[1]] rval <- rval[seq_along(pars),,drop=FALSE] rownames(rval) <- names(pars) zval <- rval[,1]/rval[,2] new("Coefmat", cbind(rval, "z value" = zval, "Pr(>|z|)" = 2 * pnorm(abs(zval), lower.tail = FALSE))) }) names(x) <- paste("Comp", seq_along(x), sep = ".") x }) setMethod("refit_optim", signature(object = "FLXMC"), function(object, components, coef, se) { Design <- FLXgetDesign(object, components) if (object@dist == "mvnorm") { p <- length(grep("Comp.1_center", colnames(Design), fixed = TRUE)) diagonal <- get("diagonal", environment(object@fit)) if (diagonal) { cov <- diag(seq_len(p)) coef_comp <- as.vector(sapply(seq_len(nrow(Design)), function(i) c(coef[(i-1) * 2 * p + seq_len(p)], as.vector(diag(diag(coef[(i-1) * 2 * p + p + seq_len(p)])))))) coef <- c(coef_comp, coef[(nrow(Design) * 2 * p + 1):length(coef)]) se_comp <- as.vector(sapply(seq_len(nrow(Design)), function(i) c(se[(i-1) * 2 * p + seq_len(p)], as.vector(diag(diag(se[(i-1) * 2 * p + p + seq_len(p)])))))) se <- c(se_comp, se[(nrow(Design) * 2 * p + 1):length(se)]) } else { cov <- matrix(NA, nrow = p, ncol = p) cov[lower.tri(cov, diag = TRUE)] <- seq_len(sum(lower.tri(cov, diag = TRUE))) cov[upper.tri(cov)] <- t(cov)[upper.tri(cov)] coef <- coef[c(as.vector(sapply(seq_len(nrow(Design)), function(i) (i-1)*(max(cov)+p) + c(seq_len(p), as.vector(cov) + p))), (nrow(Design) * (max(cov) + p)+1):length(coef))] se <- se[c(as.vector(sapply(seq_len(nrow(Design)), function(i) (i-1)*(max(cov)+p) + c(seq_len(p), as.vector(cov) + p))), (nrow(Design) * (max(cov) + p)+1):length(se))] } } callNextMethod(object = object, components = components, coef = coef, se = se) }) setMethod("refit_optim", signature(object = "FLXP"), function(object, coef, se) { x <- lapply(seq_len(ncol(object@coef))[-1], function(k) { indices <- grep(paste("Comp", k, sep = "."), names(coef)) rval <- cbind(Estimate = coef[indices], "Std. Error" = se[indices]) rval <- rval[seq_len(nrow(object@coef)),,drop=FALSE] rownames(rval) <- rownames(object@coef) zval <- rval[,1]/rval[,2] new("Coefmat", cbind(rval, "z value" = zval, "Pr(>|z|)" = 2 * pnorm(abs(zval), lower.tail = FALSE))) }) names(x) <- paste("Comp", 1 + seq_along(x), sep = ".") x }) setMethod("FLXgetDesign", signature(object = "FLXM"), function(object, components, ...) { parms <- lapply(components, function(x) unlist(slot(x, "parameters"))) nr_parms <- sapply(parms, length) cumSum <- cumsum(c(0, nr_parms)) Design <- t(sapply(seq_len(length(cumSum)-1), function(i) rep(c(0, 1, 0), c(cumSum[i], nr_parms[i], max(cumSum) - cumSum[i] - nr_parms[i])))) colnames(Design) <- paste(rep(paste("Comp", seq_len(nrow(Design)), sep = "."), nr_parms), unlist(lapply(parms, names)), sep = "_") Design }) setMethod("FLXgetDesign", signature(object = "FLXMRglmfix"), function(object, components, ...) { if (length(components) == 1) return(callNextMethod(object, components, ...)) Design <- object@design if (object@family == "gaussian") { cumSum <- cumsum(c(0, object@variance)) variance <- matrix(sapply(seq_len(length(cumSum)-1), function(i) rep(c(0, 1, 0), c(cumSum[i], object@variance[i], length(components) - cumSum[i] - object@variance[i]))), nrow = length(components)) colnames(variance) <- paste("Comp", apply(variance, 2, function(x) which(x == 1)[1]), "sigma", sep= ".") Design <- cbind(Design, variance) } Design }) ###********************************************************* setMethod("refit_mstep", signature(object="FLXM"), function(object, newdata, weights, ...) { lapply(seq_len(ncol(weights)), function(k) object@fit(object@x, object@y, weights[,k], ...)@parameters) }) setMethod("refit_mstep", signature(object="FLXMRglm"), function(object, newdata, weights, ...) { lapply(seq_len(ncol(weights)), function(k) { fit <- object@refit(object@x, object@y, weights[,k], ...) fit <- c(fit, list(formula = object@fullformula, terms = object@terms, contrasts = object@contrasts, xlevels = object@xlevels)) class(fit) <- c("glm", "lm") fit }) }) ###********************************************************** setMethod("fitted", signature(object="flexmix"), function(object, drop=TRUE, aggregate = FALSE, ...) { x<- list() for(m in seq_along(object@model)) { comp <- lapply(object@components, "[[", m) x[[m]] <- fitted(object@model[[m]], comp, ...) } if (aggregate) { group <- group(object) prior_weights <- determinePrior(object@prior, object@concomitant, group)[as.integer(group),] z <- lapply(x, function(z) matrix(rowSums(do.call("cbind", z) * prior_weights), nrow = nrow(z[[1]]))) if(drop && all(lapply(z, ncol)==1)){ z <- sapply(z, unlist) } } else { z <- list() for (k in seq_len(object@k)) { z[[k]] <- do.call("cbind", lapply(x, "[[", k)) } names(z) <- paste("Comp", seq_len(object@k), sep=".") if(drop && all(lapply(z, ncol)==1)){ z <- sapply(z, unlist) } } z }) setMethod("fitted", signature(object="FLXM"), function(object, components, ...) { lapply(components, function(z) z@predict(object@x)) }) setMethod("predict", signature(object="FLXM"), function(object, newdata, components, ...) { object <- FLXgetModelmatrix(object, newdata, formula = object@fullformula, lhs = FALSE) z <- list() for(k in seq_along(components)) z[[k]] <- components[[k]]@predict(object@x, ...) z }) ###********************************************************** setMethod("Lapply", signature(object="FLXRmstep"), function(object, FUN, model = 1, component = TRUE, ...) { X <- object@components[[model]] lapply(X[component], FUN, ...) }) ###********************************************************* setMethod("refit_mstep", signature(object="flexmix", newdata="listOrdata.frame"), function(object, newdata, ...) { z <- new("FLXR", call=sys.call(-1), k = object@k) z@components <- lapply(object@model, function(x) { x <- refit_mstep(x, newdata = newdata, weights=posterior(object, newdata = newdata)) names(x) <- paste("Comp", seq_len(object@k), sep=".") x }) z@concomitant <- if (object@k > 1) refit_mstep(object@concomitant, newdata, object@posterior$scaled, object@group, w = object@weights) else NULL z }) setMethod("refit_mstep", signature(object="FLXMRglm", newdata="listOrdata.frame"), function(object, newdata, weights, ...) { w <- weights lapply(seq_len(ncol(w)), function(k) { newdata$weights <- weights <- w[,k] weighted.glm(formula = object@fullformula, data = newdata, family = object@family, weights = weights, ...) }) }) weighted.glm <- function(weights, ...) { fit <- eval(as.call(c(as.symbol("glm"), c(list(...), list(weights = weights, x = TRUE))))) fit$df.null <- sum(weights) + fit$df.null - fit$df.residual - fit$rank fit$df.residual <- sum(weights) - fit$rank fit$method <- "weighted.glm.fit" fit } weighted.glm.fit <- function(x, y, weights, offset = NULL, family = "gaussian", ...) { if (!is.function(family) & !is(family, "family")) family <- get(family, mode = "function", envir = parent.frame()) fit <- c(glm.fit(x, y, weights = weights, offset=offset, family=family), list(call = sys.call(), offset = offset, control = eval(formals(glm.fit)$control), method = "weighted.glm.fit")) fit$df.null <- sum(weights) + fit$df.null - fit$df.residual - fit$rank fit$df.residual <- sum(weights) - fit$rank fit$x <- x fit } flexmix/R/kldiv.R0000644000176200001440000001006514404637304013372 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: kldiv.R 5079 2016-01-31 12:21:12Z gruen $ # setMethod("KLdiv", "matrix", function(object, eps=10^-4, overlap=TRUE,...) { if(!is.numeric(object)) stop("object must be a numeric matrix\n") z <- matrix(NA, nrow=ncol(object), ncol=ncol(object)) colnames(z) <- rownames(z) <- colnames(object) w <- object < eps if (any(w)) object[w] <- eps object <- sweep(object, 2, colSums(object) , "/") for(k in seq_len(ncol(object)-1)){ for(l in 2:ncol(object)){ ok <- (object[, k] > eps) & (object[, l] > eps) if (!overlap | any(ok)) { z[k,l] <- sum(object[,k] * (log(object[,k]) - log(object[,l]))) z[l,k] <- sum(object[,l] * (log(object[,l]) - log(object[,k]))) } } } diag(z)<-0 z }) setMethod("KLdiv", "flexmix", function(object, method = c("continuous", "discrete"), ...) { method <- match.arg(method) if (method == "discrete") z <- KLdiv(object@posterior$scaled, ...) else { z <- matrix(0, object@k, object@k) for (i in seq_along(object@model)) { comp <- lapply(object@components, "[[", i) z <- z + KLdiv(object@model[[i]], comp) } } z }) setMethod("KLdiv", "FLXMRglm", function(object, components, ...) { z <- matrix(NA, length(components), length(components)) mu <- lapply(components, function(x) x@predict(object@x)) if (object@family == "gaussian") { sigma <- lapply(components, function(x) x@parameters$sigma) for (k in seq_len(ncol(z)-1)) { for (l in seq_len(ncol(z))[-1]) { z[k,l] <- sum(log(sigma[[l]]) - log(sigma[[k]]) + 1/2 * (-1 + ((sigma[[k]]^2 + (mu[[k]] - mu[[l]])^2))/sigma[[l]]^2)) z[l,k] <- sum(log(sigma[[k]]) - log(sigma[[l]]) + 1/2 * (-1 + ((sigma[[l]]^2 + (mu[[l]] - mu[[k]])^2))/sigma[[k]]^2)) } } } else if (object@family == "binomial") { for (k in seq_len(ncol(z)-1)) { for (l in seq_len(ncol(z))[-1]) { z[k,l] <- sum(mu[[k]] * log(mu[[k]]/mu[[l]]) + (1-mu[[k]]) * log((1-mu[[k]])/(1-mu[[l]]))) z[l,k] <- sum(mu[[l]] * log(mu[[l]]/mu[[k]]) + (1-mu[[l]]) * log((1-mu[[l]])/(1-mu[[k]]))) } } } else if (object@family == "poisson") { for (k in seq_len(ncol(z)-1)) { for (l in seq_len(ncol(z))[-1]) { z[k,l] <- sum(mu[[k]] * log(mu[[k]]/mu[[l]]) + mu[[l]] - mu[[k]]) z[l,k] <- sum(mu[[l]] * log(mu[[l]]/mu[[k]]) + mu[[k]] - mu[[l]]) } } } else if (object@family == "gamma") { shape <- lapply(components, function(x) x@parameters$shape) for (k in seq_len(ncol(z)-1)) { for (l in seq_len(ncol(z))[-1]) { X <- mu[[k]]*shape[[l]]/mu[[l]]/shape[[k]] z[k,l] <- sum(log(gamma(shape[[l]])/gamma(shape[[k]])) + shape[[l]] * log(X) - shape[[k]] * (1 - 1/X) + (shape[[k]] - shape[[l]])*digamma(shape[[k]])) z[l,k] <- sum(log(gamma(shape[[k]])/gamma(shape[[l]])) - shape[[k]] * log(X) - shape[[l]] * (1 - X) + (shape[[l]] - shape[[k]])*digamma(shape[[l]])) } } } else stop(paste("Unknown family", object@family)) diag(z) <- 0 z }) setMethod("KLdiv", "FLXMC", function(object, components, ...) { z <- matrix(NA, length(components), length(components)) if (object@dist == "mvnorm") { center <- lapply(components, function(x) x@parameters$center) cov <- lapply(components, function(x) x@parameters$cov) for (k in seq_len(ncol(z)-1)) { for (l in seq_len(ncol(z))[-1]) { z[k,l] <- 1/2 * (log(det(cov[[l]])) - log(det(cov[[k]])) - length(center[[k]]) + sum(diag(solve(cov[[l]]) %*% (cov[[k]] + tcrossprod(center[[k]] - center[[l]]))))) z[l,k] <- 1/2 * (log(det(cov[[k]])) - log(det(cov[[l]])) - length(center[[l]]) + sum(diag(solve(cov[[k]]) %*% (cov[[l]] + tcrossprod(center[[l]] - center[[k]]))))) } } } else stop(paste("Unknown distribution", object@dist)) diag(z) <- 0 z }) ###********************************************************** flexmix/R/infocrit.R0000644000176200001440000000277614404637304014110 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: infocrit.R 5079 2016-01-31 12:21:12Z gruen $ # setMethod("nobs", signature(object="flexmix"), function(object, ...) { if (is.null(object@weights)) nrow(object@posterior$scaled) else sum(object@weights) }) setMethod("logLik", signature(object="flexmix"), function(object, newdata, ...){ if (missing(newdata)) { z <- object@logLik attr(z, "df") <- object@df attr(z, "nobs") <- nobs(object) class(z) <- "logLik" } else { z <- sum(log(rowSums(posterior(object, newdata = newdata, unscaled = TRUE)))) attr(z, "df") <- object@df attr(z, "nobs") <- nrow(newdata) class(z) <- "logLik" } z }) setMethod("ICL", signature(object="flexmix"), function(object, ...){ -2 * clogLik(object) + object@df * log(nobs(object)) }) setMethod("clogLik", signature(object="flexmix"), function(object, ...){ first <- if (length(object@group)) groupFirst(object@group) else TRUE post <- object@posterior$unscaled[first,,drop=FALSE] n <- nrow(post) sum(log(post[seq_len(n) + (clusters(object)[first] - 1)*n])) }) setMethod("EIC", signature(object="flexmix"), function(object, ...) { first <- if (length(object@group)) groupFirst(object@group) else TRUE post <- object@posterior$scaled[first,,drop=FALSE] n <- nrow(post) lpost <- log(post) if (any(is.infinite(lpost))) lpost[is.infinite(lpost)] <- -10^3 1 + sum(post * lpost)/(n * log(object@k)) }) flexmix/R/allClasses.R0000644000176200001440000002277114404637304014356 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: allClasses.R 5185 2020-06-23 13:24:06Z gruen $ # setClass("FLXcontrol", representation(iter.max="numeric", minprior="numeric", tolerance="numeric", verbose="numeric", classify="character", nrep="numeric"), prototype(iter.max=200, minprior=0.05, tolerance=10e-7, verbose=0, classify="auto", nrep=1), validity=function(object) { (object@iter.max > 0) }) setAs("list", "FLXcontrol", function(from, to){ z = list2object(from, to) z@classify = match.arg(z@classify, c("auto", "weighted", "hard", "random", "SEM", "CEM")) z }) setAs("NULL", "FLXcontrol", function(from, to){ new(to) }) ###********************************************************** setClassUnion("expressionOrfunction", c("expression", "function")) setClass("FLXM", representation(fit="function", defineComponent="expressionOrfunction", weighted="logical", name="character", formula="formula", fullformula="formula", x="matrix", y="ANY", terms="ANY", xlevels="ANY", contrasts="ANY", preproc.x="function", preproc.y="function", "VIRTUAL"), prototype(formula=.~., fullformula=.~., preproc.x = function(x) x, preproc.y = function(x) x)) ## model-based clustering setClass("FLXMC", representation(y="matrix", dist="character"), contains = "FLXM") ## regression setClass("FLXMR", representation(y="matrix", offset="ANY"), contains = "FLXM") setMethod("show", "FLXM", function(object){ cat("FlexMix model of type", object@name,"\n\nformula: ") print(object@formula) cat("Weighted likelihood possible:", object@weighted,"\n\n") if(!is.null(object@x) && nrow(object@x)>0){ cat("Regressors:\n") print(summary(object@x)) } if(!is.null(object@y) && nrow(object@y)>0){ cat("Response:\n") print(summary(object@y)) } cat("\n") }) setClass("FLXcomponent", representation(df="numeric", logLik="function", parameters="list", predict="function")) setMethod("show", "FLXcomponent", function(object){ if(length(object@parameters)>0) print(object@parameters) }) ###********************************************************** setClass("FLXP", representation(name="character", formula="formula", x="matrix", fit="function", refit="function", coef="matrix", df="function"), prototype(formula=~1, df = function(x, k, ...) (k-1)*ncol(x))) setMethod("initialize", signature(.Object="FLXP"), function(.Object, ...) { .Object <- callNextMethod(.Object=.Object, ...) if (is.null(formals(.Object@refit))) .Object@refit <- .Object@fit .Object }) setClass("FLXPmultinom", contains="FLXP") setMethod("show", "FLXP", function(object){ cat("FlexMix concomitant model of type", object@name,"\n\nformula: ") print(object@formula) if(!is.null(object@x) && nrow(object@x)>0){ cat("\nRegressors:\n") print(summary(object@x)) } cat("\n") }) ###********************************************************** setClass("FLXdist", representation(model="list", prior="numeric", components="list", concomitant="FLXP", formula="formula", call="call", k="integer"), validity=function(object) { (object@k == length(object@prior)) }, prototype(formula=.~.)) setClass("flexmix", representation(posterior="ANY", weights="ANY", iter="numeric", cluster="integer", logLik="numeric", df="numeric", control="FLXcontrol", group="factor", size="integer", converged="logical", k0="integer"), prototype(group=(factor(integer(0))), formula=.~.), contains="FLXdist") setMethod("show", "flexmix", function(object){ cat("\nCall:", deparse(object@call,0.75*getOption("width")), sep="\n") cat("\nCluster sizes:\n") print(object@size) cat("\n") if(!object@converged) cat("no ") cat("convergence after", object@iter, "iterations\n") }) ###********************************************************** setClass("summary.flexmix", representation(call="call", AIC="numeric", BIC="numeric", logLik="logLik", comptab="ANY")) setMethod("show", "summary.flexmix", function(object){ cat("\nCall:", deparse(object@call,0.75*getOption("width")), sep="\n") cat("\n") print(object@comptab, digits=3) cat("\n") print(object@logLik) cat("AIC:", object@AIC, " BIC:", object@BIC, "\n") cat("\n") }) ###********************************************************** setClass("FLXMRglm", representation(family="character", refit="function"), contains="FLXMR") setClass("FLXR", representation(k="integer", components = "list", concomitant = "ANY", call="call", "VIRTUAL")) setClass("FLXRoptim", representation(coef="vector", vcov="matrix"), contains="FLXR") setClass("FLXRmstep", contains="FLXR") setMethod("show", signature(object = "FLXR"), function(object) { cat("\nCall:", deparse(object@call,0.75*getOption("width")), sep="\n") cat("\nNumber of components:", object@k, "\n\n") }) setMethod("summary", signature(object = "FLXRoptim"), function(object, model = 1, which = c("model", "concomitant"), ...) { which <- match.arg(which) z <- if (which == "model") object@components[[model]] else object@concomitant show(z) invisible(object) }) setMethod("summary", signature(object = "FLXRmstep"), function(object, model = 1, which = c("model", "concomitant"), ...) { which <- match.arg(which) if (which == "model") { z <- object@components[[model]] if (!is.null(z)) lapply(seq_along(z), function(k) { cat(paste("$", names(z)[k], "\n", sep = "")) printCoefmat(coef(summary(z[[k]]))) cat("\n") }) } else { z <- object@concomitant fitted.summary <- summary(z) k <- nrow(coef(fitted.summary)) + 1 coefs <- lapply(2:k, function(n) { coef.p <- fitted.summary$coefficients[n - 1, , drop = FALSE] s.err <- fitted.summary$standard.errors[n - 1, , drop = FALSE] tvalue <- coef.p/s.err pvalue <- 2 * pnorm(-abs(tvalue)) coef.table <- t(rbind(coef.p, s.err, tvalue, pvalue)) dimnames(coef.table) <- list(colnames(coef.p), c("Estimate", "Std. Error", "z value", "Pr(>|z|)")) new("Coefmat", coef.table) }) names(coefs) <- paste("Comp", 2:k, sep = ".") print(coefs) } invisible(object) }) setClass("Coefmat", contains = "matrix") setMethod("show", signature(object="Coefmat"), function(object) { printCoefmat(object, signif.stars = getOption("show.signif.stars")) }) ###********************************************************** setClass("FLXnested", representation(formula = "list", k = "numeric"), validity = function(object) { length(object@formula) == length(object@k) }) setAs("numeric", "FLXnested", function(from, to) { new("FLXnested", formula = rep(list(~0), length(from)), k = from) }) setAs("list", "FLXnested", function(from, to) { z <- list2object(from, to) }) setAs("NULL", "FLXnested", function(from, to) { new(to) }) setMethod("initialize", "FLXnested", function(.Object, formula = list(), k = numeric(0), ...) { if (is(formula, "formula")) formula <- rep(list(formula), length(k)) .Object <- callNextMethod(.Object, formula = formula, k = k, ...) .Object }) ###********************************************************** setClass("FLXMRfix", representation(design = "matrix", nestedformula = "FLXnested", fixed = "formula", segment = "matrix", variance = "vector"), contains="FLXMR") setClass("FLXMRglmfix", contains=c("FLXMRfix", "FLXMRglm")) ###********************************************************** setClassUnion("listOrdata.frame", c("list", "data.frame")) ###********************************************************** flexmix/R/relabel.R0000644000176200001440000000555414404637304013676 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id$ # setGeneric("dorelabel", function(object, perm, ...) standardGeneric("dorelabel")) setMethod("dorelabel", signature(object="flexmix", perm="vector"), function(object, perm, ...) { object <- callNextMethod(object, perm) object@posterior$scaled <- object@posterior$scaled[,perm,drop=FALSE] object@posterior$unscaled <- object@posterior$unscaled[,perm,drop=FALSE] object@cluster <- order(perm)[object@cluster] object@size <- object@size[perm] names(object@size) <- seq_along(perm) object }) setMethod("dorelabel", signature(object="FLXdist", perm="vector"), function(object, perm, ...) { if (length(perm) != object@k) stop("length of order argument does not match number of components") if (any(sort(perm) != seq_len(object@k))) stop("order argument not specified correctly") object@prior <- object@prior[perm] object@components <- object@components[perm] names(object@components) <- sapply(seq_along(object@components), function(k) gsub("[0-9]+", k, names(object@components)[k])) object@concomitant <- dorelabel(object@concomitant, perm, ...) object }) setMethod("dorelabel", signature(object="FLXP", perm="vector"), function(object, perm, ...) { object@coef <- object@coef[,perm,drop=FALSE] colnames(object@coef) <- sapply(seq_len(ncol(object@coef)), function(k) gsub("[0-9]+", k, colnames(object@coef)[k])) object }) setMethod("dorelabel", signature(object="FLXPmultinom", perm="vector"), function(object, perm, ...) { object@coef <- object@coef[,perm,drop=FALSE] object@coef <- sweep(object@coef, 1, object@coef[,1], "-") colnames(object@coef) <- sapply(seq_len(ncol(object@coef)), function(k) gsub("[0-9]+", k, colnames(object@coef)[k])) object }) setMethod("relabel", signature(object="FLXdist", by="character"), function(object, by, which=NULL, ...) { by <- match.arg(by, c("prior", "model", "concomitant")) if(by=="prior"){ perm <- order(prior(object), ...) } else if(by %in% c("model", "concomitant")) { pars <- parameters(object, which = by) index <- grep(which, rownames(pars)) if (length(index) != 1) stop("no suitable ordering variable given in 'which'") perm <- order(pars[index,], ...) } object <- dorelabel(object, perm=perm) object }) setMethod("relabel", signature(object="FLXdist", by="missing"), function(object, by, ...) { object <- relabel(object, by="prior", ...) object }) setMethod("relabel", signature(object="FLXdist", by="integer"), function(object, by, ...) { if(!all(sort(by) == seq_len(object@k))) stop("if integer, ", sQuote("by"), " must be a permutation of the numbers 1 to ", object@k) object <- dorelabel(object, by) object }) flexmix/R/plot-refit.R0000644000176200001440000001125014404637304014343 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: plot-refit.R 5079 2016-01-31 12:21:12Z gruen $ # prepanel.default.coef <- function (x, y, subscripts, groups=NULL, horizontal = TRUE, nlevels, origin = NULL, ...) { if (any(!is.na(x) & !is.na(y))) { if (horizontal) { if (!is.factor(y)) { if (missing(nlevels)) nlevels <- length(unique(y)) y <- factor(y, levels = seq_len(nlevels)) } if (!is.null(groups)) { if (!is.numeric(x)) stop("x must be numeric") x <- rep(x, each = 2) + rep(groups[subscripts], each = 2) *c(-1,1) } list(xlim = if (is.numeric(x)) range(x, origin, finite = TRUE) else levels(x), ylim = levels(y), yat = sort(unique(as.numeric(y))), dx = 1, dy = 1) } else { if (!is.factor(x)) { if (missing(nlevels)) nlevels <- length(unique(x)) x <- factor(x, levels = seq_len(nlevels)) } if (!is.null(groups)) { if (!is.numeric(y)) stop("y must be numeric") y <- rep(as.numeric(y), each = 2) + rep(groups[subscripts], each = 2) *c(-1,1) } list(xlim = levels(x), xat = sort(unique(as.numeric(x))), ylim = if (is.numeric(y)) range(y, origin, finite = TRUE) else levels(y), dx = 1, dy = 1) } } else list(xlim = c(NA, NA), ylim = c(NA, NA), dx = 1, dy = 1) } panel.coef <- function(x, y, subscripts, groups, significant = NULL, horizontal = TRUE, lwd = 2, col, col.line = c("black", "grey"), ...) { col.sig <- rep(col.line[1], length(x)) if (!is.null(significant)) { if (missing(col)) col <- c("grey", "white") col.fill <- rep(col[1], length(x)) col.sig[!significant[subscripts]] <- col.line[2] col.fill[!significant[subscripts]] <- col[2] } else if (missing(col)) col.fill <- "grey" else col.fill <- col panel.barchart(x, y, border = col.sig, col = col.fill, horizontal = horizontal, ...) if (!missing(groups)) { if (horizontal) { z <- x + rep(c(-1,1), each = length(x)) * matrix(rep(groups[subscripts], 2), ncol = 2) for (i in seq_along(x)) { panel.xyplot(z[i,], rep(y[i], 2), type = "l", col = col.sig[i], lwd = lwd) } } else { z <- y + rep(c(-1,1), each = length(y)) * matrix(rep(groups[subscripts], 2), ncol = 2) for (i in seq_along(y)) { panel.xyplot(rep(x[i], 2), z[i,], type = "l", col = col.sig[i], lwd = lwd) } } } } getCoefs <- function(x, alpha = 0.05, components, ...) { names(x) <- sapply(names(x), function(z) strsplit(z, "Comp.")[[1]][2]) x <- x[names(x) %in% components] Comp <- lapply(names(x), function(n) data.frame(Value = x[[n]][,1], SD = x[[n]][,2] * qnorm(1-alpha/2), Variable = rownames(x[[n]]), Component = n, Significance = x[[n]][,4] <= alpha)) do.call("rbind", Comp) } setMethod("plot", signature(x="FLXRoptim", y="missing"), function(x, y, model = 1, which = c("model", "concomitant"), bycluster=TRUE, alpha=0.05, components, labels=NULL, significance = FALSE, xlab = NULL, ylab = NULL, ci = TRUE, scales = list(), as.table = TRUE, horizontal = TRUE, ...) { which <- match.arg(which) if (missing(components)) components <- seq_len(x@k) plot.data <- if (which == "model") getCoefs(x@components[[model]], alpha, components) else getCoefs(x@concomitant, alpha, components) if (!is.null(labels)) plot.data$Variable <- factor(plot.data$Variable, labels = labels) plot.data$Component <- with(plot.data, factor(Component, sort(unique(Component)), labels = paste("Comp.", sort(unique(Component))))) if (bycluster) { formula <- if (horizontal) Variable ~ Value | Component else Value ~ Variable | Component plot.data$Variable <- with(plot.data, factor(Variable, levels = rev(unique(Variable)))) } else { formula <- if (horizontal) Component ~ Value | Variable else Value ~ Component | Variable plot.data$Component <- with(plot.data, factor(Component, levels = rev(levels(Component)))) } groups <- if (ci) plot.data$SD else NULL significant <- if (significance) plot.data$Significance else NULL xyplot(formula, data = plot.data, xlab = xlab, ylab = ylab, origin = 0, horizontal = horizontal, scales = scales, as.table = as.table, significant = significant, groups = groups, prepanel = function(...) prepanel.default.coef(...), panel = function(x, y, subscripts, groups, ...) panel.coef(x, y, subscripts, groups, ...), ...) }) flexmix/R/lmmc.R0000644000176200001440000006522614404661473013226 0ustar liggesuserssetClass("FLXMRlmc", representation(family = "character", group = "factor", censored = "formula", C = "matrix"), contains = "FLXMR") setClass("FLXMRlmcfix", contains = "FLXMRlmc") setClass("FLXMRlmmc", representation(random = "formula", z = "matrix", which = "ANY"), contains = "FLXMRlmc") setClass("FLXMRlmmcfix", contains = "FLXMRlmmc") setMethod("allweighted", signature(model = "FLXMRlmc", control = "ANY", weights = "ANY"), function(model, control, weights) { if (!control@classify %in% c("auto", "weighted")) stop("Model class only supports weighted ML estimation.") model@weighted }) update_Residual <- function(fit, w, z, C, which, random, censored) { index <- lapply(C, function(x) x == 1) W <- rep(w, sapply(which, function(x) nrow(z[[x]]))) ZGammaZ <- sapply(seq_along(which), function(i) sum(diag(crossprod(z[[which[i]]]) %*% random$Gamma[[i]]))) WHICH <- which(sapply(C, sum) > 0) Residual <- if (length(WHICH) > 0) sum(sapply(WHICH, function(i) w[i] * sum(diag(censored$Sigma[[i]]) - 2 * z[[which[i]]][index[[i]],,drop=FALSE] * censored$psi[[i]]))) else 0 (sum(W * residuals(fit)^2) + Residual + sum(w * ZGammaZ))/sum(W) } update_latent <- function(x, y, C, fit) { AnyMissing <- which(sapply(C, sum) > 0) index <- lapply(C, function(x) x == 1) Sig <- lapply(seq_along(x), function(i) fit$sigma2 * diag(nrow = nrow(x[[i]]))) SIGMA <- rep(list(matrix(nrow = 0, ncol = 0)), length(x)) if (length(AnyMissing) > 0) { SIGMA[AnyMissing] <- lapply(AnyMissing, function(i) { S <- Sig[[i]] SIG <- S[index[[i]], index[[i]]] if (sum(!index[[i]]) > 0) SIG <- SIG - S[index[[i]],!index[[i]]] %*% solve(S[!index[[i]],!index[[i]]]) %*% S[!index[[i]],index[[i]]] SIG }) } Sigma <- MU <- rep(list(vector("numeric", length = 0)), length(x)) if (length(AnyMissing) > 0) { MU[AnyMissing] <- lapply(AnyMissing, function(i) { S <- Sig[[i]] Mu <- x[[i]][index[[i]],,drop=FALSE] %*% fit$coef if (sum(!index[[i]]) > 0) Mu <- Mu + S[index[[i]],!index[[i]]] %*% solve(S[!index[[i]],!index[[i]]]) %*% (y[[i]][!index[[i]]] - x[[i]][!index[[i]],,drop=FALSE] %*% fit$coef) Mu }) } moments <- lapply(seq_along(x), function(i) { if (sum(index[[i]]) > 0) moments_truncated(MU[[i]], SIGMA[[i]], y[[i]][C[[i]] == 1]) }) Sigma <- lapply(moments, "[[", "variance") censored <- list(mu = lapply(moments, "[[", "mean"), Sigma = Sigma) list(censored = censored) } update_latent_random <- function(x, y, z, C, which, fit) { index <- lapply(C, function(x) x == 1) AnyMissing <- which(sapply(C, sum) > 0) Residual <- fit$sigma2$Residual Psi <- fit$sigma2$Random EVbeta <- lapply(seq_along(z), function(i) solve(1/Residual * crossprod(z[[i]]) + solve(Psi))) Sig <- lapply(seq_along(z), function(i) z[[i]] %*% Psi %*% t(z[[i]]) + Residual * diag(nrow = nrow(z[[i]]))) SIGMA <- rep(list(matrix(nrow = 0, ncol = 0)), length(x)) if (length(AnyMissing) > 0) { SIGMA[AnyMissing] <- lapply(AnyMissing, function(i) { S <- Sig[[which[i]]] SIG <- S[index[[i]], index[[i]]] if (sum(!index[[i]]) > 0) SIG <- SIG - S[index[[i]],!index[[i]]] %*% solve(S[!index[[i]],!index[[i]]]) %*% S[!index[[i]],index[[i]]] SIG }) } Sigma <- MU <- rep(list(vector("numeric", length = 0)), length(x)) if (length(AnyMissing) > 0) { MU[AnyMissing] <- lapply(AnyMissing, function(i) { S <- Sig[[which[i]]] Mu <- x[[i]][index[[i]],,drop=FALSE] %*% fit$coef if (sum(!index[[i]]) > 0) { Mu <- Mu + S[index[[i]],!index[[i]]] %*% solve(S[!index[[i]],!index[[i]]]) %*% (y[[i]][!index[[i]]] - x[[i]][!index[[i]],,drop=FALSE] %*% fit$coef) } Mu }) } moments <- lapply(seq_along(x), function(i) { if (sum(index[[i]]) > 0) moments_truncated(MU[[i]], SIGMA[[i]], y[[i]][C[[i]] == 1]) }) Sigma <- lapply(moments, "[[", "variance") censored <- list(mu = lapply(moments, "[[", "mean"), Sigma = Sigma, psi = lapply(seq_along(x), function(i) { if (sum(index[[i]]) > 0) return(diag(Sigma[[i]] %*% z[[which[i]]][index[[i]],,drop=FALSE] %*% EVbeta[[which[i]]])/Residual) else return(vector("numeric", length = 0)) })) ybar <- lapply(seq_along(y), function(i) { Y <- y[[i]] Y[index[[i]]] <- censored$mu[[i]] Y }) random <- list(beta = lapply(seq_along(x), function(i) EVbeta[[which[i]]] %*% t(z[[which[i]]]) %*% (ybar[[i]] - x[[i]] %*% fit$coef)/Residual), Gamma = lapply(seq_along(x), function(i) { if (sum(index[[i]]) > 0) { return(EVbeta[[which[i]]] + (EVbeta[[which[i]]] %*% (t(z[[which[i]]][index[[i]],,drop=FALSE]) %*% censored$Sigma[[i]] %*% z[[which[i]]][index[[i]],,drop=FALSE]) %*% t(EVbeta[[which[i]]]))/Residual^2) } else return(EVbeta[[which[i]]]) })) list(random = random, censored = censored) } moments_truncated <- function(mu, Sigma, T, ...) { Sigma <- as.matrix(Sigma) mu <- as.vector(mu) T <- as.vector(T) S <- 1/sqrt(diag(Sigma)) T1 <- S * (T - mu) if (length(mu) == 1) { alpha <- pnorm(T1) dT1 <- dnorm(T1) Ex <- - dT1 / alpha Ex2 <- 1 - T1 * dT1 / alpha } else { R <- S * Sigma * rep(S, each = ncol(Sigma)) diag(R) <- 1L alpha <- mvtnorm::pmvnorm(upper = T1, sigma = R, ...) rq <- lapply(seq_along(T1), function(q) (R - tcrossprod(R[,q]))) R2 <- R^2 Vq <- 1 - R2 Sq <- sqrt(Vq) Rq <- lapply(seq_along(T1), function(q) rq[[q]]/(tcrossprod(Sq[,q]))) Tq <- lapply(seq_along(T1), function(q) (T1 - R[,q] * T1[q])/Sq[,q]) Phiq <- if (length(mu) == 1) 1 else sapply(seq_along(Rq), function(q) mvtnorm::pmvnorm(upper = Tq[[q]][-q], sigma = Rq[[q]][-q,-q], ...)) phi_Phiq <- dnorm(T1) * Phiq Ex <- - (R %*% phi_Phiq)/alpha T2_entries <- lapply(seq_along(T1), function(j) sapply(lapply(seq_along(T1)[seq_len(j)], function(i) R[,i] * T1 * phi_Phiq), function(z) sum(z * R[j,]))) T2 <- diag(length(T1)) T2[upper.tri(T2, diag = TRUE)] <- unlist(T2_entries) T2[lower.tri(T2)] <- t(T2)[lower.tri(T2)] phiqr <- lapply(seq_along(T1), function(q) sapply(seq_along(T1), function(r) { if (r == q) return(0) else return(mvtnorm::dmvnorm(T1[c(q, r)], mean = rep(0, length.out = length(c(q,r))), sigma = R[c(q,r), c(q,r)]))})) if (length(mu) == 2) { Ex2 <- R - T2 / alpha + Reduce("+", lapply(seq_along(Tq), function(q) tcrossprod(R[q,], rowSums(sapply(seq_along(Tq)[-q], function(r) phiqr[[q]][r] * (R[,r] - R[q,r] * R[q,])))))) / alpha } else { betaq <- lapply(seq_along(T1), function(q) sweep(rq[[q]], 2, Vq[,q], "/")) Rqr <- lapply(seq_along(T1), function(q) lapply(seq_along(T1), function(r) if (r == q) return(0) else return((Rq[[q]][-c(q,r),-c(q,r)] - tcrossprod(Rq[[q]][-c(q,r),r]))/tcrossprod(sqrt(1 - Rq[[q]][-c(q,r),r]^2))))) Tqr <- lapply(seq_along(T1), function(q) { lapply(seq_along(T1), function(r) if (r == q) return(0) else return((T1[-c(q,r)] - betaq[[r]][-c(r,q),q] * T1[q] - betaq[[q]][-c(r,q),r] * T1[r])/ (Sq[-c(r,q),q] * sqrt(1 - Rq[[q]][-c(r,q),r]^2))))}) T3 <- Reduce("+", lapply(seq_along(Tq), function(q) tcrossprod(R[q,], rowSums(sapply(seq_along(Tq)[-q], function(r) phiqr[[q]][r] * (R[,r] - R[q,r] * R[q,]) * mvtnorm::pmvnorm(upper = Tqr[[q]][[r]], sigma = Rqr[[q]][[r]], ...)))))) / alpha Ex2 <- R - T2 / alpha + 1/2 * (T3 + t(T3)) } } moments <- list(mean = 1/S * Ex + mu, variance = diag(1/S, nrow = length(T)) %*% (Ex2 - tcrossprod(Ex)) %*% diag(1/S, nrow = length(T))) if (!all(is.finite(unlist(moments))) || any(moments$mean > T) || any(eigen(moments$variance)$values < 0)) { moments <- list(mean = T - abs(diag(Sigma)), variance = Sigma) } moments } FLXMRlmmc <- function(formula = . ~ ., random, censored, varFix, eps = 10^-6, ...) { family <- "gaussian" censored <- if (length(censored) == 3) censored else formula(paste(".", paste(deparse(censored), collapse = ""))) if (missing(random)) { if (missing(varFix)) varFix <- FALSE else if ((length(varFix) > 1) || (is.na(as.logical(varFix)))) stop("varFix has to be a logical vector of length one") object <- new("FLXMRlmc", formula = formula, censored = censored, weighted = TRUE, family = family, name = "FLXMRlmc:gaussian") if (varFix) object <- new("FLXMRlmcfix", object) lmc.wfit <- function(x, y, w, C, censored) { W <- rep(w, sapply(x, nrow)) X <- do.call("rbind", x) AnyMissing <- which(sapply(C, sum) > 0) ybar <- lapply(seq_along(y), function(i) { Y <- y[[i]] Y[C[[i]] == 1] <- censored$mu[[i]] Y }) Y <- do.call("rbind", ybar) fit <- lm.wfit(X, Y, W, ...) fit$sigma2 <- if (length(AnyMissing) > 0) (sum(W * residuals(fit)^2) + sum(sapply(AnyMissing, function(i) w[i] * sum(diag(censored$Sigma[[i]])))))/sum(W) else sum(W * residuals(fit)^2)/sum(W) fit$df <- ncol(X) fit } object@defineComponent <- function(para) { predict <- function(x, ...) lapply(x, function(X) X %*% para$coef) logLik <- function(x, y, C, group, censored, ...) { AnyMissing <- which(sapply(C, sum) > 0) index <- lapply(C, function(x) x == 1) V <- lapply(x, function(X) diag(nrow(X)) * para$sigma2) mu <- predict(x, ...) SIGMA <- rep(list(matrix(nrow = 0, ncol = 0)), length(x)) if (length(AnyMissing) > 0) { SIGMA[AnyMissing] <- lapply(AnyMissing, function(i) { S <- V[[i]] SIG <- S[index[[i]], index[[i]]] if (sum(!index[[i]]) > 0) SIG <- SIG - S[index[[i]],!index[[i]]] %*% solve(S[!index[[i]],!index[[i]]]) %*% S[!index[[i]],index[[i]]] SIG }) } MU <- rep(list(vector("numeric", length = 0)), length(x)) if (length(AnyMissing) > 0) { MU[AnyMissing] <- lapply(AnyMissing, function(i) { S <- V[[i]] Mu <- mu[[i]][index[[i]]] if (sum(!index[[i]]) > 0) Mu <- Mu + S[index[[i]],!index[[i]]] %*% solve(S[!index[[i]],!index[[i]]]) %*% (y[[i]][!index[[i]]] - mu[[i]][!index[[i]]]) Mu }) } llh <- sapply(seq_along(x), function(i) { LLH <- 0 if (sum(index[[i]]) > 0) LLH <- log(mvtnorm::pmvnorm(upper = y[[i]][index[[i]]], mean = as.vector(MU[[i]]), sigma = SIGMA[[i]])) if (sum(!index[[i]]) > 0) LLH <- LLH + mvtnorm::dmvnorm(t(y[[i]][!index[[i]]]), mean = mu[[i]][!index[[i]]], sigma = V[[i]][!index[[i]], !index[[i]], drop = FALSE], log=TRUE) LLH/nrow(V[[i]]) }) as.vector(ungroupPriors(matrix(llh), group, !duplicated(group))) } new("FLXcomponent", parameters = list(coef = para$coef, sigma2 = para$sigma2, censored = para$censored), logLik = logLik, predict = predict, df = para$df) } object@fit <- if (varFix) { function(x, y, w, C, fit) { any_removed <- any(w <= eps) if (any_removed) { ok <- apply(w, 2, function(x) x > eps) W <- lapply(seq_len(ncol(ok)), function(i) w[ok[,i],i]) X <- lapply(seq_len(ncol(ok)), function(i) x[ok[,i],,drop = FALSE]) y <- lapply(seq_len(ncol(ok)), function(i) y[ok[,i]]) C <- lapply(seq_len(ncol(ok)), function(i) C[ok[,i]]) } else { X <- rep(list(x), ncol(w)) y <- rep(list(y), ncol(w)) C <- rep(list(C), ncol(w)) W <- lapply(seq_len(ncol(w)), function(i) w[,i]) } if ("coef" %in% names(fit[[1]])) fit <- lapply(seq_len(ncol(w)), function(k) update_latent(X[[k]], y[[k]], C[[k]], fit[[k]])) else { fit <- lapply(seq_len(ncol(w)), function(k) list(censored = list(mu = lapply(seq_along(y[[k]]), function(i) y[[k]][[i]][C[[k]][[i]] == 1]), Sigma = lapply(C[[k]], function(x) diag(1, nrow = sum(x)) * var(unlist(y[[k]])))))) } fit <- lapply(seq_len(ncol(w)), function(k) c(lmc.wfit(X[[k]], y[[k]], W[[k]], C[[k]], fit[[k]]$censored), censored = list(fit[[k]]$censored))) sigma2 <- sum(sapply(fit, function(x) x$sigma2) * colMeans(w)) for (k in seq_len(ncol(w))) fit[[k]]$sigma2 <- sigma2 lapply(fit, function(Z) object@defineComponent(list(coef = coef(Z), df = Z$df + 1/ncol(w), sigma2 = Z$sigma2, censored = Z$censored))) } } else { function(x, y, w, C, fit){ any_removed <- any(w <= eps) if (any_removed) { ok <- w > eps w <- w[ok] x <- x[ok,,drop = FALSE] y <- y[ok] C <- C[ok] } if ("coef" %in% names(fit)) { fit <- update_latent(x, y, C, fit) } else { fit$censored <- list(mu = lapply(seq_along(y), function(i) y[[i]][C[[i]] == 1]), Sigma = lapply(C, function(x) diag(1, nrow = sum(x)) * var(unlist(y)))) } fit <- c(lmc.wfit(x, y, w, C, fit$censored), censored = list(fit$censored)) object@defineComponent( list(coef = coef(fit), df = fit$df + 1, sigma2 = fit$sigma2, censored = fit$censored)) } } } else { if (missing(varFix)) varFix <- c(Random = FALSE, Residual = FALSE) else if (length(varFix) != 2 || is.null(names(varFix)) || any(is.na(pmatch(names(varFix), c("Random", "Residual"))))) stop("varFix has to be a named vector of length two") else names(varFix) <- c("Random", "Residual")[pmatch(names(varFix), c("Random", "Residual"))] random <- if (length(random) == 3) random else formula(paste(".", paste(deparse(random), collapse = ""))) object <- new("FLXMRlmmc", formula = formula, random = random, censored = censored, weighted = TRUE, family = family, name = "FLXMRlmmc:gaussian") if (any(varFix)) object <- new("FLXMRlmmcfix", object) add <- function(x) Reduce("+", x) lmmc.wfit <- function(x, y, w, z, C, which, random, censored) { effect <- lapply(seq_along(which), function(i) z[[which[i]]] %*% random$beta[[i]]) Effect <- do.call("rbind", effect) W <- rep(w, sapply(x, nrow)) X <- do.call("rbind", x) ybar <- lapply(seq_along(y), function(i) { Y <- y[[i]] Y[C[[i]] == 1] <- censored$mu[[i]] Y }) Y <- do.call("rbind", ybar) fit <- lm.wfit(X, Y - Effect, W, ...) wGamma <- add(lapply(seq_along(which), function(i) w[i] * random$Gamma[[i]])) bb <- add(lapply(seq_along(which), function(i) tcrossprod(random$beta[[i]]) * w[i])) fit$sigma2 <- list(Random = (wGamma + bb)/sum(w)) fit$df <- ncol(X) fit } object@defineComponent <- function(para) { predict <- function(x, ...) lapply(x, function(X) X %*% para$coef) logLik <- function(x, y, z, C, which, group, censored, ...) { AnyMissing <- which(sapply(C, sum) > 0) index <- lapply(C, function(x) x == 1) V <- lapply(z, function(Z) tcrossprod(tcrossprod(Z, para$sigma2$Random), Z) + diag(nrow(Z)) * para$sigma2$Residual) mu <- predict(x, ...) SIGMA <- rep(list(matrix(nrow = 0, ncol = 0)), length(x)) if (length(AnyMissing) > 0) { SIGMA[AnyMissing] <- lapply(AnyMissing, function(i) { S <- V[[which[i]]] SIG <- S[index[[i]], index[[i]]] if (sum(!index[[i]]) > 0) SIG <- SIG - S[index[[i]],!index[[i]]] %*% solve(S[!index[[i]],!index[[i]]]) %*% S[!index[[i]],index[[i]]] SIG }) } MU <- rep(list(vector("numeric", length = 0)), length(x)) if (length(AnyMissing) > 0) { MU[AnyMissing] <- lapply(AnyMissing, function(i) { S <- V[[which[i]]] Mu <- mu[[i]][index[[i]]] if (sum(!index[[i]]) > 0) Mu <- Mu + S[index[[i]],!index[[i]]] %*% solve(S[!index[[i]],!index[[i]]]) %*% (y[[i]][!index[[i]]] - mu[[i]][!index[[i]]]) Mu }) } llh <- sapply(seq_along(x), function(i) { LLH <- 0 if (sum(index[[i]]) > 0) LLH <- log(mvtnorm::pmvnorm(upper = y[[i]][index[[i]]], mean = as.vector(MU[[i]]), sigma = SIGMA[[i]])) if (sum(!index[[i]]) > 0) LLH <- LLH + mvtnorm::dmvnorm(t(y[[i]][!index[[i]]]), mean = mu[[i]][!index[[i]]], sigma = V[[which[i]]][!index[[i]], !index[[i]], drop = FALSE], log=TRUE) LLH/nrow(V[[which[i]]]) }) as.vector(ungroupPriors(matrix(llh), group, !duplicated(group))) } new("FLXcomponent", parameters = list(coef = para$coef, sigma2 = para$sigma2, censored = para$censored, random = para$random), logLik = logLik, predict = predict, df = para$df) } object@fit <- if (any(varFix)) { function(x, y, w, z, C, which, fit) { any_removed <- any(w <= eps) if (any_removed) { ok <- apply(w, 2, function(x) x > eps) W <- lapply(seq_len(ncol(ok)), function(i) w[ok[,i],i]) X <- lapply(seq_len(ncol(ok)), function(i) x[ok[,i],,drop = FALSE]) y <- lapply(seq_len(ncol(ok)), function(i) y[ok[,i]]) C <- lapply(seq_len(ncol(ok)), function(i) C[ok[,i]]) which <- lapply(seq_len(ncol(ok)), function(i) which[ok[,i]]) } else { X <- rep(list(x), ncol(w)) y <- rep(list(y), ncol(w)) C <- rep(list(C), ncol(w)) which <- rep(list(which), ncol(w)) W <- lapply(seq_len(ncol(w)), function(i) w[,i]) } if ("coef" %in% names(fit[[1]])) fit <- lapply(seq_len(ncol(w)), function(k) update_latent_random(X[[k]], y[[k]], z, C[[k]], which[[k]], fit[[k]])) else { fit <- lapply(seq_len(ncol(w)), function(k) list(random = list(beta = lapply(seq_along(W[[k]]), function(i) rep(0, ncol(z[[which[[k]][i]]]))), Gamma = lapply(seq_along(W[[k]]), function(i) diag(ncol(z[[which[[k]][i]]])))), censored = list(mu = lapply(seq_along(y[[k]]), function(i) y[[k]][[i]][C[[k]][[i]] == 1]), Sigma = lapply(C[[k]], function(x) diag(1, nrow = sum(x)) * var(unlist(y[[k]]))), psi = lapply(C[[k]], function(x) rep(0, sum(x)))))) } fit <- lapply(seq_len(ncol(w)), function(k) c(lmmc.wfit(X[[k]], y[[k]], W[[k]], z, C[[k]], which[[k]], fit[[k]]$random, fit[[k]]$censored), random = list(fit[[k]]$random), censored = list(fit[[k]]$censored))) if (varFix["Random"]) { prior_w <- apply(w, 2, weighted.mean, w = sapply(x, length)) Psi <- add(lapply(seq_len(ncol(w)), function(k) fit[[k]]$sigma2$Random * prior_w[k])) for (k in seq_len(ncol(w))) fit[[k]]$sigma2$Random <- Psi } for (k in seq_len(ncol(w))) fit[[k]]$sigma2$Residual <- update_Residual(fit[[k]], W[[k]], z, C[[k]], which[[k]], fit[[k]]$random, fit[[k]]$censored) if (varFix["Residual"]) { prior <- colMeans(w) Residual <- sum(sapply(fit[[k]]$sigma2$Residual, function(x) x) * prior) for (k in seq_len(ncol(w))) fit[[k]]$sigma2$Residual <- Residual } n <- nrow(fit[[1]]$sigma2$Random) lapply(fit, function(Z) object@defineComponent( list(coef = coef(Z), df = Z$df + n*(n+1)/(2*ifelse(varFix["Random"], ncol(w), 1)) + ifelse(varFix["Residual"], 1/ncol(w), 1), sigma2 = Z$sigma2, random = Z$random, censored = Z$censored))) } } else { function(x, y, w, z, C, which, fit){ any_removed <- any(w <= eps) if (any_removed) { ok <- w > eps w <- w[ok] x <- x[ok,,drop = FALSE] y <- y[ok] C <- C[ok] which <- which[ok] } if ("coef" %in% names(fit)) fit <- update_latent_random(x, y, z, C, which, fit) else { fit <- list(random = list(beta = lapply(which, function(i) rep(0, ncol(z[[i]]))), Gamma = lapply(which, function(i) diag(ncol(z[[i]])))), censored = list(mu = lapply(seq_along(y), function(i) y[[i]][C[[i]] == 1]), Sigma = lapply(C, function(x) diag(1, nrow = sum(x)) * var(unlist(y))), psi = lapply(C, function(x) rep(0, sum(x))))) } fit <- c(lmmc.wfit(x, y, w, z, C, which, fit$random, fit$censored), random = list(fit$random), censored = list(fit$censored)) fit$sigma2$Residual <- update_Residual(fit, w, z, C, which, fit$random, fit$censored) n <- nrow(fit$sigma2$Random) object@defineComponent( list(coef = coef(fit), df = fit$df + n*(n+1)/2 + 1, sigma2 = fit$sigma2, random = fit$random, censored = fit$censored)) } } } object } setMethod("FLXmstep", signature(model = "FLXMRlmc"), function(model, weights, components) { weights <- weights[!duplicated(model@group),,drop=FALSE] return(sapply(1:ncol(weights), function(k) model@fit(model@x, model@y, weights[,k], model@C, components[[k]]@parameters))) }) setMethod("FLXmstep", signature(model = "FLXMRlmcfix"), function(model, weights, components) { weights <- weights[!duplicated(model@group),,drop=FALSE] return(model@fit(model@x, model@y, weights, model@C, lapply(components, function(x) x@parameters))) }) setMethod("FLXmstep", signature(model = "FLXMRlmmc"), function(model, weights, components) { weights <- weights[!duplicated(model@group),,drop=FALSE] return(sapply(1:ncol(weights), function(k) model@fit(model@x, model@y, weights[,k], model@z, model@C, model@which, components[[k]]@parameters))) }) setMethod("FLXmstep", signature(model = "FLXMRlmmcfix"), function(model, weights, components) { weights <- weights[!duplicated(model@group),,drop=FALSE] return(model@fit(model@x, model@y, weights, model@z, model@C, model@which, lapply(components, function(x) x@parameters))) }) setMethod("FLXgetModelmatrix", signature(model="FLXMRlmc"), function(model, data, formula, lhs=TRUE, ...) { formula_nogrouping <- RemoveGrouping(formula) if (formula_nogrouping == formula) stop("please specify a grouping variable") model <- callNextMethod(model, data, formula, lhs) model@fullformula <- update(model@fullformula, paste(".~. |", .FLXgetGroupingVar(formula))) mt2 <- terms(model@censored, data=data) mf2 <- model.frame(delete.response(mt2), data=data, na.action = NULL) model@C <- model.matrix(attr(mf2, "terms"), data) model@group <- grouping <- .FLXgetGrouping(formula, data)$group model@x <- matrix(lapply(unique(grouping), function(g) model@x[grouping == g, , drop = FALSE]), ncol = 1) if (lhs) model@y <- matrix(lapply(unique(grouping), function(g) model@y[grouping == g, , drop = FALSE]), ncol = 1) model@C <- matrix(lapply(unique(grouping), function(g) model@C[grouping == g, , drop = FALSE]), ncol = 1) model }) setMethod("FLXgetModelmatrix", signature(model="FLXMRlmmc"), function(model, data, formula, lhs=TRUE, ...) { model <- callNextMethod(model, data, formula, lhs) mt1 <- terms(model@random, data=data) mf1 <- model.frame(delete.response(mt1), data=data, na.action = NULL) model@z <- model.matrix(attr(mf1, "terms"), data) rownames(model@z) <- NULL grouping <- .FLXgetGrouping(formula, data)$group z <- matrix(lapply(unique(grouping), function(g) model@z[grouping == g, , drop = FALSE]), ncol = 1) model@z <- unique(z) model@which <- match(z, model@z) model }) setMethod("FLXgetObs", "FLXMRlmc", function(model) sum(sapply(model@x, nrow))) setMethod("FLXdeterminePostunscaled", signature(model = "FLXMRlmc"), function(model, components, ...) { sapply(components, function(x) x@logLik(model@x, model@y, model@C, model@group, x@parameters$censored)) }) setMethod("FLXdeterminePostunscaled", signature(model = "FLXMRlmmc"), function(model, components, ...) { sapply(components, function(x) x@logLik(model@x, model@y, model@z, model@C, model@which, model@group, x@parameters$censored)) }) setMethod("predict", signature(object="FLXMRlmc"), function(object, newdata, components, ...) { object <- FLXgetModelmatrix(object, newdata, formula = object@fullformula, lhs = FALSE) lapply(components, function(comp) unlist(comp@predict(object@x, ...))) }) setMethod("rFLXM", signature(model = "FLXMRlmc", components = "FLXcomponent"), function(model, components, ...) { stop("This model driver is not implemented yet.") }) flexmix/R/concomitant.R0000644000176200001440000000647414404637304014610 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: concomitant.R 5079 2016-01-31 12:21:12Z gruen $ # FLXPmultinom <- function(formula=~1) { z <- new("FLXPmultinom", name="FLXPmultinom", formula=formula) multinom.fit <- function(x, y, w, ...) { r <- ncol(x) p <- ncol(y) if (p < 2) stop("Multinom requires at least two components.") mask <- c(rep(0, r + 1), rep(c(0, rep(1, r)), p - 1)) nnet.default(x, y, w, mask = mask, size = 0, skip = TRUE, softmax = TRUE, censored = FALSE, rang = 0, trace=FALSE,...) } z@fit <- function(x, y, w, ...) multinom.fit(x, y, w, ...)$fitted.values z@refit <- function(x, y, w, ...) { if (missing(w) || is.null(w)) w <- rep(1, nrow(y)) rownames(y) <- rownames(x) <- NULL fit <- multinom(y ~ 0 + x, weights = w, data = list(y = y, x = x), Hess = TRUE, trace = FALSE) fit$coefnames <- colnames(x) fit$vcoefnames <- fit$coefnames[seq_along(fit$coefnames)] dimnames(fit$Hessian) <- lapply(dim(fit$Hessian) / ncol(x), function(i) paste(rep(seq_len(i) + 1, each = ncol(x)), colnames(x), sep = ":")) fit } z } FLXPconstant <- function() { new("FLXP", name="FLXPconstant", formula = ~1, fit = function(x, y, w, ...){ if (missing(w) || is.null(w)) return(matrix(colMeans(y), ncol=ncol(y), dimnames = list("prior", seq_len(ncol(y))))) else return(matrix(colMeans(w*y)/mean(w), ncol=ncol(y), dimnames = list("prior", seq_len(ncol(y))))) }) } ###********************************************************** setMethod("FLXgetModelmatrix", signature(model="FLXP"), function(model, data, groups, lhs, ...) { mt <- terms(model@formula, data=data) mf <- model.frame(delete.response(mt), data=data, na.action = NULL) X <- model.matrix(mt, data=mf) if (nrow(X)){ if (!checkGroup(X, groups$group)) stop("model variables have to be constant for grouping variable") model@x <- X[groups$groupfirst,,drop=FALSE] } else{ model@x <- matrix(1, nrow=sum(groups$groupfirst)) } model }) checkGroup <- function(x, group) { check <- TRUE for(g in levels(group)){ gok <- group==g if(any(gok)){ check <- all(c(check, apply(x[gok,,drop=FALSE], 2, function(z) length(unique(z)) == 1))) } } check } ###********************************************************** setMethod("refit_mstep", signature(object="FLXP", newdata="missing"), function(object, newdata, posterior, group, ...) NULL) setMethod("refit_mstep", signature(object="FLXPmultinom", newdata="missing"), function(object, newdata, posterior, group, ...) { groupfirst <- if (length(group)) groupFirst(group) else rep(TRUE, nrow(posterior)) object@refit(object@x, posterior[groupfirst,,drop=FALSE], ...) }) ###********************************************************** setMethod("FLXfillConcomitant", signature(concomitant="FLXP"), function(concomitant, posterior, weights) { concomitant@coef <- concomitant@refit(concomitant@x, posterior, weights) concomitant }) setMethod("FLXfillConcomitant", signature(concomitant="FLXPmultinom"), function(concomitant, posterior, weights) { concomitant@coef <- cbind("1" = 0, t(coef(concomitant@refit(concomitant@x, posterior, weights)))) concomitant }) ###********************************************************** flexmix/R/group.R0000644000176200001440000000061514404637304013415 0ustar liggesuserssetMethod("group", signature(object="flexmix"), function(object) { group <- object@group if (!length(group)) group <- group(object@model[[1]]) group }) setMethod("group", signature(object="FLXM"), function(object) { factor(seq_len(nrow(object@x))) }) setMethod("group", signature(object="FLXMRglmfix"), function(object) { factor(seq_len(nrow(object@x)/sum(object@nestedformula@k))) }) flexmix/R/flexmix.R0000644000176200001440000005224414404637304013742 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: flexmix.R 5184 2020-06-20 18:27:29Z gruen $ # log_row_sums <- function(m) { M <- m[cbind(seq_len(nrow(m)), max.col(m, "first"))] M + log(rowSums(exp(m - M))) } ## The following two methods only fill in and rearrange the model argument setMethod("flexmix", signature(formula = "formula", model="missing"), function(formula, data=list(), k=NULL, cluster=NULL, model=NULL, concomitant=NULL, control=NULL, weights=NULL) { mycall = match.call() z <- flexmix(formula=formula, data=data, k=k, cluster=cluster, model=list(FLXMRglm()), concomitant=concomitant, control=control, weights = weights) z@call <- mycall z }) setMethod("flexmix", signature(formula = "formula", model="FLXM"), function(formula, data=list(), k=NULL, cluster=NULL, model=NULL, concomitant=NULL, control=NULL, weights=NULL) { mycall = match.call() z <- flexmix(formula=formula, data=data, k=k, cluster=cluster, model=list(model), concomitant=concomitant, control=control, weights=weights) z@call <- mycall z }) ## This is the real thing setMethod("flexmix", signature(formula = "formula", model="list"), function(formula, data=list(), k=NULL, cluster=NULL, model=NULL, concomitant=NULL, control=NULL, weights=NULL) { mycall = match.call() control = as(control, "FLXcontrol") if (!is(concomitant, "FLXP")) concomitant <- FLXPconstant() groups <- .FLXgetGrouping(formula, data) model <- lapply(model, FLXcheckComponent, k, cluster) k <- unique(unlist(sapply(model, FLXgetK, k))) if (length(k) > 1) stop("number of clusters not specified correctly") model <- lapply(model, FLXgetModelmatrix, data, formula) groups$groupfirst <- if (length(groups$group)) groupFirst(groups$group) else rep(TRUE, FLXgetObs(model[[1]])) if (is(weights, "formula")) { weights <- model.frame(weights, data = data, na.action = NULL)[,1] } ## check if the weights are integer ## if non-integer weights are wanted modifications e.g. ## for classify != weighted and ## plot,flexmix,missing-method are needed if (!is.null(weights) & !identical(weights, as.integer(weights))) stop("only integer weights allowed") ## if weights and grouping is specified the weights within each ## group need to be the same if (!is.null(weights) & length(groups$group)>0) { unequal <- tapply(weights, groups$group, function(x) length(unique(x)) > 1) if (any(unequal)) stop("identical weights within groups needed") } postunscaled <- initPosteriors(k, cluster, FLXgetObs(model[[1]]), groups) if (ncol(postunscaled) == 1L) concomitant <- FLXPconstant() concomitant <- FLXgetModelmatrix(concomitant, data = data, groups = groups) z <- FLXfit(model=model, concomitant=concomitant, control=control, postunscaled=postunscaled, groups=groups, weights = weights) z@formula = formula z@call = mycall z@k0 = as.integer(k) z }) ###********************************************************** setMethod("FLXgetK", signature(model = "FLXM"), function(model, k, ...) k) setMethod("FLXgetObs", signature(model = "FLXM"), function(model) nrow(model@x)) setMethod("FLXcheckComponent", signature(model = "FLXM"), function(model, ...) model) setMethod("FLXremoveComponent", signature(model = "FLXM"), function(model, ...) model) setMethod("FLXmstep", signature(model = "FLXM"), function(model, weights, components, ...) { if ("component" %in% names(formals(model@fit))) sapply(seq_len(ncol(weights)), function(k) model@fit(model@x, model@y, weights[,k], component = components[[k]]@parameters)) else sapply(seq_len(ncol(weights)), function(k) model@fit(model@x, model@y, weights[,k])) }) setMethod("FLXdeterminePostunscaled", signature(model = "FLXM"), function(model, components, ...) { matrix(sapply(components, function(x) x@logLik(model@x, model@y)), nrow = nrow(model@y)) }) ###********************************************************** setMethod("FLXfit", signature(model="list"), function(model, concomitant, control, postunscaled=NULL, groups, weights) { ### initialize k <- ncol(postunscaled) N <- nrow(postunscaled) control <- allweighted(model, control, weights) if(control@verbose>0) cat("Classification:", control@classify, "\n") if (control@classify %in% c("SEM", "random")) iter.rm <- 0 group <- groups$group groupfirst <- groups$groupfirst if(length(group)>0) postunscaled <- groupPosteriors(postunscaled, group) logpostunscaled <- log(postunscaled) postscaled <- exp(logpostunscaled - log_row_sums(logpostunscaled)) llh <- -Inf if (control@classify %in% c("SEM", "random")) llh.max <- -Inf converged <- FALSE components <- rep(list(rep(list(new("FLXcomponent")), k)), length(model)) ### EM for(iter in seq_len(control@iter.max)) { ### M-Step postscaled = .FLXgetOK(postscaled, control, weights) prior <- if (is.null(weights)) ungroupPriors(concomitant@fit(concomitant@x, postscaled[groupfirst,,drop=FALSE]), group, groupfirst) else ungroupPriors(concomitant@fit(concomitant@x, (postscaled/weights)[groupfirst & weights > 0,,drop=FALSE], weights[groupfirst & weights > 0]), group, groupfirst) # Check min.prior nok <- if (nrow(prior) == 1) which(prior < control@minprior) else { if (is.null(weights)) which(colMeans(prior[groupfirst,,drop=FALSE]) < control@minprior) else which(colSums(prior[groupfirst,] * weights[groupfirst])/sum(weights[groupfirst]) < control@minprior) } if(length(nok)) { if(control@verbose>0) cat("*** Removing", length(nok), "component(s) ***\n") prior <- prior[,-nok,drop=FALSE] prior <- prior/rowSums(prior) postscaled <- postscaled[,-nok,drop=FALSE] postscaled[rowSums(postscaled) == 0,] <- if (nrow(prior) > 1) prior[rowSums(postscaled) == 0,] else prior[rep(1, sum(rowSums(postscaled) == 0)),] postscaled <- postscaled/rowSums(postscaled) if (!is.null(weights)) postscaled <- postscaled * weights k <- ncol(prior) if (k == 0) stop("all components removed") if (control@classify=="random") { llh.max <- -Inf iter.rm <- iter } model <- lapply(model, FLXremoveComponent, nok) components <- lapply(components, "[", -nok) } components <- lapply(seq_along(model), function(i) FLXmstep(model[[i]], postscaled, components[[i]])) postunscaled <- matrix(0, nrow = N, ncol = k) for (n in seq_along(model)) postunscaled <- postunscaled + FLXdeterminePostunscaled(model[[n]], components[[n]]) if(length(group)>0) postunscaled <- groupPosteriors(postunscaled, group) ### E-Step ## Code changed thanks to Nicolas Picard ## to avoid problems with small likelihoods postunscaled <- if (nrow(prior) > 1) postunscaled + log(prior) else sweep(postunscaled, 2, log(prior), "+") logpostunscaled <- postunscaled postunscaled <- exp(postunscaled) postscaled <- exp(logpostunscaled - log_row_sums(logpostunscaled)) ##: wenn eine beobachtung in allen Komonenten extrem ## kleine postunscaled-werte hat, ist exp(-postunscaled) ## numerisch Null, und damit postscaled NaN ## log(rowSums(postunscaled)) ist -Inf ## if (any(is.nan(postscaled))) { index <- which(as.logical(rowSums(is.nan(postscaled)))) postscaled[index,] <- if(nrow(prior)==1) rep(prior, each = length(index)) else prior[index,] postunscaled[index,] <- .Machine$double.xmin } ### check convergence llh.old <- llh llh <- if (is.null(weights)) sum(log_row_sums(logpostunscaled[groupfirst,,drop=FALSE])) else sum(log_row_sums(logpostunscaled[groupfirst,,drop=FALSE])*weights[groupfirst]) if(is.na(llh) | is.infinite(llh)) stop(paste(formatC(iter, width=4), "Log-likelihood:", llh)) if (abs(llh-llh.old)/(abs(llh)+0.1) < control@tolerance){ if(control@verbose>0){ printIter(iter, llh) cat("converged\n") } converged <- TRUE break } if (control@classify=="random") { if (llh.max < llh) { components.max <- components prior.max <- prior postscaled.max <- postscaled postunscaled.max <- postunscaled llh.max <- llh } } if(control@verbose && (iter%%control@verbose==0)) printIter(iter, llh) } ### Construct return object if (control@classify=="random") { components <- components.max prior <- prior.max postscaled <- postscaled.max postunscaled <- postunscaled.max llh <- llh.max iter <- control@iter.max - iter.rm } components <- lapply(seq_len(k), function(i) lapply(components, function(x) x[[i]])) names(components) <- paste("Comp", seq_len(k), sep=".") cluster <- max.col(postscaled) size <- if (is.null(weights)) tabulate(cluster, nbins=k) else tabulate(rep(cluster, weights), nbins=k) names(size) <- seq_len(k) concomitant <- FLXfillConcomitant(concomitant, postscaled[groupfirst,,drop=FALSE], weights[groupfirst]) df <- concomitant@df(concomitant@x, k) + sum(sapply(components, sapply, slot, "df")) control@nrep <- 1 prior <- if (is.null(weights)) colMeans(postscaled[groupfirst,,drop=FALSE]) else colSums(postscaled[groupfirst,,drop=FALSE] * weights[groupfirst])/sum(weights[groupfirst]) retval <- new("flexmix", model=model, prior=prior, posterior=list(scaled=postscaled, unscaled=postunscaled), weights = weights, iter=iter, cluster=cluster, size = size, logLik=llh, components=components, concomitant=concomitant, control=control, df=df, group=group, k=as(k, "integer"), converged=converged) retval }) ###********************************************************** .FLXgetOK = function(p, control, weights){ n = ncol(p) N = seq_len(n) if (is.null(weights)) { if (control@classify == "weighted") return(p) else { z = matrix(FALSE, nrow = nrow(p), ncol = n) if(control@classify %in% c("CEM", "hard")) m = max.col(p) else if(control@classify %in% c("SEM", "random")) m = apply(p, 1, function(x) sample(N, size = 1, prob = x)) else stop("Unknown classification method") z[cbind(seq_len(nrow(p)), m)] = TRUE } }else { if(control@classify=="weighted") z <- p * weights else{ z = matrix(FALSE, nrow=nrow(p), ncol=n) if(control@classify %in% c("CEM", "hard")) { m = max.col(p) z[cbind(seq_len(nrow(p)), m)] = TRUE z <- z * weights } else if(control@classify %in% c("SEM", "random")) z = t(sapply(seq_len(nrow(p)), function(i) table(factor(sample(N, size=weights[i], prob=p[i,], replace=TRUE), N)))) else stop("Unknown classification method") } } z } ###********************************************************** RemoveGrouping <- function(formula) { lf <- length(formula) formula1 <- formula if(length(formula[[lf]])>1) { if (deparse(formula[[lf]][[1]]) == "|"){ formula1[[lf]] <- formula[[lf]][[2]] } else if (deparse(formula[[lf]][[1]]) == "("){ form <- formula[[lf]][[2]] if (length(form) == 3 && form[[1]] == "|") formula1[[lf]] <- form[[2]] } } formula1 } .FLXgetGroupingVar <- function(x) { lf <- length(x) while (lf > 1) { x <- x[[lf]] lf <- length(x) } x } .FLXgetGrouping <- function(formula, data) { group <- factor(integer(0)) formula1 <- RemoveGrouping(formula) if (!identical(formula1, formula)) group <- factor(eval(.FLXgetGroupingVar(formula), data)) return(list(group=group, formula=formula1)) } setMethod("FLXgetModelmatrix", signature(model="FLXM"), function(model, data, formula, lhs=TRUE, ...) { formula <- RemoveGrouping(formula) if (length(grep("\\|", deparse(model@formula)))) stop("no grouping variable allowed in the model") if(is.null(model@formula)) model@formula = formula ## model@fullformula = update.formula(formula, model@formula) ## : ist das der richtige weg, wenn ein punkt in beiden ## formeln ist? model@fullformula = update(terms(formula, data=data), model@formula) ## if (lhs) { mf <- if (is.null(model@terms)) model.frame(model@fullformula, data=data, na.action = NULL) else model.frame(model@terms, data=data, na.action = NULL, xlev = model@xlevels) model@terms <- attr(mf, "terms") response <- as.matrix(model.response(mf)) model@y <- model@preproc.y(response) } else { mt1 <- if (is.null(model@terms)) terms(model@fullformula, data=data) else model@terms mf <- model.frame(delete.response(mt1), data=data, na.action = NULL, xlev = model@xlevels) model@terms<- attr(mf, "terms") ## : warum war das da??? ## attr(mt, "intercept") <- attr(mt1, "intercept") ## } X <- model.matrix(model@terms, data=mf) model@contrasts <- attr(X, "contrasts") model@x <- model@preproc.x(X) model@xlevels <- .getXlevels(model@terms, mf) model }) ## groupfirst: for grouped observation we need to be able to use ## the posterior of each group, but for computational simplicity ## post(un)scaled has N rows (with mutiple identical rows for each ## group). postscaled[groupfirst,] extracts posteriors of each ## group ordered as the appear in the data set. groupFirst <- function(x) !duplicated(x) ## if we have a group variable, set the posterior to the product ## of all density values for that group (=sum in logarithm) groupPosteriors <- function(x, group) { if (length(group) > 0) { group <- as.integer(group) x.by.group <- matrix(unname(apply(x, 2, tapply, group, sum)), ncol = ncol(x)) x <- x.by.group[group,, drop = FALSE] } x } ungroupPriors <- function(x, group, groupfirst) { if (!length(group)) group <- seq_along(groupfirst) if (nrow(x) >= length(group[groupfirst])) { x <- x[order(as.integer(group[groupfirst])),,drop=FALSE] x <- x[as.integer(group),,drop=FALSE] } x } setMethod("allweighted", signature(model = "list", control = "ANY", weights = "ANY"), function(model, control, weights) { allweighted <- all(sapply(model, function(x) allweighted(x, control, weights))) if(allweighted){ if(control@classify=="auto") control@classify <- "weighted" } else{ if(control@classify=="auto") control@classify <- "hard" else if (control@classify=="weighted") { warning("only hard classification supported for the modeldrivers") control@classify <- "hard" } if(!is.null(weights)) stop("it is not possible to specify weights for models without weighted ML estimation") } control }) setMethod("allweighted", signature(model = "FLXM", control = "ANY", weights = "ANY"), function(model, control, weights) { model@weighted }) initPosteriors <- function(k, cluster, N, groups) { if(is(cluster, "matrix")){ postunscaled <- cluster if (!is.null(k)) if (k != ncol(postunscaled)) stop("specified k does not match the number of columns of cluster") } else{ if(is.null(cluster)){ if(is.null(k)) stop("either k or cluster must be specified") else cluster <- ungroupPriors(as.matrix(sample(seq_len(k), size = sum(groups$groupfirst), replace=TRUE)), groups$group, groups$groupfirst) } else{ cluster <- as(cluster, "integer") if (!is.null(k)) if (k != max(cluster)) stop("specified k does not match the values in cluster") k <- max(cluster) } postunscaled <- matrix(0.1, nrow=N, ncol=k) for(K in seq_len(k)){ postunscaled[cluster==K, K] <- 0.9 } } postunscaled } ###********************************************************** setMethod("predict", signature(object="FLXdist"), function(object, newdata=list(), aggregate=FALSE, ...){ if (missing(newdata)) return(fitted(object, aggregate=aggregate, drop=FALSE)) x = list() for(m in seq_along(object@model)) { comp <- lapply(object@components, "[[", m) x[[m]] <- predict(object@model[[m]], newdata, comp, ...) } if (aggregate) { prior_weights <- prior(object, newdata) z <- lapply(x, function(z) matrix(rowSums(do.call("cbind", z) * prior_weights), nrow = nrow(z[[1]]))) } else { z <- list() for (k in seq_len(object@k)) { z[[k]] <- do.call("cbind", lapply(x, "[[", k)) } names(z) <- paste("Comp", seq_len(object@k), sep=".") } z }) ###********************************************************** setMethod("parameters", signature(object="FLXdist"), function(object, component=NULL, model=NULL, which = c("model", "concomitant"), simplify=TRUE, drop=TRUE) { which <- match.arg(which) if (is.null(component)) component <- seq_len(object@k) if (is.null(model)) model <- seq_along(object@model) if (which == "model") { if (simplify) { parameters <- sapply(model, function(m) sapply(object@components[component], function(x) unlist(x[[m]]@parameters), simplify=TRUE), simplify = FALSE) } else { parameters <- sapply(model, function(m) sapply(object@components[component], function(x) x[[m]]@parameters, simplify=FALSE), simplify = FALSE) } if (drop) { if (length(component) == 1 && !simplify) parameters <- lapply(parameters, "[[", 1) if (length(model) == 1) parameters <- parameters[[1]] } } else { parameters <- object@concomitant@coef[,component,drop=FALSE] } parameters }) setMethod("prior", signature(object="FLXdist"), function(object, newdata, ...) { if (missing(newdata)) prior <- object@prior else { groups <- .FLXgetGrouping(object@formula, newdata) nobs <- if (is(newdata, "data.frame")) nrow(newdata) else min(sapply(newdata, function(x) { if (is.null(nrow(x))) length(x) else nrow(x) })) group <- if (length(groups$group)) groups$group else factor(seq_len(nobs)) object@concomitant <- FLXgetModelmatrix(object@concomitant, data = newdata, groups = list(group=group, groupfirst = groupFirst(group))) prior <- determinePrior(object@prior, object@concomitant, group)[as.integer(group),] } prior }) setMethod("posterior", signature(object="flexmix", newdata="missing"), function(object, newdata, unscaled = FALSE, ...) { if (unscaled) return(object@posterior$unscaled) else return(object@posterior$scaled) }) setMethod("posterior", signature(object="FLXdist", newdata="listOrdata.frame"), function(object, newdata, unscaled=FALSE,...) { comp <- lapply(object@components, "[[", 1) postunscaled <- posterior(object@model[[1]], newdata, comp, ...) for (m in seq_along(object@model)[-1]) { comp <- lapply(object@components, "[[", m) postunscaled <- postunscaled + posterior(object@model[[m]], newdata, comp, ...) } groups <- .FLXgetGrouping(object@formula, newdata) prior <- prior(object, newdata = newdata) if(length(groups$group)>0) postunscaled <- groupPosteriors(postunscaled, groups$group) postunscaled <- postunscaled + log(prior) if (unscaled) return(exp(postunscaled)) else return(exp(postunscaled - log_row_sums(postunscaled))) }) setMethod("posterior", signature(object="FLXM", newdata="listOrdata.frame"), function(object, newdata, components, ...) { object <- FLXgetModelmatrix(object, newdata, object@fullformula, lhs = TRUE) FLXdeterminePostunscaled(object, components, ...) }) setMethod("clusters", signature(object="flexmix", newdata="missing"), function(object, newdata, ...) { object@cluster }) setMethod("clusters", signature(object="FLXdist", newdata="ANY"), function(object, newdata, ...) { max.col(posterior(object, newdata, ...)) }) ###********************************************************** setMethod("summary", "flexmix", function(object, eps=1e-4, ...){ z <- new("summary.flexmix", call = object@call, AIC = AIC(object), BIC = BIC(object), logLik = logLik(object)) TAB <- data.frame(prior=object@prior, size=object@size) rownames(TAB) <- paste("Comp.", seq_len(nrow(TAB)), sep="") TAB[["post>0"]] <- if (is.null(object@weights)) colSums(object@posterior$scaled > eps) else colSums((object@posterior$scaled > eps) * object@weights) TAB[["ratio"]] <- TAB[["size"]]/TAB[["post>0"]] z@comptab = TAB z }) ###********************************************************** flexmix/R/examples.R0000644000176200001440000000411314404637304014074 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: examples.R 5079 2016-01-31 12:21:12Z gruen $ # ExNPreg = function(n) { if(n %% 2 != 0) stop("n must be even") x <- runif(2*n, 0, 10) mp <- exp(c(2-0.2*x[1:n], 1+0.1*x[(n+1):(2*n)])) mb <- binomial()$linkinv(c(x[1:n]-5, 5-x[(n+1):(2*n)])) data.frame(x=x, yn=c(5*x[1:n], 40-(x[(n+1):(2*n)]-5)^2)+3*rnorm(n), yp=rpois(2*n, mp), yb=rbinom(2*n, size=1, prob=mb), class = rep(1:2, c(n,n)), id1 = factor(rep(1:n, rep(2, n))), id2 = factor(rep(1:(n/2), rep(4, n/2)))) } ExNclus = function(n=100) { if(n %% 2 != 0) stop("n must be even") rbind(mvtnorm::rmvnorm(n, mean=rep(0,2)), mvtnorm::rmvnorm(n, mean=c(8,0), sigma=diag(1:2)), mvtnorm::rmvnorm(1.5*n, mean=c(-2,6), sigma=diag(2:1)), mvtnorm::rmvnorm(2*n, mean=c(4,4), sigma=matrix(c(1,.9,.9,1), 2))) } ExLinear <- function(beta, n, xdist="runif", xdist.args=NULL, family=c("gaussian", "poisson"), sd=1, ...) { family <- match.arg(family) X <- NULL y <- NULL k <- ncol(beta) d <- nrow(beta)-1 n <- rep(n, length.out=k) if(family=="gaussian") sd <- rep(sd, length.out=k) xdist <- rep(xdist, length.out=d) if(is.null(xdist.args)){ xdist.args <- list(list(...)) } if(!is.list(xdist.args[[1]])) xdist.args <- list(xdist.args) xdist.args <- rep(xdist.args, length.out=d) for(i in 1:k) { X1 <- 1 for(j in 1:d){ xdist.args[[j]]$n <- n[i] X1 <- cbind(X1, do.call(xdist[j], xdist.args[[j]])) } X <- rbind(X, X1) xb <- X1 %*% beta[,i,drop=FALSE] if(family=="gaussian") y1 <- xb + rnorm(n[i], sd=sd[i]) else y1 <- rpois(n[i], exp(xb)) y <- c(y, y1) } X <- X[,-1,drop=FALSE] colnames(X) <- paste("x", 1:d, sep="") z <- data.frame(y=y, X) attr(z, "clusters") <- rep(1:k, n) z } flexmix/R/rFLXmodel.R0000644000176200001440000000566714404637304014131 0ustar liggesuserssetMethod("rFLXM", signature(model="FLXM", components="list"), function(model, components, class, ...) { y <- NULL for (l in seq_along(components)) { yl <- as.matrix(rFLXM(model, components[[l]], ...)) if (is.null(y)) y <- matrix(NA, nrow = length(class), ncol = ncol(yl)) y[class == l,] <- yl[class==l,] } y }) setMethod("rFLXM", signature(model = "FLXMRglm", components="FLXcomponent"), function(model, components, ...) { family <- model@family n <- nrow(model@x) if(family == "gaussian") { sigma <- components@parameters$sigma y <- rnorm(n, mean = components@predict(model@x, ...), sd = sigma) } else if (family == "binomial") { dotarg = list(...) if ("size" %in% names(dotarg)) size <- dotarg$size else { if (nrow(model@y)!=n) stop("no y values - specify a size argument") size <- rowSums(model@y) } parms <- components@parameters y <- rbinom(n, prob = components@predict(model@x, ...), size=size) y <- cbind(y, size - y) } else if (family == "poisson") { y <- rpois(n, lambda = components@predict(model@x, ...)) } else if (family == "Gamma") { shape <- components@parameters$shape y <- rgamma(n, shape = shape, scale = components@predict(model@x, ...)/shape) } else stop("family not supported") y }) setMethod("rFLXM", signature(model = "FLXMRglmfix", components="list"), function(model, components, class, ...) { k <- sum(model@nestedformula@k) n <- nrow(model@x)/k y <- matrix(NA, nrow = length(class), ncol = ncol(model@y)) model.sub <- as(model, "FLXMRglm") for (l in seq_len(k)) { rok <- (l-1)*n + seq_len(n) model.sub@x <- model@x[rok, as.logical(model@design[l,]), drop=FALSE] model.sub@y <- model@y[rok,,drop=FALSE] yl <- as.matrix(rFLXM(model.sub, components[[l]], ...)) y[class==l,] <- yl[class==l,] } y }) rmvbinom <- function(n, size, prob) sapply(prob, function(p) rbinom(n, size, p)) rmvbinary <- function(n, center) sapply(center, function(p) rbinom(n, 1, p)) setMethod("rFLXM", signature(model = "FLXMC", components = "FLXcomponent"), function(model, components, class, ...) { rmvnorm <- function(n, center, cov) mvtnorm::rmvnorm(n = n, mean = center, sigma = cov) dots <- list(...) FUN <- paste("r", model@dist, sep = "") args <- c(n = nrow(model@x), dots, components@parameters) return(do.call(FUN, args)) }) flexmix/R/plot-flexmix.R0000644000176200001440000001353014404637304014711 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: plot-flexmix.R 5079 2016-01-31 12:21:12Z gruen $ # determine_y <- function(h, root) { y <- h$counts if (root) y <- sqrt(y) return(y) } panel.rootogram <- function (x, breaks, equal.widths = TRUE, nint = max(round(log2(length(x)) + 1), 3), alpha = plot.polygon$alpha, col = plot.polygon$col, border = plot.polygon$border, lty = plot.polygon$lty, lwd = plot.polygon$lwd, subscripts, groups, mark, root = TRUE, markcol, ...) { x <- as.numeric(x) plot.polygon <- trellis.par.get("plot.polygon") grid.lines(x = c(0.05, 0.95), y = unit(c(0, 0), "native"), gp = gpar(col = border, lty = lty, lwd = lwd, alpha = alpha), default.units = "npc") if (length(x) > 0) { if (is.null(breaks)) { breaks <- if (equal.widths) do.breaks(range(x, finite = TRUE), nint) else quantile(x, 0:nint/nint, na.rm = TRUE) } h <- hist.constructor(x, breaks = breaks, plot = FALSE, ...) y <- determine_y(h, root) if (!is.null(mark)) { h1 <- hist.constructor(x[groups[subscripts] == mark], breaks = h$breaks, plot = FALSE, ...) y1 <- determine_y(h1, root) } nb <- length(breaks) if (length(y) != nb - 1) warning("problem with hist computations") if (nb > 1) { panel.rect(x = breaks[-nb], y = 0, height = y, width = diff(breaks), col = col, alpha = alpha, border = border, lty = lty, lwd = lwd, just = c("left", "bottom")) if (!is.null(mark)) panel.rect(x = breaks[-nb], y = 0, height = y1, width = diff(breaks), col = markcol, alpha = alpha, border = border, lty = lty, lwd = lwd, just = c("left", "bottom")) } } } prepanel.rootogram <- function (x, breaks, equal.widths = TRUE, nint = max(round(log2(length(x)) + 1), 3), root = TRUE, ...) { if (length(x) < 1) list(xlim = NA, ylim = NA, dx = NA, dy = NA) else { if (is.factor(x)) { isFactor <- TRUE xlimits <- levels(x) } else isFactor <- FALSE if (!is.numeric(x)) x <- as.numeric(x) if (is.null(breaks)) { breaks <- if (equal.widths) do.breaks(range(x, finite = TRUE), nint) else quantile(x, 0:nint/nint, na.rm = TRUE) } h <- hist.constructor(x, breaks = breaks, plot = FALSE, ...) y <- determine_y(h, root) list(xlim = if (isFactor) xlimits else range(x, breaks, finite = TRUE), ylim = range(0, y, finite = TRUE), dx = 1, dy = 1) } } setMethod("plot", signature(x="flexmix", y="missing"), function(x, y, mark=NULL, markcol=NULL, col=NULL, eps=1e-4, root=TRUE, ylim=TRUE, main=NULL, xlab = "", ylab = "", as.table = TRUE, endpoints = c(-0.04, 1.04), ...){ k <- length(x@prior) if(is.null(markcol)) markcol <- FullColors[5] if(is.null(col)) col <- LightColors[4] if(is.null(main)){ main <- ifelse(root, "Rootogram of posterior probabilities", "Histogram of posterior probabilities") main <- paste(main, ">", eps) } groupfirst <- if (length(x@group)) !duplicated(x@group) else TRUE if (is.null(x@weights)) z <- data.frame(posterior = as.vector(x@posterior$scaled[groupfirst,,drop=FALSE]), component = factor(rep(seq_len(x@k), each = nrow(x@posterior$scaled[groupfirst,,drop=FALSE])), levels = seq_len(x@k), labels = paste("Comp.", seq_len(x@k))), cluster = rep(as.vector(x@cluster[groupfirst]), k)) else z <- data.frame(posterior = rep(as.vector(x@posterior$scaled[groupfirst,,drop=FALSE]), rep(x@weights[groupfirst], k)), component = factor(rep(seq_len(x@k), each = sum(x@weights[groupfirst])), seq_len(x@k), paste("Comp.", seq_len(x@k))), cluster = rep(rep(as.vector(x@cluster[groupfirst]), x@weights[groupfirst]), k)) panel <- function(x, subscripts, groups, ...) panel.rootogram(x, root = root, mark = mark, col = col, markcol = markcol, subscripts = subscripts, groups = groups, ...) prepanel <- function(x, ...) prepanel.rootogram(x, root = root, ...) z <- subset(z, posterior > eps) cluster <- NULL # make codetools happy if (is.logical(ylim)) { scales <- if (ylim) list() else list(y = list(relation = "free")) hh <- histogram(~ posterior | component, data = z, main = main, ylab = ylab, xlab = xlab, groups = cluster, panel = panel, prepanel = prepanel, scales = scales, as.table = as.table, endpoints = endpoints, ...) } else hh <- histogram(~ posterior | component, data = z, main = main, ylab = ylab, xlab = xlab, groups = cluster, ylim = ylim, panel = panel, prepanel = prepanel, as.table = as.table, endpoints = endpoints, ...) if (root) { hh$yscale.components <- function (lim, packet.number = 0, packet.list = NULL, right = TRUE, ...) { comps <- calculateAxisComponents(lim, packet.list = packet.list, packet.number = packet.number, ...) comps$at <- sqrt(seq(min(comps$at)^2, max(comps$at)^2, length.out = length(comps$at))) comps$labels <- format(comps$at^2, trim = TRUE) list(num.limit = comps$num.limit, left = list(ticks = list(at = comps$at, tck = 1), labels = list(at = comps$at, labels = comps$labels, cex = 1, check.overlap = comps$check.overlap)), right = right) } } hh }) flexmix/R/ziglm.R0000644000176200001440000000405314404637304013403 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: ziglm.R 5079 2016-01-31 12:21:12Z gruen $ # setClass("FLXMRziglm", contains = "FLXMRglm") FLXMRziglm <- function(formula = . ~ ., family = c("binomial", "poisson"), ...) { family <- match.arg(family) new("FLXMRziglm", FLXMRglm(formula, family, ...), name = paste("FLXMRziglm", family, sep=":")) } setMethod("FLXgetModelmatrix", signature(model="FLXMRziglm"), function(model, data, formula, lhs=TRUE, ...) { model <- callNextMethod(model, data, formula, lhs) if (attr(terms(model@fullformula), "intercept") == 0) stop("please include an intercept") model }) setMethod("FLXremoveComponent", signature(model = "FLXMRziglm"), function(model, nok, ...) if (1 %in% nok) as(model, "FLXMRglm") else model) setMethod("FLXmstep", signature(model = "FLXMRziglm"), function(model, weights, components, ...) { coef <- c(-Inf, rep(0, ncol(model@x)-1)) names(coef) <- colnames(model@x) comp.1 <- model@defineComponent( list(coef = coef, df = 0, offset = NULL, family = model@family)) c(list(comp.1), FLXmstep(as(model, "FLXMRglm"), weights[, -1, drop=FALSE], components[-1])) }) setMethod("FLXgetDesign", signature(object = "FLXMRziglm"), function(object, components) rbind(0, FLXgetDesign(as(object, "FLXMRglm"), components[-1]))) setMethod("FLXreplaceParameters", signature(object="FLXMRziglm"), function(object, components, parms) c(components[[1]], FLXreplaceParameters(as(object, "FLXMRglm"), components[-1], parms))) setMethod("FLXgradlogLikfun", signature(object="FLXMRziglm"), function(object, components, weights, ...) FLXgradlogLikfun(as(object, "FLXMRglm"), components[-1], weights[,-1,drop=FALSE])) setMethod("refit_optim", signature(object = "FLXMRziglm"), function(object, components, ...) { x <- refit_optim(as(object, "FLXMRglm"), components[-1], ...) names(x) <- paste("Comp", 1 + seq_along(x), sep = ".") x }) flexmix/R/stepFlexmix.R0000644000176200001440000001351314404637304014572 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: stepFlexmix.R 5079 2016-01-31 12:21:12Z gruen $ # setClass("stepFlexmix", representation(models="list", k="integer", nrep="integer", logLiks="matrix", call="call")) stepFlexmix <- function(..., k=NULL, nrep=3, verbose=TRUE, drop=TRUE, unique=FALSE) { MYCALL <- match.call() MYCALL1 <- MYCALL bestFlexmix <- function(...) { z = new("flexmix", logLik=-Inf) logLiks = rep(NA, length.out = nrep) for(m in seq_len(nrep)){ if(verbose) cat(" *") x = try(flexmix(...)) if (!is(x, "try-error")) { logLiks[m] <- logLik(x) if(logLik(x) > logLik(z)) z = x } } return(list(z = z, logLiks = logLiks)) } z = list() if(is.null(k)){ RET = bestFlexmix(...) z[[1]] <- RET$z logLiks <- as.matrix(RET$logLiks) z[[1]]@call <- MYCALL z[[1]]@control@nrep <- nrep names(z) <- as.character(z[[1]]@k) if(verbose) cat("\n") } else{ k = as.integer(k) logLiks <- matrix(nrow = length(k), ncol = nrep) for(n in seq_along(k)){ ns <- as.character(k[n]) if(verbose) cat(k[n], ":") RET <- bestFlexmix(..., k=k[n]) z[[ns]] = RET$z logLiks[n,] <- RET$logLiks MYCALL1[["k"]] <- as.numeric(k[n]) z[[ns]]@call <- MYCALL1 z[[ns]]@control@nrep <- nrep if(verbose) cat("\n") } } logLiks <- logLiks[is.finite(sapply(z, logLik)),,drop=FALSE] z <- z[is.finite(sapply(z, logLik))] rownames(logLiks) <- names(z) if (!length(z)) stop("no convergence to a suitable mixture") if(drop & (length(z)==1)){ return(z[[1]]) } else{ z <- return(new("stepFlexmix", models=z, k=as.integer(names(z)), nrep=as.integer(nrep), logLiks=logLiks, call=MYCALL)) if(unique) z <- unique(z) return(z) } } ###********************************************************** setMethod("unique", "stepFlexmix", function(x, incomparables=FALSE, ...) { z <- list() K <- sapply(x@models, function(x) x@k) logLiks <- x@logLiks keep <- rep(TRUE, nrow(logLiks)) for(k in sort(unique(K))){ n <- which(k==K) if(length(n)>1){ l <- sapply(x@models[n], logLik) z[as.character(k)] <- x@models[n][which.max(l)] keep[n[-which.max(l)]] <- FALSE } else z[as.character(k)] <- x@models[n] } logLiks <- logLiks[keep,,drop=FALSE] rownames(logLiks) <- names(z) attr(logLiks, "na.action") <- NULL mycall <- x@call mycall["unique"] <- TRUE return(new("stepFlexmix", models=z, k=as.integer(names(z)), nrep=x@nrep, logLiks=logLiks, call=mycall)) }) ###********************************************************** setMethod("show", "stepFlexmix", function(object) { cat("\nCall:", deparse(object@call,0.75*getOption("width")), sep="\n") cat("\n") z <- data.frame(iter = sapply(object@models, function(x) x@iter), converged = sapply(object@models, function(x) x@converged), k = sapply(object@models, function(x) x@k), k0 = sapply(object@models, function(x) x@k0), logLik = sapply(object@models, function(x) logLik(x)), AIC = AIC(object), BIC = BIC(object), ICL = ICL(object)) print(z, na.string="") }) setMethod("nobs", signature(object="stepFlexmix"), function(object, ...) { sapply(object@models, nobs) }) setMethod("logLik", "stepFlexmix", function(object, ..., k = 2) { ll <- lapply(object@models, function(x) logLik(x)) df <- sapply(ll, attr, "df") nobs <- sapply(ll, attr, "nobs") ll <- unlist(ll) attr(ll, "df") <- df attr(ll, "nobs") <- nobs class(ll) <- "logLik" ll }) setMethod("ICL", "stepFlexmix", function(object, ...) { sapply(object@models, function(x) ICL(x, ...)) }) setMethod("EIC", "stepFlexmix", function(object, ...) { sapply(object@models, function(x) EIC(x, ...)) }) ###********************************************************** setMethod("getModel", "stepFlexmix", function(object, which="BIC") { if(which=="AIC") which <- which.min(sapply(object@models, function(x) AIC(x))) if(which=="BIC") which <- which.min(sapply(object@models, function(x) BIC(x))) if(which=="ICL") which <- which.min(sapply(object@models, function(x) ICL(x))) object@models[[which]] } ) ###********************************************************** setMethod("plot", signature(x="stepFlexmix", y="missing"), function(x, y, what=c("AIC", "BIC", "ICL"), xlab=NULL, ylab=NULL, legend="topright", ...) { X <- x@k Y <- NULL for(w in what){ Y <- cbind(Y, do.call(w, list(object=x))) } if(is.null(xlab)) xlab <- "number of components" if(is.null(ylab)){ if(length(what)==1) ylab <- what else ylab <- "" } matplot(X, Y, xlab=xlab, ylab=ylab, type="b", lty=1, pch=seq_along(what), ...) if(legend!=FALSE && length(what)>1) legend(x=legend, legend=what, pch=seq_along(what), col=seq_along(what)) for(n in seq_len(ncol(Y))){ m <- which.min(Y[,n]) points(X[m], Y[m,n], pch=16, cex=1.5, col=n) } }) flexmix/R/plot-FLXboot.R0000644000176200001440000001421014404637304014546 0ustar liggesusersprepanel.parallel.horizontal <- function (x, y, z, horizontal = TRUE, ...) { if (horizontal) list(xlim = extend.limits(c(1, ncol(as.data.frame(z))), prop = 0.03), ylim = c(0, 1), dx = 1, dy = 1) else list(xlim = c(0, 1), ylim = extend.limits(c(1, ncol(as.data.frame(z))), prop = 0.03), dx = 1, dy = 1) } panel.parallel.horizontal <- function (x, y, z, subscripts, groups = NULL, col = superpose.line$col, lwd = superpose.line$lwd, lty = superpose.line$lty, alpha = superpose.line$alpha, common.scale = FALSE, lower = sapply(z, function(x) min(as.numeric(x), na.rm = TRUE)), upper = sapply(z, function(x) max(as.numeric(x), na.rm = TRUE)), horizontal = TRUE, ...) { superpose.line <- trellis.par.get("superpose.line") reference.line <- trellis.par.get("reference.line") n.r <- ncol(z) n.c <- length(subscripts) if (is.null(groups)) { col <- rep(col, length = n.c) lty <- rep(lty, length = n.c) lwd <- rep(lwd, length = n.c) alpha <- rep(alpha, length = n.c) } else { groups <- as.factor(groups)[subscripts] n.g <- nlevels(groups) gnum <- as.numeric(groups) col <- rep(col, length = n.g)[gnum] lty <- rep(lty, length = n.g)[gnum] lwd <- rep(lwd, length = n.g)[gnum] alpha <- rep(alpha, length = n.g)[gnum] } if (is.function(lower)) lower <- sapply(z, lower) if (is.function(upper)) upper <- sapply(z, upper) if (common.scale) { lower <- min(lower) upper <- max(upper) } lower <- rep(lower, length = n.r) upper <- rep(upper, length = n.r) dif <- upper - lower if (n.r > 1) { if (horizontal) panel.segments(y0 = 0, y1 = 1, x0 = seq_len(n.r), x1 = seq_len(n.r), col = reference.line$col, lwd = reference.line$lwd, lty = reference.line$lty) else panel.segments(x0 = 0, x1 = 1, y0 = seq_len(n.r), y1 = seq_len(n.r), col = reference.line$col, lwd = reference.line$lwd, lty = reference.line$lty) }else return(invisible()) for (i in seq_len(n.r - 1)) { x0 <- (as.numeric(z[subscripts, i]) - lower[i])/dif[i] x1 <- (as.numeric(z[subscripts, i + 1]) - lower[i + 1])/dif[i + 1] if (horizontal) panel.segments(y0 = x0, x0 = i, y1 = x1, x1 = i + 1, col = col, lty = lty, lwd = lwd, alpha = alpha, ...) else panel.segments(x0 = x0, y0 = i, x1 = x1, y1 = i + 1, col = col, lty = lty, lwd = lwd, alpha = alpha, ...) } invisible() } confidence.panel.boot <- function(x, y, z, subscripts, lwd = 1, SD = NULL, ..., lower, upper, range = c(0, 1)) { nc <- ncol(z) if (missing(lower)) lower <- sapply(z, function(x) quantile(x, range[1])) if (missing(upper)) upper <- sapply(z, function(x) quantile(x, range[2])) dif <- upper - lower if (!is.null(SD)) { SD <- lapply(SD, function(x) (x - lower)/dif) for (l in seq_along(SD)) { grid.polygon(y = unit(c(SD[[l]][,1], rev(SD[[l]][,3])), "native"), x = unit(c(seq_len(nc),rev(seq_len(nc))), "native"), gp = gpar(fill = rgb(190/225, 190/225, 190/225, 0.5), col = "darkgrey")) } } panel.parallel.horizontal(x, y, z, subscripts, ..., lower = lower, upper = upper) if (!is.null(SD)) { for (l in seq_along(SD)) { llines(y = SD[[l]][,2], x = seq_len(nc), col="white", lwd=lwd, lty = 1) } } } setMethod("plot", signature(x = "FLXboot", y = "missing"), function(x, y, ordering = NULL, range = c(0, 1), ci = FALSE, varnames = colnames(pars), strip_name = NULL, ...) { k <- x@object@k pars <- parameters(x) if (ci) { x_refit <- refit(x@object) sd <- sqrt(diag(x_refit@vcov)) CI <- x_refit@coef + qnorm(0.975) * cbind(-sd, 0, sd) indices_prior <- grep("alpha$", names(x_refit@coef)) if (length(indices_prior)) { z <- mvtnorm::rmvnorm(10000, x_refit@coef[indices_prior,drop=FALSE], x_refit@vcov[indices_prior,indices_prior,drop=FALSE]) Priors <- t(apply(cbind(1, exp(z))/rowSums(cbind(1, exp(z))), 2, quantile, c(0.025, 0.5, 0.975))) indices <- lapply(seq_len(k), function(i) grep(paste("_Comp.", i, sep = ""), names(x_refit@coef[-indices_prior]))) SD <- lapply(seq_len(k), function(i) rbind(CI[indices[[i]], ], prior = Priors[i,])) } else { indices <- lapply(seq_len(k), function(i) grep(paste("_Comp.", i, sep = ""), names(x_refit@coef))) SD <- lapply(seq_len(k), function(i) CI[indices[[i]], ]) mnrow <- max(sapply(SD, nrow)) SD <- lapply(SD, function(x) if (nrow(x) < mnrow) do.call("rbind", c(list(x), as.list(rep(0, mnrow - nrow(x))))) else x) } if (any("gaussian" %in% sapply(x@object@model, function(x) if (is(x, "FLXMRglm")) x@family else ""))) { i <- grep("sigma$", colnames(pars)) pars[,i] <- log(pars[,i]) colnames(pars)[i] <- "log(sigma)" } } else SD <- NULL range_name <- vector(mode = "character", length=2) range_name[1] <- if (range[1] == 0) "Min" else paste(round(range[1]*100), "%", sep = "") range_name[2] <- if (range[2] == 1) "Max" else paste(round(range[2]*100), "%", sep = "") Ordering <- if (is.null(ordering)) NULL else factor(as.vector(apply(matrix(pars[,ordering], nrow = k), 2, function(x) order(order(x))))) if(is.null(strip_name)) formula = ~ pars else { opt.old <- options(useFancyQuotes = FALSE) on.exit(options(opt.old)) formula <- as.formula(paste("~ pars | ", sQuote(strip_name))) } pars <- na.omit(pars) if (!is.null(attr(pars, "na.action"))) Ordering <- Ordering[-attr(na.omit(pars), "na.action")] parallel.plot <- parallelplot(formula, groups = Ordering, default.scales = list(y = list(at = c(0, 1), labels = range_name), x = list(alternating = FALSE, axs = "i", tck = 0, at = seq_len(ncol(pars)))), range = range, panel = confidence.panel.boot, prepanel = prepanel.parallel.horizontal, SD = SD, ...) parallel.plot$x.scales$labels <- varnames parallel.plot }) flexmix/R/flxdist.R0000644000176200001440000000554214404637304013742 0ustar liggesusersFLXdist <- function(formula, k = NULL, model=FLXMRglm(), components, concomitant=FLXPconstant()) { mycall <- match.call() if(is(model, "FLXM")) model <- list(model) if (length(k)==1) prior <- rep(1/k, k) else { prior <- k/sum(k) } concomitant@x <- matrix(c(1, rep(0, ncol(concomitant@coef))[-1]), nrow = 1) prior <- as.vector(evalPrior(prior, concomitant)) lf <- length(formula) formula1 <- formula if(length(formula[[lf]])>1 && deparse(formula[[lf]][[1]]) == "|") formula1[[lf]] <- formula[[lf]][[2]] for(n in seq(along.with=model)) { if(is.null(model[[n]]@formula)) model[[n]]@formula <- formula1 else if(length(model[[n]]@formula) == 3 && model[[n]]@formula[[2]] == ".") model[[n]]@formula <- model[[n]]@formula[-2] model[[n]]@fullformula <- update.formula(formula1, model[[n]]@formula) } if (missing(components)) stop("no parameter values specified") if (length(components) != length(prior)) stop("components not specified correctly") comp <- list() for (k in seq(along.with=prior)) { comp[[k]] <- list() if (length(components[[k]]) != length(model)) stop("components not specified correctly") for (n in seq(along.with=model)) { comp[[k]][[n]] <- FLXcomponent(model[[n]], components[[k]][[n]]) } } new("FLXdist", formula=formula, call=mycall, concomitant=concomitant, prior=prior, k=length(prior), model=model, components=comp) } ###********************************************************** setGeneric("FLXcomponent", function(object, ...) standardGeneric("FLXcomponent")) setMethod("FLXcomponent", signature(object="FLXM"), function(object, components, ...) { components$df <- numeric() if (is(object@defineComponent, "expression")) eval(object@defineComponent, components) else object@defineComponent(components) }) #### setMethod("FLXcomponent", signature(object="FLXMRglm"), function(object, components, ...) { components$df <- numeric() offset <- NULL family <- object@family if (is(object@defineComponent, "expression")) eval(object@defineComponent, components) else object@defineComponent(components) }) ###********************************************************** setMethod("show", "FLXdist", function(object){ cat("\nCall:", deparse(object@call,0.75*getOption("width")), sep="\n") cat("\nPriors:\n") names(object@prior) <- paste("Comp.", seq_along(object@prior), sep="") print(object@prior) cat("\n") }) ###********************************************************** evalPrior <- function(prior, concomitant) prior setGeneric("evalPrior", function(prior, concomitant) standardGeneric("evalPrior")) setMethod("evalPrior", signature(concomitant="FLXPmultinom"), function(prior, concomitant) { exps <- exp(concomitant@x %*% concomitant@coef) exps/rowSums(exps) }) flexmix/R/utils.R0000644000176200001440000000321714404637304013422 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: utils.R 5079 2016-01-31 12:21:12Z gruen $ # list2object = function(from, to){ n = names(from) s = slotNames(to) p = pmatch(n, s) if(any(is.na(p))) stop(paste("\nInvalid slot name(s) for class", to, ":", paste(n[is.na(p)], collapse=" "))) names(from) = s[p] do.call("new", c(from, Class=to)) } printIter = function(iter, logLik, label="Log-likelihood") cat(formatC(iter, width=4), label, ":", formatC(logLik, width=12, format="f"),"\n") ## library(colorspace) ## dput(x[c(1,3,5,7,2,4,6,8)]) ## x = hcl(seq(0, 360*7/8, length.out = 8), c=30) LightColors <- c("#F9C3CD", "#D0D4A8", "#9DDDD5", "#D1CCF5", "#EDCAB2", "#AFDCB8", "#ACD7ED", "#EFC4E8") ## x = hcl(seq(0, 360*7/8, length.out = 8), c=100, l=65) FullColors <- c("#FF648A", "#96A100", "#00BCA3", "#9885FF", "#DC8400", "#00B430", "#00AEEF", "#F45BE1") ###********************************************************** ## similar defaults to silhouette plots in flexclust unipolarCols <- function(n, hue=0, chr=50, lum = c(55, 90)) { lum <- seq(lum[1], lum[2], length=n) hcl(hue, chr, lum) } bipolarCols <- function(n, hue=c(10, 130), ...) { if(n%%2){ # n odd n2 <- (n-1)/2 c1 <- unipolarCols(n2, hue[1]) c2 <- rev(unipolarCols(n2, hue[2])) return(c(c1, "white", c2)) } else{ # n even n2 <- n/2 c1 <- unipolarCols(n2, hue[1]) c2 <- rev(unipolarCols(n2, hue[2])) return(c(c1, c2)) } } ###********************************************************** flexmix/R/allGenerics.R0000644000176200001440000000621014404637304014506 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: allGenerics.R 5079 2016-01-31 12:21:12Z gruen $ # setGeneric("flexmix", function(formula, data=list(), k=NULL, cluster=NULL, model=NULL, concomitant=NULL, control=NULL, weights = NULL) standardGeneric("flexmix")) setGeneric("FLXfit", function(model, concomitant, control, postunscaled=NULL, groups, weights) standardGeneric("FLXfit")) ###********************************************************** setGeneric("FLXgetModelmatrix", function(model, data, ...) standardGeneric("FLXgetModelmatrix")) setGeneric("FLXfillConcomitant", function(concomitant, ...) standardGeneric("FLXfillConcomitant")) ###********************************************************** setGeneric("logLik") setGeneric("clogLik", function(object, ...) standardGeneric("clogLik")) setGeneric("EIC", function(object, ...) standardGeneric("EIC")) ###********************************************************** setGeneric("FLXcheckComponent", function(model, ...) standardGeneric("FLXcheckComponent")) setGeneric("FLXgetK", function(model, ...) standardGeneric("FLXgetK")) setGeneric("FLXgetObs", function(model) standardGeneric("FLXgetObs")) setGeneric("FLXmstep", function(model, ...) standardGeneric("FLXmstep")) setGeneric("FLXremoveComponent", function(model, ...) standardGeneric("FLXremoveComponent")) setGeneric("FLXdeterminePostunscaled", function(model, ...) standardGeneric("FLXdeterminePostunscaled")) setGeneric("FLXgetDesign", function(object, ...) standardGeneric("FLXgetDesign")) setGeneric("FLXreplaceParameters", function(object, ...) standardGeneric("FLXreplaceParameters")) setGeneric("FLXlogLikfun", function(object, ...) standardGeneric("FLXlogLikfun")) setGeneric("FLXgradlogLikfun", function(object, ...) standardGeneric("FLXgradlogLikfun")) setGeneric("VarianceCovariance", function(object, ...) standardGeneric("VarianceCovariance")) setGeneric("FLXgetParameters", function(object, ...) standardGeneric("FLXgetParameters")) setGeneric("logLikfun_comp", function(object, ...) standardGeneric("logLikfun_comp")) setGeneric("getPriors", function(object, ...) standardGeneric("getPriors")) setGeneric("existGradient", function(object, ...) standardGeneric("existGradient")) setGeneric("refit_mstep", function(object, newdata, ...) standardGeneric("refit_mstep")) setGeneric("refit_optim", function(object, ...) standardGeneric("refit_optim")) ###********************************************************** setGeneric("group", function(object, ...) standardGeneric("group")) setGeneric("rflexmix", function(object, newdata, ...) standardGeneric("rflexmix")) setGeneric("rFLXM", function(model, components, ...) standardGeneric("rFLXM")) ## just to make sure that some S3 generics are available in S4 setGeneric("fitted", package = "stats") setGeneric("predict", package = "stats") setGeneric("simulate", package = "stats") setGeneric("summary", package = "base") setGeneric("unique", package = "base") setGeneric("allweighted", function(model, control, weights) standardGeneric("allweighted")) flexmix/R/flexmixFix.R0000644000176200001440000001415214404637304014405 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch and Bettina Gruen # $Id: flexmixFix.R 5079 2016-01-31 12:21:12Z gruen $ # setMethod("FLXcheckComponent", signature(model = "FLXMRfix"), function(model, k, cluster, ...) { if (sum(model@nestedformula@k)) { if (!is.null(k)) { if (k != sum(model@nestedformula@k)) stop("specified k does not match the nestedformula in the model") } else k <- sum(model@nestedformula@k) } else { if (is(cluster, "matrix")) { if (is.null(k)) k <- ncol(cluster) } else if (!is.null(cluster)) { if (is.null(k)) { cluster <- as(cluster, "integer") k <- max(cluster) } } if (is.null(k)) stop("either k, cluster or the nestedformula of the model must be specified") else model@nestedformula <- as(k, "FLXnested") } if (length(model@variance) > 1) { if (sum(model@variance) != k) stop("specified k does not match the specified varFix argument in the model") } else if (model@variance) model@variance <- k else model@variance <- rep(1, k) model }) setMethod("FLXgetObs", signature(model = "FLXMRfix"), function(model) nrow(model@y)/sum(model@nestedformula@k)) setMethod("FLXgetK", signature(model = "FLXMRfix"), function(model, ...) sum(model@nestedformula@k)) setMethod("FLXremoveComponent", signature(model = "FLXMRfix"), function(model, nok, ...) { if (!length(nok)) return(model) K <- model@nestedformula wnok <- sapply(nok, function(i) which(apply(rbind(i > c(0, cumsum(K@k[-length(K@k)])), i <= c(cumsum(K@k))), 2, all))) wnok <- table(wnok) if (length(wnok) > 0) { K@k[as.integer(names(wnok))] <- K@k[as.integer(names(wnok))] - wnok if (any(K@k == 0)) { keep <- K@k != 0 K@k <- K@k[keep] K@formula <- K@formula[keep] } k <- sum(K@k) model@nestedformula <- K } varnok <- sapply(nok, function(i) which(apply(rbind(i > c(0, cumsum(model@variance[-length(model@variance)])), i <= c(cumsum(model@variance))), 2, all))) varnok <- table(varnok) if (length(varnok) > 0) { model@variance[as.integer(names(varnok))] <- model@variance[as.integer(names(varnok))] - varnok if (any(model@variance == 0)) model@variance <- model@variance[model@variance != 0] } rok <- which(!apply(model@segment[,nok,drop=FALSE], 1, function(x) any(x))) model@x <- model@x[rok, which(colSums(model@design[-nok,,drop=FALSE]) > 0), drop=FALSE] model@y <- model@y[rok,, drop=FALSE] model@design <- model@design[-nok,,drop=FALSE] cok <- colSums(model@design) > 0 model@design <- model@design[,cok,drop=FALSE] model@segment <- model@segment[rok,-nok, drop=FALSE] model }) ###********************************************************** setMethod("FLXmstep", signature(model = "FLXMRfix"), function(model, weights, ...) { model@fit(model@x, model@y, as.vector(weights), model@design, model@variance) }) ###********************************************************** setMethod("FLXdeterminePostunscaled", signature(model = "FLXMRfix"), function(model, components, ...) { sapply(seq_along(components), function(m) components[[m]]@logLik(model@x[model@segment[,m], as.logical(model@design[m,]), drop=FALSE], model@y[model@segment[,m],,drop=FALSE])) }) ###********************************************************** modelMatrix <- function(random, fixed, nested, data=list(), lhs, xlevels = NULL) { if (!lhs) random <- random[-2] mf.random <- model.frame(random, data=data, na.action = NULL) response <- if (lhs) as.matrix(model.response(mf.random)) else NULL xlev <- xlevels[names(.getXlevels(terms(mf.random), mf.random))] mm.random <- if (is.null(xlev)) model.matrix(terms(mf.random), data=mf.random) else model.matrix(terms(mf.random), data=data, xlev = xlev) xlevels.random <- .getXlevels(terms(mf.random), mf.random) randomfixed <- if(identical(paste(deparse(fixed), collapse = ""), "~0")) random else update(random, paste("~.+", paste(deparse(fixed[[length(fixed)]]), collapse = ""))) mf.randomfixed <- model.frame(randomfixed, data=data) mm.randomfixed <- model.matrix(terms(mf.randomfixed), data=mf.randomfixed, xlev = xlevels[names(.getXlevels(terms(mf.randomfixed), mf))]) mm.fixed <- mm.randomfixed[,!colnames(mm.randomfixed) %in% colnames(mm.random), drop=FALSE] xlevels.fixed <- .getXlevels(terms(mf.randomfixed), mf.randomfixed) all <- mm.all <- mm.nested <- xlevels.nested <- list() for (l in seq_along(nested)) { all[[l]] <- if (identical(paste(deparse(nested[[l]]), collapse = ""), "~0")) randomfixed else update(randomfixed, paste("~.+", paste(deparse(nested[[l]][[length(nested[[l]])]]), collapse = ""))) mf <- model.frame(all[[l]], data=data) mm.all[[l]] <- model.matrix(terms(mf), data=mf, xlev = xlevels[names(.getXlevels(terms(mf), mf))]) mm.nested[[l]] <- mm.all[[l]][,!colnames(mm.all[[l]]) %in% colnames(mm.randomfixed),drop=FALSE] xlevels.nested[[l]] <- .getXlevels(terms(mf), mf) } return(list(random=mm.random, fixed=mm.fixed, nested=mm.nested, response=response, xlevels=c(xlevels.random, xlevels.fixed, unlist(xlevels.nested)))) } ###********************************************************** modelDesign <- function(mm.all, k) { design <- matrix(1, nrow=sum(k@k), ncol=ncol(mm.all$fixed)) col.names <- colnames(mm.all$fixed) nested <- matrix(0, nrow=sum(k@k), ncol=sum(sapply(mm.all$nested, ncol))) cumK <- c(0, cumsum(k@k)) i <- 0 for (l in seq_along(mm.all$nested)) { if (ncol(mm.all$nested[[l]])) { nested[(cumK[l] + 1):cumK[l+1], i+seq_len(ncol(mm.all$nested[[l]]))] <- 1 i <- i+ncol(mm.all$nested[[l]]) col.names <- c(col.names, colnames(mm.all$nested[[l]])) } } design <- cbind(design, nested) if (ncol(mm.all$random)) design <- cbind(design, kronecker(diag(sum(k@k)), matrix(1, ncol=ncol(mm.all$random)))) colnames(design) <- c(col.names, rep(colnames(mm.all$random), sum(k@k))) design } ###********************************************************** flexmix/R/flxmcsparse.R0000644000176200001440000000225214404637304014607 0ustar liggesuserssetClass("FLXMCsparse", contains = "FLXM") as.data.frame.simple_triplet_matrix <- function(x, ...) { as.data.frame.model.matrix(x, ...) } setMethod("FLXgetModelmatrix", signature(model = "FLXMCsparse"), function(model, data, formula, lhs=TRUE, ...) { formula <- RemoveGrouping(formula) if (length(grep("\\|", deparse(model@formula)))) stop("no grouping variable allowed in the model") if(is.null(model@formula)) model@formula <- formula model@fullformula <- update(terms(formula, data = data), model@formula) fullformula <- terms(model@fullformula, data = data) model@terms <- attr(fullformula, "terms") if (lhs) { env <- environment(fullformula) vars <- attr(fullformula, "variables") varnames <- vapply(vars, function(x) paste(deparse(x, backtick = FALSE), collapse = " "), " ")[-1L] variables <- eval(vars, data, env) resp <- attr(fullformula, "response") response <- variables[[resp]] model@y <- model@preproc.y(response) model@x <- matrix(nrow = nrow(model@y), ncol = 0) } else { model@x <- matrix(nrow = nrow(as.data.frame(data)), ncol = 0) } model }) flexmix/R/lmer.R0000644000176200001440000001506414404637304013224 0ustar liggesuserssigmaMethod <- getExportedValue(if(getRversion() >= "3.3.0") "stats" else "lme4", "sigma") setClass("FLXMRlmer", representation(random = "formula", lmod = "list", control = "ANY", preproc.z = "function"), prototype(preproc.z = function(x, ...) x), contains = "FLXMRglm") defineComponent_lmer <- function(para) { predict <- function(x, ...) x%*%para$coef logLik <- function(x, y, lmod, ...) { z <- as.matrix(lmod$reTrms$Zt) grouping <- lmod$reTrms$flist[[1]] llh <- vector(length=nrow(x)) for (i in seq_len(nlevels(grouping))) { index1 <- which(grouping == levels(grouping)[i]) index2 <- rownames(z) %in% levels(grouping)[i] V <- crossprod(z[index2,index1,drop=FALSE], para$sigma2$Random) %*% z[index2, index1, drop=FALSE] + diag(length(index1)) * para$sigma2$Residual llh[index1] <- mvtnorm::dmvnorm(y[index1,], mean=predict(x[index1,,drop=FALSE], ...), sigma = V, log=TRUE)/length(index1) } llh } new("FLXcomponent", parameters=list(coef=para$coef, sigma2=para$sigma2), logLik=logLik, predict=predict, df=para$df) } FLXMRlmer <- function(formula = . ~ ., random, weighted = TRUE, control = list(), eps = .Machine$double.eps) { random <- if (length(random) == 3) random else formula(paste(".", paste(deparse(random), collapse = ""))) missCtrl <- missing(control) if (missCtrl || !inherits(control, "lmerControl")) { if (!is.list(control)) stop("'control' is not a list; use lmerControl()") control <- do.call(lme4::lmerControl, control) } object <- new("FLXMRlmer", formula = formula, random = random, control = control, family = "gaussian", weighted = weighted, name = "FLXMRlmer:gaussian") if (weighted) object@preproc.z <- function(lmod) { if (length(unique(names(lmod[["reTrms"]][["flist"]]))) != 1) stop("only a single variable for random effects is allowed") for (i in seq_along(lmod[["reTrms"]][["flist"]])) { DIFF <- t(sapply(levels(lmod[["reTrms"]]$flist[[i]]), function(id) { index1 <- which(lmod[["reTrms"]]$flist[[i]] == id) index2 <- rownames(lmod[["reTrms"]]$Zt) == id sort(apply(lmod[["reTrms"]]$Zt[index2, index1, drop=FALSE], 1, paste, collapse = "")) })) if (length(unique(table(lmod[["reTrms"]][["flist"]][[i]]))) != 1 || nrow(unique(DIFF)) != 1) stop("FLXMRlmer does only work correctly if the covariates of the random effects are the same for all observations") } lmod } lmer.wfit <- function(x, y, w, lmod) { zero.weights <- any(w < eps) if (zero.weights) { ok <- w >= eps w <- w[ok] lmod[["fr"]] <- lmod[["fr"]][ok, , drop = FALSE] lmod[["X"]] <- lmod[["X"]][ok, , drop = FALSE] lmod[["reTrms"]][["Zt"]] <- lmod[["reTrms"]][["Zt"]][, ok, drop = FALSE] for (i in seq_along(lmod[["reTrms"]][["flist"]])) { lmod[["reTrms"]][["flist"]][[i]] <- lmod[["reTrms"]][["flist"]][[i]][ok] } } wts <- sqrt(w) lmod$X <- lmod$X * wts lmod$fr[[1]] <- lmod$fr[[1]] * wts devfun <- do.call(lme4::mkLmerDevfun, c(lmod, list(start = NULL, verbose = FALSE, control = control))) opt <- lme4::optimizeLmer(devfun, optimizer = control$optimizer, restart_edge = control$restart_edge, control = control$optCtrl, verbose = FALSE, start = NULL) mer <- lme4::mkMerMod(environment(devfun), opt, lmod$reTrms, fr = lmod$fr) sigma_res <- sigmaMethod(mer) / sqrt(mean(w)) vc <- lme4::VarCorr(mer) n <- c(0, cumsum(sapply(vc, ncol))) Random <- matrix(0, max(n), max(n)) for (i in seq_along(vc)) { index <- (n[i]+1):n[i+1] Random[index, index] <- vc[[i]] } Random <- Random / mean(w) list(coefficients = lme4::fixef(mer), sigma2 = list(Random = Random, Residual = sigma_res^2), df = length(lme4::fixef(mer)) + 1 + length(mer@theta)) } object@defineComponent <- defineComponent_lmer object@fit <- function(x, y, w, lmod){ fit <- lmer.wfit(x, y, w, lmod) object@defineComponent( list(coef = coef(fit), df = fit$df, sigma2 = fit$sigma2)) } object } setMethod("FLXgetModelmatrix", signature(model="FLXMRlmer"), function(model, data, formula, lhs=TRUE, contrasts = NULL, ...) { formula_nogrouping <- RemoveGrouping(formula) if (identical(paste(deparse(formula_nogrouping), collapse = ""), paste(deparse(formula), collapse = ""))) stop("please specify a grouping variable") model <- callNextMethod(model, data, formula, lhs) random_formula <- update(model@random, paste(".~. |", .FLXgetGroupingVar(formula))) fullformula <- model@fullformula if (!lhs) fullformula <- fullformula[c(1,3)] fullformula <- update(fullformula, paste(ifelse(lhs, ".", ""), "~. + ", paste(deparse(random_formula[[3]]), collapse = ""))) model@fullformula <- update(model@fullformula, paste(ifelse(lhs, ".", ""), "~. |", .FLXgetGroupingVar(formula))) model@lmod <- lme4::lFormula(fullformula, data, REML = FALSE, control = model@control) model@lmod <- model@preproc.z(model@lmod) model }) setMethod("FLXmstep", signature(model = "FLXMRlmer"), function(model, weights, ...) { apply(weights, 2, function(w) model@fit(model@x, model@y, w, model@lmod)) }) setMethod("FLXdeterminePostunscaled", signature(model = "FLXMRlmer"), function(model, components, ...) { sapply(components, function(x) x@logLik(model@x, model@y, model@lmod)) }) setMethod("rFLXM", signature(model = "FLXMRlmer", components="FLXcomponent"), function(model, components, ...) { sigma2 <- components@parameters$sigma2 z <- as.matrix(model@lmod$reTrms$Zt) grouping <- model@lmod$reTrms$flist[[1]] y <- matrix(0, nrow=nrow(model@x), ncol = 1) for (i in seq_len(nlevels(grouping))) { index1 <- which(grouping == levels(grouping)[i]) index2 <- rownames(z) %in% levels(grouping)[i] V <- crossprod(z[index2,index1,drop=FALSE], sigma2$Random) %*% z[index2, index1, drop=FALSE] + diag(length(index1)) * sigma2$Residual y[index1, 1] <- mvtnorm::rmvnorm(1, mean=components@predict(model@x[index1,,drop=FALSE], ...), sigma = V) } y }) flexmix/R/rflexmix.R0000644000176200001440000000742114404637304014121 0ustar liggesuserssetMethod("rflexmix", signature(object = "FLXdist", newdata="numeric"), function(object, newdata, ...) { newdata <- data.frame(matrix(nrow = as.integer(newdata), ncol = 0)) rflexmix(object, newdata = newdata, ...) }) setMethod("rflexmix", signature(object = "FLXdist", newdata="listOrdata.frame"), function(object, newdata, ...) { groups <- .FLXgetGrouping(object@formula, newdata) object@model <- lapply(object@model, FLXgetModelmatrix, newdata, object@formula, lhs=FALSE) group <- if (length(groups$group)) groups$group else factor(seq_len(FLXgetObs(object@model[[1]]))) object@concomitant <- FLXgetModelmatrix(object@concomitant, data = newdata, groups = list(group=group, groupfirst = groupFirst(group))) rflexmix(new("flexmix", object, group=group, weights = NULL), ...) }) setMethod("rflexmix", signature(object = "flexmix", newdata="missing"), function(object, newdata, ...) { N <- length(object@model) object <- undo_weights(object) group <- group(object) prior <- determinePrior(object@prior, object@concomitant, group) class <- apply(prior, 1, function(x) rmultinom(1, size = 1, prob = x)) class <- if (is.matrix(class)) t(class) else as.matrix(class) class <- max.col(class)[group] y <- vector("list", N) for (i in seq_len(N)) { comp <- lapply(object@components, function(x) x[[i]]) yi <- rFLXM(object@model[[i]], comp, class, group, ...) form <- object@model[[i]]@fullformula names <- if(length(form) == 3) form[[2]] else paste("y", i, seq_len(ncol(yi)), sep = ".") if (ncol(yi) > 1) { if (inherits(names, "call")) names <- as.character(names[-1]) if (length(names) != ncol(yi)) { if (length(names) == 1) names <- paste(as.character(names)[1], i, seq_len(ncol(yi)), sep = ".") else stop("left hand side not specified correctly") } } else if (inherits(names, "call")) names <- deparse(names) colnames(yi) <- as.character(names) y[[i]] <- yi } list(y = y, group=group, class = class) }) ###********************************************************** determinePrior <- function(prior, concomitant, group) { matrix(prior, nrow = length(unique(group)), ncol = length(prior), byrow=TRUE) } setGeneric("determinePrior", function(prior, concomitant, group) standardGeneric("determinePrior")) setMethod("determinePrior", signature(concomitant="FLXPmultinom"), function(prior, concomitant, group) { exps <- exp(concomitant@x %*% concomitant@coef) exps/rowSums(exps) }) undo_weights <- function(object) { if (!is.null(object@weights)) { for (i in seq_along(object@model)) { object@model[[i]]@x <- apply(object@model[[i]]@x, 2, rep, object@weights) object@model[[i]]@y <- apply(object@model[[i]]@y, 2, rep, object@weights) object@concomitant@x <- apply(object@concomitant@x, 2, rep, object@weights) } if (length(object@group) > 0) object@group <- rep(object@group, object@weights) object@weights <- NULL } object } ###********************************************************** setMethod("simulate", signature("FLXdist"), function(object, nsim, seed = NULL, ...) { if (!exists(".Random.seed", envir = .GlobalEnv, inherits = FALSE)) runif(1) if (is.null(seed)) RNGstate <- get(".Random.seed", envir = .GlobalEnv, inherits = FALSE) else { R.seed <- get(".Random.seed", envir = .GlobalEnv, inherits = FALSE) set.seed(seed) RNGstate <- structure(seed, kind = as.list(RNGkind())) on.exit(assign(".Random.seed", R.seed, envir = .GlobalEnv, inherits = FALSE)) } ans <- lapply(seq_len(nsim), function(i) rflexmix(object, ...)$y) if (all(sapply(ans, ncol) == 1)) ans <- as.data.frame(ans) attr(ans, "seed") <- RNGstate ans }) flexmix/R/lattice.R0000644000176200001440000000746614404637304013721 0ustar liggesusers# # Copyright (C) Deepayan Sarkar # Internal code copied from package lattice for use in flexmix # hist.constructor <- function (x, breaks, include.lowest = TRUE, right = TRUE, ...) { if (is.numeric(breaks) && length(breaks) > 1) hist(as.numeric(x), breaks = breaks, plot = FALSE, include.lowest = include.lowest, right = right) else hist(as.numeric(x), breaks = breaks, right = right, plot = FALSE) } checkArgsAndCall <- function (FUN, args) { if (!("..." %in% names(formals(FUN)))) args <- args[intersect(names(args), names(formals(FUN)))] do.call(FUN, args) } formattedTicksAndLabels <- function (x, at = FALSE, used.at = NULL, labels = FALSE, logsc = FALSE, ..., num.limit = NULL, abbreviate = NULL, minlength = 4, format.posixt = NULL, equispaced.log = TRUE) { rng <- if (length(x) == 2) as.numeric(x) else range(as.numeric(x)) if (is.logical(logsc) && logsc) logsc <- 10 have.log <- !is.logical(logsc) if (have.log) logbase <- if (is.numeric(logsc)) logsc else if (logsc == "e") exp(1) else stop("Invalid value of 'log'") logpaste <- if (have.log) paste(as.character(logsc), "^", sep = "") else "" check.overlap <- if (is.logical(at) && is.logical(labels)) TRUE else FALSE if (is.logical(at)) { at <- if (have.log && !equispaced.log) checkArgsAndCall(axisTicks, list(usr = log10(logbase^rng), log = TRUE, axp = NULL, ...)) else checkArgsAndCall(pretty, list(x = x[is.finite(x)], ...)) } else if (have.log && (length(at) > 0)) { if (is.logical(labels)) labels <- as.character(at) at <- log(at, base = logbase) } if (is.logical(labels)) { if (have.log && !equispaced.log) { labels <- as.character(at) at <- log(at, logbase) } else labels <- paste(logpaste, format(at, trim = TRUE), sep = "") } list(at = at, labels = labels, check.overlap = check.overlap, num.limit = rng) } calculateAxisComponents <- function (x, ..., packet.number, packet.list, abbreviate = NULL, minlength = 4) { if (all(is.na(x))) return(list(at = numeric(0), labels = numeric(0), check.overlap = TRUE, num.limit = c(0, 1))) ans <- formattedTicksAndLabels(x, ...) rng <- range(ans$num.limit) ok <- ans$at >= min(rng) & ans$at <= max(rng) ans$at <- ans$at[ok] ans$labels <- ans$labels[ok] if (is.logical(abbreviate) && abbreviate) ans$labels <- abbreviate(ans$labels, minlength) ans } extend.limits <- function (lim, length = 1, axs = "r", prop = if (axs == "i") 0 else lattice.getOption("axis.padding")$numeric) { if (all(is.na(lim))) NA_real_ else if (is.character(lim)) { c(1, length(lim)) + c(-1, 1) * if (axs == "i") 0.5 else lattice.getOption("axis.padding")$factor } else if (length(lim) == 2) { if (lim[1] > lim[2]) { ccall <- match.call() ccall$lim <- rev(lim) ans <- eval.parent(ccall) return(rev(ans)) } if (!missing(length) && !missing(prop)) stop("'length' and 'prop' cannot both be specified") if (length <= 0) stop("'length' must be positive") if (!missing(length)) { prop <- (as.numeric(length) - as.numeric(diff(lim)))/(2 * as.numeric(diff(lim))) } if (lim[1] == lim[2]) lim + 0.5 * c(-length, length) else { d <- diff(as.numeric(lim)) lim + prop * d * c(-1, 1) } } else { print(lim) stop("improper length of 'lim'") } } flexmix/R/multcomp.R0000644000176200001440000000366114757625043014135 0ustar liggesusers# # Copyright (C) 2004-2016 Friedrich Leisch # $Id: multcomp.R 5298 2025-02-26 14:50:01Z gruen $ # ###********************************************************* setGeneric("flxglht", function(model, linfct, ...) standardGeneric("flxglht")) setMethod("flxglht", signature(model="flexmix", linfct="character"), function(model, linfct, ...) { model <- refit(model) flxglht(model, linfct, ...) }) setMethod("flxglht", signature(model="FLXRoptim", linfct="character"), function(model, linfct, ...) { if (!requireNamespace("multcomp", quietly = TRUE)) { stop("install package multcomp to use this function") } if(length(model@components)>1) stop("Can currently handle only models with one response!\n") type <- match.arg(linfct, c("zero", "tukey")) k <- model@k cf <- model@coef vc <- model@vcov nc <- rownames(model@components[[1]][[1]]) nc <- as.vector(outer(paste("model.1_Comp.", 1:k, "_coef.", sep=""), nc, paste, sep="")) ## FIXME: for zero-inflated models some components are missing nc <- nc[nc %in% names(cf)] cf <- cf[nc] vc <- vc[nc, nc] nc <- sub("model.1_Comp.(.*)_coef.", "C\\1.", nc) names(cf) <- colnames(vc) <- rownames(vc) <- nc if(type=="zero"){ linfct <- diag(length(cf)) rownames(linfct) <- nc } else{ k <- length(cf)/length(rownames(model@components[[1]][[1]])) p <- length(cf) / k tmp <- rep(3, k) Ktmp <- multcomp::contrMat(tmp, "Tukey") linfct <- kronecker(diag(p), Ktmp) colnames(linfct) <- names(cf) rownames(linfct) <- 1:nrow(linfct) for (i in 1:nrow(linfct)) rownames(linfct)[i] <- paste(colnames(linfct)[linfct[i,] == 1], colnames(linfct)[linfct[i,] == -1], sep = "-") } multcomp::glht(multcomp::parm(coef = cf, vcov = vc), linfct = linfct, ...) }) flexmix/R/multinom.R0000644000176200001440000000340114404637304014121 0ustar liggesuserssetClass("FLXMRmultinom", contains = "FLXMRglm") FLXMRmultinom <- function(formula=.~., ...) { z <- new("FLXMRmultinom", weighted=TRUE, formula=formula, family = "multinom", name=paste("FLXMRglm", "multinom", sep=":")) z@preproc.y <- function(x){ x <- as.integer(factor(x)) if (min(x) < 1 | length(unique(x)) != max(x)) stop("x needs to be coercible to an integer vector containing all numbers from 1 to max(x)") y <- matrix(0, nrow = length(x), ncol = max(x)) y[cbind(seq_along(x), x)] <- 1 y } z@defineComponent <- function(para) { predict <- function(x) { p <- tcrossprod(x, para$coef) eta <- cbind(1, exp(p)) eta/rowSums(eta) } logLik <- function(x, y) { log(predict(x))[cbind(seq_len(nrow(y)), max.col(y, "first"))] } new("FLXcomponent", parameters=list(coef=para$coef), logLik=logLik, predict=predict, df=para$df) } z@fit <- function(x, y, w, component){ r <- ncol(x) p <- ncol(y) if (p < 2) stop("Multinom requires at least two components.") mask <- c(rep(0, r + 1), rep(c(0, rep(1, r)), p - 1)) fit <- nnet.default(x, y, w, mask = mask, size = 0, skip = TRUE, softmax = TRUE, censored = FALSE, rang = 0, trace=FALSE, ...) fit$coefnames <- colnames(x) fit$weights <- w fit$vcoefnames <- fit$coefnames[seq_len(ncol(x))] fit$lab <- seq_len(ncol(y)) class(fit) <- c("multinom", "nnet") coef <- coef(fit) z@defineComponent(list(coef = coef, df = length(coef))) } z } setMethod("existGradient", signature(object = "FLXMRmultinom"), function(object) FALSE) flexmix/vignettes/0000755000176200001440000000000014757625373013761 5ustar liggesusersflexmix/vignettes/mymclust.R0000644000176200001440000000205314404637307015746 0ustar liggesusersmymclust <- function (formula = .~., diagonal = TRUE) { retval <- new("FLXMC", weighted = TRUE, formula = formula, dist = "mvnorm", name = "my model-based clustering") retval@defineComponent <- function(para) { logLik <- function(x, y) { mvtnorm::dmvnorm(y, mean = para$center, sigma = para$cov, log = TRUE) } predict <- function(x) { matrix(para$center, nrow = nrow(x), ncol = length(para$center), byrow = TRUE) } new("FLXcomponent", parameters = list(center = para$center, cov = para$cov), df = para$df, logLik = logLik, predict = predict) } retval@fit <- function(x, y, w, ...) { para <- cov.wt(y, wt = w)[c("center", "cov")] df <- (3 * ncol(y) + ncol(y)^2)/2 if (diagonal) { para$cov <- diag(diag(para$cov)) df <- 2 * ncol(y) } retval@defineComponent(c(para, df = df)) } retval } flexmix/vignettes/mixture-regressions.Rnw0000644000176200001440000022017614404637307020504 0ustar liggesusers% % Copyright (C) 2008 Bettina Gruen and Friedrich Leisch % $Id: mixture-regressions.Rnw $ % \documentclass[nojss]{jss} \usepackage{amsfonts} \title{FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters} \Plaintitle{FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters} \Shorttitle{FlexMix Version 2} \author{Bettina Gr{\"u}n\\ Wirtschaftsuniversit{\"a}t Wien \And Friedrich Leisch\\ Universit\"at f\"ur Bodenkultur Wien} \Plainauthor{Bettina Gr{\"u}n, Friedrich Leisch} \Address{ Bettina Gr\"un\\ Institute for Statistics and Mathematics\\ Wirtschaftsuniversit{\"a}t Wien\\ Welthandelsplatz 1\\ 1020 Wien, Austria\\ E-mail: \email{Bettina.Gruen@R-project.org}\\ Friedrich Leisch\\ Institut f\"ur Angewandte Statistik und EDV\\ Universit\"at f\"ur Bodenkultur Wien\\ Peter Jordan Stra\ss{}e 82\\ 1190 Wien, Austria\\ E-mail: \email{Friedrich.Leisch@boku.ac.at} } \Abstract{ This article is a (slightly) modified version of \cite{mixtures:Gruen+Leisch:2008a}, published in the \emph{Journal of Statistical Software}. \pkg{flexmix} provides infrastructure for flexible fitting of finite mixture models in \proglang{R} using the expectation-maximization (EM) algorithm or one of its variants. The functionality of the package was enhanced. Now concomitant variable models as well as varying and constant parameters for the component specific generalized linear regression models can be fitted. The application of the package is demonstrated on several examples, the implementation described and examples given to illustrate how new drivers for the component specific models and the concomitant variable models can be defined. } \Keywords{\proglang{R}, finite mixture models, generalized linear models, concomitant variables} \Plainkeywords{R, finite mixture models, generalized linear models, concomitant variables} \usepackage{amsmath, listings} \def\argmax{\mathop{\rm arg\,max}} %% \usepackage{Sweave} prevent automatic inclusion \SweaveOpts{width=9, height=4.5, eps=FALSE, keep.source=TRUE} <>= options(width=60, prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE) library("graphics") library("stats") library("flexmix") library("lattice") ltheme <- canonical.theme("postscript", FALSE) lattice.options(default.theme=ltheme) data("NPreg", package = "flexmix") data("dmft", package = "flexmix") source("myConcomitant.R") @ %%\VignetteIndexEntry{FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters} %%\VignetteDepends{flexmix} %%\VignetteKeywords{R, finite mixture models, model based clustering, latent class regression} %%\VignettePackage{flexmix} \begin{document} %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Introduction}\label{sec:introduction} Finite mixture models are a popular technique for modelling unobserved heterogeneity or to approximate general distribution functions in a semi-parametric way. They are used in a lot of different areas such as astronomy, biology, economics, marketing or medicine. An overview on mixture models is given in \cite{mixtures:Everitt+Hand:1981}, \cite{mixtures:Titterington+Smith+Makov:1985}, \cite{mixtures:McLachlan+Basford:1988}, \cite{mixtures:Boehning:1999}, \cite{mixtures:McLachlan+Peel:2000} and \cite{mixtures:Fruehwirth-Schnatter:2006}. Version 1 of \proglang{R} package \pkg{flexmix} was introduced in \cite{mixtures:Leisch:2004}. The main design principles of the package are extensibility and fast prototyping for new types of mixture models. It uses \proglang{S}4 classes and methods \citep{mixtures:Chambers:1998} as implemented in the \proglang{R} package \pkg{methods} and exploits advanced features of \proglang{R} such as lexical scoping \citep{mixtures:Gentleman+Ihaka:2000}. The package implements a framework for maximum likelihood estimation with the expectation-maximization (EM) algorithm \citep{mixtures:Dempster+Laird+Rubin:1977}. The main focus is on finite mixtures of regression models and it allows for multiple independent responses and repeated measurements. The EM algorithm can be controlled through arguments such as the maximum number of iterations or a minimum improvement in the likelihood to continue. Newly introduced features in the current package version are concomitant variable models \citep{mixtures:Dayton+Macready:1988} and varying and constant parameters in the component specific regressions. Varying parameters follow a finite mixture, i.e., several groups exist in the population which have different parameters. Constant parameters are fixed for the whole population. This model is similar to mixed-effects models \citep{mixtures:Pinheiro+Bates:2000}. The main difference is that in this application the distribution of the varying parameters is unknown and has to be estimated. Thus the model is actually closer to the varying-coefficients modelling framework \citep{mixtures:Hastie+Tibshirani:1993}, using convex combinations of discrete points as functional form for the varying coefficients. The extension to constant and varying parameters allows for example to fit varying intercept models as given in \cite{mixtures:Follmann+Lambert:1989} and \cite{mixtures:Aitkin:1999}. These models are frequently applied to account for overdispersion in the data where the components follow either a binomial or Poisson distribution. The model was also extended to include nested varying parameters, i.e.~this allows to have groups of components with the same parameters \citep{mixtures:Gruen+Leisch:2006, mixtures:Gruen:2006}. In Section~\ref{sec:model-spec-estim} the extended model class is presented together with the parameter estimation using the EM algorithm. In Section~\ref{sec:using-new-funct} examples are given to demonstrate how the new functionality can be used. An overview on the implementational details is given in Section~\ref{sec:implementation}. The new model drivers are presented and changes made to improve the flexibility of the software and to enable the implementation of the new features are discussed. Examples for writing new drivers for the component specific models and the concomitant variable models are given in Section~\ref{sec:writing-your-own}. This paper gives a short overview on finite mixtures and the package in order to be self-contained. A more detailed introduction to finite mixtures and the package \pkg{flexmix} can be found in \cite{mixtures:Leisch:2004}. All computations and graphics in this paper have been done with \pkg{flexmix} version \Sexpr{packageDescription("flexmix",fields="Version")} and \proglang{R} version \Sexpr{getRversion()} using Sweave \citep{mixtures:Leisch:2002}. The newest release version of \pkg{flexmix} is always available from the Comprehensive \proglang{R} Archive Network at \url{http://CRAN.R-project.org/package=flexmix}. An up-to-date version of this paper is contained in the package as a vignette, giving full access to the \proglang{R} code behind all examples shown below. See \code{help("vignette")} or \cite{mixtures:Leisch:2003} for details on handling package vignettes. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Model specification and estimation}\label{sec:model-spec-estim} A general model class of finite mixtures of regression models is considered in the following. The mixture is assumed to consist of $K$ components where each component follows a parametric distribution. Each component has a weight assigned which indicates the a-priori probability for an observation to come from this component and the mixture distribution is given by the weighted sum over the $K$ components. If the weights depend on further variables, these are referred to as concomitant variables. In marketing choice behaviour is often modelled in dependence of marketing mix variables such as price, promotion and display. Under the assumption that groups of respondents with different price, promotion and display elasticities exist mixtures of regressions are fitted to model consumer heterogeneity and segment the market. Socio-demographic variables such as age and gender have often been shown to be related to the different market segments even though they generally do not perform well when used to a-priori segment the market. The relationships between the behavioural and the socio-demographic variables is then modelled through concomitant variable models where the group sizes (i.e.~the weights of the mixture) depend on the socio-demographic variables. The model class is given by \begin{align*} h(y|x, w, \psi) &= \sum_{k = 1}^K \pi_k(w, \alpha) f_k(y|x,\theta_{k})\\ &= \sum_{k = 1}^K \pi_k(w, \alpha) \prod_{d=1}^D f_{kd}(y_d|x_d,\theta_{kd}), \end{align*} where $\psi$ denotes the vector of all parameters for the mixture density $h()$ and is given by $(\alpha, (\theta_k)_{k=1,\ldots,K})$. $y$ denotes the response, $x$ the predictor and $w$ the concomitant variables. $f_k$ is the component specific density function. Multivariate variables $y$ are assumed to be dividable into $D$ subsets where the component densities are independent between the subsets, i.e.~the component density $f_k$ is given by a product over $D$ densities which are defined for the subset variables $y_d$ and $x_d$ for $d=1,\ldots,D$. The component specific parameters are given by $\theta_k = (\theta_{kd})_{d=1,\ldots,D}$. Under the assumption that $N$ observations are available the dimensions of the variables are given by $y = (y_d)_{d=1,\ldots,D} \in \mathbb{R}^{N \times \sum_{d=1}^D k_{yd}}$, $x = (x_d)_{d=1,\ldots,D} \in \mathbb{R}^{N \times \sum_{d=1}^D k_{xd}}$ for all $d = 1,\ldots,D$ and $w \in \mathbb{R}^{N \times k_w}$. In this notation $k_{yd}$ denotes the dimension of the $d^{\textrm{th}}$ response, $k_{xd}$ the dimension of the $d^{\textrm{th}}$ predictors and $k_w$ the dimension of the concomitant variables. For mixtures of GLMs each of the $d$ responses will in general be univariate, i.e.~multivariate responses will be conditionally independent given the segment memberships. For the component weights $\pi_k$ it holds $\forall w$ that \begin{equation}\label{eq:prior} \sum_{k=1}^K \pi_k(w,\alpha) = 1 \quad \textrm{and} \quad \pi_k(w, \alpha) > 0, \, \forall k, \end{equation} where $\alpha$ are the parameters of the concomitant variable model. For the moment focus is given to finite mixtures where the component specific densities are from the same parametric family, i.e.~$f_{kd} \equiv f_d$ for notational simplicity. If $f_d$ is from the exponential family of distributions and for each component a generalized linear model is fitted \citep[GLMs;][]{mixtures:McCullagh+Nelder:1989} these models are also called GLIMMIX models \citep{mixtures:Wedel+DeSarbo:1995}. In this case the component specific parameters are given by $\theta_{kd} = (\beta'_{kd}, \phi_{kd})$ where $\beta_{kd}$ are the regression coefficients and $\phi_{kd}$ is the dispersion parameter. The component specific parameters $\theta_{kd}$ are either restricted to be equal over all components, to vary between groups of components or to vary between all components. The varying between groups is referred to as varying parameters with one level of nesting. A disjoint partition $K_c$, $c = 1,\ldots,C$ of the set $\tilde{K} := \{1\ldots,K\}$ is defined for the regression coefficients. $C$ is the number of groups of the regression coefficients at the nesting level. The regression coefficients are accordingly split into three groups: \begin{align*} \beta_{kd} &= (\beta'_{1d}, \beta'_{2,c(k)d}, \beta'_{3,kd})', \end{align*} where $c(k) = \{c = 1,\ldots, C: k \in K_c\}$. Similar a disjoint partition $K_v$, $v = 1,\ldots,V$, of $\tilde{K}$ can be defined for the dispersion parameters if nested varying parameters are present. $V$ denotes the number of groups of the dispersion parameters at the nesting level. This gives: \begin{align*} \phi_{kd} &= \left\{\begin{array}{ll} \phi_{d} & \textrm{for constant parameters}\\ \phi_{kd} & \textrm{for varying parameters}\\ \phi_{v(k)d} & \textrm{for nested varying parameters} \end{array}\right. \end{align*} where $v(k) = \{v = 1,\ldots,V: k \in K_v\}$. The nesting structure of the component specific parameters is also described in \cite{mixtures:Gruen+Leisch:2006}. Different concomitant variable models are possible to determine the component weights \citep{mixtures:Dayton+Macready:1988}. The mapping function only has to fulfill condition \eqref{eq:prior}. In the following a multinomial logit model is assumed for the $\pi_k$ given by \begin{equation*} \pi_k(w,\alpha) = \frac{e^{w'\alpha_k}}{\sum_{u = 1}^K e^{w'\alpha_u}} \quad \forall k, \end{equation*} with $\alpha = (\alpha'_k)'_{k=1,\ldots,K}$ and $\alpha_1 \equiv 0$. %%------------------------------------------------------------------------- \subsection{Parameter estimation}\label{sec:estimation} The EM algorithm \citep{mixtures:Dempster+Laird+Rubin:1977} is the most common method for maximum likelihood estimation of finite mixture models where the number of components $K$ is fixed. The EM algorithm applies a missing data augmentation scheme. It is assumed that a latent variable $z_n \in \{0,1\}^K$ exists for each observation $n$ which indicates the component membership, i.e.~$z_{nk}$ equals 1 if observation $n$ comes from component $k$ and 0 otherwise. Furthermore it holds that $\sum_{k=1}^K z_{nk}=1$ for all $n$. In the EM algorithm these unobserved component memberships $z_{nk}$ of the observations are treated as missing values and the data is augmented by estimates of the component membership, i.e.~the estimated a-posteriori probabilities $\hat{p}_{nk}$. For a sample of $N$ observations $\{(y_1, x_1, w_1), \ldots, (y_N, x_N, w_N)\}$ the EM algorithm is given by: \begin{description} \item[E-step:] Given the current parameter estimates $\psi^{(i)}$ in the $i$-th iteration, replace the missing data $z_{nk}$ by the estimated a-posteriori probabilities \begin{align*} \hat{p}_{nk} & = \frac{\displaystyle \pi_k(w_n, \alpha^{(i)}) f(y_n| x_n, \theta_k^{(i)}) }{\displaystyle \sum_{u = 1}^K \pi_u(w_n, \alpha^{(i)}) f(y_n |x_n, \theta_u^{(i)}) }. \end{align*} \item[M-step:] Given the estimates for the a-posteriori probabilities $\hat{p}_{nk}$ (which are functions of $\psi^{(i)}$), obtain new estimates $\psi^{(i+1)}$ of the parameters by maximizing \begin{align*} Q(\psi^{(i+1)}|\psi^{(i)}) &= Q_1(\theta^{(i+1)} | \psi^{(i)}) + Q_2(\alpha^{(i+1)} | \psi^{(i)}), \end{align*} where \begin{align*} Q_1(\theta^{(i+1)} | \psi^{(i)}) &= \sum_{n = 1}^N \sum_{k = 1}^K \hat{p}_{nk} \log(f(y_n | x_n, \theta_k^{(i+1)})) \end{align*} and \begin{align*} Q_2(\alpha^{(i+1)}| \psi^{(i)}) &= \sum_{n = 1}^N \sum_{k = 1}^K \hat{p}_{nk} \log(\pi_k(w_n, \alpha^{(i+1)})). \end{align*} $Q_1$ and $Q_2$ can be maximized separately. The maximization of $Q_1$ gives new estimates $\theta^{(i+1)}$ and the maximization of $Q_2$ gives $\alpha^{(i+1)}$. $Q_1$ is maximized separately for each $d=1,\ldots,D$ using weighted ML estimation of GLMs and $Q_2$ using weighted ML estimation of multinomial logit models. \end{description} Different variants of the EM algorithm exist such as the stochastic EM \citep[SEM;][]{mixtures:Diebolt+Ip:1996} or the classification EM \citep[CEM;][]{mixtures:Celeux+Govaert:1992}. These two variants are also implemented in package \pkg{flexmix}. For both variants an additional step is made between the expectation and maximization steps. This step uses the estimated a-posteriori probabilities and assigns each observation to only one component, i.e.~classifies it into one component. For SEM this assignment is determined in a stochastic way while it is a deterministic assignment for CEM. For the SEM algorithm the additional step is given by: \begin{description} \item[S-step:] Given the a-posteriori probabilities draw \begin{align*} \hat{z}_n &\sim \textrm{Mult}((\hat{p}_{nk})_{k=1,\ldots,K}, 1) \end{align*} where $\textrm{Mult}(\theta, T)$ denotes the multinomial distribution with success probabilities $\theta$ and number of trials $T$. \end{description} Afterwards, the $\hat{z}_{nk}$ are used instead of the $\hat{p}_{nk}$ in the M-step. For the CEM the additional step is given by: \begin{description} \item[C-step:] Given the a-posteriori probabilities define \begin{align*} \hat{z}_{nk} &= \left\{\begin{array}{ll} 1&\textrm{if } k = \min\{ l : \hat{p}_{nl} \geq \hat{p}_{nk}\, \forall k=1,\ldots,K\}\\ 0&\textrm{otherwise}. \end{array}\right. \end{align*} \end{description} Please note that in this step the observation is assigned to the component with the smallest index if the same maximum a-posteriori probability is observed for several components. Both of these variants have been proposed to improve the performance of the EM algorithm, because the ordinary EM algorithm tends to converge rather slowly and only to a local optimum. The convergence behavior can be expected to be better for the CEM than ordinary EM algorithm, while SEM can escape convergence to a local optimum. However, the CEM algorithm does not give ML estimates because it maximizes the complete likelihood. For SEM good approximations of the ML estimator are obtained if the parameters where the maximum likelihood was encountered are used as estimates. Another possibility for determining parameter estimates from the SEM algorithm could be the mean after discarding a suitable number of burn-ins. An implementational advantage of both variants is that no weighted maximization is necessary in the M-step. It has been shown that the values of the likelihood are monotonically increased during the EM algorithm. On the one hand this ensures the convergence of the EM algorithm if the likelihood is bounded, but on the other hand only the detection of a local maximum can be guaranteed. Therefore, it is recommended to repeat the EM algorithm with different initializations and choose as final solution the one with the maximum likelihood. Different initialization strategies for the EM algorithm have been proposed, as its convergence to the optimal solution depends on the initialization \citep{mixtures:Biernacki+Celeux+Govaert:2003,mixtures:Karlis+Xekalaki:2003}. Proposed strategies are for example to first make several runs of the SEM or CEM algorithm with different random initializations and then start the EM at the best solution encountered. The component specific parameter estimates can be determined separately for each $d=1,\ldots,D$. For simplicity of presentation the following description assumes $D=1$. If all parameter estimates vary between the component distributions they can be determined separately for each component in the M-step. However, if also constant or nested varying parameters are specified, the component specific estimation problems are not independent from each other any more. Parameters have to be estimated which occur in several or all components and hence, the parameters of the different components have to be determined simultaneously for all components. The estimation problem for all component specific parameters is then obtained by replicating the vector of observations $y = (y_n)_{n=1,\ldots,N}$ $K$ times and defining the covariate matrix $X = (X_{\textrm{constant}}, X_{\textrm{nested}}, X_{\textrm{varying}})$ by \begin{align*} &X_{\textrm{constant}} = \mathbf{1}_K \otimes (x'_{1,n})_{n=1,\ldots,N}\\ &X_{\textrm{nested}} = \mathbf{J} \odot (x'_{2,n})_{n=1,\ldots,N}\\ &X_{\textrm{varying}} = \mathbf{I}_K \otimes(x'_{3,n})_{n=1,\ldots,N}, \end{align*} where $\mathbf{1}_K$ is a vector of 1s of length $K$, $\mathbf{J}$ is the incidence matrix for each component $k=1,\ldots,K$ and each nesting group $c \in C$ and hence is of dimension $K \times |C|$, and $\mathbf{I}_K$ is the identity matrix of dimension $K \times K$. $\otimes$ denotes the Kronecker product and $\odot$ the Khatri-Rao product (i.e., the column-wise Kronecker product). $x_{m,n}$ are the covariates of the corresponding coefficients $\beta_{m,.}$ for $m=1,2,3$. Please note that the weights used for the estimation are the a-posteriori probabilities which are stacked for all components, i.e.~a vector of length $N K$ is obtained. Due to the replication of data in the case of constant or nested varying parameters the amount of memory needed for fitting the mixture model to large datasets is substantially increased and it might be easier to fit only varying coefficients to these datasets. To overcome this problem it could be considered to implement special data structures in order to avoid storing the same data multiple times for large datasets. Before each M-step the average component sizes (over the given data points) are checked and components which are smaller than a given (relative) minimum size are omitted in order to avoid too small components where fitting problems might arise. This strategy has already been recommended for the SEM algorithm \citep{mixtures:Celeux+Diebolt:1988} because it allows to determine the suitable number of components in an automatic way given that the a-priori specified number of components is large enough. This recommendation is based on the assumption that the redundent components will be omitted during the estimation process if the algorithm is started with too many components. If omission of small components is not desired the minimum size required can be set to zero. All components will be then retained throughout the EM algorithm and a mixture with the number of components specified in the initialization will be returned. The algorithm is stopped if the relative change in the log-likelihood is smaller than a pre-specified $\epsilon$ or the maximum number of iterations is reached. For model selection different information criteria are available: AIC, BIC and ICL \citep[Integrated Complete Likelihood;][]{mixtures:Biernacki+Celeux+Govaert:2000}. They are of the form twice the negative loglikelihood plus number of parameters times $k$ where $k=2$ for the AIC and $k$ equals the logarithm of the number of observations for the BIC. The ICL is the same as the BIC except that the complete likelihood (where the missing class memberships are replaced by the assignments induced by the maximum a-posteriori probabilities) instead of the likelihood is used. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Using the new functionality} \label{sec:using-new-funct} In the following model fitting and model selection in \proglang{R} is illustrated on several examples including mixtures of Gaussian, binomial and Poisson regression models, see also \cite{mixtures:Gruen:2006} and \cite{mixtures:Gruen+Leisch:2007a}. More examples for mixtures of GLMs are provided as part of the software package through a collection of artificial and real world datasets, most of which have been previously used in the literature (see references in the online help pages). Each dataset can be loaded to \proglang{R} with \code{data("}\textit{name}\code{")} and the fitting of the proposed models can be replayed using \code{example("}\textit{name}\code{")}. Further details on these examples are given in a user guide which can be accessed using \code{vignette("regression-examples", package="flexmix")} from within \proglang{R}. %%----------------------------------------------------------------------- \subsection{Artificial example}\label{sec:artificial-example} In the following the artificial dataset \code{NPreg} is used which has already been used in \cite{mixtures:Leisch:2004} to illustrate the application of package \pkg{flexmix}. The data comes from two latent classes of size \Sexpr{nrow(NPreg)/2} each and for each of the classes the data is drawn with respect to the following structure: \begin{center} \begin{tabular}{ll} Class~1: & $ \mathit{yn} = 5x+\epsilon$\\ Class~2: & $ \mathit{yn} = 15+10x-x^2+\epsilon$ \end{tabular} \end{center} with $\epsilon\sim N(0,9)$, see the left panel of Figure~\ref{fig:npreg}. The dataset \code{NPreg} also includes a response $\mathit{yp}$ which is given by a generalized linear model following a Poisson distribution and using the logarithm as link function. The parameters of the mean are given for the two classes by: \begin{center} \begin{tabular}{ll} Class~1: & $ \mu_1 = 2 - 0.2x$\\ Class~2: & $ \mu_2 = 1 + 0.1x$. \end{tabular} \end{center} This signifies that given $x$ the response $\mathit{yp}$ in group $k$ follows a Poisson distribution with mean $e^{\mu_k}$, see the right panel of Figure~\ref{fig:npreg}. \setkeys{Gin}{width=\textwidth} \begin{figure} \centering <>= par(mfrow=c(1,2)) plot(yn~x, col=class, pch=class, data=NPreg) plot(yp~x, col=class, pch=class, data=NPreg) @ \caption{Standard regression example (left) and Poisson regression (right).} \label{fig:npreg} \end{figure} This model can be fitted in \proglang{R} using the commands: <<>>= suppressWarnings(RNGversion("3.5.0")) set.seed(1802) library("flexmix") data("NPreg", package = "flexmix") Model_n <- FLXMRglm(yn ~ . + I(x^2)) Model_p <- FLXMRglm(yp ~ ., family = "poisson") m1 <- flexmix(. ~ x, data = NPreg, k = 2, model = list(Model_n, Model_p), control = list(verbose = 10)) @ If the dimensions are independent the component specific model for multivariate observations can be specified as a list of models for each dimension. The estimation can be controlled with the \code{control} argument which is specified with an object of class \code{"FLXcontrol"}. For convenience also a named list can be provided which is used to construct and set the respective slots of the \code{"FLXcontrol"} object. Elements of the control object are \code{classify} to select ordinary EM, CEM or SEM, \code{minprior} for the minimum relative size of components, \code{iter.max} for the maximum number of iterations and \code{verbose} for monitoring. If \code{verbose} is a positive integer the log-likelihood is reported every \code{verbose} iterations and at convergence together with the number of iterations made. The default is to not report any log-likelihood information during the fitting process. The estimated model \code{m1} is of class \code{"flexmix"} and the result of the default plot method for this class is given in Figure~\ref{fig:root1}. This plot method uses package \pkg{lattice} \citep{mixtures:Sarkar:2008} and the usual parameters can be specified to alter the plot, e.g.~the argument \code{layout} determines the arrangement of the panels. The returned object is of class \code{"trellis"} and the plotting can also be influenced by the arguments of its show method. The default plot prints rootograms (i.e., a histogram of the square root of counts) of the a-posteriori probabilities of each observation separately for each component. For each component the observations with a-posteriori probabilities less than a pre-specified $\epsilon$ (default is $10^{-4}$) for this component are omitted in order to avoid that the bar at zero dominates the plot \citep{mixtures:Leisch:2004a}. Please note that the labels of the y-axis report the number of observations in each bar, i.e.~the squared values used for the rootograms. \begin{figure} \centering <>= print(plot(m1)) @ \caption{The plot method for \code{"flexmix"} objects, here obtained by \code{plot(m1)}, shows rootograms of the posterior class probabilities.} \label{fig:root1} \end{figure} More detailed information on the estimated parameters with respect to standard deviations and significance tests can be obtained with function \code{refit()}. This function determines the variance-covariance matrix of the estimated parameters by using the inverted negative Hesse matrix as computed by the general purpose optimizer \code{optim()} on the full likelihood of the model. \code{optim()} is initialized in the solution obtained with the EM algorithm. For mixtures of GLMs we also implemented the gradient, which speeds up convergence and gives more precise estimates of the Hessian. Naturally, function \code{refit()} will also work for models which have been determined by applying some model selection strategy depending on the data (AIC, BIC, \ldots). The same caution is necessary as when using \code{summary()} on standard linear models selected using \code{step()}: The p-values shown are not correct because they have not been adjusted for the fact that the same data are used to select the model and compute the p-values. So use them only in an exploratory manner in this context, see also \cite{mixtures:Harrell:2001} for more details on the general problem. The returned object can be inspected using \code{summary()} with arguments \code{which} to specify if information for the component model or the concomitant variable model should be shown and \code{model} to indicate for which dimension of the component models this should be done. Selecting \code{model=1} gives the parameter estimates for the dimension where the response variable follows a Gaussian distribution. <<>>= m1.refit <- refit(m1) summary(m1.refit, which = "model", model = 1) @ \begin{figure} \centering <>= print(plot(m1.refit, layout = c(1,3), bycluster = FALSE, main = expression(paste(yn *tilde(" ")* x + x^2))), split= c(1,1,2,1), more = TRUE) print(plot(m1.refit, model = 2, main = expression(paste(yp *tilde(" ")* x)), layout = c(1,2), bycluster = FALSE), split = c(2,1,2,1)) @ \caption{The default plot for refitted \code{"flexmix"} objects, here obtained by \code{plot(refit(m1), model = 1)} and \code{plot(refit(m1), model = 2)}, shows the coefficient estimates and their confidence intervals.} \label{fig:refit} \end{figure} The default plot method for the refitted \code{"flexmix"} object depicts the estimated coefficients with corresponding confidence intervals and is given in Figure~\ref{fig:refit}. It can be seen that for the first model the confidence intervals of the coefficients of the intercept and the quadratic term of \code{x} overlap with zero. A model where these coefficients are set to zero can be estimated with the model driver function \code{FLXMRglmfix()} and the following commands for specifying the nesting structure. The argument \code{nested} needs input for the number of components in each group (given by \code{k}) and the formula which determines the model matrix for the nesting (given by \code{formula}). This information can be provided in a named list. For the restricted model the element \code{k} is a vector with two 1s because each of the components has different parameters. The formulas specifying the model matrices of these coefficients are \verb/~ 1 + I(x^2)/ for an intercept and a quadratic term of $x$ for component 1 and \code{~ 0} for no additional coefficients for component 2. The EM algorithm is initialized in the previously fitted model by passing the posterior probabilities in the argument \code{cluster}. <<>>= Model_n2 <- FLXMRglmfix(yn ~ . + 0, nested = list(k = c(1, 1), formula = c(~ 1 + I(x^2), ~ 0))) m2 <- flexmix(. ~ x, data = NPreg, cluster = posterior(m1), model = list(Model_n2, Model_p)) m2 @ Model selection based on the BIC would suggest the smaller model which also corresponds to the true underlying model. <<>>= c(BIC(m1), BIC(m2)) @ %%----------------------------------------------------------------------- \subsection{Beta-blockers dataset} \label{sec:beta-blockers} The dataset is analyzed in \cite{mixtures:Aitkin:1999, mixtures:Aitkin:1999a} using a finite mixture of binomial regression models. Furthermore, it is described in \citet[p.~165]{mixtures:McLachlan+Peel:2000}. The dataset is from a 22-center clinical trial of beta-blockers for reducing mortality after myocardial infarction. A two-level model is assumed to represent the data, where centers are at the upper level and patients at the lower level. The data is illustrated in Figure~\ref{fig:beta}. First, the center information is ignored and a binomial logit regression model with treatment as covariate is fitted using \code{glm}, i.e.~$K=1$ and it is assumed that the different centers are comparable: <<>>= data("betablocker", package = "flexmix") betaGlm <- glm(cbind(Deaths, Total - Deaths) ~ Treatment, family = "binomial", data = betablocker) betaGlm @ The residual deviance suggests that overdispersion is present in the data. In the next step the intercept is allowed to follow a mixture distribution given the centers. This signifies that the component membership is fixed for each center. This grouping is specified in \proglang{R} by adding \code{| Center} to the formula similar to the notation used in \pkg{nlme} \citep{mixtures:Pinheiro+Bates:2000}. Under the assumption of homogeneity within centers identifiability of the model class can be ensured as induced by the sufficient conditions for identifability given in \cite{mixtures:Follmann+Lambert:1991} for binomial logit models with varying intercepts and \cite{mixtures:Gruen+Leisch:2008} for multinomial logit models with varying and constant parameters. In order to determine the suitable number of components, the mixture is fitted with different numbers of components. <<>>= betaMixFix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, model = FLXMRglmfix(family = "binomial", fixed = ~ Treatment), k = 2:4, nrep = 5, data = betablocker) @ The returned object is of class \code{"stepFlexmix"} and printing the object gives the information on the number of iterations until termination of the EM algorithm, a logical indicating if the EM algorithm has converged, the log-likelihood and some model information criteria. The plot method compares the fitted models using the different model information criteria. <<>>= betaMixFix @ A specific \code{"flexmix"} model contained in the \code{"stepFlexmix"} object can be selected using \code{getModel()} with argument \code{which} to specify the selection criterion. The best model with respect to the BIC is selected with: <<>>= betaMixFix_3 <- getModel(betaMixFix, which = "BIC") betaMixFix_3 <- relabel(betaMixFix_3, "model", "Intercept") @ The components of the selected model are ordered with respect to the estimated intercept values. In this case a model with three components is selected with respect to the BIC. The fitted values for the model with three components are given in Figure~\ref{fig:beta} separately for each component and the treatment and control groups. The fitted parameters of the component specific models can be accessed with: <<>>= parameters(betaMixFix_3) @ Please note that the coefficients of variable \code{Treatment} are the same for all three components. \begin{figure} \centering <>= library("grid") betablocker$Center <- with(betablocker, factor(Center, levels = Center[order((Deaths/Total)[1:22])])) clusters <- factor(clusters(betaMixFix_3), labels = paste("Cluster", 1:3)) print(dotplot(Deaths/Total ~ Center | clusters, groups = Treatment, as.table = TRUE, data = betablocker, xlab = "Center", layout = c(3, 1), scales = list(x = list(cex = 0.7, tck = c(1, 0))), key = simpleKey(levels(betablocker$Treatment), lines = TRUE, corner = c(1,0)))) betaMixFix.fitted <- fitted(betaMixFix_3) for (i in 1:3) { seekViewport(trellis.vpname("panel", i, 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[1:22, i], "native"), gp = gpar(lty = 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[23:44, i], "native"), gp = gpar(lty = 2)) } @ \setkeys{Gin}{width=0.8\textwidth} \caption{Relative number of deaths for the treatment and the control group for each center in the beta-blocker dataset. The centers are sorted by the relative number of deaths in the control group. The lines indicate the fitted values for each component of the 3-component mixture model with varying intercept and constant parameters for treatment.} \label{fig:beta} \end{figure} The variable \code{Treatment} can also be included in the varying part of the model. This signifies that a mixture distribution is assumed where for each component different values are allowed for the intercept and the treatment coefficient. This mixture distribution can be specified using function \code{FLXMRglm()}. Again it is assumed that the heterogeneity is only between centers and therefore the aggregated data for each center can be used. <<>>= betaMix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ Treatment | Center, model = FLXMRglm(family = "binomial"), k = 3, nrep = 5, data = betablocker) betaMix <- relabel(betaMix, "model", "Treatment") parameters(betaMix) c(BIC(betaMixFix_3), BIC(betaMix)) @ The difference between model \code{betaMix} and \code{betaMixFix\_3} is that the treatment coefficients are the same for all three components for \code{betaMixFix\_3} while they have different values for \code{betaMix} which can easily be seen when comparing the fitted component specific parameters. The larger model \code{betaMix} which also allows varying parameters for treatment has a higher BIC and therefore the smaller model \code{betaMixFix\_3} would be preferred. The default plot for \code{"flexmix"} objects gives a rootogram of the posterior probabilities for each component. Argument \code{mark} can be used to inspect with which components the specified component overlaps as all observations are coloured in the different panels which are assigned to this component based on the maximum a-posteriori probabilities. \begin{figure} \centering <>= print(plot(betaMixFix_3, nint = 10, mark = 1, col = "grey", layout = c(3, 1))) @ \caption{Default plot of \code{"flexmix"} objects where the observations assigned to the first component are marked.}\label{fig:default} \end{figure} \begin{figure} \centering <>= print(plot(betaMixFix_3, nint = 10, mark = 2, col = "grey", layout = c(3, 1))) @ \caption{Default plot of \code{"flexmix"} objects where the observations assigned to the third component are marked.}\label{fig:default-2} \end{figure} The rootogram indicates that the components are well separated. In Figure~\ref{fig:default} it can be seen that component 1 is completely separated from the other two components, while Figure~\ref{fig:default-2} shows that component 2 has a slight overlap with both other components. The cluster assignments using the maximum a-posteriori probabilities are obtained with: <<>>= table(clusters(betaMix)) @ The estimated probabilities of death for each component for the treated patients and those in the control group can be obtained with: <<>>= predict(betaMix, newdata = data.frame(Treatment = c("Control", "Treated"))) @ or by obtaining the fitted values for two observations (e.g.~rows 1 and 23) with the desired levels of the predictor \code{Treatment} <<>>= betablocker[c(1, 23), ] fitted(betaMix)[c(1, 23), ] @ A further analysis of the model is possible with function \code{refit()} which returns the estimated coefficients together with the standard deviations, z-values and corresponding p-values. Please note that the p-values are only approximate in the sense that they have not been corrected for the fact that the data has already been used to determine the specific fitted model. <<>>= summary(refit(betaMix)) @ Given the estimated treatment coefficients we now also compare this model to a model where the treatment coefficient is assumed to be the same for components 1 and 2. Such a model is specified using the model driver \code{FLXMRglmfix()}. As the first two components are assumed to have the same coeffcients for treatment and for the third component the coefficient for treatment shall be set to zero the argument \code{nested} has \code{k = c(2,1)} and \code{formula = c(\~{}Treatment, \~{})}. <<>>= ModelNested <- FLXMRglmfix(family = "binomial", nested = list(k = c(2, 1), formula = c(~ Treatment, ~ 0))) betaMixNested <- flexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, model = ModelNested, k = 3, data = betablocker, cluster = posterior(betaMix)) parameters(betaMixNested) c(BIC(betaMix), BIC(betaMixNested), BIC(betaMixFix_3)) @ The comparison of the BIC values suggests that the nested model with the same treatment effect for two components and no treatment effect for the third component is the best. %%----------------------------------------------------------------------- \subsection[Productivity of Ph.D. students in biochemistry]{Productivity of Ph.D.~students in biochemistry} \label{sec:bioChemists} <>= data("bioChemists", package = "flexmix") @ This dataset is taken from \cite{mixtures:Long:1990}. It contains \Sexpr{nrow(bioChemists)} observations from academics who obtained their Ph.D.~degree in biochemistry in the 1950s and 60s. It includes \Sexpr{sum(bioChemists$fem=="Women")} women and \Sexpr{sum(bioChemists$fem=="Men")} men. The productivity was measured by counting the number of publications in scientific journals during the three years period ending the year after the Ph.D.~was received. In addition data on the productivity and the prestige of the mentor and the Ph.D.~department was collected. Two measures of family characteristics were recorded: marriage status and number of children of age 5 and lower by the year of the Ph.D. First, mixtures with one, two and three components and only varying parameters are fitted, and the model minimizing the BIC is selected. This is based on the assumption that unobserved heterogeneity is present in the data due to latent differences between the students in order to be productive and achieve publications. Starting with the most general model to determine the number of components using information criteria and checking for possible model restrictions after having the number of components fixed is a common strategy in finite mixture modelling \citep[see][]{mixtures:Wang+Puterman+Cockburn:1996}. Function \code{refit()} is used to determine confidence intervals for the parameters in order to choose suitable alternative models. However, it has to be noted that in the course of the procedure these confidence intervals will not be correct any more because the specific fitted models have already been determined using the same data. <<>>= data("bioChemists", package = "flexmix") Model1 <- FLXMRglm(family = "poisson") ff_1 <- stepFlexmix(art ~ ., data = bioChemists, k = 1:3, model = Model1) ff_1 <- getModel(ff_1, "BIC") @ The selected model has \Sexpr{ff_1@k} components. The estimated coefficients of the components are given in Figure~\ref{fig:coefficients-1} together with the corresponding 95\% confidence intervals using the plot method for objects returned by \code{refit()}. The plot shows that the confidence intervals of the parameters for \code{kid5}, \code{mar}, \code{ment} and \code{phd} overlap for the two components. In a next step a mixture with two components is therefore fitted where only a varying intercept and a varying coefficient for \code{fem} is specified and all other coefficients are constant. The EM algorithm is initialized with the fitted mixture model using \code{posterior()}. \begin{figure} \centering <>= print(plot(refit(ff_1), bycluster = FALSE, scales = list(x = list(relation = "free")))) @ \caption{Coefficient estimates and confidence intervals for the model with only varying parameters.}\label{fig:coefficients-1} \end{figure} <<>>= Model2 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment) ff_2 <- flexmix(art ~ fem + phd, data = bioChemists, cluster = posterior(ff_1), model = Model2) c(BIC(ff_1), BIC(ff_2)) @ If the BIC is used for model comparison the smaller model including only varying coefficients for the intercept and \code{fem} is preferred. The coefficients of the fitted model can be obtained using \code{refit()}: <<>>= summary(refit(ff_2)) @ It can be seen that the coefficient of \code{phd} does for both components not differ significantly from zero and might be omitted. This again improves the BIC. <<>>= Model3 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment) ff_3 <- flexmix(art ~ fem, data = bioChemists, cluster = posterior(ff_2), model = Model3) c(BIC(ff_2), BIC(ff_3)) @ The coefficients of the restricted model without \code{phd} are given in Figure~\ref{fig:coefficients-2}. \begin{figure}[t] \centering <>= print(plot(refit(ff_3), bycluster = FALSE, scales = list(x = list(relation = "free")))) @ \caption{Coefficient estimates and confidence intervals for the model with varying and constant parameters where the variable \code{phd} is not used in the regression.}\label{fig:coefficients-2} \end{figure} An alternative model would be to assume that gender does not directly influence the number of articles but has an impact on the segment sizes. <<>>= Model4 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment) ff_4 <- flexmix(art ~ 1, data = bioChemists, cluster = posterior(ff_2), concomitant = FLXPmultinom(~ fem), model = Model4) parameters(ff_4) summary(refit(ff_4), which = "concomitant") BIC(ff_4) @ This suggests that the proportion of women is lower in the second component which is the more productive segment. The alternative modelling strategy where homogeneity is assumed at the beginning and a varying interept is added if overdispersion is observed leads to the following model which is the best with respect to the BIC. <<>>= Model5 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + ment + fem) ff_5 <- flexmix(art ~ 1, data = bioChemists, cluster = posterior(ff_2), model = Model5) BIC(ff_5) @ \begin{figure} \centering \setkeys{Gin}{width=0.8\textwidth} <>= pp <- predict(ff_5, newdata = data.frame(kid5 = 0, mar = factor("Married", levels = c("Single", "Married")), fem = c("Men", "Women"), ment = mean(bioChemists$ment))) matplot(0:12, sapply(unlist(pp), function(x) dpois(0:12, x)), type = "b", lty = 1, xlab = "Number of articles", ylab = "Probability") legend("topright", paste("Comp.", rep(1:2, each = 2), ":", c("Men", "Women")), lty = 1, col = 1:4, pch = paste(1:4), bty = "n") @ \caption{The estimated productivity for each compoment for men and women.} \label{fig:estimated} \end{figure} \setkeys{Gin}{width=0.98\textwidth} In Figure~\ref{fig:estimated} the estimated distribution of productivity for model \code{ff\_5} are given separately for men and women as well as for each component where for all other variables the mean values are used for the numeric variables and the most frequent category for the categorical variables. The two components differ in that component 1 contains the students who publish no article or only a single article, while the students in component 2 write on average several articles. With a constant coefficient for gender women publish less articles than men in both components. This example shows that different optimal models are chosen for different modelling procedures. However, the distributions induced by the different variants of the model class may be similar and therefore it is not suprising that they then will have similar BIC values. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Implementation}\label{sec:implementation} The new features extend the available model class described in \cite{mixtures:Leisch:2004} by providing infrastructure for concomitant variable models and for fitting mixtures of GLMs with varying and constant parameters for the component specific parameters. The implementation of the extensions of the model class made it necessary to define a better class structure for the component specific models and to modify the fit functions \code{flexmix()} and \code{FLXfit()}. An overview on the \proglang{S}4 class structure of the package is given in Figure~\ref{fig:class structure}. There is a class for unfitted finite mixture distributions given by \code{"FLXdist"} which contains a list of \code{"FLXM"} objects which determine the component specific models, a list of \code{"FLXcomponent"} objects which specify functions to determine the component specific log-likelihoods and predictions and which contain the component specific parameters, and an object of class \code{"FLXP"} which specifies the concomitant variable model. Class \code{"flexmix"} extends \code{"FLXdist"}. It represents a fitted finite mixture distribution and it contains the information about the fitting with the EM algorithm in the object of class \code{"FLXcontrol"}. Repeated fitting with the EM algorithm with different number of components is provided by function \code{stepFlexmix()} which returns an object of class \code{"stepFlexmix"}. Objects of class \code{"stepFlexmix"} contain the list of the fitted mixture models for each number of components in the slot \code{"models"}. \setkeys{Gin}{width=.9\textwidth} \begin{figure}[t] \centering \includegraphics{flexmix} \caption{UML class diagram \citep[see][]{mixtures:Fowler:2004} of the \pkg{flexmix} package.} \label{fig:class structure} \end{figure} \setkeys{Gin}{width=\textwidth} For the component specific model a virtual class \code{"FLXM"} is introduced which (currently) has two subclasses: \code{"FLXMC"} for model-based clustering and \code{"FLXMR"} for clusterwise regression, where predictor variables are given. Additional slots have been introduced to allow for data preprocessing and the construction of the components was separated from the fit and is implemented using lexical scoping \citep{mixtures:Gentleman+Ihaka:2000} in the slot \code{defineComponent}. \code{"FLXMC"} has an additional slot \code{dist} to specify the name of the distribution of the variable. In the future functionality shall be provided for sampling from a fitted or unfitted finite mixture. Using this slot observations can be generated by using the function which results from adding an \code{r} at the beginnning of the distribution name. This allows to only implement the (missing) random number generator functions and otherwise use the same method for sampling from mixtures with component specific models of class \code{"FLXMC"}. For \code{flexmix()} and \code{FLXfit()} code blocks which are model dependent have been identified and different methods implemented. Finite mixtures of regressions with varying, nested and constant parameters were a suitable model class for this identification task as they are different from models previously implemented. The main differences are: \begin{itemize} \item The number of components is related to the component specific model and the omission of small components during the EM algorithm impacts on the model. \item The parameters of the component specific models can not be determined separately in the M-step and a joint model matrix is needed. \end{itemize} This makes it also necessary to have different model dependent methods for \code{fitted()} which extracts the fitted values from a \code{"flexmix"} object, \code{predict()} which predicts new values for a \code{"flexmix"} object and \code{refit()} which refits an estimated model to obtain additional information for a \code{"flexmix"} object. %%----------------------------------------------------------------------- \subsection{Component specific models with varying and constant parameters}\label{sec:comp-models-with} A new M-step driver is provided which fits finite mixtures of GLMs with constant and nested varying parameters for the coefficients and the dispersion parameters. The class \code{"FLXMRglmfix"} returned by the driver \code{FLXMRglmfix()} has the following additional slots with respect to \code{"FLXMRglm"}: \begin{description} \item[\code{design}:] An incidence matrix indicating which columns of the model matrix are used for which component, i.e.~$\mathbf{D}=(\mathbf{1}_K,\mathbf{J}, \mathbf{I}_K)$. \item[\code{nestedformula}:] An object of class \code{"FLXnested"} containing the formula for the nested regression coefficients and the number of components in each $K_c$, $c \in C$. \item[\code{fixed}:] The formula for the constant regression coefficients. \item[\code{variance}:] A logical indicating if different variances shall be estimated for the components following a Gaussian distribution or a vector specifying the nested structure for estimating these variances. \end{description} The difference between estimating finite mixtures including only varying parameters using models specified with \code{FLXMRglm()} and those with varying and constant parameters using function \code{FLXMRglmfix()} is hidden from the user, as only the specified model is different. The fitted model is also of class \code{"flexmix"} and can be analyzed using the same functions as for any model fitted using package \pkg{flexmix}. The methods used are the same except if the slot containing the model is accessed and method dispatching is made via the model class. New methods are provided for models of class \code{"FLXMRglmfix"} for functions \code{refit()}, \code{fitted()} and \code{predict()} which can be used for analyzing the fitted model. The implementation allows repeated measurements by specifying a grouping variable in the formula argument of \code{flexmix()}. Furthermore, it has to be noticed that the model matrix is determined by updating the formula of the varying parameters successively with the formula of the constant and then of the nested varying parameters. This ensures that if a mixture distribution is fitted for the intercept, the model matrix of a categorical variable includes only the remaining columns for the constant parameters to have full column rank. However, this updating scheme makes it impossible to estimate a constant intercept while allowing varying parameters for a categorical variable. For this model one big model matrix is constructed where the observations are repeated $K$ times and suitable columns of zero added. The coefficients of all $K$ components are determined simultaneously in the M-step, while if only varying parameters are specified the maximization of the likelihood is made separately for all components. For large datasets the estimation of a combination of constant and varying parameters might therefore be more challenging than only varying parameters. %% ----------------------------------------------------------------------- \subsection{Concomitant variable models}\label{sec:conc-vari-models} For representing concomitant variable models the class \code{"FLXP"} is defined. It specifies how the concomitant variable model is fitted using the concomitant variable model matrix as predictor variables and the current a-posteriori probability estimates as response variables. The object has the following slots: \begin{description} \item[\code{fit}:] A \code{function (x, y, ...)} returning the fitted values for the component weights during the EM algorithm. \item[\code{refit}:] A \code{function (x, y, ...)} used for refitting the model. \item[\code{df}:] A \code{function (x, k, ...)} returning the degrees of freedom used for estimating the concomitant variable model given the model matrix \code{x} and the number of components \code{k}. \item[\code{x}:] A matrix containing the model matrix of the concomitant variables. \item[\code{formula}:] The formula for determining the model matrix \code{x}. \item[\code{name}:] A character string describing the model, which is only used for print output. \end{description} Two constructor functions for concomitant variable models are provided at the moment. \code{FLXPconstant()} is for constant component weights without concomitant variables and for multinomial logit models \code{FLXPmultinom()} can be used. \code{FLXPmultinom()} has its own class \code{"FLXPmultinom"} which extends \code{"FLXP"} and has an additional slot \code{coef} for the fitted coefficients. The multinomial logit models are fitted using package \pkg{nnet} \citep{mixtures:Venables+Ripley:2002}. %%----------------------------------------------------------------------- \subsection{Further changes} The estimation of the model with the EM algorithm was improved by adapting the variants to correspond to the CEM and SEM variants as outlined in the literature. To make this more explicit it is now also possible to use \code{"CEM"} or \code{"SEM"} to specify an EM variant in the \code{classify} argument of the \code{"FLXcontrol"} object. Even though the SEM algorithm can in general not be expected to converge the fitting procedure is also terminated for the SEM algorithm if the change in the relative log-likelhood is smaller than the pre-specified threshold. This is motivated by the fact that for well separated clusters the posteriors might converge to an indicator function with all weight concentrated in one component. The fitted model with the maximum likelihood encountered during the SEM algorithm is returned. For discrete data in general multiple observations with the same values are given in a dataset. A \code{weights} argument was added to the fitting function \code{flexmix()} in order to avoid repeating these observations in the provided dataset. The specification is through a \code{formula} in order to allow selecting a column of the data frame given in the \code{data} argument. The weights argument allows to avoid replicating the same observations and hence enables more efficient memory use in these applications. This possibitliy is especially useful in the context of model-based clustering for mixtures of Poisson distributions or latent class analysis with multivariate binary observations. In order to be able to apply different initialization strategies such as for example first running several different random initializations with CEM and then switching to ordinary EM using the best solution found by CEM for initialization a \code{posterior()} function was implemented. \code{posterior()} also takes a \code{newdata} argument and hence, it is possible to apply subset strategies for large datasets as suggested in \cite{mixtures:Wehrens+Buydens+Fraley:2004}. The returned matrix of the posterior probabilities can be used to specify the \code{cluster} argument for \code{flexmix()} and the posteriors are then used as weights in the first M-step. The default plot methods now use trellis graphics as implemented in package \pkg{lattice} \citep{mixtures:Sarkar:2008}. Users familiar with the syntax of these graphics and with the plotting and printing arguments will find the application intuitive as a lot of plotting arguments are passed to functions from \pkg{lattice} as for example \code{xyplot()} and \code{histogram()}. In fact only new panel, pre-panel and group-panel functions were implemented. The returned object is of class \code{"trellis"} and the show method for this class is used to create the plot. Function \code{refit()} was modified and has now two different estimation methods: \code{"optim"} and \code{"mstep"}. The default method \code{"optim"} determines the variance-covariance matrix of the parameters from the inverse Hessian of the full log-likelihood. The general purpose optimizer \code{optim()} is used to maximize the log-likelihood and initialized in the solution obtained with the EM algorithm. For mixtures of GLMs there are also functions implemented to determine the gradient which can be used to speed up convergence. The second method \code{"mstep"} is only a raw approximation. It performs an M-step where the a-posteriori probabilities are treated as given instead of estimated and returns for the component specific models nearly complete \code{"glm"} objects which can be further analyzed. The advantage of this method is that the return value is basically a list of standard \code{"glm"} objects, such that the regular methods for this class can be used. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Writing your own drivers}\label{sec:writing-your-own} Two examples are given in the following to demonstrate how new drivers can be provided for concomitant variable models and for component specific models. Easy extensibility is one of the main implementation aims of the package and it can be seen that writing new drivers requires only a few lines of code for providing the constructor functions which include the fit functions. %%----------------------------------------------------------------------- \subsection{Component specific models: Zero-inflated models}\label{sec:component-models} \lstset{frame=trbl,basicstyle=\small\tt,stepnumber=5,numbers=left} In Poisson or binomial regression models it can be often encountered that the observed number of zeros is higher than expected. A mixture with two components where one has mean zero can be used to model such data. These models are also referred to as zero-inflated models \citep[see for example][]{mixtures:Boehning+Dietz+Schlattmann:1999}. A generalization of this model class would be to fit mixtures with more than two components where one component has a mean fixed at zero. So this model class is a special case of a mixture of generalized linear models where (a) the family is restricted to Poisson and binomial and (b) the parameters of one component are fixed. For simplicity the implementation assumes that the component with mean zero is the first component. In addition we assume that the model matrix contains an intercept and to have the first component absorbing the access zeros the coefficient of the intercept is set to $-\infty$ and all other coefficients are set to zero. Hence, to implement this model using package \pkg{flexmix} an appropriate model class is needed with a corresponding convenience function for construction. During the fitting of the EM algorithm using \code{flexmix()} different methods for this model class are needed when determining the model matrix (to check the presence of an intercept), to check the model after a component is removed and for the M-step to account for the fact that the coefficients of the first component are fixed. For all other methods those available for \code{"FLXMRglm"} can be re-used. The code is given in Figure~\ref{fig:ziglm.R}. \begin{figure} \centering \begin{minipage}{0.98\textwidth} \lstinputlisting{ziglm.R} \end{minipage} \caption{Driver for a zero-inflated component specific model.} \label{fig:ziglm.R} \end{figure} The model class \code{"FLXMRziglm"} is defined as extending \code{"FLXMRglm"} in order to be able to inherit methods from this model class. For construction of a \code{"FLXMRziglm"} class the convenicence function \code{FLXMRziglm()} is used which calls \code{FLXMRglm()}. The only differences are that the family is restricted to binomial or Poisson, that a different name is assigned and that an object of the correct class is returned. The presence of the intercept in the model matrix is checked in \code{FLXgetModelmatrix()} after using the method available for \code{"FLXMRglm"} models as indicated by the call to \code{callNextMethod()}. During the EM algorithm \code{FLXremoveComponent()} is called if one component is removed. For this model class it checks if the first component has been removed and if this is the case the model class is changed to \code{"FLXMRglm"}. In the M-step the coefficients of the first component are fixed and not estimated, while for the remaining components the M-step of \code{"FLXMRglm"} objects can be used. During the EM algorithm \code{FLXmstep()} is called to perform the M-step and returns a list of \code{"FLXcomponent"} objects with the fitted parameters. A new method for this function is needed for \code{"FLXMRziglm"} objects in order to account for the fixed coefficients in the first component, i.e.~for the first component the \code{"FLXcomponent"} object is constructed and concatenated with the list of \code{"FLXcomponent"} objects returned by using the \code{FLXmstep()} method for \code{"FLXMRglm"} models for the remaining components. Similar modifications are necessary in order to be able to use \code{refit()} for this model class. The code for implementing the \code{refit()} method using \code{optim()} for \code{"FLXMRziglm"} is not shown, but can be inspected in the source code of the package. \subsubsection{Example: Using the driver} This new M-step driver can be used to estimate a zero-inflated Poisson model to the data given in \cite{mixtures:Boehning+Dietz+Schlattmann:1999}. The dataset \code{dmft} consists of count data from a dental epidemiological study for evaluation of various programs for reducing caries collected among school children from an urban area of Belo Horizonte (Brazil). The variables included are the number of decayed, missing or filled teeth (DMFT index) at the beginning and at the end of the observation period, the gender, the ethnic background and the specific treatment for \Sexpr{nrow(dmft)} children. The model can be fitted with the new driver function using the following commands: <<>>= data("dmft", package = "flexmix") Model <- FLXMRziglm(family = "poisson") Fitted <- flexmix(End ~ log(Begin + 0.5) + Gender + Ethnic + Treatment, model = Model, k = 2 , data = dmft, control = list(minprior = 0.01)) summary(refit(Fitted)) @ Please note that \cite{mixtures:Boehning+Dietz+Schlattmann:1999} added the predictor \code{log(Begin + 0.5)} to serve as an offset in order to be able to analyse the improvement in the DMFT index from the beginning to the end of the study. The linear predictor with the offset subtracted is intended to be an estimate for $\log(\mathbb{E}(\textrm{End})) - \log(\mathbb{E}(\textrm{Begin}))$. This is justified by the fact that for a Poisson distributed variable $Y$ with mean between 1 and 10 it holds that $\mathbb{E}(\log(Y + 0.5))$ is approximately equal to $\log(\mathbb{E}(Y))$. $\log(\textrm{Begin} + 0.5)$ can therefore be seen as an estimate for $\log(\mathbb{E}(\textrm{Begin}))$. The estimated coefficients with corresponding confidence intervals are given in Figure~\ref{fig:dmft}. As the coefficients of the first component are restricted a-priori to minus infinity for the intercept and to zero for the other variables, they are of no interest and only the second component is plotted. The box ratio can be modified as for \code{barchart()} in package \pkg{lattice}. The code to produce this plot is given by: <>= print(plot(refit(Fitted), components = 2, box.ratio = 3)) @ \begin{figure} \centering \setkeys{Gin}{width=0.9\textwidth} <>= <> @ \caption{The estimated coefficients of the zero-inflated model for the \code{dmft} dataset. The first component is not plotted as this component captures the inflated zeros and its coefficients are fixed a-priori.} \label{fig:dmft} \end{figure} %%----------------------------------------------------------------------- \subsection{Concomitant variable models}\label{sec:concomitant-models} If the concomitant variable is a categorical variable, the multinomial logit model is equivalent to a model where the component weights for each level of the concomitant variable are determined by the mean values of the a-posteriori probabilities. The driver which implements this \code{"FLXP"} model is given in Figure~\ref{fig:myConcomitant.R}. A name for the driver has to be specified and a \code{fit()} function. In the \code{fit()} function the mean posterior probability for all observations with the same covariate points is determined, assigned to the corresponding observations and the full new a-posteriori probability matrix returned. By contrast \code{refit()} only returns the new a-posteriori probability matrix for the number of unique covariate points. \lstset{frame=trbl,basicstyle=\small\tt,stepnumber=5,numbers=left} \begin{figure} \centering \begin{minipage}{0.98\textwidth} \lstinputlisting{myConcomitant.R} \end{minipage} \caption{Driver for a concomitant variable model where the component weights are determined by averaging over the a-posteriori probabilities for each level of the concomitant variable.} \label{fig:myConcomitant.R} \end{figure} \subsubsection{Example: Using the driver} If the concomitant variable model returned by \code{myConcomitant()} is used for the artificial example in Section~\ref{sec:using-new-funct} the same fitted model is returned as if a multinomial logit model is specified. An advantage is that in this case no problems occur if the fitted probabilities are close to zero or one. <>= Concomitant <- FLXPmultinom(~ yb) MyConcomitant <- myConcomitant(~ yb) set.seed(1234) m2 <- flexmix(. ~ x, data = NPreg, k = 2, model = list(Model_n, Model_p), concomitant = Concomitant) m3 <- flexmix(. ~ x, data = NPreg, k = 2, model = list(Model_n, Model_p), cluster = posterior(m2), concomitant = MyConcomitant) @ <<>>= summary(m2) summary(m3) @ For comparing the estimated component weights for each value of $\mathit{yb}$ the following function can be used: <<>>= determinePrior <- function(object) { object@concomitant@fit(object@concomitant@x, posterior(object))[!duplicated(object@concomitant@x), ] } @ <<>>= determinePrior(m2) determinePrior(m3) @ Obviously the fitted values of the two models correspond to each other. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Summary and outlook}\label{sec:summary-outlook} Package \pkg{flexmix} was extended to cover finite mixtures of GLMs with (nested) varying and constant parameters. This allows for example the estimation of varying intercept models. In order to be able to characterize the components given some variables concomitant variable models can be estimated for the component weights. The implementation of these extensions have triggered some modifications in the class structure and in the fit functions \code{flexmix()} and \code{FLXfit()}. For certain steps, as e.g.~the M-step, methods which depend on the component specific models are defined in order to enable the estimation of finite mixtures of GLMs with only varying parameters and those with (nested) varying and constant parameters with the same fit function. The flexibility of this modified implementation is demonstrated by illustrating how a driver for zero-inflated models can be defined. In the future diagnostic tools based on resampling methods shall be implemented as bootstrap results can give valuable insights into the model fit \citep{mixtures:Gruen+Leisch:2004}. A function which conveniently allows to test linear hypotheses about the parameters using the variance-covariance matrix returned by \code{refit()} would be a further valuable diagnostic tool. The implementation of zero-inflated Poisson and binomial regression models are a first step towards relaxing the assumption that all component specific distributions are from the same parametric family. As mixtures with components which follow distributions from different parametric families can be useful for example to model outliers \citep{mixtures:Dasgupta+Raftery:1998,mixtures:Leisch:2008}, it is intended to also make this functionality available in \pkg{flexmix} in the future. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section*{Computational details} <>= SI <- sessionInfo() pkgs <- paste(sapply(c(SI$otherPkgs, SI$loadedOnly), function(x) paste("\\\\pkg{", x$Package, "} ", x$Version, sep = "")), collapse = ", ") @ All computations and graphics in this paper have been done using \proglang{R} version \Sexpr{getRversion()} with the packages \Sexpr{pkgs}. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section*{Acknowledgments} This research was supported by the the Austrian Science Foundation (FWF) under grants P17382 and T351. Thanks also to Achim Zeileis for helpful discussions on implementation details and an anonymous referee for asking a good question about parameter significance which initiated the new version of function \code{refit()}. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \bibliography{mixture} %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \end{document} flexmix/vignettes/flexmix.bib0000644000176200001440000002335214404637307016105 0ustar liggesusers@STRING{jcgs = {Journal of Computational and Graphical Statistics} } @STRING{tuwien = {Technische Universit{\"a}t Wien, Vienna, Austria} } @STRING{jasa = {Journal of the American Statistical Association} } @Article{ flexmix:Aitkin:1996, author = {Murray Aitkin}, title = {A General Maximum Likelihood Analysis of Overdispersion in Generalized Linear Models}, journal = {Statistics and Computing}, year = 1996, volume = 6, pages = {251--262} } @Article{ flexmix:Aitkin:1999, author = {Murray Aitkin}, title = {A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models}, journal = {Biometrics}, year = 1999, volume = 55, pages = {117--128} } @Article{ flexmix:Aitkin:1999a, author = {Murray Aitkin}, title = {Meta-Analysis by Random Effect Modelling in Generalized Linear Models}, journal = {Statistics in Medicine}, year = 1999, volume = 18, number = {17--18}, month = {September}, pages = {2343--2351} } @Manual{ flexmix:Buyske:2003, title = {{R} Package \texttt{mmlcr}: Mixed-Mode Latent Class Regression}, author = {Steve Buyske}, year = 2003, note = {version 1.3.2}, url = {http://www.stat.rutgers.edu/~buyske/software.html} } @Book{ flexmix:Chambers:1998, author = {John M. Chambers}, title = {Programming with Data: A Guide to the {S} Language}, publisher = {Springer Verlag}, year = 1998, address = {Berlin, Germany} } @Article{ flexmix:DeSarbo+Cron:1988, author = {Wayne S. DeSarbo and W. L. Cron}, title = {A Maximum Likelihood Methodology for Clusterwise Linear Regression}, journal = {Journal of Classification}, year = 1988, volume = 5, pages = {249--282} } @Article{ flexmix:Dempster+Laird+Rubin:1977, author = {A.P. Dempster and N.M. Laird and D.B. Rubin}, title = {Maximum Likelihood from Incomplete Data via the {EM}-Alogrithm}, journal = {Journal of the Royal Statistical Society, B}, volume = 39, pages = {1--38}, year = 1977 } @Article{ flexmix:Diebolt+Robert:1994, author = {J. Diebolt and C. P. Robert}, title = {Estimation of Finite Mixture Distributions Through {B}ayesian Sampling}, journal = {Journal of the Royal Statistical Society, Series B}, year = 1994, volume = 56, pages = {363--375} } @Book{ flexmix:Everitt+Hand:1981, author = {Brian S. Everitt and David J. Hand}, title = {Finite Mixture Distributions}, publisher = {Chapman and Hall}, address = {London}, year = 1981 } @Article{ flexmix:Follmann+Lambert:1989, author = {Dean A. Follmann and Diane Lambert}, title = {Generalizing Logistic Regression by Non-Parametric Mixing}, journal = jasa, volume = 84, number = 405, month = {March}, pages = {295--300}, year = 1989 } @Article{ flexmix:Fraley+Raftery:2002, author = {Chris Fraley and Adrian E. Raftery}, title = {Model-Based Clustering, Discriminant Analysis and dDnsity Estimation}, journal = jasa, year = 2002, volume = 97, pages = {611-631} } @TechReport{ flexmix:Fraley+Raftery:2002a, author = {Chris Fraley and Adrian E. Raftery}, title = {{MCLUST}: Software for Model-Based Clustering, Discriminant Analysis and Density Estimation}, institution = {Department of Statistics, University of Washington}, year = 2002, number = 415, address = {Seattle, WA, USA}, url = {http://www.stat.washington.edu/raftery} } @Article{ flexmix:Gentleman+Ihaka:2000, author = {Robert Gentleman and Ross Ihaka}, title = {Lexical Scope and Statistical Computing}, journal = jcgs, year = 2000, volume = 9, number = 3, pages = {491--508}, keywords = {statistical computing, function closure, lexical scope, random number generators} } @InProceedings{ flexmix:Gruen+Leisch:2006, author = {Bettina Gr{\" u}n and Friedrich Leisch}, title = {Fitting Finite Mixtures of Linear Regression Models with Varying \& Fixed Effects in \textsf{R}}, booktitle = {Compstat 2006---Proceedings in Computational Statistics}, pages = {853--860}, editor = {Alfredo Rizzi and Maurizio Vichi}, publisher = {Physica Verlag}, address = {Heidelberg, Germany}, isbn = {3-7908-1708-2}, year = 2006 } @InProceedings{ flexmix:Grun+Leisch:2004, author = {Bettina Gr{\" u}n and Friedrich Leisch}, title = {Bootstrapping Finite Mixture Models}, booktitle = {Compstat 2004---Proceedings in Computational Statistics}, year = 2004, editor = {Jaromir Antoch}, publisher = {Physica Verlag}, address = {Heidelberg, Germany}, isbn = {3-7908-1554-3}, pages = {1115--1122}, pdf = {http://www.stat.uni-muenchen.de/~leisch/papers/Grun+Leisch-2004.pdf} } @MastersThesis{ flexmix:Grun:2002, author = {Bettina Gr{\"u}n}, title = {{I}dentifizierbarkeit von multinomialen {M}ischmodellen}, school = tuwien, year = 2002, note = {Kurt Hornik and Friedrich Leisch, advisors} } @Article{ flexmix:Hennig:2000, author = {Christian Hennig}, title = {Identifiability of Models for Clusterwise Linear Regression}, journal = {Journal of Classification}, volume = 17, pages = {273--296}, year = 2000 } @InProceedings{ flexmix:Leisch:2004, author = {Friedrich Leisch}, title = {Exploring the Structure of Mixture Model Components}, booktitle = {Compstat 2004---Proceedings in Computational Statistics}, year = 2004, editor = {Jaromir Antoch}, publisher = {Physica Verlag}, address = {Heidelberg, Germany}, isbn = {3-7908-1554-3}, pages = {1405--1412}, pdf = {http://www.stat.uni-muenchen.de/~leisch/papers/Leisch-2004.pdf} } @Article{ flexmix:Leisch:2004a, author = {Friedrich Leisch}, title = {{FlexMix}: A General Framework for Finite Mixture Models and Latent Class Regression in {R}}, journal = {Journal of Statistical Software}, year = 2004, volume = 11, number = 8, doi = {10.18637/jss.v011.i08}, } @Book{ flexmix:McLachlan+Peel:2000, author = {Geoffrey McLachlan and David Peel}, title = {Finite Mixture Models}, publisher = {John Wiley and Sons Inc.}, year = 2000 } @Manual{ flexmix:R-Core:2004, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = 2004, isbn = {3-900051-07-0}, url = {http://www.R-project.org} } @InProceedings{ flexmix:Tantrum+Murua+Stuetzle:2003, author = {Jeremy Tantrum and Alejandro Murua and Werner Stuetzle}, title = {Assessment and Pruning of Hierarchical Model Based Clustering}, booktitle = {Proceedings of the ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining}, pages = {197--205}, year = 2003, publisher = {ACM Press}, address = {New York, NY, USA}, isbn = {1-58113-737-0}, } @Book{ flexmix:Titterington+Smith+Makov:1985, author = {D.M. Titterington and A.F.M. Smith and U.E. Makov}, title = {Statistical Analysis of Finite Mixture Distributions}, publisher = {John Wiley and Sons Inc.}, year = 1985 } @InProceedings{ flexmix:Urbanek+Theus:2003, author = {Simon Urbanek and Martin Theus}, title = {{iPlots}---High Interaction Graphics for {R}}, booktitle = {Proceedings of the 3rd International Workshop on Distributed Statistical Computing, Vienna, Austria}, editor = {Kurt Hornik and Friedrich Leisch and Achim Zeileis}, year = 2003, url = {http://www.ci.tuwien.ac.at/Conferences/DSC-2003/Proceedings/}, note = {{ISSN 1609-395X}} } @Book{ flexmix:Venables+Ripley:2002, title = {Modern Applied Statistics with S}, author = {William N. Venables and Brian D. Ripley}, publisher = {Springer Verlag}, edition = {Fourth}, address = {New York}, year = 2002, isbn = {0-387-95457-0} } @Article{ flexmix:Wang+Cockburn+Puterman:1998, author = {Peiming Wang and Iain M. Cockburn and Martin L. Puterman}, title = {Analysis of Patent Data---{A} Mixed-{P}oisson-Regression-Model Approach}, journal = {Journal of Business \& Economic Statistics}, year = 1998, volume = 16, number = 1, pages = {27--41} } @Article{ flexmix:Wang+Puterman+Cockburn:1996, author = {Peiming Wang and Martin L. Puterman and Iain M. Cockburn and Nhu D. Le}, title = {Mixed {P}oisson Regression Models with Covariate Dependent Rates}, journal = {Biometrics}, year = 1996, volume = 52, pages = {381--400} } @Article{ flexmix:Wang+Puterman:1998, author = {Peiming Wang and Martin L. Puterman}, title = {Mixed Logistic Regression Models}, journal = {Journal of Agricultural, Biological, and Environmental Statistics}, year = 1998, volume = 3, number = 2, pages = {175--200} } @Article{ flexmix:Wedel+DeSarbo:1995, author = {Michel Wedel and Wayne S. DeSarbo}, title = {A Mixture Likelihood Approach for Generalized Linear Models}, journal = {Journal of Classification}, year = 1995, volume = 12, pages = {21--55} } @Book{ flexmix:Wedel+Kamakura:2001, author = {Michel Wedel and Wagner A. Kamakura}, title = {Market Segmentation -- Conceptual and Methodological Foundations}, publisher = {Kluwer Academic Publishers}, year = 2001, address = {Boston, MA, USA}, edition = {2nd} } flexmix/vignettes/regression-examples.Rnw0000644000176200001440000012407214404637307020440 0ustar liggesusers\documentclass[nojss]{jss} \usepackage{amsfonts,bm,amsmath,amssymb} %%\usepackage{Sweave} %% already provided by jss.cls %%%\VignetteIndexEntry{Applications of finite mixtures of regression models} %%\VignetteDepends{flexmix} %%\VignetteKeywords{R, finite mixture model, generalized linear model, latent class regression} %%\VignettePackage{flexmix} \title{Applications of finite mixtures of regression models} <>= library("stats") library("graphics") library("flexmix") @ \author{Bettina Gr{\"u}n\\ Wirtschaftsuniversit{\"a}t Wien \And Friedrich Leisch\\ Universit\"at f\"ur Bodenkultur Wien} \Plainauthor{Bettina Gr{\"u}n, Friedrich Leisch} \Address{ Bettina Gr\"un\\ Institute for Statistics and Mathematics\\ Wirtschaftsuniversit{\"a}t Wien\\ Welthandelsplatz 1\\ 1020 Wien, Austria\\ E-mail: \email{Bettina.Gruen@R-project.org}\\ Friedrich Leisch\\ Institut f\"ur Angewandte Statistik und EDV\\ Universit\"at f\"ur Bodenkultur Wien\\ Peter Jordan Stra\ss{}e 82\\ 1190 Wien, Austria\\ E-mail: \email{Friedrich.Leisch@boku.ac.at} } \Abstract{ Package \pkg{flexmix} provides functionality for fitting finite mixtures of regression models. The available model class includes generalized linear models with varying and fixed effects for the component specific models and multinomial logit models for the concomitant variable models. This model class includes random intercept models where the random part is modelled by a finite mixture instead of a-priori selecting a suitable distribution. The application of the package is illustrated on various datasets which have been previously used in the literature to fit finite mixtures of Gaussian, binomial or Poisson regression models. The \proglang{R} commands are given to fit the proposed models and additional insights are gained by visualizing the data and the fitted models as well as by fitting slightly modified models. } \Keywords{\proglang{R}, finite mixture models, generalized linear models, concomitant variables} \Plainkeywords{R, finite mixture models, generalized linear models, concomitant variables} %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \begin{document} \SweaveOpts{engine=R, echo=true, height=5, width=8, eps=FALSE, keep.source=TRUE} \setkeys{Gin}{width=0.8\textwidth} <>= options(width=70, prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE) suppressWarnings(RNGversion("3.5.0")) set.seed(1802) library("lattice") ltheme <- canonical.theme("postscript", FALSE) lattice.options(default.theme=ltheme) @ %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \section{Introduction} Package \pkg{flexmix} provides infrastructure for flexible fitting of finite mixtures models. The design principles of the package allow easy extensibility and rapid prototyping. In addition, the main focus of the available functionality is on fitting finite mixtures of regression models, as other packages in \proglang{R} exist which have specialized functionality for model-based clustering, such as e.g.~\pkg{mclust} \citep{flexmix:Fraley+Raftery:2002a} for finite mixtures of Gaussian distributions. \cite{flexmix:Leisch:2004a} gives a general introduction into the package outlining the main implementational principles and illustrating the use of the package. The paper is also contained as a vignette in the package. An example for fitting mixtures of Gaussian regression models is given in \cite{flexmix:Gruen+Leisch:2006}. This paper focuses on examples of finite mixtures of binomial logit and Poisson regression models. Several datasets which have been previously used in the literature to demonstrate the use of finite mixtures of regression models have been selected to illustrate the application of the package. The model class covered are finite mixtures of generalized linear model with focus on binomial logit and Poisson regressions. The regression coefficients as well as the dispersion parameters of the component specific models are assumed to vary for all components, vary between groups of components, i.e.~to have a nesting, or to be fixed over all components. In addition it is possible to specify concomitant variable models in order to be able to characterize the components. Random intercept models are a special case of finite mixtures with varying and fixed effects as fixed effects are assumed for the coefficients of all covariates and varying effects for the intercept. These models are often used to capture overdispersion in the data which can occur for example if important covariates are omitted in the regression. It is then assumed that the influence of these covariates can be captured by allowing a random distribution for the intercept. This illustration does not only show how the package \pkg{flexmix} can be used for fitting finite mixtures of regression models but also indicates the advantages of using an extension package of an environment for statistical computing and graphics instead of a stand-alone package as available visualization techniques can be used for inspecting the data and the fitted models. In addition users already familiar with \proglang{R} and its formula interface should find the model specification and a lot of commands for exploring the fitted model intuitive. %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \section{Model specification} Finite mixtures of Gaussian regressions with concomitant variable models are given by: \begin{align*} H(y\,|\,\bm{x}, \bm{w}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\bm{w}, \bm{\alpha}) \textrm{N}(y\,|\, \mu_s(\bm{x}), \sigma^2_s), \end{align*} where $\textrm{N}(\cdot\,|\, \mu_s(\bm{x}), \sigma^2_s)$ is the Gaussian distribution with mean $\mu_s(\bm{x}) = \bm{x}' \bm{\beta}^s$ and variance $\sigma^2_s$. $\Theta$ denotes the vector of all parameters of the mixture distribution and the dependent variables are $y$, the independent $\bm{x}$ and the concomitant $\bm{w}$. Finite mixtures of binomial regressions with concomitant variable models are given by: \begin{align*} H(y\,|\,T, \bm{x}, \bm{w}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\bm{w}, \bm{\alpha}) \textrm{Bi}(y\,|\,T, \theta_s(\bm{x})), \end{align*} where $\textrm{Bi}(\cdot\,|\,T, \theta_s(\bm{x}))$ is the binomial distribution with number of trials equal to $T$ and success probability $\theta_s(\bm{x}) \in (0,1)$ given by $\textrm{logit}(\theta_s(\bm{x})) = \bm{x}' \bm{\beta}^s$. Finite mixtures of Poisson regressions are given by: \begin{align*} H(y \,|\, \bm{x}, \bm{w}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\bm{w}, \bm{\alpha}) \textrm{Poi} (y \,|\, \lambda_s(\bm{x})), \end{align*} where $\textrm{Poi}(\cdot\,|\,\lambda_s(\bm{x}))$ denotes the Poisson distribution and $\log(\lambda_s(\bm{x})) = \bm{x}'\bm{\beta}^s$. For all these mixture distributions the coefficients are split into three different groups depending on if fixed, nested or varying effects are specified: \begin{align*} \bm{\beta}^s &= (\bm{\beta}_1, \bm{\beta}^{c(s)}_{2}, \bm{\beta}^{s}_3) \end{align*} where the first group represents the fixed, the second the nested and the third the varying effects. For the nested effects a partition $\mathcal{C} = \{c_s \,|\, s = 1,\ldots S\}$ of the $S$ components is determined where $c_s = \{s^* = 1,\ldots,S \,|\, c(s^*) = c(s)\}$. A similar splitting is possible for the variance of mixtures of Gaussian regression models. The function for maximum likelihood (ML) estimation with the Expectation-Maximization (EM) algorithm is \code{flexmix()} which is described in detail in \cite{flexmix:Leisch:2004a}. It takes as arguments a specification of the component specific model and of the concomitant variable model. The component specific model with varying, nested and fixed effects can be specified with the M-step driver \code{FLXMRglmfix()} which has arguments \code{formula} for the varying, \code{nested} for the nested and \code{fixed} for the fixed effects. \code{formula} and \code{fixed} take an argument of class \code{"formula"}, whereas \code{nested} expects an object of class \code{"FLXnested"} or a named list specifying the nested structure with a component \code{k} which is a vector of the number of components in each group of the partition and a component \code{formula} which is a vector of formulas for each group of the partition. In addition there is an argument \code{family} which has to be one of \code{gaussian}, \code{binomial}, \code{poisson} or \code{Gamma} and determines the component specific distribution function as well as an \code{offset} argument. The argument \code{varFix} can be used to determine the structure of the dispersion parameters. If only varying effects are specified the M-step driver \code{FLXMRglm()} can be used which only has an argument \code{formula} for the varying effects and also a \code{family} and an \code{offset} argument. This driver has the advantage that in the M-step the weighted ML estimation is made separately for each component which signifies that smaller model matrices are used. If a mixture model with a lot of components $S$ is fitted to a large data set with $N$ observations and the model matrix used in the M-step of \code{FLXMRglm()} has $N$ rows and $K$ columns, the model matrix used in the M-step of \code{FLXMRglmfix()} has $S N$ rows and up to $S K$ columns. In general the concomitant variable model is assumed to be a multinomial logit model, i.e.~: \begin{align*} \pi_s(\bm{w},\bm{\alpha}) &= \frac{e^{\bm{w}'\bm{\alpha}_s}}{\sum_{u = 1}^S e^{\bm{w}'\bm{\alpha}_u}} \quad \forall s, \end{align*} with $\bm{\alpha} = (\bm{\alpha}'_s)_{s=1,\ldots,S}$ and $\bm{\alpha}_1 \equiv \bm{0}$. This model can be fitted in \pkg{flexmix} with \code{FLXPmultinom()} which takes as argument \code{formula} the formula specification of the multinomial logit part. For fitting the function \code{nnet()} is used from package \pkg{MASS} \citep{flexmix:Venables+Ripley:2002} with the independent variables specified by the formula argument and the dependent variables are given by the a-posteriori probability estimates. %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \section[Using package flexmix]{Using package \pkg{flexmix}} In the following datasets from different areas such as medicine, biology and economics are used. There are three subsections: for finite mixtures of Gaussian regressions, for finite mixtures of binomial regression models and for finite mixtures of Poisson regression models. %%------------------------------------------------------------------------- \subsection{Finite mixtures of Gaussian regressions} This artificial dataset with 200 observations is given in \cite{flexmix:Gruen+Leisch:2006}. The data is generated from a mixture of Gaussian regression models with three components. There is an intercept with varying effects, an independent variable $x1$, which is a numeric variable, with fixed effects and another independent variable $x2$, which is a categorical variable with two levels, with nested effects. The prior probabilities depend on a concomitant variable $w$, which is also a categorical variable with two levels. Fixed effects are also assumed for the variance. The data is illustrated in Figure~\ref{fig:artificialData} and the true underlying model is given by: \begin{align*} H(y\,|\,(x1, x2), w, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(w, \bm{\alpha}) \textrm{N}(y\,|\, \mu_s, \sigma^2), \end{align*} with $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \beta^{c(s)}_{\textrm{x1}}, \beta_{\textrm{x2}})$. The nesting signifies that $c(1) = c(2)$ and $\beta^{c(3)}_{\textrm{x1}} = 0$. The mixture model is fitted by first loading the package and the dataset and then specifying the component specific model. In a first step a component specific model with only varying effects is specified. Then the fitting function \code{flexmix()} is called repeatedly using \code{stepFlexmix()}. Finally, we order the components such that they are in ascending order with respect to the coefficients of the variable \code{x1}. <>= set.seed(2807) library("flexmix") data("NregFix", package = "flexmix") Model <- FLXMRglm(~ x2 + x1) fittedModel <- stepFlexmix(y ~ 1, model = Model, nrep = 3, k = 3, data = NregFix, concomitant = FLXPmultinom(~ w)) fittedModel <- relabel(fittedModel, "model", "x1") summary(refit(fittedModel)) @ The estimated coefficients indicate that the components differ for the intercept, but that they are not significantly different for the coefficients of $x2$. For $x1$ the coefficient of the first component is not significantly different from zero and the confidence intervals for the other two components overlap. Therefore we fit a modified model, which is equivalent to the true underlying model. The previously fitted model is used for initializing the EM algorithm: <>= Model2 <- FLXMRglmfix(fixed = ~ x2, nested = list(k = c(1, 2), formula = c(~ 0, ~ x1)), varFix = TRUE) fittedModel2 <- flexmix(y ~ 1, model = Model2, cluster = posterior(fittedModel), data = NregFix, concomitant = FLXPmultinom(~ w)) BIC(fittedModel) BIC(fittedModel2) @ The BIC suggests that the restricted model should be preferred. \begin{figure}[tb] \centering \setkeys{Gin}{width=0.95\textwidth} <>= plotNregFix <- NregFix plotNregFix$w <- factor(NregFix$w, levels = 0:1, labels = paste("w =", 0:1)) plotNregFix$x2 <- factor(NregFix$x2, levels = 0:1, labels = paste("x2 =", 0:1)) plotNregFix$class <- factor(NregFix$class, levels = 1:3, labels = paste("Class", 1:3)) print(xyplot(y ~ x1 | x2*w, groups = class, data = plotNregFix, cex = 0.6, auto.key = list(space="right"), layout = c(2,2))) @ \setkeys{Gin}{width=0.8\textwidth} \caption{Sample with 200 observations from the artificial example.} \label{fig:artificialData} \end{figure} <>= summary(refit(fittedModel2)) @ The coefficients are ordered such that the fixed coefficients are first, the nested varying coefficients second and the varying coefficients last. %%------------------------------------------------------------------------- \subsection{Finite mixtures of binomial logit regressions} %%------------------------------------------------------------------------- \subsubsection{Beta blockers} The dataset is analyzed in \cite{flexmix:Aitkin:1999, flexmix:Aitkin:1999a} using a finite mixture of binomial regression models. Furthermore, it is described in \cite{flexmix:McLachlan+Peel:2000} on page 165. The dataset is from a 22-center clinical trial of beta-blockers for reducing mortality after myocardial infarction. A two-level model is assumed to represent the data, where centers are at the upper level and patients at the lower level. The data is illustrated in Figure~\ref{fig:beta} and the model is given by: \begin{align*} H(\textrm{Deaths} \,|\, \textrm{Total}, \textrm{Treatment}, \textrm{Center}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Bi}( \textrm{Deaths} \,|\, \textrm{Total}, \theta_s). \end{align*} First, the center classification is ignored and a binomial logit regression model with treatment as covariate is fitted using \code{glm}, i.e.~$S=1$: <>= data("betablocker", package = "flexmix") betaGlm <- glm(cbind(Deaths, Total - Deaths) ~ Treatment, family = "binomial", data = betablocker) betaGlm @ In the next step the center classification is included by allowing a random effect for the intercept given the centers, i.e.~the coefficients $\bm{\beta}^s$ are given by $(\beta^s_{\textrm{Intercept|Center}}, \beta_{\textrm{Treatment}})$. This signifies that the component membership is fixed for each center. In order to determine the suitable number of components, the mixture is fitted with different numbers of components and the BIC information criterion is used to select an appropriate model. In this case a model with three components is selected. The fitted values for the model with three components are given in Figure~\ref{fig:beta}. <>= betaMixFix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, model = FLXMRglmfix(family = "binomial", fixed = ~ Treatment), k = 2:4, nrep = 3, data = betablocker) betaMixFix @ \begin{figure} \centering <>= library("grid") betaMixFix_3 <- getModel(betaMixFix, "3") betaMixFix_3 <- relabel(betaMixFix_3, "model", "Intercept") betablocker$Center <- with(betablocker, factor(Center, levels = Center[order((Deaths/Total)[1:22])])) clusters <- factor(clusters(betaMixFix_3), labels = paste("Cluster", 1:3)) print(dotplot(Deaths/Total ~ Center | clusters, groups = Treatment, as.table = TRUE, data = betablocker, xlab = "Center", layout = c(3, 1), scales = list(x = list(draw = FALSE)), key = simpleKey(levels(betablocker$Treatment), lines = TRUE, corner = c(1,0)))) betaMixFix.fitted <- fitted(betaMixFix_3) for (i in 1:3) { seekViewport(trellis.vpname("panel", i, 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[1:22, i], "native"), gp = gpar(lty = 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[23:44, i], "native"), gp = gpar(lty = 2)) } @ \caption{Relative number of deaths for the treatment and the control group for each center in the beta blocker dataset. The centers are sorted by the relative number of deaths in the control group. The lines indicate the fitted values for each component of the 3-component mixture model with random intercept and fixed effect for treatment.} \label{fig:beta} \end{figure} In addition the treatment effect can also be included in the random part of the model. As then all coefficients for the covariates and the intercept follow a mixture distribution the component specific model can be specified using \code{FLXMRglm()}. The coefficients are $\bm{\beta}^s=(\beta^s_{\textrm{Intercept|Center}}, \beta^s_{\textrm{Treatment|Center}})$, i.e.~it is assumed that the heterogeneity is only between centers and therefore the aggregated data for each center can be used. <>= betaMix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ Treatment | Center, model = FLXMRglm(family = "binomial"), k = 3, nrep = 3, data = betablocker) summary(betaMix) @ The full model with a random effect for treatment has a higher BIC and therefore the smaller would be preferred. The default plot of the returned \code{flexmix} object is a rootogramm of the a-posteriori probabilities where observations with a-posteriori probabilities smaller than \code{eps} are omitted. With argument \code{mark} the component is specified to have those observations marked which are assigned to this component based on the maximum a-posteriori probabilities. This indicates which components overlap. <>= print(plot(betaMixFix_3, mark = 1, col = "grey", markcol = 1)) @ The default plot of the fitted model indicates that the components are well separated. In addition component 1 has a slight overlap with component 2 but none with component 3. The fitted parameters of the component specific models can be accessed with: <>= parameters(betaMix) @ The cluster assignments using the maximum a-posteriori probabilities are obtained with: <>= table(clusters(betaMix)) @ The estimated probabilities for each component for the treated patients and those in the control group can be obtained with: <>= predict(betaMix, newdata = data.frame(Treatment = c("Control", "Treated"))) @ or <>= fitted(betaMix)[c(1, 23), ] @ A further analysis of the model is possible with function \code{refit()} which returns the estimated coefficients together with the standard deviations, z-values and corresponding p-values: <>= summary(refit(getModel(betaMixFix, "3"))) @ The printed coefficients are ordered to have the fixed effects before the varying effects. %%----------------------------------------------------------------------- \subsubsection{Mehta et al. trial} This dataset is similar to the beta blocker dataset and is also analyzed in \cite{flexmix:Aitkin:1999a}. The dataset is visualized in Figure~\ref{fig:mehta}. The observation for the control group in center 15 is slightly conspicuous and might classify as an outlier. The model is given by: \begin{align*} H(\textrm{Response} \,|\, \textrm{Total}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Bi}( \textrm{Response} \,|\, \textrm{Total}, \theta_s), \end{align*} with $\bm{\beta}^s = (\beta^s_{\textrm{Intercept|Site}}, \beta_{\textrm{Drug}})$. This model is fitted with: <>= data("Mehta", package = "flexmix") mehtaMix <- stepFlexmix(cbind(Response, Total - Response)~ 1 | Site, model = FLXMRglmfix(family = "binomial", fixed = ~ Drug), control = list(minprior = 0.04), nrep = 3, k = 3, data = Mehta) summary(mehtaMix) @ One component only contains the observations for center 15 and in order to be able to fit a mixture with such a small component it is necessary to modify the default argument for \code{minprior} which is 0.05. The fitted values for this model are given separately for each component in Figure~\ref{fig:mehta}. \begin{figure} \centering <>= Mehta$Site <- with(Mehta, factor(Site, levels = Site[order((Response/Total)[1:22])])) clusters <- factor(clusters(mehtaMix), labels = paste("Cluster", 1:3)) print(dotplot(Response/Total ~ Site | clusters, groups = Drug, layout = c(3,1), data = Mehta, xlab = "Site", scales = list(x = list(draw = FALSE)), key = simpleKey(levels(Mehta$Drug), lines = TRUE, corner = c(1,0)))) mehtaMix.fitted <- fitted(mehtaMix) for (i in 1:3) { seekViewport(trellis.vpname("panel", i, 1)) sapply(1:nlevels(Mehta$Drug), function(j) grid.lines(unit(1:22, "native"), unit(mehtaMix.fitted[Mehta$Drug == levels(Mehta$Drug)[j], i], "native"), gp = gpar(lty = j))) } @ \caption{Relative number of responses for the treatment and the control group for each site in the Mehta et al.~trial dataset together with the fitted values. The sites are sorted by the relative number of responses in the control group.} \label{fig:mehta} \end{figure} If also a random effect for the coefficient of $\textrm{Drug}$ is fitted, i.e.~$\bm{\beta}^s = (\beta^s_{\textrm{Intercept|Site}}, \beta^s_{\textrm{Drug|Site}})$, this is estimated by: <>= mehtaMix <- stepFlexmix(cbind(Response, Total - Response) ~ Drug | Site, model = FLXMRglm(family = "binomial"), k = 3, data = Mehta, nrep = 3, control = list(minprior = 0.04)) summary(mehtaMix) @ The BIC is smaller for the larger model and this indicates that the assumption of an equal drug effect for all centers is not confirmed by the data. Given Figure~\ref{fig:mehta} a two-component model with fixed treatment is also fitted to the data where site 15 is omitted: <>= Mehta.sub <- subset(Mehta, Site != 15) mehtaMix <- stepFlexmix(cbind(Response, Total - Response) ~ 1 | Site, model = FLXMRglmfix(family = "binomial", fixed = ~ Drug), data = Mehta.sub, k = 2, nrep = 3) summary(mehtaMix) @ %%----------------------------------------------------------------------- \subsubsection{Tribolium} A finite mixture of binomial regressions is fitted to the Tribolium dataset given in \cite{flexmix:Wang+Puterman:1998}. The data was collected to investigate whether the adult Tribolium species Castaneum has developed an evolutionary advantage to recognize and avoid eggs of its own species while foraging, as beetles of the genus Tribolium are cannibalistic in the sense that adults eat the eggs of their own species as well as those of closely related species. The experiment isolated a number of adult beetles of the same species and presented them with a vial of 150 eggs (50 of each type), the eggs being thoroughly mixed to ensure uniformity throughout the vial. The data gives the consumption data for adult Castaneum species. It reports the number of Castaneum, Confusum and Madens eggs, respectively, that remain uneaten after two day exposure to the adult beetles. Replicates 1, 2, and 3 correspond to different occasions on which the experiment was conducted. The data is visualized in Figure~\ref{fig:tribolium} and the model is given by: \begin{align*} H(\textrm{Remaining} \,|\, \textrm{Total}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\textrm{Replicate}, \bm{\alpha}) \textrm{Bi}( \textrm{Remaining} \,|\, \textrm{Total}, \theta_s), \end{align*} with $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \bm{\beta}_{\textrm{Species}})$. This model is fitted with: <>= data("tribolium", package = "flexmix") TribMix <- stepFlexmix(cbind(Remaining, Total - Remaining) ~ 1, k = 2:3, model = FLXMRglmfix(fixed = ~ Species, family = "binomial"), concomitant = FLXPmultinom(~ Replicate), data = tribolium) @ The model which is selected as the best in \cite{flexmix:Wang+Puterman:1998} can be estimated with: <>= modelWang <- FLXMRglmfix(fixed = ~ I(Species == "Confusum"), family = "binomial") concomitantWang <- FLXPmultinom(~ I(Replicate == 3)) TribMixWang <- stepFlexmix(cbind(Remaining, Total - Remaining) ~ 1, data = tribolium, model = modelWang, concomitant = concomitantWang, k = 2) summary(refit(TribMixWang)) @ \begin{figure} \centering <>= clusters <- factor(clusters(TribMixWang), labels = paste("Cluster", 1:TribMixWang@k)) print(dotplot(Remaining/Total ~ factor(Replicate) | clusters, groups = Species, data = tribolium[rep(1:9, each = 3) + c(0:2)*9,], xlab = "Replicate", auto.key = list(corner = c(1,0)))) @ \caption{Relative number of remaining beetles for the number of replicate. The different panels are according to the cluster assignemnts based on the a-posteriori probabilities of the model suggested in \cite{flexmix:Wang+Puterman:1998}.} \label{fig:tribolium} \end{figure} \cite{flexmix:Wang+Puterman:1998} also considered a model where they omit one conspicuous observation. This model can be estimated with: <>= TribMixWangSub <- stepFlexmix(cbind(Remaining, Total - Remaining) ~ 1, k = 2, data = tribolium[-7,], model = modelWang, concomitant = concomitantWang) @ %%----------------------------------------------------------------------- \subsubsection{Trypanosome} The data is used in \cite{flexmix:Follmann+Lambert:1989}. It is from a dosage-response analysis where the proportion of organisms belonging to different populations shall be assessed. It is assumed that organisms belonging to different populations are indistinguishable other than in terms of their reaction to the stimulus. The experimental technique involved inspection under the microscope of a representative aliquot of a suspension, all organisms appearing within two fields of view being classified either alive or dead. Hence the total numbers of organisms present at each dose and the number showing the quantal response were both random variables. The data is illustrated in Figure~\ref{fig:trypanosome}. The model which is proposed in \cite{flexmix:Follmann+Lambert:1989} is given by: \begin{align*} H(\textrm{Dead} \,|\,\bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Bi}( \textrm{Dead} \,|\, \theta_s), \end{align*} where $\textrm{Dead} \in \{0,1\}$ and with $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \bm{\beta}_{\textrm{log(Dose)}})$. This model is fitted with: <>= data("trypanosome", package = "flexmix") TrypMix <- stepFlexmix(cbind(Dead, 1-Dead) ~ 1, k = 2, nrep = 3, data = trypanosome, model = FLXMRglmfix(family = "binomial", fixed = ~ log(Dose))) summary(refit(TrypMix)) @ The fitted values are given in Figure~\ref{fig:trypanosome} together with the fitted values of a generalized linear model in order to facilitate comparison of the two models. \begin{figure} \centering <>= tab <- with(trypanosome, table(Dead, Dose)) Tryp.dat <- data.frame(Dead = tab["1",], Alive = tab["0",], Dose = as.numeric(colnames(tab))) plot(Dead/(Dead+Alive) ~ Dose, data = Tryp.dat) Tryp.pred <- predict(glm(cbind(Dead, 1-Dead) ~ log(Dose), family = "binomial", data = trypanosome), newdata=Tryp.dat, type = "response") TrypMix.pred <- predict(TrypMix, newdata = Tryp.dat, aggregate = TRUE)[[1]] lines(Tryp.dat$Dose, Tryp.pred, lty = 2) lines(Tryp.dat$Dose, TrypMix.pred, lty = 3) legend(4.7, 1, c("GLM", "Mixture model"), lty=c(2, 3), xjust=0, yjust=1) @ \caption{Relative number of deaths for each dose level together with the fitted values for the generalized linear model (``GLM'') and the random intercept model (``Mixture model'').} \label{fig:trypanosome} \end{figure} %%------------------------------------------------------------------------- \subsection{Finite mixtures of Poisson regressions} % %%----------------------------------------------------------------------- \subsubsection{Fabric faults} The dataset is analyzed using a finite mixture of Poisson regression models in \cite{flexmix:Aitkin:1996}. Furthermore, it is described in \cite{flexmix:McLachlan+Peel:2000} on page 155. It contains 32 observations on the number of faults in rolls of a textile fabric. A random intercept model is used where a fixed effect is assumed for the logarithm of length: <>= data("fabricfault", package = "flexmix") fabricMix <- stepFlexmix(Faults ~ 1, model = FLXMRglmfix(family="poisson", fixed = ~ log(Length)), data = fabricfault, k = 2, nrep = 3) summary(fabricMix) summary(refit(fabricMix)) Lnew <- seq(0, 1000, by = 50) fabricMix.pred <- predict(fabricMix, newdata = data.frame(Length = Lnew)) @ The intercept of the first component is not significantly different from zero for a signficance level of 0.05. We therefore also fit a modified model where the intercept is a-priori set to zero for the first component. This nested structure is given as part of the model specification with argument \code{nested}. <>= fabricMix2 <- flexmix(Faults ~ 0, data = fabricfault, cluster = posterior(fabricMix), model = FLXMRglmfix(family = "poisson", fixed = ~ log(Length), nested = list(k=c(1,1), formula=list(~0,~1)))) summary(refit(fabricMix2)) fabricMix2.pred <- predict(fabricMix2, newdata = data.frame(Length = Lnew)) @ The data and the fitted values for each of the components for both models are given in Figure~\ref{fig:fabric}. \begin{figure} \centering <>= plot(Faults ~ Length, data = fabricfault) sapply(fabricMix.pred, function(y) lines(Lnew, y, lty = 1)) sapply(fabricMix2.pred, function(y) lines(Lnew, y, lty = 2)) legend(190, 25, paste("Model", 1:2), lty=c(1, 2), xjust=0, yjust=1) @ \caption{Observed values of the fabric faults dataset together with the fitted values for the components of each of the two fitted models.} \label{fig:fabric} \end{figure} %%----------------------------------------------------------------------- \subsubsection{Patent} The patent data given in \cite{flexmix:Wang+Cockburn+Puterman:1998} consist of 70 observations on patent applications, R\&D spending and sales in millions of dollar from pharmaceutical and biomedical companies in 1976 taken from the National Bureau of Economic Research R\&D Masterfile. The observations are displayed in Figure~\ref{fig:patent}. The model which is chosen as the best in \cite{flexmix:Wang+Cockburn+Puterman:1998} is given by: \begin{align*} H(\textrm{Patents} \,|\, \textrm{lgRD}, \textrm{RDS}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\textrm{RDS}, \bm{\alpha}) \textrm{Poi} ( \textrm{Patents} \,|\, \lambda_s), \end{align*} and $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \beta^s_{\textrm{lgRD}})$. The model is fitted with: <>= data("patent", package = "flexmix") ModelPat <- FLXMRglm(family = "poisson") FittedPat <- stepFlexmix(Patents ~ lgRD, k = 3, nrep = 3, model = ModelPat, data = patent, concomitant = FLXPmultinom(~ RDS)) summary(FittedPat) @ The fitted values for the component specific models and the concomitant variable model are given in Figure~\ref{fig:patent}. The plotting symbol of the observations corresponds to the induced clustering given by \code{clusters(FittedPat)}. This model is modified to have fixed effects for the logarithmized R\&D spendings, i.e.~$\bm(\beta)^s = (\beta^s_{\textrm{Intercept}}, \beta_{\textrm{lgRD}})$. The already fitted model is used for initialization, i.e.~the EM algorithm is started with an M-step given the a-posteriori probabilities. <>= ModelFixed <- FLXMRglmfix(family = "poisson", fixed = ~ lgRD) FittedPatFixed <- flexmix(Patents ~ 1, model = ModelFixed, cluster = posterior(FittedPat), concomitant = FLXPmultinom(~ RDS), data = patent) summary(FittedPatFixed) @ The fitted values for the component specific models and the concomitant variable model of this model are also given in Figure~\ref{fig:patent}. \begin{figure} \centering \setkeys{Gin}{width=0.95\textwidth} <>= lgRDv <- seq(-3, 5, by = 0.05) newdata <- data.frame(lgRD = lgRDv) plotData <- function(fitted) { with(patent, data.frame(Patents = c(Patents, unlist(predict(fitted, newdata = newdata))), lgRD = c(lgRD, rep(lgRDv, 3)), class = c(clusters(fitted), rep(1:3, each = nrow(newdata))), type = rep(c("data", "fit"), c(nrow(patent), nrow(newdata)*3)))) } plotPatents <- cbind(plotData(FittedPat), which = "Wang et al.") plotPatentsFixed <- cbind(plotData(FittedPatFixed), which = "Fixed effects") plotP <- rbind(plotPatents, plotPatentsFixed) rds <- seq(0, 3, by = 0.02) x <- model.matrix(FittedPat@concomitant@formula, data = data.frame(RDS = rds)) plotConc <- function(fitted) { E <- exp(x%*%fitted@concomitant@coef) data.frame(Probability = as.vector(E/rowSums(E)), class = rep(1:3, each = nrow(x)), RDS = rep(rds, 3)) } plotConc1 <- cbind(plotConc(FittedPat), which = "Wang et al.") plotConc2 <- cbind(plotConc(FittedPatFixed), which = "Fixed effects") plotC <- rbind(plotConc1, plotConc2) print(xyplot(Patents ~ lgRD | which, data = plotP, groups=class, xlab = "log(R&D)", panel = "panel.superpose", type = plotP$type, panel.groups = function(x, y, type = "p", subscripts, ...) { ind <- plotP$type[subscripts] == "data" panel.xyplot(x[ind], y[ind], ...) panel.xyplot(x[!ind], y[!ind], type = "l", ...) }, scales = list(alternating=FALSE), layout=c(1,2), as.table=TRUE), more=TRUE, position=c(0,0,0.6, 1)) print(xyplot(Probability ~ RDS | which, groups = class, data = plotC, type = "l", scales = list(alternating=FALSE), layout=c(1,2), as.table=TRUE), position=c(0.6, 0.01, 1, 0.99)) @ \caption{Patent data with the fitted values of the component specific models (left) and the concomitant variable model (right) for the model in \citeauthor{flexmix:Wang+Cockburn+Puterman:1998} and with fixed effects for $\log(\textrm{R\&D})$. The plotting symbol for each observation is determined by the component with the maximum a-posteriori probability.} \label{fig:patent} \end{figure} \setkeys{Gin}{width=0.8\textwidth} With respect to the BIC the full model is better than the model with the fixed effects. However, fixed effects have the advantage that the different components differ only in their baseline and the relation between the components in return of investment for each additional unit of R\&D spending is constant. Due to a-priori domain knowledge this model might seem more plausible. The fitted values for the constrained model are also given in Figure~\ref{fig:patent}. %%----------------------------------------------------------------------- \subsubsection{Seizure} The data is used in \cite{flexmix:Wang+Puterman+Cockburn:1996} and is from a clinical trial where the effect of intravenous gamma-globulin on suppression of epileptic seizures is studied. There are daily observations for a period of 140 days on one patient, where the first 27 days are a baseline period without treatment, the remaining 113 days are the treatment period. The model proposed in \cite{flexmix:Wang+Puterman+Cockburn:1996} is given by: \begin{align*} H(\textrm{Seizures} \,|\, (\textrm{Treatment}, \textrm{log(Day)}, \textrm{log(Hours)}), \bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Poi} ( \textrm{Seizures} \,|\, \lambda_s), \end{align*} where $\bm(\beta)^s = (\beta^s_{\textrm{Intercept}}, \beta^s_{\textrm{Treatment}}, \beta^s_{\textrm{log(Day)}}, \beta^s_{\textrm{Treatment:log(Day)}})$ and $\textrm{log(Hours)}$ is used as offset. This model is fitted with: <>= data("seizure", package = "flexmix") seizMix <- stepFlexmix(Seizures ~ Treatment * log(Day), data = seizure, k = 2, nrep = 3, model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix) summary(refit(seizMix)) @ A different model with different contrasts to directly estimate the coefficients for the jump when changing between base and treatment period is given by: <>= seizMix2 <- flexmix(Seizures ~ Treatment * log(Day/27), data = seizure, cluster = posterior(seizMix), model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix2) summary(refit(seizMix2)) @ A different model which allows no jump at the change between base and treatment period is fitted with: <>= seizMix3 <- flexmix(Seizures ~ log(Day/27)/Treatment, data = seizure, cluster = posterior(seizMix), model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix3) summary(refit(seizMix3)) @ With respect to the BIC criterion the smaller model with no jump is preferred. This is also the more intuitive model from a practitioner's point of view, as it does not seem to be plausible that starting the treatment already gives a significant improvement, but improvement develops over time. The data points together with the fitted values for each component of the two models are given in Figure~\ref{fig:seizure}. It can clearly be seen that the fitted values are nearly equal which also supports the smaller model. \begin{figure} \centering <>= plot(Seizures/Hours~Day, pch = c(1,3)[as.integer(Treatment)], data=seizure) abline(v=27.5, lty=2, col="grey") legend(140, 9, c("Baseline", "Treatment"), pch=c(1, 3), xjust=1, yjust=1) matplot(seizure$Day, fitted(seizMix)/seizure$Hours, type="l", add=TRUE, lty = 1, col = 1) matplot(seizure$Day, fitted(seizMix3)/seizure$Hours, type="l", add=TRUE, lty = 3, col = 1) legend(140, 7, paste("Model", c(1,3)), lty=c(1, 3), xjust=1, yjust=1) @ \caption{Observed values for the seizure dataset together with the fitted values for the components of the two different models.} \label{fig:seizure} \end{figure} %%----------------------------------------------------------------------- \subsubsection{Ames salmonella assay data} The ames salomnella assay dataset was used in \cite{flexmix:Wang+Puterman+Cockburn:1996}. They propose a model given by: \begin{align*} H(\textrm{y} \,|\, \textrm{x}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Poi} ( \textrm{y} \,|\, \lambda_s), \end{align*} where $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \beta_{\textrm{x}}, \beta_{\textrm{log(x+10)}})$. The model is fitted with: <>= data("salmonellaTA98", package = "flexmix") salmonMix <- stepFlexmix(y ~ 1, data = salmonellaTA98, k = 2, nrep = 3, model = FLXMRglmfix(family = "poisson", fixed = ~ x + log(x + 10))) @ \begin{figure} \centering <>= salmonMix.pr <- predict(salmonMix, newdata=salmonellaTA98) plot(y~x, data=salmonellaTA98, pch=as.character(clusters(salmonMix)), xlab="Dose of quinoline", ylab="Number of revertant colonies of salmonella", ylim=range(c(salmonellaTA98$y, unlist(salmonMix.pr)))) for (i in 1:2) lines(salmonellaTA98$x, salmonMix.pr[[i]], lty=i) @ \caption{Means and classification for assay data according to the estimated posterior probabilities based on the fitted model.} \label{fig:almes} \end{figure} %%----------------------------------------------------------------------- \section{Conclusions and future work} Package \pkg{flexmix} can be used to fit finite mixtures of regressions to datasets used in the literature to illustrate these models. The results can be reproduced and additional insights can be gained using visualization methods available in \proglang{R}. The fitted model is an object in \proglang{R} which can be explored using \code{show()}, \code{summary()} or \code{plot()}, as suitable methods have been implemented for objects of class \code{"flexmix"} which are returned by \code{flexmix()}. In the future it would be desirable to have more diagnostic tools available to analyze the model fit and compare different models. The use of resampling methods would be convenient as they can be applied to all kinds of mixtures models and would therefore suit well the purpose of the package which is flexible modelling of various finite mixture models. Furthermore, an additional visualization method for the fitted coefficients of the mixture would facilitate the comparison of the components. %%----------------------------------------------------------------------- \section*{Computational details} <>= SI <- sessionInfo() pkgs <- paste(sapply(c(SI$otherPkgs, SI$loadedOnly), function(x) paste("\\\\pkg{", x$Package, "} ", x$Version, sep = "")), collapse = ", ") @ All computations and graphics in this paper have been done using \proglang{R} version \Sexpr{getRversion()} with the packages \Sexpr{pkgs}. %%----------------------------------------------------------------------- \section*{Acknowledgments} This research was supported by the the Austrian Science Foundation (FWF) under grant P17382 and the Austrian Academy of Sciences ({\"O}AW) through a DOC-FFORTE scholarship for Bettina Gr{\"u}n. %%----------------------------------------------------------------------- \bibliography{flexmix} \end{document} flexmix/vignettes/flexmix.png0000644000176200001440000022746114404637307016144 0ustar liggesusers‰PNG  IHDRݲêÛsBITÛáOà pHYs   jŒw IDATxœìÝi@WÛ7ðIØqW6w©UqƒZ¨­¨Xµ¨`Å]¬Õ‚€hk«µRën¥7ŠâŠ÷ÝÞÔ­®ÕªuC±*¶¨ˆ²+*BBï‡yïy¦3É0Ùføÿ>M®9sÎ5I€äâÌIuu5‚“Š@…º €8P—‡¹Ø €±¨¬¬ÌÉÉ; 0;;»† Šü ê2ðÿ=~üØÍÍMì,ÀPÃÃÃÅÎþ×1ˆóeÀdŒ?þåË—bgâøòË/ýýýÅÎBÏP—“qüøñ‚‚±³qŒ1BìôuP­Y³fݺu; ÐÞ£G²²²Äθ .ªuïÞýرcbgÚ[¹rå¬Y³Äθ`Ý_q`¾ ˜$[[Û«W¯ŠPbbbBB‚ØYê2`’¤R©‡‡‡ØY€ÙÛÛ‹‚Áá:&q . 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FlexMix implements a general framework for fitting discrete mixtures of regression models in the \R{} statistical computing environment: three variants of the EM algorithm can be used for parameter estimation, regressors and responses may be multivariate with arbitrary dimension, data may be grouped, e.g., to account for multiple observations per individual, the usual formula interface of the \proglang{S} language is used for convenient model specification, and a modular concept of driver functions allows to interface many different types of regression models. Existing drivers implement mixtures of standard linear models, generalized linear models and model-based clustering. FlexMix provides the E-step and all data handling, while the M-step can be supplied by the user to easily define new models. } \Keywords{\proglang{R}, finite mixture models, model based clustering, latent class regression} \Plainkeywords{R, finite mixture models, model based clustering, latent class regression} \Volume{11} \Issue{8} \Month{October} \Year{2004} \Submitdate{2004-04-19} \Acceptdate{2004-10-18} %%\usepackage{Sweave} %% already provided by jss.cls %%\VignetteIndexEntry{FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R} %%\VignetteDepends{flexmix} %%\VignetteKeywords{R, finite mixture models, model based clustering, latent class regression} %%\VignettePackage{flexmix} \begin{document} \section{Introduction} \label{sec:introduction} Finite mixture models have been used for more than 100 years, but have seen a real boost in popularity over the last decade due to the tremendous increase in available computing power. The areas of application of mixture models range from biology and medicine to physics, economics and marketing. On the one hand these models can be applied to data where observations originate from various groups and the group affiliations are not known, and on the other hand to provide approximations for multi-modal distributions \citep{flexmix:Everitt+Hand:1981,flexmix:Titterington+Smith+Makov:1985,flexmix:McLachlan+Peel:2000}. In the 1990s finite mixture models have been extended by mixing standard linear regression models as well as generalized linear models \citep{flexmix:Wedel+DeSarbo:1995}. An important area of application of mixture models is market segmentation \citep{flexmix:Wedel+Kamakura:2001}, where finite mixture models replace more traditional cluster analysis and cluster-wise regression techniques as state of the art. Finite mixture models with a fixed number of components are usually estimated with the expectation-maximization (EM) algorithm within a maximum likelihood framework \citep{flexmix:Dempster+Laird+Rubin:1977} and with MCMC sampling \citep{flexmix:Diebolt+Robert:1994} within a Bayesian framework. \newpage The \R{} environment for statistical computing \citep{flexmix:R-Core:2004} features several packages for finite mixture models, including \pkg{mclust} for mixtures of multivariate Gaussian distributions \citep{flexmix:Fraley+Raftery:2002,flexmix:Fraley+Raftery:2002a}, \pkg{fpc} for mixtures of linear regression models \citep{flexmix:Hennig:2000} and \pkg{mmlcr} for mixed-mode latent class regression \citep{flexmix:Buyske:2003}. There are three main reasons why we have chosen to write yet another software package for EM estimation of mixture models: \begin{itemize} \item The existing implementations did not cover all cases we needed for our own research (mainly marketing applications). \item While all \R{} packages mentioned above are open source and hence can be extended by the user by modifying the source code, we wanted an implementation where extensibility is a main design principle to enable rapid prototyping of new mixture models. \item We include a sampling-based variant of the EM-algorithm for models where weighted maximum likelihood estimation is not available. FlexMix has a clean interface between E- and M-step such that variations of both are easy to combine. \end{itemize} This paper is organized as follows: First we introduce the mathematical models for latent class regression in Section~\ref{sec:latent-class-regr} and shortly discuss parameter estimation and identifiability. Section~\ref{sec:using-flexmix} demonstrates how to use FlexMix to fit models with the standard driver for generalized linear models. Finally, Section~\ref{sec:extending-flexmix} shows how to extend FlexMix by writing new drivers using the well-known model-based clustering procedure as an example. \section{Latent class regression} \label{sec:latent-class-regr} Consider finite mixture models with $K$ components of form \begin{equation}\label{eq:1} h(y|x,\psi) = \sum_{k = 1}^K \pi_k f(y|x,\theta_k) \end{equation} \begin{displaymath} \pi_k \geq 0, \quad \sum_{k = 1}^K \pi_k = 1 \end{displaymath} where $y$ is a (possibly multivariate) dependent variable with conditional density $h$, $x$ is a vector of independent variables, $\pi_k$ is the prior probability of component $k$, $\theta_k$ is the component specific parameter vector for the density function $f$, and $\psi=(\pi_1,,\ldots,\pi_K,\theta_1',\ldots,\theta_K')'$ is the vector of all parameters. If $f$ is a univariate normal density with component-specific mean $\beta_k'x$ and variance $\sigma^2_k$, we have $\theta_k = (\beta_k', \sigma_k^2)'$ and Equation~(\ref{eq:1}) describes a mixture of standard linear regression models, also called \emph{latent class regression} or \emph{cluster-wise regression} \citep{flexmix:DeSarbo+Cron:1988}. If $f$ is a member of the exponential family, we get a mixture of generalized linear models \citep{flexmix:Wedel+DeSarbo:1995}, known as \emph{GLIMMIX} models in the marketing literature \citep{flexmix:Wedel+Kamakura:2001}. For multivariate normal $f$ and $x\equiv1$ we get a mixture of Gaussians without a regression part, also known as \emph{model-based clustering}. The posterior probability that observation $(x,y)$ belongs to class $j$ is given by \begin{equation}\label{eq:3} \Prob(j|x, y, \psi) = \frac{\pi_j f(y | x, \theta_j)}{\sum_k \pi_k f(y | x, \theta_k)} \end{equation} The posterior probabilities can be used to segment data by assigning each observation to the class with maximum posterior probability. In the following we will refer to $f(\cdot|\cdot, \theta_k)$ as \emph{mixture components} or \emph{classes}, and the groups in the data induced by these components as \emph{clusters}. \subsection{Parameter estimation} \label{sec:parameter-estimation} The log-likelihood of a sample of $N$ observations $\{(x_1,y_1),\ldots,(x_N,y_N)\}$ is given by \begin{equation}\label{eq:4} \log L = \sum_{n=1}^N \log h(y_n|x_n,\psi) = \sum_{n=1}^N \log\left(\sum_{k = 1}^K \pi_kf(y_n|x_n,\theta_k) \right) \end{equation} and can usually not be maximized directly. The most popular method for maximum likelihood estimation of the parameter vector $\psi$ is the iterative EM algorithm \citep{flexmix:Dempster+Laird+Rubin:1977}: \begin{description} \item[Estimate] the posterior class probabilities for each observation \begin{displaymath} \hat p_{nk} = \Prob(k|x_n, y_n, \hat \psi) \end{displaymath} using Equation~(\ref{eq:3}) and derive the prior class probabilities as \begin{displaymath} \hat\pi_k = \frac1N \sum_{n=1}^N \hat p_{nk} \end{displaymath} \item[Maximize] the log-likelihood for each component separately using the posterior probabilities as weights \begin{equation}\label{eq:2} \max_{\theta_k} \sum_{n=1}^N \hat p_{nk} \log f(y_n | x_n, \theta_k) \end{equation} \end{description} The E- and M-steps are repeated until the likelihood improvement falls under a pre-specified threshold or a maximum number of iterations is reached. The EM algorithm cannot be used for mixture models only, but rather provides a general framework for fitting models on incomplete data. Suppose we augment each observation $(x_n,y_n)$ with an unobserved multinomial variable $z_n = (z_{n1},\ldots,z_{nK})$, where $z_{nk}=1$ if $(x_n,y_n)$ belongs to class $k$ and $z_{nk}=0$ otherwise. The EM algorithm can be shown to maximize the likelihood on the ``complete data'' $(x_n,y_n,z_n)$; the $z_n$ encode the missing class information. If the $z_n$ were known, maximum likelihood estimation of all parameters would be easy, as we could separate the data set into the $K$ classes and estimate the parameters $\theta_k$ for each class independently from the other classes. If the weighted likelihood estimation in Equation~(\ref{eq:2}) is infeasible for analytical, computational, or other reasons, then we have to resort to approximations of the true EM procedure by assigning the observations to disjoint classes and do unweighted estimation within the groups: \begin{displaymath} \max_{\theta_k} \sum_{n: z_{nk=1}} \log f(y_n | x_n, \theta_k) \end{displaymath} This corresponds to allow only 0 and 1 as weights. Possible ways of assigning the data into the $K$ classes are \begin{itemize} \item \textbf{hard} \label{hard} assignment to the class with maximum posterior probability $p_{nk}$, the resulting procedure is called maximizing the \emph{classification likelihood} by \cite{flexmix:Fraley+Raftery:2002}. Another idea is to do \item \textbf{random} assignment to classes with probabilities $p_{nk}$, which is similar to the sampling techniques used in Bayesian estimation (although for the $z_n$ only). \end{itemize} Well known limitations of the EM algorithm include that convergence can be slow and is to a local maximum of the likelihood surface only. There can also be numerical instabilities at the margin of parameter space, and if a component gets to contain only a few observations during the iterations, parameter estimation in the respective component may be problematic. E.g., the likelihood of Gaussians increases without bounds for $\sigma^2\to 0$. As a result, numerous variations of the basic EM algorithm described above exist, most of them exploiting features of special cases for $f$. \subsection{Identifiability} \label{sec:identifiability} An open question is still identifiability of many mixture models. A comprehensive overview of this topic is beyond the scope of this paper, however, users of mixture models should be aware of the problem: \begin{description} \item[Relabelling of components:] Mixture models are only identifiable up to a permutation of the component labels. For EM-based approaches this only affects interpretation of results, but is no problem for parameter estimation itself. \item[Overfitting:] If a component is empty or two or more components have the same parameters, the data generating process can be represented by a smaller model with fewer components. This kind of unidentifiability can be avoided by requiring that the prior weights $\pi_k$ are not equal to zero and that the component specific parameters are different. \item[Generic unidentifiability:] It has been shown that mixtures of univariate normal, gamma, exponential, Cauchy and Poisson distributions are identifiable, while mixtures of discrete or continuous uniform distributions are not identifiable. A special case is the class of mixtures of binomial and multinomial distributions which are only identifiable if the number of components is limited with respect to, e.g., the number of observations per person. See \cite{flexmix:Everitt+Hand:1981}, \cite{flexmix:Titterington+Smith+Makov:1985}, \cite{flexmix:Grun:2002} and references therein for details. \end{description} FlexMix tries to avoid overfitting because of vanishing prior probabilities by automatically removing components where the prior $\pi_k$ falls below a user-specified threshold. Automated diagnostics for generic identifiability are currently under investigation. Relabelling of components is in some cases more of a nuisance than a real problem (``component 2 of the first run may be component 3 in the second run''), more serious are interactions of component relabelling and categorical predictor variables, see \cite{flexmix:Grun+Leisch:2004} for a discussion and how bootstrapping can be used to assess identifiability of mixture models. \pagebreak[4] \section{Using FlexMix} \label{sec:using-flexmix} \SweaveOpts{width=12,height=8,eps=FALSE,keep.source=TRUE} The standard M-step \texttt{FLXMRglm()} of FlexMix is an interface to R's generalized linear modelling facilities (the \texttt{glm()} function). As a simple example we use artificial data with two latent classes of size \Sexpr{nrow(NPreg)/2} each: \begin{center} \begin{tabular}{ll} Class~1: & $ y = 5x+\epsilon$\\ Class~2: & $ y = 15+10x-x^2+\epsilon$\\ \end{tabular} \end{center} with $\epsilon\sim N(0,9)$ and prior class probabilities $\pi_1=\pi_2=0.5$, see the left panel of Figure~\ref{fig:npreg}. We can fit this model in \R{} using the commands <<>>= library("flexmix") data("NPreg") m1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2) m1 @ and get a first look at the estimated parameters of mixture component~1 by <<>>= parameters(m1, component = 1) @ and <<>>= parameters(m1, component = 2) @ for component~2. The paramter estimates of both components are close to the true values. A cross-tabulation of true classes and cluster memberships can be obtained by <<>>= table(NPreg$class, clusters(m1)) @ The summary method <<>>= summary(m1) @ gives the estimated prior probabilities $\hat\pi_k$, the number of observations assigned to the corresponding clusters, the number of observations where $p_{nk}>\delta$ (with a default of $\delta=10^{-4}$), and the ratio of the latter two numbers. For well-seperated components, a large proportion of observations with non-vanishing posteriors $p_{nk}$ should also be assigned to the corresponding cluster, giving a ratio close to 1. For our example data the ratios of both components are approximately 0.7, indicating the overlap of the classes at the cross-section of line and parabola. \begin{figure}[htbp] \centering <>= par(mfrow=c(1,2)) plot(yn~x, col=class, pch=class, data=NPreg) plot(yp~x, col=class, pch=class, data=NPreg) @ \caption{Standard regression example (left) and Poisson regression (right).} \label{fig:npreg} \end{figure} Histograms or rootograms of the posterior class probabilities can be used to visually assess the cluster structure \citep{flexmix:Tantrum+Murua+Stuetzle:2003}, this is now the default plot method for \texttt{"flexmix"} objects \citep{flexmix:Leisch:2004}. Rootograms are very similar to histograms, the only difference is that the height of the bars correspond to square roots of counts rather than the counts themselves, hence low counts are more visible and peaks less emphasized. \begin{figure}[htbp] \centering <>= print(plot(m1)) @ \caption{The plot method for \texttt{"flexmix"} objects, here obtained by \texttt{plot(m1)}, shows rootograms of the posterior class probabilities.} \label{fig:root1} \end{figure} Usually in each component a lot of observations have posteriors close to zero, resulting in a high count for the corresponing bin in the rootogram which obscures the information in the other bins. To avoid this problem, all probabilities with a posterior below a threshold are ignored (we again use $10^{-4}$). A peak at probability 1 indicates that a mixture component is well seperated from the other components, while no peak at 1 and/or significant mass in the middle of the unit interval indicates overlap with other components. In our simple example the components are medium well separated, see Figure~\ref{fig:root1}. Tests for significance of regression coefficients can be obtained by <<>>= rm1 <- refit(m1) summary(rm1) @ Function \texttt{refit()} fits weighted generalized linear models to each component using the standard \R{} function \texttt{glm()} and the posterior probabilities as weights, see \texttt{help("refit")} for details. The data set \texttt{NPreg} also includes a response from a generalized linear model with a Poisson distribution and exponential link function. The two classes of size \Sexpr{nrow(NPreg)/2} each have parameters \begin{center} \begin{tabular}{ll} Class~1: & $ \mu_1 = 2 - 0.2x$\\ Class~2: & $ \mu_2 = 1 + 0.1x$\\ \end{tabular} \end{center} and given $x$ the response $y$ in group $k$ has a Poisson distribution with mean $e^{\mu_k}$, see the right panel of Figure~\ref{fig:npreg}. The model can be estimated using <>= options(width=55) @ <<>>= m2 <- flexmix(yp ~ x, data = NPreg, k = 2, model = FLXMRglm(family = "poisson")) summary(m2) @ <>= options(width=65) @ \begin{figure}[htbp] \centering <>= print(plot(m2)) @ \caption{\texttt{plot(m2)}} \label{fig:root2} \end{figure} Both the summary table and the rootograms in Figure~\ref{fig:root2} clearly show that the clusters of the Poisson response have much more overlap. For our simple low-dimensional example data the overlap of the classes is obvious by looking at scatterplots of the data. For data in higher dimensions this is not an option. The rootograms and summary tables for \texttt{"flexmix"} objects work off the densities or posterior probabilities of the observations and thus do not depend on the dimensionality of the input space. While we use simple 2-dimensional examples to demonstrate the techniques, they can easily be used on high-dimensional data sets or models with complicated covariate structures. \subsection{Multiple independent responses} \label{sec:mult-indep-resp} If the response $y=(y_1,\ldots,y_D)'$ is $D$-dimensional and the $y_d$ are mutually independent the mixture density in Equation~(\ref{eq:1}) can be written as \begin{eqnarray*} h(y|x,\psi) &=& \sum_{k = 1}^K \pi_k f(y|x,\theta_k)\\ &=& \sum_{k = 1}^K \pi_k \prod_{d=1}^D f_d(y|x,\theta_{kd}) \end{eqnarray*} To specify such models in FlexMix we pass it a list of models, where each list element corresponds to one $f_d$, and each can have a different set of dependent and independent variables. To use the Gaussian and Poisson responses of data \texttt{NPreg} simultaneously, we use the model specification \begin{Sinput} > m3 = flexmix(~x, data=NPreg, k=2, + model=list(FLXMRglm(yn~.+I(x^2)), + FLXMRglm(yp~., family="poisson"))) \end{Sinput} <>= m3 <- flexmix(~ x, data = NPreg, k = 2, model=list(FLXMRglm(yn ~ . + I(x^2)), FLXMRglm(yp ~ ., family = "poisson"))) @ Note that now three model formulas are involved: An overall formula as first argument to function \texttt{flexmix()} and one formula per response. The latter ones are interpreted relative to the overall formula such that common predictors have to be specified only once, see \texttt{help("update.formula")} for details on the syntax. The basic principle is that the dots get replaced by the respective terms from the overall formula. The rootograms show that the posteriors of the two-response model are shifted towards 0 and 1 (compared with either of the two univariate models), the clusters are now well-separated. \begin{figure}[htbp] \centering <>= print(plot(m3)) @ \caption{\texttt{plot(m3)}} \label{fig:root3} \end{figure} \subsection{Repeated measurements} \label{sec:repe-meas} If the data are repeated measurements on $M$ individuals, and we have $N_m$ observations from individual $m$, then the log-likelihood in Equation~(\ref{eq:4}) can be written as \begin{displaymath} \log L = \sum_{m=1}^M \sum_{n=1}^{N_m} \log h(y_{mn}|x_{mn},\psi), \qquad \sum_{m=1}^M N_m = N \end{displaymath} and the posterior probability that individual $m$ belongs to class $j$ is given by \begin{displaymath} \Prob(j|m) = \frac{\pi_j \prod_{n=1}^{N_m} f(y_{mn} | x_{mn}, \theta_j)}{\sum_k \pi_k \prod_{n=1}^{N_m} f(y_{mn} | x_{mn}, \theta_k)} \end{displaymath} where $(x_{mn}, y_{mn})$ is the $n$-th observation from individual $m$. As an example, assume that the data in \texttt{NPreg} are not 200 independent observations, but 4 measurements each from 50 persons such that $\forall m: N_m=4$. Column \texttt{id2} of the data frame encodes such a grouping and can easily be used in FlexMix: <<>>= m4 <- flexmix(yn ~ x + I(x^2) | id2, data = NPreg, k = 2) summary(m4) @ Note that convergence of the EM algorithm is much faster with grouping and the two clusters are now perfectly separated. \subsection{Control of the EM algorithm} \label{sec:control-em-algorithm} Details of the EM algorithm can be tuned using the \texttt{control} argument of function \texttt{flexmix()}. E.g., to use a maximum number of 15 iterations, report the log-likelihood at every 3rd step and use hard assignment of observations to clusters (cf. page~\pageref{hard}) the call is <<>>= m5 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2, control = list(iter.max = 15, verbose = 3, classify = "hard")) @ Another control parameter (\texttt{minprior}, see below for an example) is the minimum prior probability components are enforced to have, components falling below this threshold (the current default is 0.05) are removed during EM iteration to avoid numerical instabilities for components containing only a few observations. Using a minimum prior of 0 disables component removal. \subsection{Automated model search} In real applications the number of components is unknown and has to be estimated. Tuning the minimum prior parameter allows for simplistic model selection, which works surprisingly well in some situations: <<>>= m6 <- flexmix(yp ~ x + I(x^2), data = NPreg, k = 4, control = list(minprior = 0.2)) m6 @ Although we started with four components, the algorithm converged at the correct two component solution. A better approach is to fit models with an increasing number of components and compare them using AIC or BIC. As the EM algorithm converges only to the next local maximum of the likelihood, it should be run repeatedly using different starting values. The function \texttt{stepFlexmix()} can be used to repeatedly fit models, e.g., <<>>= m7 <- stepFlexmix(yp ~ x + I(x^2), data = NPreg, control = list(verbose = 0), k = 1:5, nrep = 5) @ runs \texttt{flexmix()} 5 times for $k=1,2,\ldots,5$ components, totalling in 25 runs. It returns a list with the best solution found for each number of components, each list element is simply an object of class \texttt{"flexmix"}. To find the best model we can use <<>>= getModel(m7, "BIC") @ and choose the number of components minimizing the BIC. \section{Extending FlexMix} \label{sec:extending-flexmix} One of the main design principles of FlexMix was extensibility, users can provide their own M-step for rapid prototyping of new mixture models. FlexMix was written using S4 classes and methods \citep{flexmix:Chambers:1998} as implemented in \R{} package \pkg{methods}. The central classes for writing M-steps are \texttt{"FLXM"} and \texttt{"FLXcomponent"}. Class \texttt{"FLXM"} specifies how the model is fitted using the following slots: \begin{description} \item[fit:] A \texttt{function(x,y,w)} returning an object of class \texttt{"FLXcomponent"}. \item[defineComponent:] Expression or function constructing the object of class \texttt{"FLXcomponent"}. \item[weighted:] Logical, specifies if the model may be fitted using weighted likelihoods. If \texttt{FALSE}, only hard and random classification are allowed (and hard classification becomes the default). \item[formula:] Formula relative to the overall model formula, default is \verb|.~.| \item[name:] A character string describing the model, this is only used for print output. \end{description} The remaining slots of class \texttt{"FLXM"} are used internally by FlexMix to hold data, etc. and omitted here, because they are not needed to write an M-step driver. The most important slot doing all the work is \texttt{fit} holding a function performing the maximum likelihood estimation described in Equation~(\ref{eq:2}). The \texttt{fit()} function returns an object of class \texttt{"FLXcomponent"} which holds a fitted component using the slots: \begin{description} \item[logLik:] A \texttt{function(x,y)} returning the log-likelihood for observations in matrices \texttt{x} and \texttt{y}. \item[predict:] A \texttt{function(x)} predicting \texttt{y} given \texttt{x}. \item[df:] The degrees of freedom used by the component, i.e., the number of estimated parameters. \item[parameters:] An optional list containing model parameters. \end{description} In a nutshell class \texttt{"FLXM"} describes an \emph{unfitted} model, whereas class \texttt{"FLXcomponent"} holds a \emph{fitted} model. \lstset{frame=trbl,basicstyle=\small\tt,stepnumber=5,numbers=left} \begin{figure}[tb] \centering \begin{minipage}{0.94\textwidth} \lstinputlisting{mymclust.R} \end{minipage} \caption{M-step for model-based clustering: \texttt{mymclust} is a simplified version of the standard FlexMix driver \texttt{FLXmclust}.} \label{fig:mymclust.R} \end{figure} \subsection{Writing an M-step driver} \label{sec:writing-an-m} Figure~\ref{fig:mymclust.R} shows an example driver for model-based clustering. We use function \texttt{dmvnorm()} from package \pkg{mvtnorm} for calculation of multivariate Gaussian densities. In line~5 we create a new \texttt{"FLXMC"} object named \texttt{retval}, which is also the return value of the driver. Class \texttt{"FLXMC"} extends \texttt{"FLXM"} and is used for model-based clustering. It contains an additional slot with the name of the distribution used. All drivers should take a formula as their first argument, this formula is directly passed on to \texttt{retval}. In most cases authors of new FlexMix drivers need not worry about formula parsing etc., this is done by \texttt{flexmix} itself. In addition we have to declare whether the driver can do weighted ML estimation (\texttt{weighted=TRUE}) and give a name to our model. The remainder of the driver creates a \texttt{fit()} function, which takes regressors \texttt{x}, response \texttt{y} and weights \texttt{w}. For multivariate Gaussians the maximum likelihood estimates correspond to mean and covariance matrix, the standard R function \texttt{cov.wt()} returns a list containing estimates of the weighted covariance matrix and the mean for given data. Our simple example performs clustering without a regression part, hence $x$ is ignored. If \texttt{y} has $D$ columns, we estimate $D$ parameters for the mean and $D(D-1)/2$ parameters for the covariance matrix, giving a total of $(3D+D^2)/2$ parameters (line~11). As an additional feature we allow the user to specify whether the covariance matrix is assumed to be diagonal or a full matrix. For \texttt{diagonal=TRUE} we use only the main diagonal of the covariance matrix (line~14) and the number of parameters is reduced to $2D$. In addition to parameter estimates, \texttt{flexmix()} needs a function calculating the log-likelihood of given data $x$ and $y$, which in our example is the log-density of a multivariate Gaussian. In addition we have to provide a function predicting $y$ given $x$, in our example simply the mean of the Gaussian. Finally we create a new \texttt{"FLXcomponent"} as return value of function \texttt{fit()}. Note that our internal functions \texttt{fit()}, \texttt{logLik()} and \texttt{predict()} take only \texttt{x}, \texttt{y} and \texttt{w} as arguments, but none of the model-specific parameters like means and covariances, although they use them of course. \R{} uses \emph{lexical scoping} rules for finding free variables \citep{flexmix:Gentleman+Ihaka:2000}, hence it searches for them first in the environment where a function is defined. E.g., the \texttt{fit()} function uses the variable \texttt{diagonal} in line~24, and finds it in the environment where the function itself was defined, which is the body of function \texttt{mymclust()}. Function \texttt{logLik()} uses the list \texttt{para} in lines~8 and 9, and uses the one found in the body of \texttt{defineComponent()}. Function \texttt{flexmix()} on the other hand never sees the model parameters, all it uses are function calls of form \texttt{fit(x,y,w)} or \texttt{logLik(x,y)}, which are exactly the same for all kinds of mixture models. In fact, it would not be necessary to even store the component parameters in the \texttt{"FLXcomponent"} object, they are there only for convenience such that users can easily extract and use them after \texttt{flexmix()} has finished. Lexical scope allows to write clean interfaces in a very elegant way, the driver abstracts all model details from the FlexMix main engine. \subsection{Example: Using the driver} \label{sec:example:-model-based} \SweaveOpts{width=12,height=6,eps=FALSE} <>= library("flexmix") set.seed(1504) options(width=60) grDevices::ps.options(family="Times") suppressMessages(require("ellipse")) suppressMessages(require("mvtnorm")) source("mymclust.R") @ As a simple example we use the four 2-dimensional Gaussian clusters from data set \texttt{Nclus}. Fitting a wrong model with diagonal covariance matrix is done by <<>>= data("Nclus") m1 <- flexmix(Nclus ~ 1, k = 4, model = mymclust()) summary(m1) @ The result can be seen in the left panel of Figure~\ref{fig:ell}, the result is ``wrong'' because we forced the ellipses to be parallel to the axes. The overlap between three of the four clusters can also be inferred from the low ratio statistics in the summary table (around 0.5 for components 1, 3 and 4), while the much better separated upper left cluster has a much higher ratio of 0.85. Using the correct model with a full covariance matrix can be done by setting \texttt{diagonal=FALSE} in the call to our driver \texttt{mymclust()}: <<>>= m2 <- flexmix(Nclus ~ 1, k = 4, model = mymclust(diagonal = FALSE)) summary(m2) @ \begin{figure}[htbp] \centering <>= par(mfrow=1:2) plotEll(m1, Nclus) plotEll(m2, Nclus) @ \caption{Fitting a mixture model with diagonal covariance matrix (left) and full covariance matrix (right).} \label{fig:ell} \end{figure} \pagebreak[4] \section{Summary and outlook} \label{sec:summary} The primary goal of FlexMix is extensibility, this makes the package ideal for rapid development of new mixture models. There is no intent to replace packages implementing more specialized mixture models like \pkg{mclust} for mixtures of Gaussians, FlexMix should rather be seen as a complement to those. By interfacing R's facilities for generalized linear models, FlexMix allows the user to estimate complex latent class regression models. Using lexical scope to resolve model-specific parameters hides all model details from the programming interface, FlexMix can in principle fit almost arbitrary finite mixture models for which the EM algorithm is applicable. The downside of this is that FlexMix can in principle fit almost arbitrary finite mixture models, even models where no proper theoretical results for model identification etc.\ are available. We are currently working on a toolset for diagnostic checks on mixture models to test necessary identifiability conditions for those cases where results are available. We also want to implement newer variations of the classic EM algorithm, especially for faster convergence. Another plan is to have an interactive version of the rootograms using \texttt{iPlots} \citep{flexmix:Urbanek+Theus:2003} such that the user can explore the relations between mixture components, possibly linked to background variables. Other planned extensions include covariates for the prior probabilities and to allow to mix different distributions for components, e.g., to include a Poisson point process for background noise. \section*{Computational details} <>= SI <- sessionInfo() pkgs <- paste(sapply(c(SI$otherPkgs, SI$loadedOnly), function(x) paste("\\\\pkg{", x$Package, "} ", x$Version, sep = "")), collapse = ", ") @ All computations and graphics in this paper have been done using \proglang{R} version \Sexpr{getRversion()} with the packages \Sexpr{pkgs}. \section*{Acknowledgments} This research was supported by the Austrian Science Foundation (FWF) under grant SFB\#010 (`Adaptive Information Systems and Modeling in Economics and Management Science'). Bettina Gr\"un has modified the original version to include and reflect the changes of the package. \bibliography{flexmix} \end{document} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End: flexmix/vignettes/ziglm.R0000644000176200001440000000220514404637307015212 0ustar liggesuserssetClass("FLXMRziglm", contains = "FLXMRglm") FLXMRziglm <- function(formula = . ~ ., family = c("binomial", "poisson"), ...) { family <- match.arg(family) new("FLXMRziglm", FLXMRglm(formula, family, ...), name = paste("FLXMRziglm", family, sep=":")) } setMethod("FLXgetModelmatrix", signature(model="FLXMRziglm"), function(model, data, formula, lhs=TRUE, ...) { model <- callNextMethod(model, data, formula, lhs) if (attr(terms(model@fullformula), "intercept") == 0) stop("please include an intercept") model }) setMethod("FLXremoveComponent", signature(model = "FLXMRziglm"), function(model, nok, ...) { if (1 %in% nok) as(model, "FLXMRglm") else model }) setMethod("FLXmstep", signature(model = "FLXMRziglm"), function(model, weights, components, ...) { coef <- c(-Inf, rep(0, ncol(model@x)-1)) names(coef) <- colnames(model@x) comp.1 <- with(list(coef = coef, df = 0, offset = NULL, family = model@family), eval(model@defineComponent)) c(list(comp.1), FLXmstep(as(model, "FLXMRglm"), weights[, -1, drop=FALSE], components[-1])) }) flexmix/vignettes/bootstrapping.Rnw0000644000176200001440000004660014404637307017337 0ustar liggesusers\documentclass[nojss]{jss} \usepackage{amsfonts,bm,amsmath,amssymb} %%\usepackage{Sweave} %% already provided by jss.cls %%%\VignetteIndexEntry{Finite Mixture Model Diagnostics Using Resampling Methods} %%\VignetteDepends{flexmix} %%\VignetteKeywords{R, finite mixture model, resampling, bootstrap} %%\VignettePackage{flexmix} \title{Finite Mixture Model Diagnostics Using Resampling Methods} <>= options(useFancyQuotes = FALSE) digits <- 3 Colors <- c("#E495A5", "#39BEB1") critical_values <- function(n, p = "0.95") { data("qDiptab", package = "diptest") if (n %in% rownames(qDiptab)) { return(qDiptab[as.character(n), p]) }else { n.approx <- as.numeric(rownames(qDiptab)[which.min(abs(n - as.numeric(rownames(qDiptab))))]) return(sqrt(n.approx)/sqrt(n) * qDiptab[as.character(n.approx), p]) } } library("graphics") library("flexmix") combine <- function(x, sep, width) { cs <- cumsum(nchar(x)) remaining <- if (any(cs[-1] > width)) combine(x[c(FALSE, cs[-1] > width)], sep, width) c(paste(x[c(TRUE, cs[-1] <= width)], collapse= sep), remaining) } prettyPrint <- function(x, sep = " ", linebreak = "\n\t", width = getOption("width")) { x <- strsplit(x, sep)[[1]] paste(combine(x, sep, width), collapse = paste(sep, linebreak, collapse = "")) } @ \author{Bettina Gr{\"u}n\\ Wirtschaftsuniversit{\"a}t Wien \And Friedrich Leisch\\ Universit\"at f\"ur Bodenkultur Wien} \Plainauthor{Bettina Gr{\"u}n, Friedrich Leisch} \Address{ Bettina Gr\"un\\ Institute for Statistics and Mathematics\\ Wirtschaftsuniversit{\"a}t Wien\\ Welthandelsplatz 1\\ 1020 Wien, Austria\\ E-mail: \email{Bettina.Gruen@R-project.org}\\ Friedrich Leisch\\ Institut f\"ur Angewandte Statistik und EDV\\ Universit\"at f\"ur Bodenkultur Wien\\ Peter Jordan Stra\ss{}e 82\\ 1190 Wien, Austria\\ E-mail: \email{Friedrich.Leisch@boku.ac.at} } \Abstract{ This paper illustrates the implementation of resampling methods in \pkg{flexmix} as well as the application of resampling methods for model diagnostics of fitted finite mixture models. Convenience functions to perform these methods are available in package \pkg{flexmix}. The use of the methods is illustrated with an artificial example and the \code{seizure} data set. } \Keywords{\proglang{R}, finite mixture models, resampling, bootstrap} \Plainkeywords{R, finite mixture models, resampling, bootstrap} %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \begin{document} \SweaveOpts{engine=R, echo=true, height=5, width=8, eps=FALSE, keep.source=TRUE} \setkeys{Gin}{width=0.95\textwidth} \section{Implementation of resampling methods}\label{sec:implementation} The proposed framework for model diagnostics using resampling \citep{mixtures:gruen+leisch:2004} equally allows to investigate model fit for all kinds of mixture models. The procedure is applicable to mixture models with different component specific models and does not impose any limitation such as for example on the dimension of the parameter space of the component specific model. In addition to the fitting step different component specific models only require different random number generators for the parametric bootstrap. The \code{boot()} function in \pkg{flexmix} is a generic \proglang{S4} function with a method for fitted finite mixtures of class \code{"flexmix"} and is applicable to general finite mixture models. The function with arguments and their defaults is given by: <>= cat(prettyPrint(gsub("boot_flexmix", "boot", prompt(flexmix:::boot_flexmix, filename = NA)$usage[[2]]), sep = ", ", linebreak = paste("\n", paste(rep(" ", 2), collapse = ""), sep= ""), width = 70)) @ The interface is similar to the \code{boot()} function in package \pkg{boot} \citep{mixtures:Davison+Hinkley:1997, mixtures:Canty+Ripley:2010}. The \code{object} is a fitted finite mixture of class \code{"flexmix"} and \code{R} denotes the number of resamples. The possible bootstrapping method are \code{"empirical"} (also available as \code{"ordinary"}) and \code{"parametric"}. For the parametric bootstrap sampling from the fitted mixture is performed using \code{rflexmix()}. For mixture models with different component specific models \code{rflexmix()} requires a sampling method for the component specific model. Argument \code{initialize\_solution} allows to select if the EM algorithm is started in the original finite mixture solution or if random initialization is performed. The fitted mixture model might contain weights and group indicators. The weights are case weights and allow to reduce the amount of data if observations are identical. This is useful for example for latent class analysis of multivariate binary data. The argument \code{keep\_weights} allows to indicate if they should be kept for the bootstrapping. Group indicators allow to specify that the component membership is identical over several observations, e.g., for repeated measurements of the same individual. Argument \code{keep\_groups} allows to indicate if the grouping information should also be used in the bootstrapping. \code{verbose} indicates if information on the progress should be printed. The \code{control} argument allows to control the EM algorithm for fitting the model to each of the bootstrap samples. By default the \code{control} argument is extracted from the fitted model provided by \code{object}. \code{k} allows to specify the number of components and by default this is also taken from the fitted model provided. The \code{model} argument determines if also the model and the weights slot for each sample are stored and returned. The returned object is of class \code{"FLXboot"} and otherwise only contains the fitted parameters, the fitted priors, the log likelihoods, the number of components of the fitted mixtures and the information if the EM algorithm has converged. The likelihood ratio test is implemented based on \code{boot()} in function \code{LR\_test()} and returns an object of class \code{"htest"} containing the number of valid bootstrap replicates, the p-value, the double negative log likelihood ratio test statistics for the original data and the bootstrap replicates. The \code{plot} method for \code{"FLXboot"} objects returns a parallel coordinate plot with the fitted parameters separately for each of the components. \section{Artificial data set} In the following a finite mixture model is used as the underlying data generating process which is theoretically not identifiable. We are assuming a finite mixture of linear regression models with two components of equal size where the coverage condition is not fulfilled \citep{mixtures:Hennig:2000}. Hence, intra-component label switching is possible, i.e., there exist two parameterizations implying the same mixture distribution which differ how the components between the covariate points are combined. We assume that one measurement per object and a single categorical regressor with two levels are given. The usual design matrix for a model with intercept uses the two covariate points $\mathbf{x}_1 = (1, 0)'$ and $\mathbf{x}_2 = (1, 1)'$. The mixture distribution is given by \begin{eqnarray*} H(y|\mathbf{x}, \Theta) &=& \frac{1}{2} N(\mu_1, 0.1) + \frac{1}{2} N(\mu_2, 0.1), \end{eqnarray*} where $\mu_k(\mathbf{x}) = \mathbf{x}'\bm{\alpha}_k$ and $N(\mu, \sigma^2)$ is the normal distribution. Now let $\mu_1(\mathbf{x}_1) = 1$, $\mu_2(\mathbf{x}_1) = 2$, $\mu_1(\mathbf{x}_2) = -1$ and $\mu_2(\mathbf{x}_2) = 4$. As Gaussian mixture distributions are generically identifiable the means, variances and component weights are uniquely determined in each covariate point given the mixture distribution. However, as the coverage condition is not fulfilled, the two possible solutions for $\bm{\alpha}$ are: \begin{description} \item[Solution 1:] $\bm{\alpha}_1^{(1)} = (2,\phantom{-}2)'$, $\bm{\alpha}_2^{(1)} = (1,-2)'$, \item[Solution 2:] $\bm{\alpha}_1^{(2)} = (2,-3)'$, $\bm{\alpha}_2^{(2)} = (1,\phantom{-}3)'$. \end{description} We specify this artificial mixture distribution using \code{FLXdist()}. \code{FLXdist()} returns an unfitted finite mixture of class \code{"FLXdist"}. The class of fitted finite mixture models \code{"flexmix"} extends class \code{"FLXdist"}. Each component follows a normal distribution. The parameters specified in a named list therefore consist of the regression coefficients and the standard deviation. Function \code{FLXdist()} has an argument \code{formula} for specifying the regression in each of the components, an argument \code{k} for the component weights and \code{components} for the parameters of each of the components. <<>>= library("flexmix") Component_1 <- list(Model_1 = list(coef = c(1, -2), sigma = sqrt(0.1))) Component_2 <- list(Model_1 = list(coef = c(2, 2), sigma = sqrt(0.1))) ArtEx.mix <- FLXdist(y ~ x, k = rep(0.5, 2), components = list(Component_1, Component_2)) @ We draw a balanced sample with 50 observations in each covariate point from the mixture model using \code{rflexmix()} after defining the data points for the covariates. \code{rflexmix()} can either have an unfitted or a fitted finite mixture as input. For unfitted mixtures data has to be provided using the \code{newdata} argument. For already fitted mixtures data can be optionally provided, otherwise the data used for fitting the mixture is used. <<>>= ArtEx.data <- data.frame(x = rep(0:1, each = 100/2)) suppressWarnings(RNGversion("3.5.0")) set.seed(123) ArtEx.sim <- rflexmix(ArtEx.mix, newdata = ArtEx.data) ArtEx.data$y <- ArtEx.sim$y[[1]] ArtEx.data$class <- ArtEx.sim$class @ In Figure~\ref{fig:art} the sample is plotted together with the two solutions for combining $x_1$ and $x_2$, i.e., this illustrates intra-component label switching. \begin{figure} \centering <>= par(mar = c(5, 4, 2, 0) + 0.1) plot(y ~ x, data = ArtEx.data, pch = with(ArtEx.data, 2*class + x)) pars <- list(matrix(c(1, -2, 2, 2), ncol = 2), matrix(c(1, 3, 2, -3), ncol = 2)) for (i in 1:2) apply(pars[[i]], 2, abline, col = Colors[i]) @ \caption{Balanced sample from the artificial example with the two theoretical solutions.} \label{fig:art} \end{figure} We fit a finite mixture to the sample using \code{stepFlexmix()}. <<>>= set.seed(123) ArtEx.fit <- stepFlexmix(y ~ x, data = ArtEx.data, k = 2, nrep = 5, control = list(iter = 1000, tol = 1e-8, verbose = 0)) @ The fitted mixture can be inspected using \code{summary()} and \code{parameters()}. <<>>= summary(ArtEx.fit) parameters(ArtEx.fit) @ Obviously the fitted mixture parameters correspond to the parameterization we used to specify the mixture distribution. Using standard asymptotic theory to analyze the fitted mixture model gives the following estimates for the standard deviations. <<>>= ArtEx.refit <- refit(ArtEx.fit) summary(ArtEx.refit) @ The fitted mixture can also be analyzed using resampling techniques. For analyzing the stability of the parameter estimates where the possibility of identifiability problems is also taken into account the parametric bootstrap is used with random initialization. Function \code{boot()} can be used for empirical or parametric bootstrap (specified by the argument \code{sim}). The logical argument \code{initialize_solution} specifies if the initialization is in the original solution or random. By default random initialization is made. The number of bootstrap samples is set by the argument \code{R}. Please note that the arguments are chosen to correspond to those for function \code{boot} in package \pkg{boot} \citep{mixtures:Davison+Hinkley:1997}. <>= set.seed(123) ArtEx.bs <- boot(ArtEx.fit, R = 200, sim = "parametric") ArtEx.bs @ <>= if (file.exists("ArtEx.bs.rda")) { load("ArtEx.bs.rda") } else { set.seed(123) ArtEx.bs <- boot(ArtEx.fit, R = 200, sim = "parametric") save(ArtEx.bs, file = "ArtEx.bs.rda") } ArtEx.bs @ Function \code{boot()} returns an object of class \code{"\Sexpr{class(ArtEx.bs)}"}. The default plot compares the bootstrap parameter estimates to the confidence intervals derived using standard asymptotic theory in a parallel coordinate plot (see Figure~\ref{fig:plot.FLXboot-art}). Clearly two groups of parameter estimates can be distinguished which are about of equal size. One subset of the parameter estimates stays within the confidence intervals induced by standard asymptotic theory, while the second group corresponds to the second solution and clusters around these parameter values. \begin{figure}[h!] \centering <>= print(plot(ArtEx.bs, ordering = "coef.x", col = Colors)) @ \caption{Diagnostic plot of the bootstrap results for the artificial example.} \label{fig:plot.FLXboot-art} \end{figure} In the following the DIP-test is applied to check if the parameter estimates follow a unimodal distribution. This is done for the aggregated parameter esimates where unimodality implies that this parameter is not suitable for imposing an ordering constraint which induces a unique labelling. For the separate component analysis which is made after imposing an ordering constraint on the coefficient of $x$ rejection the null hypothesis of unimodality implies that identifiability problems are present, e.g.~due to intra-component label switching. <<>>= require("diptest") parameters <- parameters(ArtEx.bs) Ordering <- factor(as.vector(apply(matrix(parameters[,"coef.x"], nrow = 2), 2, order))) Comp1 <- parameters[Ordering == 1,] Comp2 <- parameters[Ordering == 2,] dip.values.art <- matrix(nrow = ncol(parameters), ncol = 3, dimnames=list(colnames(parameters), c("Aggregated", "Comp 1", "Comp 2"))) dip.values.art[,"Aggregated"] <- apply(parameters, 2, dip) dip.values.art[,"Comp 1"] <- apply(Comp1, 2, dip) dip.values.art[,"Comp 2"] <- apply(Comp2, 2, dip) dip.values.art @ The critical value for column \code{Aggregated} is \Sexpr{round(critical_values(nrow(parameters)), digits = digits)} and for the columns of the separate components \Sexpr{round(critical_values(nrow(Comp1)), digits = digits)}. The component sizes as well as the standard deviations follow a unimodal distribution for the aggregated data as well as for each of the components. The regression coefficients are multimodal for the aggregate data as well as for each of the components. While from the aggregated case it might be concluded that imposing an ordering constraint on the intercept or the coefficient of $x$ is suitable, the component-specific analyses reveal that a unique labelling was not achieved. \section{Seizure} In \cite{mixtures:Wang+Puterman+Cockburn:1996} a Poisson mixture regression is fitted to data from a clinical trial where the effect of intravenous gammaglobulin on suppression of epileptic seizures is investigated. The data used were 140 observations from one treated patient, where treatment started on the $28^\textrm{th}$ day. In the regression model three independent variables were included: treatment, trend and interaction treatment-trend. Treatment is a dummy variable indicating if the treatment period has already started. Furthermore, the number of parental observation hours per day were available and it is assumed that the number of epileptic seizures per observation hour follows a Poisson mixture distribution. The number of epileptic seizures per parental observation hour for each day are plotted in Figure~\ref{fig:seizure}. The fitted mixture distribution consists of two components which can be interpreted as representing 'good' and 'bad' days of the patients. The mixture model can be formulated by \begin{equation*} H(y|\mathbf{x}, \Theta) = \pi_1 P(\lambda_1) + \pi_2 P(\lambda_2), \end{equation*} where $\lambda_k = e^{\mathbf{x}'\bm{\alpha}_k}$ for $k = 1,2$ and $P(\lambda)$ is the Poisson distribution. The data is loaded and the mixture fitted with two components. <<>>= data("seizure", package = "flexmix") model <- FLXMRglm(family = "poisson", offset = log(seizure$Hours)) control <- list(iter = 1000, tol = 1e-10, verbose = 0) set.seed(123) seizMix <- stepFlexmix(Seizures ~ Treatment * log(Day), data = seizure, k = 2, nrep = 5, model = model, control = control) @ The fitted regression lines for each of the two components are shown in Figure~\ref{fig:seizure}. \begin{figure}[h!] \begin{center} <>= par(mar = c(5, 4, 2, 0) + 0.1) plot(Seizures/Hours~Day, data=seizure, pch = as.integer(seizure$Treatment)) abline(v = 27.5, lty = 2, col = "grey") matplot(seizure$Day, fitted(seizMix)/seizure$Hours, type="l", add = TRUE, col = 1, lty = 1, lwd = 2) @ \caption{Seizure data with the fitted values for the \citeauthor{mixtures:Wang+Puterman+Cockburn:1996} model. The plotting character for the observed values in the base period is a circle and for those in the treatment period a triangle.} \label{fig:seizure} \end{center} \end{figure} The parameteric bootstrap with random initialization is used to investigate identifiability problems and parameter stability. The diagnostic plot is given in Figure~\ref{fig:plot.FLXboot-seiz}. The coloring is according to an ordering constraint on the intercept. Clearly the parameter estimates corresponding to the solution where the bad days from the base period are combined with the good days from the treatement period and vice versa for the good days of the base period can be distinguished and indicate the slight identifiability problems of the fitted mixture. <>= set.seed(123) seizMix.bs <- boot(seizMix, R = 200, sim = "parametric") seizMix.bs @ <>= if (file.exists("seizMix.bs.rda")) { load("seizMix.bs.rda") } else { set.seed(123) seizMix.bs <- boot(seizMix, R = 200, sim = "parametric") save(seizMix.bs, file = "seizMix.bs.rda") } seizMix.bs @ \begin{figure}[h!] \centering <>= print(plot(seizMix.bs, ordering = "coef.(Intercept)", col = Colors)) @ \label{fig:plot.FLXboot-seiz} \caption{Diagnostic plot of the bootstrap results for the \code{seizure} data.} \end{figure} <<>>= parameters <- parameters(seizMix.bs) Ordering <- factor(as.vector(apply(matrix(parameters[,"coef.(Intercept)"], nrow = 2), 2, order))) Comp1 <- parameters[Ordering == 1,] Comp2 <- parameters[Ordering == 2,] @ For applying the DIP test also an ordering constraint on the intercept is used. The critical value for column \code{Aggregated} is \Sexpr{round(critical_values(nrow(parameters)), digits = digits)} and for the columns of the separate components \Sexpr{round(critical_values(nrow(Comp1)), digits = digits)}. <<>>= dip.values.art <- matrix(nrow = ncol(parameters), ncol = 3, dimnames = list(colnames(parameters), c("Aggregated", "Comp 1", "Comp 2"))) dip.values.art[,"Aggregated"] <- apply(parameters, 2, dip) dip.values.art[,"Comp 1"] <- apply(Comp1, 2, dip) dip.values.art[,"Comp 2"] <- apply(Comp2, 2, dip) dip.values.art @ For the aggregate results the hypothesis of unimodality cannot be rejected for the trend. For the component-specific analyses unimodality cannot be rejected only for the intercept (where the ordering condition was imposed on) and again the trend. For all other parameter estimates unimodality is rejected which indicates that the ordering constraint was able to impose a unique labelling only for the own parameter and not for the other parameters. This suggests identifiability problems. %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \bibliography{mixture} \end{document} flexmix/vignettes/.install_extras0000644000176200001440000000004614404637307017003 0ustar liggesusersmyConcomitant.R$ mymclust.R$ ziglm.R$ flexmix/vignettes/myConcomitant.R0000644000176200001440000000130314404637307016712 0ustar liggesusersmyConcomitant <- function(formula = ~ 1) { z <- new("FLXP", name = "myConcomitant", formula = formula) z@fit <- function(x, y, w, ...) { if (missing(w) || is.null(w)) w <- rep(1, length(x)) f <- as.integer(factor(apply(x, 1, paste, collapse = ""))) AVG <- apply(w*y, 2, tapply, f, mean) (AVG/rowSums(AVG))[f,,drop=FALSE] } z@refit <- function(x, y, w, ...) { if (missing(w) || is.null(w)) w <- rep(1, length(x)) f <- as.integer(factor(apply(x, 1, paste, collapse = ""))) AVG <- apply(w*y, 2, tapply, f, mean) (AVG/rowSums(AVG)) } z } flexmix/vignettes/mixture.bib0000644000176200001440000003621114404637307016124 0ustar liggesusers@STRING{csda = {Computational Statistics \& Data Analysis} } @STRING{jasa = {Journal of the American Statistical Association} } @STRING{jcgs = {Journal of Computational and Graphical Statistics} } @STRING{jrssa = {Journal of the Royal Statistical Society A} } @STRING{jrssb = {Journal of the Royal Statistical Society B} } @Article{ mixtures:aitkin:1999, author = {Murray Aitkin}, title = {A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models}, journal = {Biometrics}, year = 1999, volume = 55, pages = {117--128} } @Article{ mixtures:aitkin:1999a, author = {Murray Aitkin}, title = {Meta-Analysis by Random Effect Modelling in Generalized Linear Models}, journal = {Statistics in Medicine}, year = 1999, volume = 18, number = {17--18}, month = {September}, pages = {2343--2351} } @Article{ mixtures:biernacki+celeux+govaert:2000, author = {Christophe Biernacki and Gilles Celeux and G{\'e}rard Govaert}, title = {Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, year = 2000, volume = 22, number = 7, pages = {719--725}, month = {July} } @Article{ mixtures:biernacki+celeux+govaert:2003, author = {Christophe Biernacki and Gilles Celeux and G{\'e}rard Govaert}, title = {Choosing Starting Values for the {EM} Algorithm for Getting the Highest Likelihood in Multivariate {G}aussian Mixture Models}, journal = csda, year = 2003, volume = 41, pages = {561--575} } @Article{ mixtures:boehning+dietz+schlattmann:1999, author = {Dankmar B{\"o}hning and Ekkehart Dietz and Peter Schlattmann and Lisette Mendon{\c c}a and Ursula Kirchner}, title = {The Zero-Inflated {P}oisson Model and the Decayed, Missing and Filled Teeth Index in Dental Epidemiology}, journal = jrssa, year = 1999, volume = 162, number = 2, pages = {195--209}, month = {August} } @Book{ mixtures:boehning:1999, author = {Dankmar B{\"o}hning}, title = {Computer Assisted Analysis of Mixtures and Applications: Meta-Analysis, Disease Mapping, and Others}, publisher = {Chapman \& Hall/CRC}, year = 1999, volume = 81, series = {Monographs on Statistics and Applied Probability}, address = {London} } @Manual{ mixtures:canty+ripley:2010, title = {boot: Bootstrap R (S-Plus) Functions}, author = {Angelo Canty and Brian Ripley}, year = 2010, note = {R package version 1.2-43}, url = {http://CRAN.R-project.org/package=boot} } @TechReport{ mixtures:celeux+diebolt:1988, author = {Gilles Celeux and Jean Diebolt}, title = {A Random Imputation Principle: The Stochastic {EM} Algorithm}, institution = {INRIA}, year = 1988, type = {Rapports de Recherche}, number = 901, month = {September} } @Article{ mixtures:celeux+govaert:1992, author = {Gilles Celeux and G{\'e}rard Govaert}, title = {A {C}lassification {EM} Algorithm for Clustering and Two Stochastic Versions}, journal = {Computational Statistics \& Data Analysis}, year = 1992, volume = 14, number = 3, pages = {315--332}, month = {October} } @Book{ mixtures:chambers:1998, author = {John M. 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Macready}, title = {Concomitant-Variable Latent-Class Models}, journal = jasa, year = 1988, volume = 83, number = 401, pages = {173--178}, month = {March} } @Article{ mixtures:dempster+laird+rubin:1977, author = {A. P. Dempster and N. M. Laird and D. B. Rubin}, title = {Maximum Likelihood from Incomplete Data Via the {EM}-Algorithm}, journal = jrssb, volume = 39, pages = {1--38}, year = 1977 } @InCollection{ mixtures:diebolt+ip:1996, author = {Jean Diebolt and Eddie H. S. Ip}, editor = {W. R. Gilks and S. Richardson and D. J. Spiegelhalter}, booktitle = {Markov Chain {M}onte {C}arlo in Practice}, title = {Stochastic {EM}: Method and Application}, publisher = {Chapman and Hall}, year = 1996, pages = {259--273} } @Book{ mixtures:everitt+hand:1981, author = {B. S. Everitt and D. J. Hand}, title = {Finite Mixture Distributions}, publisher = {Chapman and Hall}, address = {London}, year = 1981 } @Article{ mixtures:follmann+lambert:1989, author = {Dean A. Follmann and Diane Lambert}, title = {Generalizing Logistic Regression by Non-Parametric Mixing}, journal = jasa, volume = 84, number = 405, month = {March}, pages = {295--300}, year = 1989 } @Article{ mixtures:follmann+lambert:1991, author = {Dean A. Follmann and Diane Lambert}, title = {Identifiability of Finite Mixtures of Logistic Regression Models}, journal = {Journal of Statistical Planning and Inference}, volume = 27, number = 3, month = {March}, pages = {375--381}, year = 1991 } @Book{ mixtures:fowler:2004, author = {Martin Fowler}, title = {{UML} Distilled: A Brief Guide to the Standard Object Modeling Language}, publisher = {Addison-Wesley Professional}, year = 2004, edition = {3rd} } @Book{ mixtures:fruehwirth-schnatter:2006, author = {Sylvia Fr{\"u}hwirth-Schnatter}, title = {Finite Mixture and Markov Switching Models}, publisher = {Springer-Verlag}, address = {New York}, series = {Springer-Verlag Series in Statistics}, isbn = {0-387-32909-9}, year = 2006 } @Article{ mixtures:gentleman+ihaka:2000, author = {Robert Gentleman and Ross Ihaka}, title = {Lexical Scope and Statistical Computing}, journal = jcgs, year = 2000, volume = 9, number = 3, pages = {491--508} } @InProceedings{ mixtures:gruen+leisch:2004, author = {Bettina Gr{\" u}n and Friedrich Leisch}, title = {Bootstrapping Finite Mixture Models}, booktitle = {COMPSTAT 2004 -- Proceedings in Computational Statistics}, year = 2004, editor = {Jaromir Antoch}, publisher = {Physica Verlag, Heidelberg}, isbn = {3-7908-1554-3}, pages = {1115--1122} } @InProceedings{ mixtures:gruen+leisch:2006, author = {Bettina Gr{\" u}n and Friedrich Leisch}, title = {Fitting Finite Mixtures of Linear Regression Models with Varying \& Fixed Effects in \proglang{R}}, booktitle = {COMPSTAT 2006 -- Proceedings in Computational Statistics}, pages = {853--860}, editor = {Alfredo Rizzi and Maurizio Vichi}, publisher = {Physica Verlag, Heidelberg, Germany}, isbn = {3-7908-1708-2}, year = 2006 } @Article{ mixtures:gruen+leisch:2007a, author = {Bettina Gr{\" u}n and Friedrich Leisch}, title = {Fitting Finite Mixtures of Generalized Linear Regressions in \proglang{R}}, journal = csda, year = 2007, volume = 51, number = 11, month = {July}, pages = {5247--5252} } @Article{ mixtures:gruen+leisch:2008, author = {Bettina Gr\"un and Friedrich Leisch}, title = {Identifiability of Finite Mixtures of Multinomial Logit Models with Varying and Fixed Effects}, journal = {Journal of Classification}, year = 2008, note = {Accepted for publication on 2008-03-28} } @Article{ mixtures:gruen+leisch:2008a, author = {Bettina Gr\"un and Friedrich Leisch}, title = {{F}lex{M}ix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters}, journal = {Journal of Statistical Software}, year = 2008, volume = 28, number = 4, pages = {1--35}, doi = {10.18637/jss.v028.i04}, } @Unpublished{mixtures:gruen+leisch:2010, author = {Bettina Gr\"un and Friedrich Leisch}, title = {Finite Mixture Model Diagnostics Using Resampling Methods}, note = {Unpublished manuscript}, year = 2010, } @PhDThesis{ mixtures:gruen:2006, author = {Bettina Gr{\"u}n}, title = {Identification and Estimation of Finite Mixture Models}, school = {Institut f{\"u}r Statistik und Wahrscheinlichkeitstheorie, Technische Universit{\"a}t Wien}, year = 2006, month = {September}, note = {{Friedrich Leisch, advisor}} } @Book{ mixtures:harrell:2001, author = {Frank E. Harrell}, title = {Regression Modeling Strategies}, publisher = {Springer-Verlag}, address = {New York}, year = 2001 } @Article{ mixtures:hastie+tibshirani:1993, author = {Trevor Hastie and Robert Tibshirani}, title = {Varying-Coefficient Models}, journal = jrssb, year = 1993, volume = 55, number = 4, pages = {757--796} } @Article{mixtures:hennig:2000, author = {Christian Hennig}, title = {Identifiability of Models for Clusterwise Linear Regression}, journal = {Journal of Classification}, volume = 17, number = 2, month = {July}, pages = {273--296}, year = 2000 } @Article{ mixtures:karlis+xekalaki:2003, author = {Dimitris Karlis and Evdokia Xekalaki}, title = {Choosing Initial Values for the {EM} Algorithm for Finite Mixtures}, journal = csda, year = 2003, volume = 41, pages = {577--590} } @InProceedings{ mixtures:leisch:2002, author = {Friedrich Leisch}, title = {Sweave: Dynamic Generation of Statistical Reports Using Literate Data Analysis}, booktitle = {COMPSTAT 2002 -- Proceedings in Computational Statistics}, pages = {575--580}, year = 2002, editor = {Wolfgang H{\"a}rdle and Bernd R{\"o}nz}, publisher = {Physica Verlag, Heidelberg}, note = {ISBN 3-7908-1517-9} } @Article{ mixtures:leisch:2003, author = {Friedrich Leisch}, title = {Sweave, Part {II}: Package Vignettes}, journal = {\proglang{R} News}, year = 2003, volume = 3, number = 2, pages = {21--24}, month = {October}, url = {http://CRAN.R-project.org/doc/Rnews/} } @Article{ mixtures:leisch:2004, author = {Friedrich Leisch}, title = {\pkg{FlexMix}: A General Framework for Finite Mixture Models and Latent Class Regression in \proglang{R}}, journal = {Journal of Statistical Software}, year = 2004, volume = 11, number = 8, pages = {1--18}, doi = {10.18637/jss.v011.i08}, } @InProceedings{ mixtures:leisch:2004a, author = {Friedrich Leisch}, title = {Exploring the Structure of Mixture Model Components}, booktitle = {COMPSTAT 2004 -- Proceedings in Computational Statistics}, year = 2004, editor = {Jaromir Antoch}, publisher = {Physica Verlag, Heidelberg}, isbn = {3-7908-1554-3}, pages = {1405--1412} } @InProceedings{ mixtures:leisch:2008, author = {Friedrich Leisch}, title = {Modelling Background Noise in Finite Mixtures of Generalized Linear Regression Models}, booktitle = {COMPSTAT 2008 -- Proceedings in Computational Statistics}, volume = {I}, pages = {385-396}, editor = {Paula Brito}, publisher = {Physica Verlag, Heidelberg, Germany}, isbn = {978-3-7908-2083-6}, year = 2008 } @Article{ mixtures:long:1990, author = {J. Scott Long}, title = {The Origins of Sex Differences in Science}, journal = {Social Forces}, year = 1990, volume = 68, number = 4, pages = {1297--1315}, month = {June} } @Book{ mixtures:mccullagh+nelder:1989, author = {Peter McCullagh and John A. Nelder}, title = {Generalized Linear Models}, edition = {2nd}, publisher = {Chapman and Hall}, year = 1989, location = {London} } @Book{ mixtures:mclachlan+basford:1988, author = {Geoffrey J. McLachlan and Kaye E. Basford}, title = {Mixture Models: Inference and Applications to Clustering}, publisher = {Marcel Dekker}, year = 1988, address = {New York} } @Book{ mixtures:mclachlan+peel:2000, author = {Geoffrey J. McLachlan and David Peel}, title = {Finite Mixture Models}, publisher = {John Wiley \& Sons}, year = 2000 } @Book{ mixtures:pinheiro+bates:2000, author = {Jose C. Pinheiro and Douglas M. Bates}, title = {Mixed-Effects Models in \proglang{S} and \proglang{S-Plus}}, publisher = {Springer-Verlag}, year = 2000, isbn = {0-387-98957-0} } @Book{ mixtures:sarkar:2008, title = {\pkg{lattice}: Multivariate Data Visualization with \proglang{R}}, author = {Deepayan Sarkar}, year = 2008, publisher = {Springer-Verlag}, address = {New York}, isbn = {978-0-387-75968-5} } @Book{ mixtures:titterington+smith+makov:1985, author = {D. M. Titterington and A. F. M. Smith and U. E. Makov}, title = {Statistical Analysis of Finite Mixture Distributions}, publisher = {John Wiley \& Sons}, year = 1985 } @Book{ mixtures:venables+ripley:2002, title = {Modern Applied Statistics with \proglang{S}}, author = {William N. Venables and Brian D. Ripley}, publisher = {Springer-Verlag}, edition = {4th}, address = {New York}, year = 2002, isbn = {0-387-95457-0} } @Article{ mixtures:wang+puterman+cockburn:1996, author = {Peiming Wang and Martin L. Puterman and Iain M. Cockburn and Nhu D. Le}, title = {Mixed {P}oisson Regression Models with Covariate Dependent Rates}, journal = {Biometrics}, year = 1996, volume = 52, pages = {381--400} } @Article{ mixtures:wedel+desarbo:1995, author = {Michel Wedel and Wagner S. DeSarbo}, title = {A Mixture Likelihood Approach for Generalized Linear Models}, journal = {Journal of Classification}, year = 1995, volume = 12, number = 1, month = {March}, pages = {21--55} } @Article{ mixtures:wehrens+buydens+fraley:2004, author = {Ron Wehrens and Lutgarde M.C. Buydens and Chris Fraley and Adrian E. Raftery}, title = {Model-Based Clustering for Image Segmentation and Large Datasets Via Sampling}, journal = {Journal of Classification}, year = 2004, volume = 21, number = 2, pages = {231--253} } flexmix/data/0000755000176200001440000000000014757625374012663 5ustar liggesusersflexmix/data/dmft.RData0000644000176200001440000000741014404637305014516 0ustar liggesusers‹íÚMo×Æñ)JJ€ºîWÌsßÈmÑ û¢‹lU›‰Ú2 ¨ úåÓJ6Ïý?<žªA7L4âÌÜç¾þfFÎ_þô½}ýý×Ã0¬†Õzø´ —«Çÿ\ 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W«ý‹/U}?~ŒŒLLÌê1˜3X0X2Ôg°b°f°a°e°chÀÐÁžÁÁ‘Á‰Á™Á…¡ƒ+ƒƒ;ƒƒ'ŸÁ‹Á›Á‡Á—¡1C?†¦ Íüš3021´`f0ß=V†u¼?s…|i~ùý|¢£7Òý_¾DßçŽè?|°îk¦;áqºÇ µQ¤6×ÈûZû>O$ U!£1O96èÿ«N}IÊQRâÚ—ßvÿ¦ßvºª€V…´*¢U1­JhUJ«2Z•Ó*µ ¨M@mjP›€ÚÔ& 6µ ¨M@mBjR›Ú„Ô&¤6!µ ©MHmBjR›ˆÚDÔ&¢6µ‰¨MDm"jQ›ˆÚDÔ&¦61µ‰©MLmbjS›˜ÚÄÔ&¦61µI¨MBmj“P›„Ú$Ô&¡6 µI¨MBmRj“R›”Ú¤Ô&¥6)µI©MJmRj“R›ŒÚdÔ&£6µÉ¨MFm2j“Q›ŒÚdÔ&§69µÉ©MNmrj“S›œÚäÔ&§69µ)¨MAm jSP›‚ÚÔ¦ 6µ)¨¾K„Áú~ÕX ê?¦ÐîgOûˆWûŽßgðð1flexmix/NAMESPACE0000644000176200001440000001002414757625043013157 0ustar liggesusersimportFrom("graphics", "hist", "lines", "matplot", "plot", "points", "text") importFrom("grid", "gpar", "grid.lines", "grid.polygon", "unit") importFrom("grDevices", "axisTicks", "hcl", "rgb") importFrom("lattice", "barchart", "do.breaks", "histogram", "lattice.getOption", "llines", "panel.abline", "panel.barchart", "panel.rect", "panel.segments", "panel.xyplot", "parallelplot", "trellis.par.get", "xyplot") import("methods") importFrom("modeltools", "clusters", "getModel", "ICL", "KLdiv", "Lapply", "parameters", "posterior", "prior", "refit", "relabel") importFrom("nnet", "multinom", "nnet.default") importFrom("stats", "AIC", "as.formula", "BIC", "binomial", ".checkMFClasses", "coef", "cov.wt", "dbinom", "delete.response", "dexp", "dgamma", "dlnorm", "dnorm", "dpois", "dweibull", "factanal", "Gamma", ".getXlevels", "glm.fit", "lm.wfit", "model.frame", "model.matrix", "model.response", "na.omit", "optim", "pnorm", "poisson", "predict", "printCoefmat", "qnorm", "quantile", "rbinom", "residuals", "rgamma", "rmultinom", "rnorm", "rpois", "runif", "terms", "update", "update.formula", "var", "weighted.mean") importFrom("stats4", "logLik", "nobs", "plot", "summary") importFrom("utils", "getS3method") export( "ExLinear", "ExNPreg", "ExNclus", "FLXdist", "FLXgradlogLikfun", "FLXlogLikfun", "FLXMCdist1", "FLXMCfactanal", "FLXMCmvbinary", "FLXMCmvcombi", "FLXMCmvnorm", "FLXMCmvpois", "FLXMCnorm1", "FLXPmultinom", "FLXPconstant", "FLXfit", "FLXglm", "FLXglmFix", "FLXbclust", "FLXmclust", "FLXconstant", "FLXmultinom", "FLXMRcondlogit", "FLXMRglm", "FLXMRglmfix", "FLXMRglmnet", "FLXMRlmer", "FLXMRlmm", "FLXMRlmmc", "FLXMRmgcv", "FLXMRmultinom", "FLXMRrobglm", "FLXMRziglm", "FLXgetDesign", "FLXgetParameters", "FLXreplaceParameters", "boot", "existGradient", "flexmix", "flxglht", "group", "initFlexmix", "LR_test", "plotEll", "refit_optim", "relabel", "stepFlexmix" ) exportClasses( "FLXcomponent", "FLXP", "FLXPmultinom", "FLXcontrol", "FLXdist", "FLXMRfix", "FLXMRglmfix", "FLXMRglm", "FLXMRlmer", "FLXMRlmm", "FLXMRlmmfix", "FLXMRlmmc", "FLXMRlmc", "FLXMRlmmcfix", "FLXMRlmcfix", "FLXMRmgcv", "FLXMRrobglm", "FLXMRziglm", "FLXM", "FLXMR", "FLXMC", "FLXMCsparse", "FLXnested", "FLXR", "FLXRoptim", "FLXRmstep", "flexmix", "listOrdata.frame", "stepFlexmix", "summary.flexmix" ) exportMethods( "EIC", "FLXcheckComponent", "FLXdeterminePostunscaled", "FLXfit", "FLXgetK", "FLXgetModelmatrix", "FLXgetObs", "FLXmstep", "FLXremoveComponent", "KLdiv", "ICL", "Lapply", "coerce", "clusters", "fitted", "flexmix", "flxglht", "getModel", "initialize", "logLik", "parameters", "plot", "posterior", "predict", "prior", "rFLXM", "refit", "relabel", "rflexmix", "show", "summary", "unique" ) S3method("as.data.frame", "simple_triplet_matrix") flexmix/inst/0000755000176200001440000000000014757625370012723 5ustar liggesusersflexmix/inst/CITATION0000644000176200001440000000276314404661473014061 0ustar liggesuserscitHeader(sprintf("To cite package %s in publications use:", sQuote(meta$Package))) bibentry("Manual", other = unlist(citation(auto = meta), recursive = FALSE)) bibentry(bibtype = "Article", title = "{FlexMix}: A General Framework for Finite Mixture Models and Latent Class Regression in {R}", author = person(given = "Friedrich", family = "Leisch"), journal = "Journal of Statistical Software", year = "2004", volume = "11", number = "8", pages = "1--18", doi = "10.18637/jss.v011.i08" ) bibentry(bibtype = "Article", title = "Fitting Finite Mixtures of Generalized Linear Regressions in {R}", author = c(person(given = "Bettina", family = "Gr\\\"un"), person(given = "Friedrich", family = "Leisch")), journal = "Computational Statistics \\& Data Analysis", year = "2007", volume = "51", number = "11", pages = "5247--5252", doi = "10.1016/j.csda.2006.08.014" ) bibentry(bibtype = "Article", title = "{FlexMix} Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters", author = c(person(given = "Bettina", family = "Gr\\\"un"), person(given = "Friedrich", family = "Leisch")), journal = "Journal of Statistical Software", year = "2008", volume = "28", number = "4", pages = "1--35", doi = "10.18637/jss.v028.i04" ) flexmix/inst/doc/0000755000176200001440000000000014757625370013470 5ustar liggesusersflexmix/inst/doc/mymclust.R0000644000176200001440000000205314404637307015460 0ustar liggesusersmymclust <- function (formula = .~., diagonal = TRUE) { retval <- new("FLXMC", weighted = TRUE, formula = formula, dist = "mvnorm", name = "my model-based clustering") retval@defineComponent <- function(para) { logLik <- function(x, y) { mvtnorm::dmvnorm(y, mean = para$center, sigma = para$cov, log = TRUE) } predict <- function(x) { matrix(para$center, nrow = nrow(x), ncol = length(para$center), byrow = TRUE) } new("FLXcomponent", parameters = list(center = para$center, cov = para$cov), df = para$df, logLik = logLik, predict = predict) } retval@fit <- function(x, y, w, ...) { para <- cov.wt(y, wt = w)[c("center", "cov")] df <- (3 * ncol(y) + ncol(y)^2)/2 if (diagonal) { para$cov <- diag(diag(para$cov)) df <- 2 * ncol(y) } retval@defineComponent(c(para, df = df)) } retval } flexmix/inst/doc/mixture-regressions.Rnw0000644000176200001440000022017614404637307020216 0ustar liggesusers% % Copyright (C) 2008 Bettina Gruen and Friedrich Leisch % $Id: mixture-regressions.Rnw $ % \documentclass[nojss]{jss} \usepackage{amsfonts} \title{FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters} \Plaintitle{FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters} \Shorttitle{FlexMix Version 2} \author{Bettina Gr{\"u}n\\ Wirtschaftsuniversit{\"a}t Wien \And Friedrich Leisch\\ Universit\"at f\"ur Bodenkultur Wien} \Plainauthor{Bettina Gr{\"u}n, Friedrich Leisch} \Address{ Bettina Gr\"un\\ Institute for Statistics and Mathematics\\ Wirtschaftsuniversit{\"a}t Wien\\ Welthandelsplatz 1\\ 1020 Wien, Austria\\ E-mail: \email{Bettina.Gruen@R-project.org}\\ Friedrich Leisch\\ Institut f\"ur Angewandte Statistik und EDV\\ Universit\"at f\"ur Bodenkultur Wien\\ Peter Jordan Stra\ss{}e 82\\ 1190 Wien, Austria\\ E-mail: \email{Friedrich.Leisch@boku.ac.at} } \Abstract{ This article is a (slightly) modified version of \cite{mixtures:Gruen+Leisch:2008a}, published in the \emph{Journal of Statistical Software}. \pkg{flexmix} provides infrastructure for flexible fitting of finite mixture models in \proglang{R} using the expectation-maximization (EM) algorithm or one of its variants. The functionality of the package was enhanced. Now concomitant variable models as well as varying and constant parameters for the component specific generalized linear regression models can be fitted. The application of the package is demonstrated on several examples, the implementation described and examples given to illustrate how new drivers for the component specific models and the concomitant variable models can be defined. } \Keywords{\proglang{R}, finite mixture models, generalized linear models, concomitant variables} \Plainkeywords{R, finite mixture models, generalized linear models, concomitant variables} \usepackage{amsmath, listings} \def\argmax{\mathop{\rm arg\,max}} %% \usepackage{Sweave} prevent automatic inclusion \SweaveOpts{width=9, height=4.5, eps=FALSE, keep.source=TRUE} <>= options(width=60, prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE) library("graphics") library("stats") library("flexmix") library("lattice") ltheme <- canonical.theme("postscript", FALSE) lattice.options(default.theme=ltheme) data("NPreg", package = "flexmix") data("dmft", package = "flexmix") source("myConcomitant.R") @ %%\VignetteIndexEntry{FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters} %%\VignetteDepends{flexmix} %%\VignetteKeywords{R, finite mixture models, model based clustering, latent class regression} %%\VignettePackage{flexmix} \begin{document} %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Introduction}\label{sec:introduction} Finite mixture models are a popular technique for modelling unobserved heterogeneity or to approximate general distribution functions in a semi-parametric way. They are used in a lot of different areas such as astronomy, biology, economics, marketing or medicine. An overview on mixture models is given in \cite{mixtures:Everitt+Hand:1981}, \cite{mixtures:Titterington+Smith+Makov:1985}, \cite{mixtures:McLachlan+Basford:1988}, \cite{mixtures:Boehning:1999}, \cite{mixtures:McLachlan+Peel:2000} and \cite{mixtures:Fruehwirth-Schnatter:2006}. Version 1 of \proglang{R} package \pkg{flexmix} was introduced in \cite{mixtures:Leisch:2004}. The main design principles of the package are extensibility and fast prototyping for new types of mixture models. It uses \proglang{S}4 classes and methods \citep{mixtures:Chambers:1998} as implemented in the \proglang{R} package \pkg{methods} and exploits advanced features of \proglang{R} such as lexical scoping \citep{mixtures:Gentleman+Ihaka:2000}. The package implements a framework for maximum likelihood estimation with the expectation-maximization (EM) algorithm \citep{mixtures:Dempster+Laird+Rubin:1977}. The main focus is on finite mixtures of regression models and it allows for multiple independent responses and repeated measurements. The EM algorithm can be controlled through arguments such as the maximum number of iterations or a minimum improvement in the likelihood to continue. Newly introduced features in the current package version are concomitant variable models \citep{mixtures:Dayton+Macready:1988} and varying and constant parameters in the component specific regressions. Varying parameters follow a finite mixture, i.e., several groups exist in the population which have different parameters. Constant parameters are fixed for the whole population. This model is similar to mixed-effects models \citep{mixtures:Pinheiro+Bates:2000}. The main difference is that in this application the distribution of the varying parameters is unknown and has to be estimated. Thus the model is actually closer to the varying-coefficients modelling framework \citep{mixtures:Hastie+Tibshirani:1993}, using convex combinations of discrete points as functional form for the varying coefficients. The extension to constant and varying parameters allows for example to fit varying intercept models as given in \cite{mixtures:Follmann+Lambert:1989} and \cite{mixtures:Aitkin:1999}. These models are frequently applied to account for overdispersion in the data where the components follow either a binomial or Poisson distribution. The model was also extended to include nested varying parameters, i.e.~this allows to have groups of components with the same parameters \citep{mixtures:Gruen+Leisch:2006, mixtures:Gruen:2006}. In Section~\ref{sec:model-spec-estim} the extended model class is presented together with the parameter estimation using the EM algorithm. In Section~\ref{sec:using-new-funct} examples are given to demonstrate how the new functionality can be used. An overview on the implementational details is given in Section~\ref{sec:implementation}. The new model drivers are presented and changes made to improve the flexibility of the software and to enable the implementation of the new features are discussed. Examples for writing new drivers for the component specific models and the concomitant variable models are given in Section~\ref{sec:writing-your-own}. This paper gives a short overview on finite mixtures and the package in order to be self-contained. A more detailed introduction to finite mixtures and the package \pkg{flexmix} can be found in \cite{mixtures:Leisch:2004}. All computations and graphics in this paper have been done with \pkg{flexmix} version \Sexpr{packageDescription("flexmix",fields="Version")} and \proglang{R} version \Sexpr{getRversion()} using Sweave \citep{mixtures:Leisch:2002}. The newest release version of \pkg{flexmix} is always available from the Comprehensive \proglang{R} Archive Network at \url{http://CRAN.R-project.org/package=flexmix}. An up-to-date version of this paper is contained in the package as a vignette, giving full access to the \proglang{R} code behind all examples shown below. See \code{help("vignette")} or \cite{mixtures:Leisch:2003} for details on handling package vignettes. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Model specification and estimation}\label{sec:model-spec-estim} A general model class of finite mixtures of regression models is considered in the following. The mixture is assumed to consist of $K$ components where each component follows a parametric distribution. Each component has a weight assigned which indicates the a-priori probability for an observation to come from this component and the mixture distribution is given by the weighted sum over the $K$ components. If the weights depend on further variables, these are referred to as concomitant variables. In marketing choice behaviour is often modelled in dependence of marketing mix variables such as price, promotion and display. Under the assumption that groups of respondents with different price, promotion and display elasticities exist mixtures of regressions are fitted to model consumer heterogeneity and segment the market. Socio-demographic variables such as age and gender have often been shown to be related to the different market segments even though they generally do not perform well when used to a-priori segment the market. The relationships between the behavioural and the socio-demographic variables is then modelled through concomitant variable models where the group sizes (i.e.~the weights of the mixture) depend on the socio-demographic variables. The model class is given by \begin{align*} h(y|x, w, \psi) &= \sum_{k = 1}^K \pi_k(w, \alpha) f_k(y|x,\theta_{k})\\ &= \sum_{k = 1}^K \pi_k(w, \alpha) \prod_{d=1}^D f_{kd}(y_d|x_d,\theta_{kd}), \end{align*} where $\psi$ denotes the vector of all parameters for the mixture density $h()$ and is given by $(\alpha, (\theta_k)_{k=1,\ldots,K})$. $y$ denotes the response, $x$ the predictor and $w$ the concomitant variables. $f_k$ is the component specific density function. Multivariate variables $y$ are assumed to be dividable into $D$ subsets where the component densities are independent between the subsets, i.e.~the component density $f_k$ is given by a product over $D$ densities which are defined for the subset variables $y_d$ and $x_d$ for $d=1,\ldots,D$. The component specific parameters are given by $\theta_k = (\theta_{kd})_{d=1,\ldots,D}$. Under the assumption that $N$ observations are available the dimensions of the variables are given by $y = (y_d)_{d=1,\ldots,D} \in \mathbb{R}^{N \times \sum_{d=1}^D k_{yd}}$, $x = (x_d)_{d=1,\ldots,D} \in \mathbb{R}^{N \times \sum_{d=1}^D k_{xd}}$ for all $d = 1,\ldots,D$ and $w \in \mathbb{R}^{N \times k_w}$. In this notation $k_{yd}$ denotes the dimension of the $d^{\textrm{th}}$ response, $k_{xd}$ the dimension of the $d^{\textrm{th}}$ predictors and $k_w$ the dimension of the concomitant variables. For mixtures of GLMs each of the $d$ responses will in general be univariate, i.e.~multivariate responses will be conditionally independent given the segment memberships. For the component weights $\pi_k$ it holds $\forall w$ that \begin{equation}\label{eq:prior} \sum_{k=1}^K \pi_k(w,\alpha) = 1 \quad \textrm{and} \quad \pi_k(w, \alpha) > 0, \, \forall k, \end{equation} where $\alpha$ are the parameters of the concomitant variable model. For the moment focus is given to finite mixtures where the component specific densities are from the same parametric family, i.e.~$f_{kd} \equiv f_d$ for notational simplicity. If $f_d$ is from the exponential family of distributions and for each component a generalized linear model is fitted \citep[GLMs;][]{mixtures:McCullagh+Nelder:1989} these models are also called GLIMMIX models \citep{mixtures:Wedel+DeSarbo:1995}. In this case the component specific parameters are given by $\theta_{kd} = (\beta'_{kd}, \phi_{kd})$ where $\beta_{kd}$ are the regression coefficients and $\phi_{kd}$ is the dispersion parameter. The component specific parameters $\theta_{kd}$ are either restricted to be equal over all components, to vary between groups of components or to vary between all components. The varying between groups is referred to as varying parameters with one level of nesting. A disjoint partition $K_c$, $c = 1,\ldots,C$ of the set $\tilde{K} := \{1\ldots,K\}$ is defined for the regression coefficients. $C$ is the number of groups of the regression coefficients at the nesting level. The regression coefficients are accordingly split into three groups: \begin{align*} \beta_{kd} &= (\beta'_{1d}, \beta'_{2,c(k)d}, \beta'_{3,kd})', \end{align*} where $c(k) = \{c = 1,\ldots, C: k \in K_c\}$. Similar a disjoint partition $K_v$, $v = 1,\ldots,V$, of $\tilde{K}$ can be defined for the dispersion parameters if nested varying parameters are present. $V$ denotes the number of groups of the dispersion parameters at the nesting level. This gives: \begin{align*} \phi_{kd} &= \left\{\begin{array}{ll} \phi_{d} & \textrm{for constant parameters}\\ \phi_{kd} & \textrm{for varying parameters}\\ \phi_{v(k)d} & \textrm{for nested varying parameters} \end{array}\right. \end{align*} where $v(k) = \{v = 1,\ldots,V: k \in K_v\}$. The nesting structure of the component specific parameters is also described in \cite{mixtures:Gruen+Leisch:2006}. Different concomitant variable models are possible to determine the component weights \citep{mixtures:Dayton+Macready:1988}. The mapping function only has to fulfill condition \eqref{eq:prior}. In the following a multinomial logit model is assumed for the $\pi_k$ given by \begin{equation*} \pi_k(w,\alpha) = \frac{e^{w'\alpha_k}}{\sum_{u = 1}^K e^{w'\alpha_u}} \quad \forall k, \end{equation*} with $\alpha = (\alpha'_k)'_{k=1,\ldots,K}$ and $\alpha_1 \equiv 0$. %%------------------------------------------------------------------------- \subsection{Parameter estimation}\label{sec:estimation} The EM algorithm \citep{mixtures:Dempster+Laird+Rubin:1977} is the most common method for maximum likelihood estimation of finite mixture models where the number of components $K$ is fixed. The EM algorithm applies a missing data augmentation scheme. It is assumed that a latent variable $z_n \in \{0,1\}^K$ exists for each observation $n$ which indicates the component membership, i.e.~$z_{nk}$ equals 1 if observation $n$ comes from component $k$ and 0 otherwise. Furthermore it holds that $\sum_{k=1}^K z_{nk}=1$ for all $n$. In the EM algorithm these unobserved component memberships $z_{nk}$ of the observations are treated as missing values and the data is augmented by estimates of the component membership, i.e.~the estimated a-posteriori probabilities $\hat{p}_{nk}$. For a sample of $N$ observations $\{(y_1, x_1, w_1), \ldots, (y_N, x_N, w_N)\}$ the EM algorithm is given by: \begin{description} \item[E-step:] Given the current parameter estimates $\psi^{(i)}$ in the $i$-th iteration, replace the missing data $z_{nk}$ by the estimated a-posteriori probabilities \begin{align*} \hat{p}_{nk} & = \frac{\displaystyle \pi_k(w_n, \alpha^{(i)}) f(y_n| x_n, \theta_k^{(i)}) }{\displaystyle \sum_{u = 1}^K \pi_u(w_n, \alpha^{(i)}) f(y_n |x_n, \theta_u^{(i)}) }. \end{align*} \item[M-step:] Given the estimates for the a-posteriori probabilities $\hat{p}_{nk}$ (which are functions of $\psi^{(i)}$), obtain new estimates $\psi^{(i+1)}$ of the parameters by maximizing \begin{align*} Q(\psi^{(i+1)}|\psi^{(i)}) &= Q_1(\theta^{(i+1)} | \psi^{(i)}) + Q_2(\alpha^{(i+1)} | \psi^{(i)}), \end{align*} where \begin{align*} Q_1(\theta^{(i+1)} | \psi^{(i)}) &= \sum_{n = 1}^N \sum_{k = 1}^K \hat{p}_{nk} \log(f(y_n | x_n, \theta_k^{(i+1)})) \end{align*} and \begin{align*} Q_2(\alpha^{(i+1)}| \psi^{(i)}) &= \sum_{n = 1}^N \sum_{k = 1}^K \hat{p}_{nk} \log(\pi_k(w_n, \alpha^{(i+1)})). \end{align*} $Q_1$ and $Q_2$ can be maximized separately. The maximization of $Q_1$ gives new estimates $\theta^{(i+1)}$ and the maximization of $Q_2$ gives $\alpha^{(i+1)}$. $Q_1$ is maximized separately for each $d=1,\ldots,D$ using weighted ML estimation of GLMs and $Q_2$ using weighted ML estimation of multinomial logit models. \end{description} Different variants of the EM algorithm exist such as the stochastic EM \citep[SEM;][]{mixtures:Diebolt+Ip:1996} or the classification EM \citep[CEM;][]{mixtures:Celeux+Govaert:1992}. These two variants are also implemented in package \pkg{flexmix}. For both variants an additional step is made between the expectation and maximization steps. This step uses the estimated a-posteriori probabilities and assigns each observation to only one component, i.e.~classifies it into one component. For SEM this assignment is determined in a stochastic way while it is a deterministic assignment for CEM. For the SEM algorithm the additional step is given by: \begin{description} \item[S-step:] Given the a-posteriori probabilities draw \begin{align*} \hat{z}_n &\sim \textrm{Mult}((\hat{p}_{nk})_{k=1,\ldots,K}, 1) \end{align*} where $\textrm{Mult}(\theta, T)$ denotes the multinomial distribution with success probabilities $\theta$ and number of trials $T$. \end{description} Afterwards, the $\hat{z}_{nk}$ are used instead of the $\hat{p}_{nk}$ in the M-step. For the CEM the additional step is given by: \begin{description} \item[C-step:] Given the a-posteriori probabilities define \begin{align*} \hat{z}_{nk} &= \left\{\begin{array}{ll} 1&\textrm{if } k = \min\{ l : \hat{p}_{nl} \geq \hat{p}_{nk}\, \forall k=1,\ldots,K\}\\ 0&\textrm{otherwise}. \end{array}\right. \end{align*} \end{description} Please note that in this step the observation is assigned to the component with the smallest index if the same maximum a-posteriori probability is observed for several components. Both of these variants have been proposed to improve the performance of the EM algorithm, because the ordinary EM algorithm tends to converge rather slowly and only to a local optimum. The convergence behavior can be expected to be better for the CEM than ordinary EM algorithm, while SEM can escape convergence to a local optimum. However, the CEM algorithm does not give ML estimates because it maximizes the complete likelihood. For SEM good approximations of the ML estimator are obtained if the parameters where the maximum likelihood was encountered are used as estimates. Another possibility for determining parameter estimates from the SEM algorithm could be the mean after discarding a suitable number of burn-ins. An implementational advantage of both variants is that no weighted maximization is necessary in the M-step. It has been shown that the values of the likelihood are monotonically increased during the EM algorithm. On the one hand this ensures the convergence of the EM algorithm if the likelihood is bounded, but on the other hand only the detection of a local maximum can be guaranteed. Therefore, it is recommended to repeat the EM algorithm with different initializations and choose as final solution the one with the maximum likelihood. Different initialization strategies for the EM algorithm have been proposed, as its convergence to the optimal solution depends on the initialization \citep{mixtures:Biernacki+Celeux+Govaert:2003,mixtures:Karlis+Xekalaki:2003}. Proposed strategies are for example to first make several runs of the SEM or CEM algorithm with different random initializations and then start the EM at the best solution encountered. The component specific parameter estimates can be determined separately for each $d=1,\ldots,D$. For simplicity of presentation the following description assumes $D=1$. If all parameter estimates vary between the component distributions they can be determined separately for each component in the M-step. However, if also constant or nested varying parameters are specified, the component specific estimation problems are not independent from each other any more. Parameters have to be estimated which occur in several or all components and hence, the parameters of the different components have to be determined simultaneously for all components. The estimation problem for all component specific parameters is then obtained by replicating the vector of observations $y = (y_n)_{n=1,\ldots,N}$ $K$ times and defining the covariate matrix $X = (X_{\textrm{constant}}, X_{\textrm{nested}}, X_{\textrm{varying}})$ by \begin{align*} &X_{\textrm{constant}} = \mathbf{1}_K \otimes (x'_{1,n})_{n=1,\ldots,N}\\ &X_{\textrm{nested}} = \mathbf{J} \odot (x'_{2,n})_{n=1,\ldots,N}\\ &X_{\textrm{varying}} = \mathbf{I}_K \otimes(x'_{3,n})_{n=1,\ldots,N}, \end{align*} where $\mathbf{1}_K$ is a vector of 1s of length $K$, $\mathbf{J}$ is the incidence matrix for each component $k=1,\ldots,K$ and each nesting group $c \in C$ and hence is of dimension $K \times |C|$, and $\mathbf{I}_K$ is the identity matrix of dimension $K \times K$. $\otimes$ denotes the Kronecker product and $\odot$ the Khatri-Rao product (i.e., the column-wise Kronecker product). $x_{m,n}$ are the covariates of the corresponding coefficients $\beta_{m,.}$ for $m=1,2,3$. Please note that the weights used for the estimation are the a-posteriori probabilities which are stacked for all components, i.e.~a vector of length $N K$ is obtained. Due to the replication of data in the case of constant or nested varying parameters the amount of memory needed for fitting the mixture model to large datasets is substantially increased and it might be easier to fit only varying coefficients to these datasets. To overcome this problem it could be considered to implement special data structures in order to avoid storing the same data multiple times for large datasets. Before each M-step the average component sizes (over the given data points) are checked and components which are smaller than a given (relative) minimum size are omitted in order to avoid too small components where fitting problems might arise. This strategy has already been recommended for the SEM algorithm \citep{mixtures:Celeux+Diebolt:1988} because it allows to determine the suitable number of components in an automatic way given that the a-priori specified number of components is large enough. This recommendation is based on the assumption that the redundent components will be omitted during the estimation process if the algorithm is started with too many components. If omission of small components is not desired the minimum size required can be set to zero. All components will be then retained throughout the EM algorithm and a mixture with the number of components specified in the initialization will be returned. The algorithm is stopped if the relative change in the log-likelihood is smaller than a pre-specified $\epsilon$ or the maximum number of iterations is reached. For model selection different information criteria are available: AIC, BIC and ICL \citep[Integrated Complete Likelihood;][]{mixtures:Biernacki+Celeux+Govaert:2000}. They are of the form twice the negative loglikelihood plus number of parameters times $k$ where $k=2$ for the AIC and $k$ equals the logarithm of the number of observations for the BIC. The ICL is the same as the BIC except that the complete likelihood (where the missing class memberships are replaced by the assignments induced by the maximum a-posteriori probabilities) instead of the likelihood is used. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Using the new functionality} \label{sec:using-new-funct} In the following model fitting and model selection in \proglang{R} is illustrated on several examples including mixtures of Gaussian, binomial and Poisson regression models, see also \cite{mixtures:Gruen:2006} and \cite{mixtures:Gruen+Leisch:2007a}. More examples for mixtures of GLMs are provided as part of the software package through a collection of artificial and real world datasets, most of which have been previously used in the literature (see references in the online help pages). Each dataset can be loaded to \proglang{R} with \code{data("}\textit{name}\code{")} and the fitting of the proposed models can be replayed using \code{example("}\textit{name}\code{")}. Further details on these examples are given in a user guide which can be accessed using \code{vignette("regression-examples", package="flexmix")} from within \proglang{R}. %%----------------------------------------------------------------------- \subsection{Artificial example}\label{sec:artificial-example} In the following the artificial dataset \code{NPreg} is used which has already been used in \cite{mixtures:Leisch:2004} to illustrate the application of package \pkg{flexmix}. The data comes from two latent classes of size \Sexpr{nrow(NPreg)/2} each and for each of the classes the data is drawn with respect to the following structure: \begin{center} \begin{tabular}{ll} Class~1: & $ \mathit{yn} = 5x+\epsilon$\\ Class~2: & $ \mathit{yn} = 15+10x-x^2+\epsilon$ \end{tabular} \end{center} with $\epsilon\sim N(0,9)$, see the left panel of Figure~\ref{fig:npreg}. The dataset \code{NPreg} also includes a response $\mathit{yp}$ which is given by a generalized linear model following a Poisson distribution and using the logarithm as link function. The parameters of the mean are given for the two classes by: \begin{center} \begin{tabular}{ll} Class~1: & $ \mu_1 = 2 - 0.2x$\\ Class~2: & $ \mu_2 = 1 + 0.1x$. \end{tabular} \end{center} This signifies that given $x$ the response $\mathit{yp}$ in group $k$ follows a Poisson distribution with mean $e^{\mu_k}$, see the right panel of Figure~\ref{fig:npreg}. \setkeys{Gin}{width=\textwidth} \begin{figure} \centering <>= par(mfrow=c(1,2)) plot(yn~x, col=class, pch=class, data=NPreg) plot(yp~x, col=class, pch=class, data=NPreg) @ \caption{Standard regression example (left) and Poisson regression (right).} \label{fig:npreg} \end{figure} This model can be fitted in \proglang{R} using the commands: <<>>= suppressWarnings(RNGversion("3.5.0")) set.seed(1802) library("flexmix") data("NPreg", package = "flexmix") Model_n <- FLXMRglm(yn ~ . + I(x^2)) Model_p <- FLXMRglm(yp ~ ., family = "poisson") m1 <- flexmix(. ~ x, data = NPreg, k = 2, model = list(Model_n, Model_p), control = list(verbose = 10)) @ If the dimensions are independent the component specific model for multivariate observations can be specified as a list of models for each dimension. The estimation can be controlled with the \code{control} argument which is specified with an object of class \code{"FLXcontrol"}. For convenience also a named list can be provided which is used to construct and set the respective slots of the \code{"FLXcontrol"} object. Elements of the control object are \code{classify} to select ordinary EM, CEM or SEM, \code{minprior} for the minimum relative size of components, \code{iter.max} for the maximum number of iterations and \code{verbose} for monitoring. If \code{verbose} is a positive integer the log-likelihood is reported every \code{verbose} iterations and at convergence together with the number of iterations made. The default is to not report any log-likelihood information during the fitting process. The estimated model \code{m1} is of class \code{"flexmix"} and the result of the default plot method for this class is given in Figure~\ref{fig:root1}. This plot method uses package \pkg{lattice} \citep{mixtures:Sarkar:2008} and the usual parameters can be specified to alter the plot, e.g.~the argument \code{layout} determines the arrangement of the panels. The returned object is of class \code{"trellis"} and the plotting can also be influenced by the arguments of its show method. The default plot prints rootograms (i.e., a histogram of the square root of counts) of the a-posteriori probabilities of each observation separately for each component. For each component the observations with a-posteriori probabilities less than a pre-specified $\epsilon$ (default is $10^{-4}$) for this component are omitted in order to avoid that the bar at zero dominates the plot \citep{mixtures:Leisch:2004a}. Please note that the labels of the y-axis report the number of observations in each bar, i.e.~the squared values used for the rootograms. \begin{figure} \centering <>= print(plot(m1)) @ \caption{The plot method for \code{"flexmix"} objects, here obtained by \code{plot(m1)}, shows rootograms of the posterior class probabilities.} \label{fig:root1} \end{figure} More detailed information on the estimated parameters with respect to standard deviations and significance tests can be obtained with function \code{refit()}. This function determines the variance-covariance matrix of the estimated parameters by using the inverted negative Hesse matrix as computed by the general purpose optimizer \code{optim()} on the full likelihood of the model. \code{optim()} is initialized in the solution obtained with the EM algorithm. For mixtures of GLMs we also implemented the gradient, which speeds up convergence and gives more precise estimates of the Hessian. Naturally, function \code{refit()} will also work for models which have been determined by applying some model selection strategy depending on the data (AIC, BIC, \ldots). The same caution is necessary as when using \code{summary()} on standard linear models selected using \code{step()}: The p-values shown are not correct because they have not been adjusted for the fact that the same data are used to select the model and compute the p-values. So use them only in an exploratory manner in this context, see also \cite{mixtures:Harrell:2001} for more details on the general problem. The returned object can be inspected using \code{summary()} with arguments \code{which} to specify if information for the component model or the concomitant variable model should be shown and \code{model} to indicate for which dimension of the component models this should be done. Selecting \code{model=1} gives the parameter estimates for the dimension where the response variable follows a Gaussian distribution. <<>>= m1.refit <- refit(m1) summary(m1.refit, which = "model", model = 1) @ \begin{figure} \centering <>= print(plot(m1.refit, layout = c(1,3), bycluster = FALSE, main = expression(paste(yn *tilde(" ")* x + x^2))), split= c(1,1,2,1), more = TRUE) print(plot(m1.refit, model = 2, main = expression(paste(yp *tilde(" ")* x)), layout = c(1,2), bycluster = FALSE), split = c(2,1,2,1)) @ \caption{The default plot for refitted \code{"flexmix"} objects, here obtained by \code{plot(refit(m1), model = 1)} and \code{plot(refit(m1), model = 2)}, shows the coefficient estimates and their confidence intervals.} \label{fig:refit} \end{figure} The default plot method for the refitted \code{"flexmix"} object depicts the estimated coefficients with corresponding confidence intervals and is given in Figure~\ref{fig:refit}. It can be seen that for the first model the confidence intervals of the coefficients of the intercept and the quadratic term of \code{x} overlap with zero. A model where these coefficients are set to zero can be estimated with the model driver function \code{FLXMRglmfix()} and the following commands for specifying the nesting structure. The argument \code{nested} needs input for the number of components in each group (given by \code{k}) and the formula which determines the model matrix for the nesting (given by \code{formula}). This information can be provided in a named list. For the restricted model the element \code{k} is a vector with two 1s because each of the components has different parameters. The formulas specifying the model matrices of these coefficients are \verb/~ 1 + I(x^2)/ for an intercept and a quadratic term of $x$ for component 1 and \code{~ 0} for no additional coefficients for component 2. The EM algorithm is initialized in the previously fitted model by passing the posterior probabilities in the argument \code{cluster}. <<>>= Model_n2 <- FLXMRglmfix(yn ~ . + 0, nested = list(k = c(1, 1), formula = c(~ 1 + I(x^2), ~ 0))) m2 <- flexmix(. ~ x, data = NPreg, cluster = posterior(m1), model = list(Model_n2, Model_p)) m2 @ Model selection based on the BIC would suggest the smaller model which also corresponds to the true underlying model. <<>>= c(BIC(m1), BIC(m2)) @ %%----------------------------------------------------------------------- \subsection{Beta-blockers dataset} \label{sec:beta-blockers} The dataset is analyzed in \cite{mixtures:Aitkin:1999, mixtures:Aitkin:1999a} using a finite mixture of binomial regression models. Furthermore, it is described in \citet[p.~165]{mixtures:McLachlan+Peel:2000}. The dataset is from a 22-center clinical trial of beta-blockers for reducing mortality after myocardial infarction. A two-level model is assumed to represent the data, where centers are at the upper level and patients at the lower level. The data is illustrated in Figure~\ref{fig:beta}. First, the center information is ignored and a binomial logit regression model with treatment as covariate is fitted using \code{glm}, i.e.~$K=1$ and it is assumed that the different centers are comparable: <<>>= data("betablocker", package = "flexmix") betaGlm <- glm(cbind(Deaths, Total - Deaths) ~ Treatment, family = "binomial", data = betablocker) betaGlm @ The residual deviance suggests that overdispersion is present in the data. In the next step the intercept is allowed to follow a mixture distribution given the centers. This signifies that the component membership is fixed for each center. This grouping is specified in \proglang{R} by adding \code{| Center} to the formula similar to the notation used in \pkg{nlme} \citep{mixtures:Pinheiro+Bates:2000}. Under the assumption of homogeneity within centers identifiability of the model class can be ensured as induced by the sufficient conditions for identifability given in \cite{mixtures:Follmann+Lambert:1991} for binomial logit models with varying intercepts and \cite{mixtures:Gruen+Leisch:2008} for multinomial logit models with varying and constant parameters. In order to determine the suitable number of components, the mixture is fitted with different numbers of components. <<>>= betaMixFix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, model = FLXMRglmfix(family = "binomial", fixed = ~ Treatment), k = 2:4, nrep = 5, data = betablocker) @ The returned object is of class \code{"stepFlexmix"} and printing the object gives the information on the number of iterations until termination of the EM algorithm, a logical indicating if the EM algorithm has converged, the log-likelihood and some model information criteria. The plot method compares the fitted models using the different model information criteria. <<>>= betaMixFix @ A specific \code{"flexmix"} model contained in the \code{"stepFlexmix"} object can be selected using \code{getModel()} with argument \code{which} to specify the selection criterion. The best model with respect to the BIC is selected with: <<>>= betaMixFix_3 <- getModel(betaMixFix, which = "BIC") betaMixFix_3 <- relabel(betaMixFix_3, "model", "Intercept") @ The components of the selected model are ordered with respect to the estimated intercept values. In this case a model with three components is selected with respect to the BIC. The fitted values for the model with three components are given in Figure~\ref{fig:beta} separately for each component and the treatment and control groups. The fitted parameters of the component specific models can be accessed with: <<>>= parameters(betaMixFix_3) @ Please note that the coefficients of variable \code{Treatment} are the same for all three components. \begin{figure} \centering <>= library("grid") betablocker$Center <- with(betablocker, factor(Center, levels = Center[order((Deaths/Total)[1:22])])) clusters <- factor(clusters(betaMixFix_3), labels = paste("Cluster", 1:3)) print(dotplot(Deaths/Total ~ Center | clusters, groups = Treatment, as.table = TRUE, data = betablocker, xlab = "Center", layout = c(3, 1), scales = list(x = list(cex = 0.7, tck = c(1, 0))), key = simpleKey(levels(betablocker$Treatment), lines = TRUE, corner = c(1,0)))) betaMixFix.fitted <- fitted(betaMixFix_3) for (i in 1:3) { seekViewport(trellis.vpname("panel", i, 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[1:22, i], "native"), gp = gpar(lty = 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[23:44, i], "native"), gp = gpar(lty = 2)) } @ \setkeys{Gin}{width=0.8\textwidth} \caption{Relative number of deaths for the treatment and the control group for each center in the beta-blocker dataset. The centers are sorted by the relative number of deaths in the control group. The lines indicate the fitted values for each component of the 3-component mixture model with varying intercept and constant parameters for treatment.} \label{fig:beta} \end{figure} The variable \code{Treatment} can also be included in the varying part of the model. This signifies that a mixture distribution is assumed where for each component different values are allowed for the intercept and the treatment coefficient. This mixture distribution can be specified using function \code{FLXMRglm()}. Again it is assumed that the heterogeneity is only between centers and therefore the aggregated data for each center can be used. <<>>= betaMix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ Treatment | Center, model = FLXMRglm(family = "binomial"), k = 3, nrep = 5, data = betablocker) betaMix <- relabel(betaMix, "model", "Treatment") parameters(betaMix) c(BIC(betaMixFix_3), BIC(betaMix)) @ The difference between model \code{betaMix} and \code{betaMixFix\_3} is that the treatment coefficients are the same for all three components for \code{betaMixFix\_3} while they have different values for \code{betaMix} which can easily be seen when comparing the fitted component specific parameters. The larger model \code{betaMix} which also allows varying parameters for treatment has a higher BIC and therefore the smaller model \code{betaMixFix\_3} would be preferred. The default plot for \code{"flexmix"} objects gives a rootogram of the posterior probabilities for each component. Argument \code{mark} can be used to inspect with which components the specified component overlaps as all observations are coloured in the different panels which are assigned to this component based on the maximum a-posteriori probabilities. \begin{figure} \centering <>= print(plot(betaMixFix_3, nint = 10, mark = 1, col = "grey", layout = c(3, 1))) @ \caption{Default plot of \code{"flexmix"} objects where the observations assigned to the first component are marked.}\label{fig:default} \end{figure} \begin{figure} \centering <>= print(plot(betaMixFix_3, nint = 10, mark = 2, col = "grey", layout = c(3, 1))) @ \caption{Default plot of \code{"flexmix"} objects where the observations assigned to the third component are marked.}\label{fig:default-2} \end{figure} The rootogram indicates that the components are well separated. In Figure~\ref{fig:default} it can be seen that component 1 is completely separated from the other two components, while Figure~\ref{fig:default-2} shows that component 2 has a slight overlap with both other components. The cluster assignments using the maximum a-posteriori probabilities are obtained with: <<>>= table(clusters(betaMix)) @ The estimated probabilities of death for each component for the treated patients and those in the control group can be obtained with: <<>>= predict(betaMix, newdata = data.frame(Treatment = c("Control", "Treated"))) @ or by obtaining the fitted values for two observations (e.g.~rows 1 and 23) with the desired levels of the predictor \code{Treatment} <<>>= betablocker[c(1, 23), ] fitted(betaMix)[c(1, 23), ] @ A further analysis of the model is possible with function \code{refit()} which returns the estimated coefficients together with the standard deviations, z-values and corresponding p-values. Please note that the p-values are only approximate in the sense that they have not been corrected for the fact that the data has already been used to determine the specific fitted model. <<>>= summary(refit(betaMix)) @ Given the estimated treatment coefficients we now also compare this model to a model where the treatment coefficient is assumed to be the same for components 1 and 2. Such a model is specified using the model driver \code{FLXMRglmfix()}. As the first two components are assumed to have the same coeffcients for treatment and for the third component the coefficient for treatment shall be set to zero the argument \code{nested} has \code{k = c(2,1)} and \code{formula = c(\~{}Treatment, \~{})}. <<>>= ModelNested <- FLXMRglmfix(family = "binomial", nested = list(k = c(2, 1), formula = c(~ Treatment, ~ 0))) betaMixNested <- flexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, model = ModelNested, k = 3, data = betablocker, cluster = posterior(betaMix)) parameters(betaMixNested) c(BIC(betaMix), BIC(betaMixNested), BIC(betaMixFix_3)) @ The comparison of the BIC values suggests that the nested model with the same treatment effect for two components and no treatment effect for the third component is the best. %%----------------------------------------------------------------------- \subsection[Productivity of Ph.D. students in biochemistry]{Productivity of Ph.D.~students in biochemistry} \label{sec:bioChemists} <>= data("bioChemists", package = "flexmix") @ This dataset is taken from \cite{mixtures:Long:1990}. It contains \Sexpr{nrow(bioChemists)} observations from academics who obtained their Ph.D.~degree in biochemistry in the 1950s and 60s. It includes \Sexpr{sum(bioChemists$fem=="Women")} women and \Sexpr{sum(bioChemists$fem=="Men")} men. The productivity was measured by counting the number of publications in scientific journals during the three years period ending the year after the Ph.D.~was received. In addition data on the productivity and the prestige of the mentor and the Ph.D.~department was collected. Two measures of family characteristics were recorded: marriage status and number of children of age 5 and lower by the year of the Ph.D. First, mixtures with one, two and three components and only varying parameters are fitted, and the model minimizing the BIC is selected. This is based on the assumption that unobserved heterogeneity is present in the data due to latent differences between the students in order to be productive and achieve publications. Starting with the most general model to determine the number of components using information criteria and checking for possible model restrictions after having the number of components fixed is a common strategy in finite mixture modelling \citep[see][]{mixtures:Wang+Puterman+Cockburn:1996}. Function \code{refit()} is used to determine confidence intervals for the parameters in order to choose suitable alternative models. However, it has to be noted that in the course of the procedure these confidence intervals will not be correct any more because the specific fitted models have already been determined using the same data. <<>>= data("bioChemists", package = "flexmix") Model1 <- FLXMRglm(family = "poisson") ff_1 <- stepFlexmix(art ~ ., data = bioChemists, k = 1:3, model = Model1) ff_1 <- getModel(ff_1, "BIC") @ The selected model has \Sexpr{ff_1@k} components. The estimated coefficients of the components are given in Figure~\ref{fig:coefficients-1} together with the corresponding 95\% confidence intervals using the plot method for objects returned by \code{refit()}. The plot shows that the confidence intervals of the parameters for \code{kid5}, \code{mar}, \code{ment} and \code{phd} overlap for the two components. In a next step a mixture with two components is therefore fitted where only a varying intercept and a varying coefficient for \code{fem} is specified and all other coefficients are constant. The EM algorithm is initialized with the fitted mixture model using \code{posterior()}. \begin{figure} \centering <>= print(plot(refit(ff_1), bycluster = FALSE, scales = list(x = list(relation = "free")))) @ \caption{Coefficient estimates and confidence intervals for the model with only varying parameters.}\label{fig:coefficients-1} \end{figure} <<>>= Model2 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment) ff_2 <- flexmix(art ~ fem + phd, data = bioChemists, cluster = posterior(ff_1), model = Model2) c(BIC(ff_1), BIC(ff_2)) @ If the BIC is used for model comparison the smaller model including only varying coefficients for the intercept and \code{fem} is preferred. The coefficients of the fitted model can be obtained using \code{refit()}: <<>>= summary(refit(ff_2)) @ It can be seen that the coefficient of \code{phd} does for both components not differ significantly from zero and might be omitted. This again improves the BIC. <<>>= Model3 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment) ff_3 <- flexmix(art ~ fem, data = bioChemists, cluster = posterior(ff_2), model = Model3) c(BIC(ff_2), BIC(ff_3)) @ The coefficients of the restricted model without \code{phd} are given in Figure~\ref{fig:coefficients-2}. \begin{figure}[t] \centering <>= print(plot(refit(ff_3), bycluster = FALSE, scales = list(x = list(relation = "free")))) @ \caption{Coefficient estimates and confidence intervals for the model with varying and constant parameters where the variable \code{phd} is not used in the regression.}\label{fig:coefficients-2} \end{figure} An alternative model would be to assume that gender does not directly influence the number of articles but has an impact on the segment sizes. <<>>= Model4 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment) ff_4 <- flexmix(art ~ 1, data = bioChemists, cluster = posterior(ff_2), concomitant = FLXPmultinom(~ fem), model = Model4) parameters(ff_4) summary(refit(ff_4), which = "concomitant") BIC(ff_4) @ This suggests that the proportion of women is lower in the second component which is the more productive segment. The alternative modelling strategy where homogeneity is assumed at the beginning and a varying interept is added if overdispersion is observed leads to the following model which is the best with respect to the BIC. <<>>= Model5 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + ment + fem) ff_5 <- flexmix(art ~ 1, data = bioChemists, cluster = posterior(ff_2), model = Model5) BIC(ff_5) @ \begin{figure} \centering \setkeys{Gin}{width=0.8\textwidth} <>= pp <- predict(ff_5, newdata = data.frame(kid5 = 0, mar = factor("Married", levels = c("Single", "Married")), fem = c("Men", "Women"), ment = mean(bioChemists$ment))) matplot(0:12, sapply(unlist(pp), function(x) dpois(0:12, x)), type = "b", lty = 1, xlab = "Number of articles", ylab = "Probability") legend("topright", paste("Comp.", rep(1:2, each = 2), ":", c("Men", "Women")), lty = 1, col = 1:4, pch = paste(1:4), bty = "n") @ \caption{The estimated productivity for each compoment for men and women.} \label{fig:estimated} \end{figure} \setkeys{Gin}{width=0.98\textwidth} In Figure~\ref{fig:estimated} the estimated distribution of productivity for model \code{ff\_5} are given separately for men and women as well as for each component where for all other variables the mean values are used for the numeric variables and the most frequent category for the categorical variables. The two components differ in that component 1 contains the students who publish no article or only a single article, while the students in component 2 write on average several articles. With a constant coefficient for gender women publish less articles than men in both components. This example shows that different optimal models are chosen for different modelling procedures. However, the distributions induced by the different variants of the model class may be similar and therefore it is not suprising that they then will have similar BIC values. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Implementation}\label{sec:implementation} The new features extend the available model class described in \cite{mixtures:Leisch:2004} by providing infrastructure for concomitant variable models and for fitting mixtures of GLMs with varying and constant parameters for the component specific parameters. The implementation of the extensions of the model class made it necessary to define a better class structure for the component specific models and to modify the fit functions \code{flexmix()} and \code{FLXfit()}. An overview on the \proglang{S}4 class structure of the package is given in Figure~\ref{fig:class structure}. There is a class for unfitted finite mixture distributions given by \code{"FLXdist"} which contains a list of \code{"FLXM"} objects which determine the component specific models, a list of \code{"FLXcomponent"} objects which specify functions to determine the component specific log-likelihoods and predictions and which contain the component specific parameters, and an object of class \code{"FLXP"} which specifies the concomitant variable model. Class \code{"flexmix"} extends \code{"FLXdist"}. It represents a fitted finite mixture distribution and it contains the information about the fitting with the EM algorithm in the object of class \code{"FLXcontrol"}. Repeated fitting with the EM algorithm with different number of components is provided by function \code{stepFlexmix()} which returns an object of class \code{"stepFlexmix"}. Objects of class \code{"stepFlexmix"} contain the list of the fitted mixture models for each number of components in the slot \code{"models"}. \setkeys{Gin}{width=.9\textwidth} \begin{figure}[t] \centering \includegraphics{flexmix} \caption{UML class diagram \citep[see][]{mixtures:Fowler:2004} of the \pkg{flexmix} package.} \label{fig:class structure} \end{figure} \setkeys{Gin}{width=\textwidth} For the component specific model a virtual class \code{"FLXM"} is introduced which (currently) has two subclasses: \code{"FLXMC"} for model-based clustering and \code{"FLXMR"} for clusterwise regression, where predictor variables are given. Additional slots have been introduced to allow for data preprocessing and the construction of the components was separated from the fit and is implemented using lexical scoping \citep{mixtures:Gentleman+Ihaka:2000} in the slot \code{defineComponent}. \code{"FLXMC"} has an additional slot \code{dist} to specify the name of the distribution of the variable. In the future functionality shall be provided for sampling from a fitted or unfitted finite mixture. Using this slot observations can be generated by using the function which results from adding an \code{r} at the beginnning of the distribution name. This allows to only implement the (missing) random number generator functions and otherwise use the same method for sampling from mixtures with component specific models of class \code{"FLXMC"}. For \code{flexmix()} and \code{FLXfit()} code blocks which are model dependent have been identified and different methods implemented. Finite mixtures of regressions with varying, nested and constant parameters were a suitable model class for this identification task as they are different from models previously implemented. The main differences are: \begin{itemize} \item The number of components is related to the component specific model and the omission of small components during the EM algorithm impacts on the model. \item The parameters of the component specific models can not be determined separately in the M-step and a joint model matrix is needed. \end{itemize} This makes it also necessary to have different model dependent methods for \code{fitted()} which extracts the fitted values from a \code{"flexmix"} object, \code{predict()} which predicts new values for a \code{"flexmix"} object and \code{refit()} which refits an estimated model to obtain additional information for a \code{"flexmix"} object. %%----------------------------------------------------------------------- \subsection{Component specific models with varying and constant parameters}\label{sec:comp-models-with} A new M-step driver is provided which fits finite mixtures of GLMs with constant and nested varying parameters for the coefficients and the dispersion parameters. The class \code{"FLXMRglmfix"} returned by the driver \code{FLXMRglmfix()} has the following additional slots with respect to \code{"FLXMRglm"}: \begin{description} \item[\code{design}:] An incidence matrix indicating which columns of the model matrix are used for which component, i.e.~$\mathbf{D}=(\mathbf{1}_K,\mathbf{J}, \mathbf{I}_K)$. \item[\code{nestedformula}:] An object of class \code{"FLXnested"} containing the formula for the nested regression coefficients and the number of components in each $K_c$, $c \in C$. \item[\code{fixed}:] The formula for the constant regression coefficients. \item[\code{variance}:] A logical indicating if different variances shall be estimated for the components following a Gaussian distribution or a vector specifying the nested structure for estimating these variances. \end{description} The difference between estimating finite mixtures including only varying parameters using models specified with \code{FLXMRglm()} and those with varying and constant parameters using function \code{FLXMRglmfix()} is hidden from the user, as only the specified model is different. The fitted model is also of class \code{"flexmix"} and can be analyzed using the same functions as for any model fitted using package \pkg{flexmix}. The methods used are the same except if the slot containing the model is accessed and method dispatching is made via the model class. New methods are provided for models of class \code{"FLXMRglmfix"} for functions \code{refit()}, \code{fitted()} and \code{predict()} which can be used for analyzing the fitted model. The implementation allows repeated measurements by specifying a grouping variable in the formula argument of \code{flexmix()}. Furthermore, it has to be noticed that the model matrix is determined by updating the formula of the varying parameters successively with the formula of the constant and then of the nested varying parameters. This ensures that if a mixture distribution is fitted for the intercept, the model matrix of a categorical variable includes only the remaining columns for the constant parameters to have full column rank. However, this updating scheme makes it impossible to estimate a constant intercept while allowing varying parameters for a categorical variable. For this model one big model matrix is constructed where the observations are repeated $K$ times and suitable columns of zero added. The coefficients of all $K$ components are determined simultaneously in the M-step, while if only varying parameters are specified the maximization of the likelihood is made separately for all components. For large datasets the estimation of a combination of constant and varying parameters might therefore be more challenging than only varying parameters. %% ----------------------------------------------------------------------- \subsection{Concomitant variable models}\label{sec:conc-vari-models} For representing concomitant variable models the class \code{"FLXP"} is defined. It specifies how the concomitant variable model is fitted using the concomitant variable model matrix as predictor variables and the current a-posteriori probability estimates as response variables. The object has the following slots: \begin{description} \item[\code{fit}:] A \code{function (x, y, ...)} returning the fitted values for the component weights during the EM algorithm. \item[\code{refit}:] A \code{function (x, y, ...)} used for refitting the model. \item[\code{df}:] A \code{function (x, k, ...)} returning the degrees of freedom used for estimating the concomitant variable model given the model matrix \code{x} and the number of components \code{k}. \item[\code{x}:] A matrix containing the model matrix of the concomitant variables. \item[\code{formula}:] The formula for determining the model matrix \code{x}. \item[\code{name}:] A character string describing the model, which is only used for print output. \end{description} Two constructor functions for concomitant variable models are provided at the moment. \code{FLXPconstant()} is for constant component weights without concomitant variables and for multinomial logit models \code{FLXPmultinom()} can be used. \code{FLXPmultinom()} has its own class \code{"FLXPmultinom"} which extends \code{"FLXP"} and has an additional slot \code{coef} for the fitted coefficients. The multinomial logit models are fitted using package \pkg{nnet} \citep{mixtures:Venables+Ripley:2002}. %%----------------------------------------------------------------------- \subsection{Further changes} The estimation of the model with the EM algorithm was improved by adapting the variants to correspond to the CEM and SEM variants as outlined in the literature. To make this more explicit it is now also possible to use \code{"CEM"} or \code{"SEM"} to specify an EM variant in the \code{classify} argument of the \code{"FLXcontrol"} object. Even though the SEM algorithm can in general not be expected to converge the fitting procedure is also terminated for the SEM algorithm if the change in the relative log-likelhood is smaller than the pre-specified threshold. This is motivated by the fact that for well separated clusters the posteriors might converge to an indicator function with all weight concentrated in one component. The fitted model with the maximum likelihood encountered during the SEM algorithm is returned. For discrete data in general multiple observations with the same values are given in a dataset. A \code{weights} argument was added to the fitting function \code{flexmix()} in order to avoid repeating these observations in the provided dataset. The specification is through a \code{formula} in order to allow selecting a column of the data frame given in the \code{data} argument. The weights argument allows to avoid replicating the same observations and hence enables more efficient memory use in these applications. This possibitliy is especially useful in the context of model-based clustering for mixtures of Poisson distributions or latent class analysis with multivariate binary observations. In order to be able to apply different initialization strategies such as for example first running several different random initializations with CEM and then switching to ordinary EM using the best solution found by CEM for initialization a \code{posterior()} function was implemented. \code{posterior()} also takes a \code{newdata} argument and hence, it is possible to apply subset strategies for large datasets as suggested in \cite{mixtures:Wehrens+Buydens+Fraley:2004}. The returned matrix of the posterior probabilities can be used to specify the \code{cluster} argument for \code{flexmix()} and the posteriors are then used as weights in the first M-step. The default plot methods now use trellis graphics as implemented in package \pkg{lattice} \citep{mixtures:Sarkar:2008}. Users familiar with the syntax of these graphics and with the plotting and printing arguments will find the application intuitive as a lot of plotting arguments are passed to functions from \pkg{lattice} as for example \code{xyplot()} and \code{histogram()}. In fact only new panel, pre-panel and group-panel functions were implemented. The returned object is of class \code{"trellis"} and the show method for this class is used to create the plot. Function \code{refit()} was modified and has now two different estimation methods: \code{"optim"} and \code{"mstep"}. The default method \code{"optim"} determines the variance-covariance matrix of the parameters from the inverse Hessian of the full log-likelihood. The general purpose optimizer \code{optim()} is used to maximize the log-likelihood and initialized in the solution obtained with the EM algorithm. For mixtures of GLMs there are also functions implemented to determine the gradient which can be used to speed up convergence. The second method \code{"mstep"} is only a raw approximation. It performs an M-step where the a-posteriori probabilities are treated as given instead of estimated and returns for the component specific models nearly complete \code{"glm"} objects which can be further analyzed. The advantage of this method is that the return value is basically a list of standard \code{"glm"} objects, such that the regular methods for this class can be used. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Writing your own drivers}\label{sec:writing-your-own} Two examples are given in the following to demonstrate how new drivers can be provided for concomitant variable models and for component specific models. Easy extensibility is one of the main implementation aims of the package and it can be seen that writing new drivers requires only a few lines of code for providing the constructor functions which include the fit functions. %%----------------------------------------------------------------------- \subsection{Component specific models: Zero-inflated models}\label{sec:component-models} \lstset{frame=trbl,basicstyle=\small\tt,stepnumber=5,numbers=left} In Poisson or binomial regression models it can be often encountered that the observed number of zeros is higher than expected. A mixture with two components where one has mean zero can be used to model such data. These models are also referred to as zero-inflated models \citep[see for example][]{mixtures:Boehning+Dietz+Schlattmann:1999}. A generalization of this model class would be to fit mixtures with more than two components where one component has a mean fixed at zero. So this model class is a special case of a mixture of generalized linear models where (a) the family is restricted to Poisson and binomial and (b) the parameters of one component are fixed. For simplicity the implementation assumes that the component with mean zero is the first component. In addition we assume that the model matrix contains an intercept and to have the first component absorbing the access zeros the coefficient of the intercept is set to $-\infty$ and all other coefficients are set to zero. Hence, to implement this model using package \pkg{flexmix} an appropriate model class is needed with a corresponding convenience function for construction. During the fitting of the EM algorithm using \code{flexmix()} different methods for this model class are needed when determining the model matrix (to check the presence of an intercept), to check the model after a component is removed and for the M-step to account for the fact that the coefficients of the first component are fixed. For all other methods those available for \code{"FLXMRglm"} can be re-used. The code is given in Figure~\ref{fig:ziglm.R}. \begin{figure} \centering \begin{minipage}{0.98\textwidth} \lstinputlisting{ziglm.R} \end{minipage} \caption{Driver for a zero-inflated component specific model.} \label{fig:ziglm.R} \end{figure} The model class \code{"FLXMRziglm"} is defined as extending \code{"FLXMRglm"} in order to be able to inherit methods from this model class. For construction of a \code{"FLXMRziglm"} class the convenicence function \code{FLXMRziglm()} is used which calls \code{FLXMRglm()}. The only differences are that the family is restricted to binomial or Poisson, that a different name is assigned and that an object of the correct class is returned. The presence of the intercept in the model matrix is checked in \code{FLXgetModelmatrix()} after using the method available for \code{"FLXMRglm"} models as indicated by the call to \code{callNextMethod()}. During the EM algorithm \code{FLXremoveComponent()} is called if one component is removed. For this model class it checks if the first component has been removed and if this is the case the model class is changed to \code{"FLXMRglm"}. In the M-step the coefficients of the first component are fixed and not estimated, while for the remaining components the M-step of \code{"FLXMRglm"} objects can be used. During the EM algorithm \code{FLXmstep()} is called to perform the M-step and returns a list of \code{"FLXcomponent"} objects with the fitted parameters. A new method for this function is needed for \code{"FLXMRziglm"} objects in order to account for the fixed coefficients in the first component, i.e.~for the first component the \code{"FLXcomponent"} object is constructed and concatenated with the list of \code{"FLXcomponent"} objects returned by using the \code{FLXmstep()} method for \code{"FLXMRglm"} models for the remaining components. Similar modifications are necessary in order to be able to use \code{refit()} for this model class. The code for implementing the \code{refit()} method using \code{optim()} for \code{"FLXMRziglm"} is not shown, but can be inspected in the source code of the package. \subsubsection{Example: Using the driver} This new M-step driver can be used to estimate a zero-inflated Poisson model to the data given in \cite{mixtures:Boehning+Dietz+Schlattmann:1999}. The dataset \code{dmft} consists of count data from a dental epidemiological study for evaluation of various programs for reducing caries collected among school children from an urban area of Belo Horizonte (Brazil). The variables included are the number of decayed, missing or filled teeth (DMFT index) at the beginning and at the end of the observation period, the gender, the ethnic background and the specific treatment for \Sexpr{nrow(dmft)} children. The model can be fitted with the new driver function using the following commands: <<>>= data("dmft", package = "flexmix") Model <- FLXMRziglm(family = "poisson") Fitted <- flexmix(End ~ log(Begin + 0.5) + Gender + Ethnic + Treatment, model = Model, k = 2 , data = dmft, control = list(minprior = 0.01)) summary(refit(Fitted)) @ Please note that \cite{mixtures:Boehning+Dietz+Schlattmann:1999} added the predictor \code{log(Begin + 0.5)} to serve as an offset in order to be able to analyse the improvement in the DMFT index from the beginning to the end of the study. The linear predictor with the offset subtracted is intended to be an estimate for $\log(\mathbb{E}(\textrm{End})) - \log(\mathbb{E}(\textrm{Begin}))$. This is justified by the fact that for a Poisson distributed variable $Y$ with mean between 1 and 10 it holds that $\mathbb{E}(\log(Y + 0.5))$ is approximately equal to $\log(\mathbb{E}(Y))$. $\log(\textrm{Begin} + 0.5)$ can therefore be seen as an estimate for $\log(\mathbb{E}(\textrm{Begin}))$. The estimated coefficients with corresponding confidence intervals are given in Figure~\ref{fig:dmft}. As the coefficients of the first component are restricted a-priori to minus infinity for the intercept and to zero for the other variables, they are of no interest and only the second component is plotted. The box ratio can be modified as for \code{barchart()} in package \pkg{lattice}. The code to produce this plot is given by: <>= print(plot(refit(Fitted), components = 2, box.ratio = 3)) @ \begin{figure} \centering \setkeys{Gin}{width=0.9\textwidth} <>= <> @ \caption{The estimated coefficients of the zero-inflated model for the \code{dmft} dataset. The first component is not plotted as this component captures the inflated zeros and its coefficients are fixed a-priori.} \label{fig:dmft} \end{figure} %%----------------------------------------------------------------------- \subsection{Concomitant variable models}\label{sec:concomitant-models} If the concomitant variable is a categorical variable, the multinomial logit model is equivalent to a model where the component weights for each level of the concomitant variable are determined by the mean values of the a-posteriori probabilities. The driver which implements this \code{"FLXP"} model is given in Figure~\ref{fig:myConcomitant.R}. A name for the driver has to be specified and a \code{fit()} function. In the \code{fit()} function the mean posterior probability for all observations with the same covariate points is determined, assigned to the corresponding observations and the full new a-posteriori probability matrix returned. By contrast \code{refit()} only returns the new a-posteriori probability matrix for the number of unique covariate points. \lstset{frame=trbl,basicstyle=\small\tt,stepnumber=5,numbers=left} \begin{figure} \centering \begin{minipage}{0.98\textwidth} \lstinputlisting{myConcomitant.R} \end{minipage} \caption{Driver for a concomitant variable model where the component weights are determined by averaging over the a-posteriori probabilities for each level of the concomitant variable.} \label{fig:myConcomitant.R} \end{figure} \subsubsection{Example: Using the driver} If the concomitant variable model returned by \code{myConcomitant()} is used for the artificial example in Section~\ref{sec:using-new-funct} the same fitted model is returned as if a multinomial logit model is specified. An advantage is that in this case no problems occur if the fitted probabilities are close to zero or one. <>= Concomitant <- FLXPmultinom(~ yb) MyConcomitant <- myConcomitant(~ yb) set.seed(1234) m2 <- flexmix(. ~ x, data = NPreg, k = 2, model = list(Model_n, Model_p), concomitant = Concomitant) m3 <- flexmix(. ~ x, data = NPreg, k = 2, model = list(Model_n, Model_p), cluster = posterior(m2), concomitant = MyConcomitant) @ <<>>= summary(m2) summary(m3) @ For comparing the estimated component weights for each value of $\mathit{yb}$ the following function can be used: <<>>= determinePrior <- function(object) { object@concomitant@fit(object@concomitant@x, posterior(object))[!duplicated(object@concomitant@x), ] } @ <<>>= determinePrior(m2) determinePrior(m3) @ Obviously the fitted values of the two models correspond to each other. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section{Summary and outlook}\label{sec:summary-outlook} Package \pkg{flexmix} was extended to cover finite mixtures of GLMs with (nested) varying and constant parameters. This allows for example the estimation of varying intercept models. In order to be able to characterize the components given some variables concomitant variable models can be estimated for the component weights. The implementation of these extensions have triggered some modifications in the class structure and in the fit functions \code{flexmix()} and \code{FLXfit()}. For certain steps, as e.g.~the M-step, methods which depend on the component specific models are defined in order to enable the estimation of finite mixtures of GLMs with only varying parameters and those with (nested) varying and constant parameters with the same fit function. The flexibility of this modified implementation is demonstrated by illustrating how a driver for zero-inflated models can be defined. In the future diagnostic tools based on resampling methods shall be implemented as bootstrap results can give valuable insights into the model fit \citep{mixtures:Gruen+Leisch:2004}. A function which conveniently allows to test linear hypotheses about the parameters using the variance-covariance matrix returned by \code{refit()} would be a further valuable diagnostic tool. The implementation of zero-inflated Poisson and binomial regression models are a first step towards relaxing the assumption that all component specific distributions are from the same parametric family. As mixtures with components which follow distributions from different parametric families can be useful for example to model outliers \citep{mixtures:Dasgupta+Raftery:1998,mixtures:Leisch:2008}, it is intended to also make this functionality available in \pkg{flexmix} in the future. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section*{Computational details} <>= SI <- sessionInfo() pkgs <- paste(sapply(c(SI$otherPkgs, SI$loadedOnly), function(x) paste("\\\\pkg{", x$Package, "} ", x$Version, sep = "")), collapse = ", ") @ All computations and graphics in this paper have been done using \proglang{R} version \Sexpr{getRversion()} with the packages \Sexpr{pkgs}. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \section*{Acknowledgments} This research was supported by the the Austrian Science Foundation (FWF) under grants P17382 and T351. Thanks also to Achim Zeileis for helpful discussions on implementation details and an anonymous referee for asking a good question about parameter significance which initiated the new version of function \code{refit()}. %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \bibliography{mixture} %%----------------------------------------------------------------------- %%----------------------------------------------------------------------- \end{document} flexmix/inst/doc/regression-examples.Rnw0000644000176200001440000012407214404637307020152 0ustar liggesusers\documentclass[nojss]{jss} \usepackage{amsfonts,bm,amsmath,amssymb} %%\usepackage{Sweave} %% already provided by jss.cls %%%\VignetteIndexEntry{Applications of finite mixtures of regression models} %%\VignetteDepends{flexmix} %%\VignetteKeywords{R, finite mixture model, generalized linear model, latent class regression} %%\VignettePackage{flexmix} \title{Applications of finite mixtures of regression models} <>= library("stats") library("graphics") library("flexmix") @ \author{Bettina Gr{\"u}n\\ Wirtschaftsuniversit{\"a}t Wien \And Friedrich Leisch\\ Universit\"at f\"ur Bodenkultur Wien} \Plainauthor{Bettina Gr{\"u}n, Friedrich Leisch} \Address{ Bettina Gr\"un\\ Institute for Statistics and Mathematics\\ Wirtschaftsuniversit{\"a}t Wien\\ Welthandelsplatz 1\\ 1020 Wien, Austria\\ E-mail: \email{Bettina.Gruen@R-project.org}\\ Friedrich Leisch\\ Institut f\"ur Angewandte Statistik und EDV\\ Universit\"at f\"ur Bodenkultur Wien\\ Peter Jordan Stra\ss{}e 82\\ 1190 Wien, Austria\\ E-mail: \email{Friedrich.Leisch@boku.ac.at} } \Abstract{ Package \pkg{flexmix} provides functionality for fitting finite mixtures of regression models. The available model class includes generalized linear models with varying and fixed effects for the component specific models and multinomial logit models for the concomitant variable models. This model class includes random intercept models where the random part is modelled by a finite mixture instead of a-priori selecting a suitable distribution. The application of the package is illustrated on various datasets which have been previously used in the literature to fit finite mixtures of Gaussian, binomial or Poisson regression models. The \proglang{R} commands are given to fit the proposed models and additional insights are gained by visualizing the data and the fitted models as well as by fitting slightly modified models. } \Keywords{\proglang{R}, finite mixture models, generalized linear models, concomitant variables} \Plainkeywords{R, finite mixture models, generalized linear models, concomitant variables} %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \begin{document} \SweaveOpts{engine=R, echo=true, height=5, width=8, eps=FALSE, keep.source=TRUE} \setkeys{Gin}{width=0.8\textwidth} <>= options(width=70, prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE) suppressWarnings(RNGversion("3.5.0")) set.seed(1802) library("lattice") ltheme <- canonical.theme("postscript", FALSE) lattice.options(default.theme=ltheme) @ %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \section{Introduction} Package \pkg{flexmix} provides infrastructure for flexible fitting of finite mixtures models. The design principles of the package allow easy extensibility and rapid prototyping. In addition, the main focus of the available functionality is on fitting finite mixtures of regression models, as other packages in \proglang{R} exist which have specialized functionality for model-based clustering, such as e.g.~\pkg{mclust} \citep{flexmix:Fraley+Raftery:2002a} for finite mixtures of Gaussian distributions. \cite{flexmix:Leisch:2004a} gives a general introduction into the package outlining the main implementational principles and illustrating the use of the package. The paper is also contained as a vignette in the package. An example for fitting mixtures of Gaussian regression models is given in \cite{flexmix:Gruen+Leisch:2006}. This paper focuses on examples of finite mixtures of binomial logit and Poisson regression models. Several datasets which have been previously used in the literature to demonstrate the use of finite mixtures of regression models have been selected to illustrate the application of the package. The model class covered are finite mixtures of generalized linear model with focus on binomial logit and Poisson regressions. The regression coefficients as well as the dispersion parameters of the component specific models are assumed to vary for all components, vary between groups of components, i.e.~to have a nesting, or to be fixed over all components. In addition it is possible to specify concomitant variable models in order to be able to characterize the components. Random intercept models are a special case of finite mixtures with varying and fixed effects as fixed effects are assumed for the coefficients of all covariates and varying effects for the intercept. These models are often used to capture overdispersion in the data which can occur for example if important covariates are omitted in the regression. It is then assumed that the influence of these covariates can be captured by allowing a random distribution for the intercept. This illustration does not only show how the package \pkg{flexmix} can be used for fitting finite mixtures of regression models but also indicates the advantages of using an extension package of an environment for statistical computing and graphics instead of a stand-alone package as available visualization techniques can be used for inspecting the data and the fitted models. In addition users already familiar with \proglang{R} and its formula interface should find the model specification and a lot of commands for exploring the fitted model intuitive. %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \section{Model specification} Finite mixtures of Gaussian regressions with concomitant variable models are given by: \begin{align*} H(y\,|\,\bm{x}, \bm{w}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\bm{w}, \bm{\alpha}) \textrm{N}(y\,|\, \mu_s(\bm{x}), \sigma^2_s), \end{align*} where $\textrm{N}(\cdot\,|\, \mu_s(\bm{x}), \sigma^2_s)$ is the Gaussian distribution with mean $\mu_s(\bm{x}) = \bm{x}' \bm{\beta}^s$ and variance $\sigma^2_s$. $\Theta$ denotes the vector of all parameters of the mixture distribution and the dependent variables are $y$, the independent $\bm{x}$ and the concomitant $\bm{w}$. Finite mixtures of binomial regressions with concomitant variable models are given by: \begin{align*} H(y\,|\,T, \bm{x}, \bm{w}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\bm{w}, \bm{\alpha}) \textrm{Bi}(y\,|\,T, \theta_s(\bm{x})), \end{align*} where $\textrm{Bi}(\cdot\,|\,T, \theta_s(\bm{x}))$ is the binomial distribution with number of trials equal to $T$ and success probability $\theta_s(\bm{x}) \in (0,1)$ given by $\textrm{logit}(\theta_s(\bm{x})) = \bm{x}' \bm{\beta}^s$. Finite mixtures of Poisson regressions are given by: \begin{align*} H(y \,|\, \bm{x}, \bm{w}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\bm{w}, \bm{\alpha}) \textrm{Poi} (y \,|\, \lambda_s(\bm{x})), \end{align*} where $\textrm{Poi}(\cdot\,|\,\lambda_s(\bm{x}))$ denotes the Poisson distribution and $\log(\lambda_s(\bm{x})) = \bm{x}'\bm{\beta}^s$. For all these mixture distributions the coefficients are split into three different groups depending on if fixed, nested or varying effects are specified: \begin{align*} \bm{\beta}^s &= (\bm{\beta}_1, \bm{\beta}^{c(s)}_{2}, \bm{\beta}^{s}_3) \end{align*} where the first group represents the fixed, the second the nested and the third the varying effects. For the nested effects a partition $\mathcal{C} = \{c_s \,|\, s = 1,\ldots S\}$ of the $S$ components is determined where $c_s = \{s^* = 1,\ldots,S \,|\, c(s^*) = c(s)\}$. A similar splitting is possible for the variance of mixtures of Gaussian regression models. The function for maximum likelihood (ML) estimation with the Expectation-Maximization (EM) algorithm is \code{flexmix()} which is described in detail in \cite{flexmix:Leisch:2004a}. It takes as arguments a specification of the component specific model and of the concomitant variable model. The component specific model with varying, nested and fixed effects can be specified with the M-step driver \code{FLXMRglmfix()} which has arguments \code{formula} for the varying, \code{nested} for the nested and \code{fixed} for the fixed effects. \code{formula} and \code{fixed} take an argument of class \code{"formula"}, whereas \code{nested} expects an object of class \code{"FLXnested"} or a named list specifying the nested structure with a component \code{k} which is a vector of the number of components in each group of the partition and a component \code{formula} which is a vector of formulas for each group of the partition. In addition there is an argument \code{family} which has to be one of \code{gaussian}, \code{binomial}, \code{poisson} or \code{Gamma} and determines the component specific distribution function as well as an \code{offset} argument. The argument \code{varFix} can be used to determine the structure of the dispersion parameters. If only varying effects are specified the M-step driver \code{FLXMRglm()} can be used which only has an argument \code{formula} for the varying effects and also a \code{family} and an \code{offset} argument. This driver has the advantage that in the M-step the weighted ML estimation is made separately for each component which signifies that smaller model matrices are used. If a mixture model with a lot of components $S$ is fitted to a large data set with $N$ observations and the model matrix used in the M-step of \code{FLXMRglm()} has $N$ rows and $K$ columns, the model matrix used in the M-step of \code{FLXMRglmfix()} has $S N$ rows and up to $S K$ columns. In general the concomitant variable model is assumed to be a multinomial logit model, i.e.~: \begin{align*} \pi_s(\bm{w},\bm{\alpha}) &= \frac{e^{\bm{w}'\bm{\alpha}_s}}{\sum_{u = 1}^S e^{\bm{w}'\bm{\alpha}_u}} \quad \forall s, \end{align*} with $\bm{\alpha} = (\bm{\alpha}'_s)_{s=1,\ldots,S}$ and $\bm{\alpha}_1 \equiv \bm{0}$. This model can be fitted in \pkg{flexmix} with \code{FLXPmultinom()} which takes as argument \code{formula} the formula specification of the multinomial logit part. For fitting the function \code{nnet()} is used from package \pkg{MASS} \citep{flexmix:Venables+Ripley:2002} with the independent variables specified by the formula argument and the dependent variables are given by the a-posteriori probability estimates. %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \section[Using package flexmix]{Using package \pkg{flexmix}} In the following datasets from different areas such as medicine, biology and economics are used. There are three subsections: for finite mixtures of Gaussian regressions, for finite mixtures of binomial regression models and for finite mixtures of Poisson regression models. %%------------------------------------------------------------------------- \subsection{Finite mixtures of Gaussian regressions} This artificial dataset with 200 observations is given in \cite{flexmix:Gruen+Leisch:2006}. The data is generated from a mixture of Gaussian regression models with three components. There is an intercept with varying effects, an independent variable $x1$, which is a numeric variable, with fixed effects and another independent variable $x2$, which is a categorical variable with two levels, with nested effects. The prior probabilities depend on a concomitant variable $w$, which is also a categorical variable with two levels. Fixed effects are also assumed for the variance. The data is illustrated in Figure~\ref{fig:artificialData} and the true underlying model is given by: \begin{align*} H(y\,|\,(x1, x2), w, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(w, \bm{\alpha}) \textrm{N}(y\,|\, \mu_s, \sigma^2), \end{align*} with $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \beta^{c(s)}_{\textrm{x1}}, \beta_{\textrm{x2}})$. The nesting signifies that $c(1) = c(2)$ and $\beta^{c(3)}_{\textrm{x1}} = 0$. The mixture model is fitted by first loading the package and the dataset and then specifying the component specific model. In a first step a component specific model with only varying effects is specified. Then the fitting function \code{flexmix()} is called repeatedly using \code{stepFlexmix()}. Finally, we order the components such that they are in ascending order with respect to the coefficients of the variable \code{x1}. <>= set.seed(2807) library("flexmix") data("NregFix", package = "flexmix") Model <- FLXMRglm(~ x2 + x1) fittedModel <- stepFlexmix(y ~ 1, model = Model, nrep = 3, k = 3, data = NregFix, concomitant = FLXPmultinom(~ w)) fittedModel <- relabel(fittedModel, "model", "x1") summary(refit(fittedModel)) @ The estimated coefficients indicate that the components differ for the intercept, but that they are not significantly different for the coefficients of $x2$. For $x1$ the coefficient of the first component is not significantly different from zero and the confidence intervals for the other two components overlap. Therefore we fit a modified model, which is equivalent to the true underlying model. The previously fitted model is used for initializing the EM algorithm: <>= Model2 <- FLXMRglmfix(fixed = ~ x2, nested = list(k = c(1, 2), formula = c(~ 0, ~ x1)), varFix = TRUE) fittedModel2 <- flexmix(y ~ 1, model = Model2, cluster = posterior(fittedModel), data = NregFix, concomitant = FLXPmultinom(~ w)) BIC(fittedModel) BIC(fittedModel2) @ The BIC suggests that the restricted model should be preferred. \begin{figure}[tb] \centering \setkeys{Gin}{width=0.95\textwidth} <>= plotNregFix <- NregFix plotNregFix$w <- factor(NregFix$w, levels = 0:1, labels = paste("w =", 0:1)) plotNregFix$x2 <- factor(NregFix$x2, levels = 0:1, labels = paste("x2 =", 0:1)) plotNregFix$class <- factor(NregFix$class, levels = 1:3, labels = paste("Class", 1:3)) print(xyplot(y ~ x1 | x2*w, groups = class, data = plotNregFix, cex = 0.6, auto.key = list(space="right"), layout = c(2,2))) @ \setkeys{Gin}{width=0.8\textwidth} \caption{Sample with 200 observations from the artificial example.} \label{fig:artificialData} \end{figure} <>= summary(refit(fittedModel2)) @ The coefficients are ordered such that the fixed coefficients are first, the nested varying coefficients second and the varying coefficients last. %%------------------------------------------------------------------------- \subsection{Finite mixtures of binomial logit regressions} %%------------------------------------------------------------------------- \subsubsection{Beta blockers} The dataset is analyzed in \cite{flexmix:Aitkin:1999, flexmix:Aitkin:1999a} using a finite mixture of binomial regression models. Furthermore, it is described in \cite{flexmix:McLachlan+Peel:2000} on page 165. The dataset is from a 22-center clinical trial of beta-blockers for reducing mortality after myocardial infarction. A two-level model is assumed to represent the data, where centers are at the upper level and patients at the lower level. The data is illustrated in Figure~\ref{fig:beta} and the model is given by: \begin{align*} H(\textrm{Deaths} \,|\, \textrm{Total}, \textrm{Treatment}, \textrm{Center}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Bi}( \textrm{Deaths} \,|\, \textrm{Total}, \theta_s). \end{align*} First, the center classification is ignored and a binomial logit regression model with treatment as covariate is fitted using \code{glm}, i.e.~$S=1$: <>= data("betablocker", package = "flexmix") betaGlm <- glm(cbind(Deaths, Total - Deaths) ~ Treatment, family = "binomial", data = betablocker) betaGlm @ In the next step the center classification is included by allowing a random effect for the intercept given the centers, i.e.~the coefficients $\bm{\beta}^s$ are given by $(\beta^s_{\textrm{Intercept|Center}}, \beta_{\textrm{Treatment}})$. This signifies that the component membership is fixed for each center. In order to determine the suitable number of components, the mixture is fitted with different numbers of components and the BIC information criterion is used to select an appropriate model. In this case a model with three components is selected. The fitted values for the model with three components are given in Figure~\ref{fig:beta}. <>= betaMixFix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, model = FLXMRglmfix(family = "binomial", fixed = ~ Treatment), k = 2:4, nrep = 3, data = betablocker) betaMixFix @ \begin{figure} \centering <>= library("grid") betaMixFix_3 <- getModel(betaMixFix, "3") betaMixFix_3 <- relabel(betaMixFix_3, "model", "Intercept") betablocker$Center <- with(betablocker, factor(Center, levels = Center[order((Deaths/Total)[1:22])])) clusters <- factor(clusters(betaMixFix_3), labels = paste("Cluster", 1:3)) print(dotplot(Deaths/Total ~ Center | clusters, groups = Treatment, as.table = TRUE, data = betablocker, xlab = "Center", layout = c(3, 1), scales = list(x = list(draw = FALSE)), key = simpleKey(levels(betablocker$Treatment), lines = TRUE, corner = c(1,0)))) betaMixFix.fitted <- fitted(betaMixFix_3) for (i in 1:3) { seekViewport(trellis.vpname("panel", i, 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[1:22, i], "native"), gp = gpar(lty = 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[23:44, i], "native"), gp = gpar(lty = 2)) } @ \caption{Relative number of deaths for the treatment and the control group for each center in the beta blocker dataset. The centers are sorted by the relative number of deaths in the control group. The lines indicate the fitted values for each component of the 3-component mixture model with random intercept and fixed effect for treatment.} \label{fig:beta} \end{figure} In addition the treatment effect can also be included in the random part of the model. As then all coefficients for the covariates and the intercept follow a mixture distribution the component specific model can be specified using \code{FLXMRglm()}. The coefficients are $\bm{\beta}^s=(\beta^s_{\textrm{Intercept|Center}}, \beta^s_{\textrm{Treatment|Center}})$, i.e.~it is assumed that the heterogeneity is only between centers and therefore the aggregated data for each center can be used. <>= betaMix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ Treatment | Center, model = FLXMRglm(family = "binomial"), k = 3, nrep = 3, data = betablocker) summary(betaMix) @ The full model with a random effect for treatment has a higher BIC and therefore the smaller would be preferred. The default plot of the returned \code{flexmix} object is a rootogramm of the a-posteriori probabilities where observations with a-posteriori probabilities smaller than \code{eps} are omitted. With argument \code{mark} the component is specified to have those observations marked which are assigned to this component based on the maximum a-posteriori probabilities. This indicates which components overlap. <>= print(plot(betaMixFix_3, mark = 1, col = "grey", markcol = 1)) @ The default plot of the fitted model indicates that the components are well separated. In addition component 1 has a slight overlap with component 2 but none with component 3. The fitted parameters of the component specific models can be accessed with: <>= parameters(betaMix) @ The cluster assignments using the maximum a-posteriori probabilities are obtained with: <>= table(clusters(betaMix)) @ The estimated probabilities for each component for the treated patients and those in the control group can be obtained with: <>= predict(betaMix, newdata = data.frame(Treatment = c("Control", "Treated"))) @ or <>= fitted(betaMix)[c(1, 23), ] @ A further analysis of the model is possible with function \code{refit()} which returns the estimated coefficients together with the standard deviations, z-values and corresponding p-values: <>= summary(refit(getModel(betaMixFix, "3"))) @ The printed coefficients are ordered to have the fixed effects before the varying effects. %%----------------------------------------------------------------------- \subsubsection{Mehta et al. trial} This dataset is similar to the beta blocker dataset and is also analyzed in \cite{flexmix:Aitkin:1999a}. The dataset is visualized in Figure~\ref{fig:mehta}. The observation for the control group in center 15 is slightly conspicuous and might classify as an outlier. The model is given by: \begin{align*} H(\textrm{Response} \,|\, \textrm{Total}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Bi}( \textrm{Response} \,|\, \textrm{Total}, \theta_s), \end{align*} with $\bm{\beta}^s = (\beta^s_{\textrm{Intercept|Site}}, \beta_{\textrm{Drug}})$. This model is fitted with: <>= data("Mehta", package = "flexmix") mehtaMix <- stepFlexmix(cbind(Response, Total - Response)~ 1 | Site, model = FLXMRglmfix(family = "binomial", fixed = ~ Drug), control = list(minprior = 0.04), nrep = 3, k = 3, data = Mehta) summary(mehtaMix) @ One component only contains the observations for center 15 and in order to be able to fit a mixture with such a small component it is necessary to modify the default argument for \code{minprior} which is 0.05. The fitted values for this model are given separately for each component in Figure~\ref{fig:mehta}. \begin{figure} \centering <>= Mehta$Site <- with(Mehta, factor(Site, levels = Site[order((Response/Total)[1:22])])) clusters <- factor(clusters(mehtaMix), labels = paste("Cluster", 1:3)) print(dotplot(Response/Total ~ Site | clusters, groups = Drug, layout = c(3,1), data = Mehta, xlab = "Site", scales = list(x = list(draw = FALSE)), key = simpleKey(levels(Mehta$Drug), lines = TRUE, corner = c(1,0)))) mehtaMix.fitted <- fitted(mehtaMix) for (i in 1:3) { seekViewport(trellis.vpname("panel", i, 1)) sapply(1:nlevels(Mehta$Drug), function(j) grid.lines(unit(1:22, "native"), unit(mehtaMix.fitted[Mehta$Drug == levels(Mehta$Drug)[j], i], "native"), gp = gpar(lty = j))) } @ \caption{Relative number of responses for the treatment and the control group for each site in the Mehta et al.~trial dataset together with the fitted values. The sites are sorted by the relative number of responses in the control group.} \label{fig:mehta} \end{figure} If also a random effect for the coefficient of $\textrm{Drug}$ is fitted, i.e.~$\bm{\beta}^s = (\beta^s_{\textrm{Intercept|Site}}, \beta^s_{\textrm{Drug|Site}})$, this is estimated by: <>= mehtaMix <- stepFlexmix(cbind(Response, Total - Response) ~ Drug | Site, model = FLXMRglm(family = "binomial"), k = 3, data = Mehta, nrep = 3, control = list(minprior = 0.04)) summary(mehtaMix) @ The BIC is smaller for the larger model and this indicates that the assumption of an equal drug effect for all centers is not confirmed by the data. Given Figure~\ref{fig:mehta} a two-component model with fixed treatment is also fitted to the data where site 15 is omitted: <>= Mehta.sub <- subset(Mehta, Site != 15) mehtaMix <- stepFlexmix(cbind(Response, Total - Response) ~ 1 | Site, model = FLXMRglmfix(family = "binomial", fixed = ~ Drug), data = Mehta.sub, k = 2, nrep = 3) summary(mehtaMix) @ %%----------------------------------------------------------------------- \subsubsection{Tribolium} A finite mixture of binomial regressions is fitted to the Tribolium dataset given in \cite{flexmix:Wang+Puterman:1998}. The data was collected to investigate whether the adult Tribolium species Castaneum has developed an evolutionary advantage to recognize and avoid eggs of its own species while foraging, as beetles of the genus Tribolium are cannibalistic in the sense that adults eat the eggs of their own species as well as those of closely related species. The experiment isolated a number of adult beetles of the same species and presented them with a vial of 150 eggs (50 of each type), the eggs being thoroughly mixed to ensure uniformity throughout the vial. The data gives the consumption data for adult Castaneum species. It reports the number of Castaneum, Confusum and Madens eggs, respectively, that remain uneaten after two day exposure to the adult beetles. Replicates 1, 2, and 3 correspond to different occasions on which the experiment was conducted. The data is visualized in Figure~\ref{fig:tribolium} and the model is given by: \begin{align*} H(\textrm{Remaining} \,|\, \textrm{Total}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\textrm{Replicate}, \bm{\alpha}) \textrm{Bi}( \textrm{Remaining} \,|\, \textrm{Total}, \theta_s), \end{align*} with $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \bm{\beta}_{\textrm{Species}})$. This model is fitted with: <>= data("tribolium", package = "flexmix") TribMix <- stepFlexmix(cbind(Remaining, Total - Remaining) ~ 1, k = 2:3, model = FLXMRglmfix(fixed = ~ Species, family = "binomial"), concomitant = FLXPmultinom(~ Replicate), data = tribolium) @ The model which is selected as the best in \cite{flexmix:Wang+Puterman:1998} can be estimated with: <>= modelWang <- FLXMRglmfix(fixed = ~ I(Species == "Confusum"), family = "binomial") concomitantWang <- FLXPmultinom(~ I(Replicate == 3)) TribMixWang <- stepFlexmix(cbind(Remaining, Total - Remaining) ~ 1, data = tribolium, model = modelWang, concomitant = concomitantWang, k = 2) summary(refit(TribMixWang)) @ \begin{figure} \centering <>= clusters <- factor(clusters(TribMixWang), labels = paste("Cluster", 1:TribMixWang@k)) print(dotplot(Remaining/Total ~ factor(Replicate) | clusters, groups = Species, data = tribolium[rep(1:9, each = 3) + c(0:2)*9,], xlab = "Replicate", auto.key = list(corner = c(1,0)))) @ \caption{Relative number of remaining beetles for the number of replicate. The different panels are according to the cluster assignemnts based on the a-posteriori probabilities of the model suggested in \cite{flexmix:Wang+Puterman:1998}.} \label{fig:tribolium} \end{figure} \cite{flexmix:Wang+Puterman:1998} also considered a model where they omit one conspicuous observation. This model can be estimated with: <>= TribMixWangSub <- stepFlexmix(cbind(Remaining, Total - Remaining) ~ 1, k = 2, data = tribolium[-7,], model = modelWang, concomitant = concomitantWang) @ %%----------------------------------------------------------------------- \subsubsection{Trypanosome} The data is used in \cite{flexmix:Follmann+Lambert:1989}. It is from a dosage-response analysis where the proportion of organisms belonging to different populations shall be assessed. It is assumed that organisms belonging to different populations are indistinguishable other than in terms of their reaction to the stimulus. The experimental technique involved inspection under the microscope of a representative aliquot of a suspension, all organisms appearing within two fields of view being classified either alive or dead. Hence the total numbers of organisms present at each dose and the number showing the quantal response were both random variables. The data is illustrated in Figure~\ref{fig:trypanosome}. The model which is proposed in \cite{flexmix:Follmann+Lambert:1989} is given by: \begin{align*} H(\textrm{Dead} \,|\,\bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Bi}( \textrm{Dead} \,|\, \theta_s), \end{align*} where $\textrm{Dead} \in \{0,1\}$ and with $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \bm{\beta}_{\textrm{log(Dose)}})$. This model is fitted with: <>= data("trypanosome", package = "flexmix") TrypMix <- stepFlexmix(cbind(Dead, 1-Dead) ~ 1, k = 2, nrep = 3, data = trypanosome, model = FLXMRglmfix(family = "binomial", fixed = ~ log(Dose))) summary(refit(TrypMix)) @ The fitted values are given in Figure~\ref{fig:trypanosome} together with the fitted values of a generalized linear model in order to facilitate comparison of the two models. \begin{figure} \centering <>= tab <- with(trypanosome, table(Dead, Dose)) Tryp.dat <- data.frame(Dead = tab["1",], Alive = tab["0",], Dose = as.numeric(colnames(tab))) plot(Dead/(Dead+Alive) ~ Dose, data = Tryp.dat) Tryp.pred <- predict(glm(cbind(Dead, 1-Dead) ~ log(Dose), family = "binomial", data = trypanosome), newdata=Tryp.dat, type = "response") TrypMix.pred <- predict(TrypMix, newdata = Tryp.dat, aggregate = TRUE)[[1]] lines(Tryp.dat$Dose, Tryp.pred, lty = 2) lines(Tryp.dat$Dose, TrypMix.pred, lty = 3) legend(4.7, 1, c("GLM", "Mixture model"), lty=c(2, 3), xjust=0, yjust=1) @ \caption{Relative number of deaths for each dose level together with the fitted values for the generalized linear model (``GLM'') and the random intercept model (``Mixture model'').} \label{fig:trypanosome} \end{figure} %%------------------------------------------------------------------------- \subsection{Finite mixtures of Poisson regressions} % %%----------------------------------------------------------------------- \subsubsection{Fabric faults} The dataset is analyzed using a finite mixture of Poisson regression models in \cite{flexmix:Aitkin:1996}. Furthermore, it is described in \cite{flexmix:McLachlan+Peel:2000} on page 155. It contains 32 observations on the number of faults in rolls of a textile fabric. A random intercept model is used where a fixed effect is assumed for the logarithm of length: <>= data("fabricfault", package = "flexmix") fabricMix <- stepFlexmix(Faults ~ 1, model = FLXMRglmfix(family="poisson", fixed = ~ log(Length)), data = fabricfault, k = 2, nrep = 3) summary(fabricMix) summary(refit(fabricMix)) Lnew <- seq(0, 1000, by = 50) fabricMix.pred <- predict(fabricMix, newdata = data.frame(Length = Lnew)) @ The intercept of the first component is not significantly different from zero for a signficance level of 0.05. We therefore also fit a modified model where the intercept is a-priori set to zero for the first component. This nested structure is given as part of the model specification with argument \code{nested}. <>= fabricMix2 <- flexmix(Faults ~ 0, data = fabricfault, cluster = posterior(fabricMix), model = FLXMRglmfix(family = "poisson", fixed = ~ log(Length), nested = list(k=c(1,1), formula=list(~0,~1)))) summary(refit(fabricMix2)) fabricMix2.pred <- predict(fabricMix2, newdata = data.frame(Length = Lnew)) @ The data and the fitted values for each of the components for both models are given in Figure~\ref{fig:fabric}. \begin{figure} \centering <>= plot(Faults ~ Length, data = fabricfault) sapply(fabricMix.pred, function(y) lines(Lnew, y, lty = 1)) sapply(fabricMix2.pred, function(y) lines(Lnew, y, lty = 2)) legend(190, 25, paste("Model", 1:2), lty=c(1, 2), xjust=0, yjust=1) @ \caption{Observed values of the fabric faults dataset together with the fitted values for the components of each of the two fitted models.} \label{fig:fabric} \end{figure} %%----------------------------------------------------------------------- \subsubsection{Patent} The patent data given in \cite{flexmix:Wang+Cockburn+Puterman:1998} consist of 70 observations on patent applications, R\&D spending and sales in millions of dollar from pharmaceutical and biomedical companies in 1976 taken from the National Bureau of Economic Research R\&D Masterfile. The observations are displayed in Figure~\ref{fig:patent}. The model which is chosen as the best in \cite{flexmix:Wang+Cockburn+Puterman:1998} is given by: \begin{align*} H(\textrm{Patents} \,|\, \textrm{lgRD}, \textrm{RDS}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s(\textrm{RDS}, \bm{\alpha}) \textrm{Poi} ( \textrm{Patents} \,|\, \lambda_s), \end{align*} and $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \beta^s_{\textrm{lgRD}})$. The model is fitted with: <>= data("patent", package = "flexmix") ModelPat <- FLXMRglm(family = "poisson") FittedPat <- stepFlexmix(Patents ~ lgRD, k = 3, nrep = 3, model = ModelPat, data = patent, concomitant = FLXPmultinom(~ RDS)) summary(FittedPat) @ The fitted values for the component specific models and the concomitant variable model are given in Figure~\ref{fig:patent}. The plotting symbol of the observations corresponds to the induced clustering given by \code{clusters(FittedPat)}. This model is modified to have fixed effects for the logarithmized R\&D spendings, i.e.~$\bm(\beta)^s = (\beta^s_{\textrm{Intercept}}, \beta_{\textrm{lgRD}})$. The already fitted model is used for initialization, i.e.~the EM algorithm is started with an M-step given the a-posteriori probabilities. <>= ModelFixed <- FLXMRglmfix(family = "poisson", fixed = ~ lgRD) FittedPatFixed <- flexmix(Patents ~ 1, model = ModelFixed, cluster = posterior(FittedPat), concomitant = FLXPmultinom(~ RDS), data = patent) summary(FittedPatFixed) @ The fitted values for the component specific models and the concomitant variable model of this model are also given in Figure~\ref{fig:patent}. \begin{figure} \centering \setkeys{Gin}{width=0.95\textwidth} <>= lgRDv <- seq(-3, 5, by = 0.05) newdata <- data.frame(lgRD = lgRDv) plotData <- function(fitted) { with(patent, data.frame(Patents = c(Patents, unlist(predict(fitted, newdata = newdata))), lgRD = c(lgRD, rep(lgRDv, 3)), class = c(clusters(fitted), rep(1:3, each = nrow(newdata))), type = rep(c("data", "fit"), c(nrow(patent), nrow(newdata)*3)))) } plotPatents <- cbind(plotData(FittedPat), which = "Wang et al.") plotPatentsFixed <- cbind(plotData(FittedPatFixed), which = "Fixed effects") plotP <- rbind(plotPatents, plotPatentsFixed) rds <- seq(0, 3, by = 0.02) x <- model.matrix(FittedPat@concomitant@formula, data = data.frame(RDS = rds)) plotConc <- function(fitted) { E <- exp(x%*%fitted@concomitant@coef) data.frame(Probability = as.vector(E/rowSums(E)), class = rep(1:3, each = nrow(x)), RDS = rep(rds, 3)) } plotConc1 <- cbind(plotConc(FittedPat), which = "Wang et al.") plotConc2 <- cbind(plotConc(FittedPatFixed), which = "Fixed effects") plotC <- rbind(plotConc1, plotConc2) print(xyplot(Patents ~ lgRD | which, data = plotP, groups=class, xlab = "log(R&D)", panel = "panel.superpose", type = plotP$type, panel.groups = function(x, y, type = "p", subscripts, ...) { ind <- plotP$type[subscripts] == "data" panel.xyplot(x[ind], y[ind], ...) panel.xyplot(x[!ind], y[!ind], type = "l", ...) }, scales = list(alternating=FALSE), layout=c(1,2), as.table=TRUE), more=TRUE, position=c(0,0,0.6, 1)) print(xyplot(Probability ~ RDS | which, groups = class, data = plotC, type = "l", scales = list(alternating=FALSE), layout=c(1,2), as.table=TRUE), position=c(0.6, 0.01, 1, 0.99)) @ \caption{Patent data with the fitted values of the component specific models (left) and the concomitant variable model (right) for the model in \citeauthor{flexmix:Wang+Cockburn+Puterman:1998} and with fixed effects for $\log(\textrm{R\&D})$. The plotting symbol for each observation is determined by the component with the maximum a-posteriori probability.} \label{fig:patent} \end{figure} \setkeys{Gin}{width=0.8\textwidth} With respect to the BIC the full model is better than the model with the fixed effects. However, fixed effects have the advantage that the different components differ only in their baseline and the relation between the components in return of investment for each additional unit of R\&D spending is constant. Due to a-priori domain knowledge this model might seem more plausible. The fitted values for the constrained model are also given in Figure~\ref{fig:patent}. %%----------------------------------------------------------------------- \subsubsection{Seizure} The data is used in \cite{flexmix:Wang+Puterman+Cockburn:1996} and is from a clinical trial where the effect of intravenous gamma-globulin on suppression of epileptic seizures is studied. There are daily observations for a period of 140 days on one patient, where the first 27 days are a baseline period without treatment, the remaining 113 days are the treatment period. The model proposed in \cite{flexmix:Wang+Puterman+Cockburn:1996} is given by: \begin{align*} H(\textrm{Seizures} \,|\, (\textrm{Treatment}, \textrm{log(Day)}, \textrm{log(Hours)}), \bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Poi} ( \textrm{Seizures} \,|\, \lambda_s), \end{align*} where $\bm(\beta)^s = (\beta^s_{\textrm{Intercept}}, \beta^s_{\textrm{Treatment}}, \beta^s_{\textrm{log(Day)}}, \beta^s_{\textrm{Treatment:log(Day)}})$ and $\textrm{log(Hours)}$ is used as offset. This model is fitted with: <>= data("seizure", package = "flexmix") seizMix <- stepFlexmix(Seizures ~ Treatment * log(Day), data = seizure, k = 2, nrep = 3, model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix) summary(refit(seizMix)) @ A different model with different contrasts to directly estimate the coefficients for the jump when changing between base and treatment period is given by: <>= seizMix2 <- flexmix(Seizures ~ Treatment * log(Day/27), data = seizure, cluster = posterior(seizMix), model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix2) summary(refit(seizMix2)) @ A different model which allows no jump at the change between base and treatment period is fitted with: <>= seizMix3 <- flexmix(Seizures ~ log(Day/27)/Treatment, data = seizure, cluster = posterior(seizMix), model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix3) summary(refit(seizMix3)) @ With respect to the BIC criterion the smaller model with no jump is preferred. This is also the more intuitive model from a practitioner's point of view, as it does not seem to be plausible that starting the treatment already gives a significant improvement, but improvement develops over time. The data points together with the fitted values for each component of the two models are given in Figure~\ref{fig:seizure}. It can clearly be seen that the fitted values are nearly equal which also supports the smaller model. \begin{figure} \centering <>= plot(Seizures/Hours~Day, pch = c(1,3)[as.integer(Treatment)], data=seizure) abline(v=27.5, lty=2, col="grey") legend(140, 9, c("Baseline", "Treatment"), pch=c(1, 3), xjust=1, yjust=1) matplot(seizure$Day, fitted(seizMix)/seizure$Hours, type="l", add=TRUE, lty = 1, col = 1) matplot(seizure$Day, fitted(seizMix3)/seizure$Hours, type="l", add=TRUE, lty = 3, col = 1) legend(140, 7, paste("Model", c(1,3)), lty=c(1, 3), xjust=1, yjust=1) @ \caption{Observed values for the seizure dataset together with the fitted values for the components of the two different models.} \label{fig:seizure} \end{figure} %%----------------------------------------------------------------------- \subsubsection{Ames salmonella assay data} The ames salomnella assay dataset was used in \cite{flexmix:Wang+Puterman+Cockburn:1996}. They propose a model given by: \begin{align*} H(\textrm{y} \,|\, \textrm{x}, \bm{\Theta}) &= \sum_{s = 1}^S \pi_s \textrm{Poi} ( \textrm{y} \,|\, \lambda_s), \end{align*} where $\bm{\beta}^s = (\beta^s_{\textrm{Intercept}}, \beta_{\textrm{x}}, \beta_{\textrm{log(x+10)}})$. The model is fitted with: <>= data("salmonellaTA98", package = "flexmix") salmonMix <- stepFlexmix(y ~ 1, data = salmonellaTA98, k = 2, nrep = 3, model = FLXMRglmfix(family = "poisson", fixed = ~ x + log(x + 10))) @ \begin{figure} \centering <>= salmonMix.pr <- predict(salmonMix, newdata=salmonellaTA98) plot(y~x, data=salmonellaTA98, pch=as.character(clusters(salmonMix)), xlab="Dose of quinoline", ylab="Number of revertant colonies of salmonella", ylim=range(c(salmonellaTA98$y, unlist(salmonMix.pr)))) for (i in 1:2) lines(salmonellaTA98$x, salmonMix.pr[[i]], lty=i) @ \caption{Means and classification for assay data according to the estimated posterior probabilities based on the fitted model.} \label{fig:almes} \end{figure} %%----------------------------------------------------------------------- \section{Conclusions and future work} Package \pkg{flexmix} can be used to fit finite mixtures of regressions to datasets used in the literature to illustrate these models. The results can be reproduced and additional insights can be gained using visualization methods available in \proglang{R}. The fitted model is an object in \proglang{R} which can be explored using \code{show()}, \code{summary()} or \code{plot()}, as suitable methods have been implemented for objects of class \code{"flexmix"} which are returned by \code{flexmix()}. In the future it would be desirable to have more diagnostic tools available to analyze the model fit and compare different models. The use of resampling methods would be convenient as they can be applied to all kinds of mixtures models and would therefore suit well the purpose of the package which is flexible modelling of various finite mixture models. Furthermore, an additional visualization method for the fitted coefficients of the mixture would facilitate the comparison of the components. %%----------------------------------------------------------------------- \section*{Computational details} <>= SI <- sessionInfo() pkgs <- paste(sapply(c(SI$otherPkgs, SI$loadedOnly), function(x) paste("\\\\pkg{", x$Package, "} ", x$Version, sep = "")), collapse = ", ") @ All computations and graphics in this paper have been done using \proglang{R} version \Sexpr{getRversion()} with the packages \Sexpr{pkgs}. %%----------------------------------------------------------------------- \section*{Acknowledgments} This research was supported by the the Austrian Science Foundation (FWF) under grant P17382 and the Austrian Academy of Sciences ({\"O}AW) through a DOC-FFORTE scholarship for Bettina Gr{\"u}n. %%----------------------------------------------------------------------- \bibliography{flexmix} \end{document} flexmix/inst/doc/flexmix-intro.R0000644000176200001440000001333414757625321016420 0ustar liggesusers### R code from vignette source 'flexmix-intro.Rnw' ################################################### ### code chunk number 1: flexmix-intro.Rnw:30-37 ################################################### suppressWarnings(RNGversion("3.5.0")) set.seed(1504) options(width=70, prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE) grDevices::ps.options(family="Times") library("graphics") library("flexmix") data("NPreg") ################################################### ### code chunk number 2: flexmix-intro.Rnw:323-327 ################################################### library("flexmix") data("NPreg") m1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2) m1 ################################################### ### code chunk number 3: flexmix-intro.Rnw:330-331 ################################################### parameters(m1, component = 1) ################################################### ### code chunk number 4: flexmix-intro.Rnw:334-335 ################################################### parameters(m1, component = 2) ################################################### ### code chunk number 5: flexmix-intro.Rnw:340-341 ################################################### table(NPreg$class, clusters(m1)) ################################################### ### code chunk number 6: flexmix-intro.Rnw:344-345 ################################################### summary(m1) ################################################### ### code chunk number 7: flexmix-intro.Rnw:361-364 ################################################### par(mfrow=c(1,2)) plot(yn~x, col=class, pch=class, data=NPreg) plot(yp~x, col=class, pch=class, data=NPreg) ################################################### ### code chunk number 8: flexmix-intro.Rnw:382-383 ################################################### print(plot(m1)) ################################################### ### code chunk number 9: flexmix-intro.Rnw:403-405 ################################################### rm1 <- refit(m1) summary(rm1) ################################################### ### code chunk number 10: flexmix-intro.Rnw:426-427 ################################################### options(width=55) ################################################### ### code chunk number 11: flexmix-intro.Rnw:429-432 ################################################### m2 <- flexmix(yp ~ x, data = NPreg, k = 2, model = FLXMRglm(family = "poisson")) summary(m2) ################################################### ### code chunk number 12: flexmix-intro.Rnw:434-435 ################################################### options(width=65) ################################################### ### code chunk number 13: flexmix-intro.Rnw:439-440 ################################################### print(plot(m2)) ################################################### ### code chunk number 14: flexmix-intro.Rnw:483-486 ################################################### m3 <- flexmix(~ x, data = NPreg, k = 2, model=list(FLXMRglm(yn ~ . + I(x^2)), FLXMRglm(yp ~ ., family = "poisson"))) ################################################### ### code chunk number 15: flexmix-intro.Rnw:501-502 ################################################### print(plot(m3)) ################################################### ### code chunk number 16: flexmix-intro.Rnw:531-533 ################################################### m4 <- flexmix(yn ~ x + I(x^2) | id2, data = NPreg, k = 2) summary(m4) ################################################### ### code chunk number 17: flexmix-intro.Rnw:549-551 ################################################### m5 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2, control = list(iter.max = 15, verbose = 3, classify = "hard")) ################################################### ### code chunk number 18: flexmix-intro.Rnw:568-572 ################################################### m6 <- flexmix(yp ~ x + I(x^2), data = NPreg, k = 4, control = list(minprior = 0.2)) m6 ################################################### ### code chunk number 19: flexmix-intro.Rnw:582-585 ################################################### m7 <- stepFlexmix(yp ~ x + I(x^2), data = NPreg, control = list(verbose = 0), k = 1:5, nrep = 5) ################################################### ### code chunk number 20: flexmix-intro.Rnw:591-592 ################################################### getModel(m7, "BIC") ################################################### ### code chunk number 21: flexmix-intro.Rnw:727-734 ################################################### library("flexmix") set.seed(1504) options(width=60) grDevices::ps.options(family="Times") suppressMessages(require("ellipse")) suppressMessages(require("mvtnorm")) source("mymclust.R") ################################################### ### code chunk number 22: flexmix-intro.Rnw:740-743 ################################################### data("Nclus") m1 <- flexmix(Nclus ~ 1, k = 4, model = mymclust()) summary(m1) ################################################### ### code chunk number 23: flexmix-intro.Rnw:754-756 ################################################### m2 <- flexmix(Nclus ~ 1, k = 4, model = mymclust(diagonal = FALSE)) summary(m2) ################################################### ### code chunk number 24: flexmix-intro.Rnw:761-764 ################################################### par(mfrow=1:2) plotEll(m1, Nclus) plotEll(m2, Nclus) ################################################### ### code chunk number 25: flexmix-intro.Rnw:803-807 ################################################### SI <- sessionInfo() pkgs <- paste(sapply(c(SI$otherPkgs, SI$loadedOnly), function(x) paste("\\\\pkg{", x$Package, "} ", x$Version, sep = "")), collapse = ", ") flexmix/inst/doc/mixture-regressions.R0000644000176200001440000003131214757625350017647 0ustar liggesusers### R code from vignette source 'mixture-regressions.Rnw' ################################################### ### code chunk number 1: mixture-regressions.Rnw:62-72 ################################################### options(width=60, prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE) library("graphics") library("stats") library("flexmix") library("lattice") ltheme <- canonical.theme("postscript", FALSE) lattice.options(default.theme=ltheme) data("NPreg", package = "flexmix") data("dmft", package = "flexmix") source("myConcomitant.R") ################################################### ### code chunk number 2: mixture-regressions.Rnw:499-502 ################################################### par(mfrow=c(1,2)) plot(yn~x, col=class, pch=class, data=NPreg) plot(yp~x, col=class, pch=class, data=NPreg) ################################################### ### code chunk number 3: mixture-regressions.Rnw:509-517 ################################################### suppressWarnings(RNGversion("3.5.0")) set.seed(1802) library("flexmix") data("NPreg", package = "flexmix") Model_n <- FLXMRglm(yn ~ . + I(x^2)) Model_p <- FLXMRglm(yp ~ ., family = "poisson") m1 <- flexmix(. ~ x, data = NPreg, k = 2, model = list(Model_n, Model_p), control = list(verbose = 10)) ################################################### ### code chunk number 4: mixture-regressions.Rnw:558-559 ################################################### print(plot(m1)) ################################################### ### code chunk number 5: mixture-regressions.Rnw:598-600 ################################################### m1.refit <- refit(m1) summary(m1.refit, which = "model", model = 1) ################################################### ### code chunk number 6: mixture-regressions.Rnw:605-612 ################################################### print(plot(m1.refit, layout = c(1,3), bycluster = FALSE, main = expression(paste(yn *tilde(" ")* x + x^2))), split= c(1,1,2,1), more = TRUE) print(plot(m1.refit, model = 2, main = expression(paste(yp *tilde(" ")* x)), layout = c(1,2), bycluster = FALSE), split = c(2,1,2,1)) ################################################### ### code chunk number 7: mixture-regressions.Rnw:643-648 ################################################### Model_n2 <- FLXMRglmfix(yn ~ . + 0, nested = list(k = c(1, 1), formula = c(~ 1 + I(x^2), ~ 0))) m2 <- flexmix(. ~ x, data = NPreg, cluster = posterior(m1), model = list(Model_n2, Model_p)) m2 ################################################### ### code chunk number 8: mixture-regressions.Rnw:653-654 ################################################### c(BIC(m1), BIC(m2)) ################################################### ### code chunk number 9: mixture-regressions.Rnw:672-676 ################################################### data("betablocker", package = "flexmix") betaGlm <- glm(cbind(Deaths, Total - Deaths) ~ Treatment, family = "binomial", data = betablocker) betaGlm ################################################### ### code chunk number 10: mixture-regressions.Rnw:693-696 ################################################### betaMixFix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, model = FLXMRglmfix(family = "binomial", fixed = ~ Treatment), k = 2:4, nrep = 5, data = betablocker) ################################################### ### code chunk number 11: mixture-regressions.Rnw:705-706 ################################################### betaMixFix ################################################### ### code chunk number 12: mixture-regressions.Rnw:713-715 ################################################### betaMixFix_3 <- getModel(betaMixFix, which = "BIC") betaMixFix_3 <- relabel(betaMixFix_3, "model", "Intercept") ################################################### ### code chunk number 13: mixture-regressions.Rnw:728-729 ################################################### parameters(betaMixFix_3) ################################################### ### code chunk number 14: mixture-regressions.Rnw:737-750 ################################################### library("grid") betablocker$Center <- with(betablocker, factor(Center, levels = Center[order((Deaths/Total)[1:22])])) clusters <- factor(clusters(betaMixFix_3), labels = paste("Cluster", 1:3)) print(dotplot(Deaths/Total ~ Center | clusters, groups = Treatment, as.table = TRUE, data = betablocker, xlab = "Center", layout = c(3, 1), scales = list(x = list(cex = 0.7, tck = c(1, 0))), key = simpleKey(levels(betablocker$Treatment), lines = TRUE, corner = c(1,0)))) betaMixFix.fitted <- fitted(betaMixFix_3) for (i in 1:3) { seekViewport(trellis.vpname("panel", i, 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[1:22, i], "native"), gp = gpar(lty = 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[23:44, i], "native"), gp = gpar(lty = 2)) } ################################################### ### code chunk number 15: mixture-regressions.Rnw:769-775 ################################################### betaMix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ Treatment | Center, model = FLXMRglm(family = "binomial"), k = 3, nrep = 5, data = betablocker) betaMix <- relabel(betaMix, "model", "Treatment") parameters(betaMix) c(BIC(betaMixFix_3), BIC(betaMix)) ################################################### ### code chunk number 16: mixture-regressions.Rnw:795-796 ################################################### print(plot(betaMixFix_3, nint = 10, mark = 1, col = "grey", layout = c(3, 1))) ################################################### ### code chunk number 17: mixture-regressions.Rnw:805-806 ################################################### print(plot(betaMixFix_3, nint = 10, mark = 2, col = "grey", layout = c(3, 1))) ################################################### ### code chunk number 18: mixture-regressions.Rnw:820-821 ################################################### table(clusters(betaMix)) ################################################### ### code chunk number 19: mixture-regressions.Rnw:826-828 ################################################### predict(betaMix, newdata = data.frame(Treatment = c("Control", "Treated"))) ################################################### ### code chunk number 20: mixture-regressions.Rnw:834-836 ################################################### betablocker[c(1, 23), ] fitted(betaMix)[c(1, 23), ] ################################################### ### code chunk number 21: mixture-regressions.Rnw:846-847 ################################################### summary(refit(betaMix)) ################################################### ### code chunk number 22: mixture-regressions.Rnw:858-865 ################################################### ModelNested <- FLXMRglmfix(family = "binomial", nested = list(k = c(2, 1), formula = c(~ Treatment, ~ 0))) betaMixNested <- flexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, model = ModelNested, k = 3, data = betablocker, cluster = posterior(betaMix)) parameters(betaMixNested) c(BIC(betaMix), BIC(betaMixNested), BIC(betaMixFix_3)) ################################################### ### code chunk number 23: mixture-regressions.Rnw:876-877 ################################################### data("bioChemists", package = "flexmix") ################################################### ### code chunk number 24: mixture-regressions.Rnw:908-912 ################################################### data("bioChemists", package = "flexmix") Model1 <- FLXMRglm(family = "poisson") ff_1 <- stepFlexmix(art ~ ., data = bioChemists, k = 1:3, model = Model1) ff_1 <- getModel(ff_1, "BIC") ################################################### ### code chunk number 25: mixture-regressions.Rnw:929-931 ################################################### print(plot(refit(ff_1), bycluster = FALSE, scales = list(x = list(relation = "free")))) ################################################### ### code chunk number 26: mixture-regressions.Rnw:938-942 ################################################### Model2 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment) ff_2 <- flexmix(art ~ fem + phd, data = bioChemists, cluster = posterior(ff_1), model = Model2) c(BIC(ff_1), BIC(ff_2)) ################################################### ### code chunk number 27: mixture-regressions.Rnw:950-951 ################################################### summary(refit(ff_2)) ################################################### ### code chunk number 28: mixture-regressions.Rnw:958-962 ################################################### Model3 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment) ff_3 <- flexmix(art ~ fem, data = bioChemists, cluster = posterior(ff_2), model = Model3) c(BIC(ff_2), BIC(ff_3)) ################################################### ### code chunk number 29: mixture-regressions.Rnw:970-971 ################################################### print(plot(refit(ff_3), bycluster = FALSE, scales = list(x = list(relation = "free")))) ################################################### ### code chunk number 30: mixture-regressions.Rnw:981-987 ################################################### Model4 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment) ff_4 <- flexmix(art ~ 1, data = bioChemists, cluster = posterior(ff_2), concomitant = FLXPmultinom(~ fem), model = Model4) parameters(ff_4) summary(refit(ff_4), which = "concomitant") BIC(ff_4) ################################################### ### code chunk number 31: mixture-regressions.Rnw:996-1000 ################################################### Model5 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + ment + fem) ff_5 <- flexmix(art ~ 1, data = bioChemists, cluster = posterior(ff_2), model = Model5) BIC(ff_5) ################################################### ### code chunk number 32: mixture-regressions.Rnw:1006-1013 ################################################### pp <- predict(ff_5, newdata = data.frame(kid5 = 0, mar = factor("Married", levels = c("Single", "Married")), fem = c("Men", "Women"), ment = mean(bioChemists$ment))) matplot(0:12, sapply(unlist(pp), function(x) dpois(0:12, x)), type = "b", lty = 1, xlab = "Number of articles", ylab = "Probability") legend("topright", paste("Comp.", rep(1:2, each = 2), ":", c("Men", "Women")), lty = 1, col = 1:4, pch = paste(1:4), bty = "n") ################################################### ### code chunk number 33: mixture-regressions.Rnw:1362-1367 ################################################### data("dmft", package = "flexmix") Model <- FLXMRziglm(family = "poisson") Fitted <- flexmix(End ~ log(Begin + 0.5) + Gender + Ethnic + Treatment, model = Model, k = 2 , data = dmft, control = list(minprior = 0.01)) summary(refit(Fitted)) ################################################### ### code chunk number 34: refit (eval = FALSE) ################################################### ## print(plot(refit(Fitted), components = 2, box.ratio = 3)) ################################################### ### code chunk number 35: mixture-regressions.Rnw:1396-1397 ################################################### print(plot(refit(Fitted), components = 2, box.ratio = 3)) ################################################### ### code chunk number 36: mixture-regressions.Rnw:1442-1449 ################################################### Concomitant <- FLXPmultinom(~ yb) MyConcomitant <- myConcomitant(~ yb) set.seed(1234) m2 <- flexmix(. ~ x, data = NPreg, k = 2, model = list(Model_n, Model_p), concomitant = Concomitant) m3 <- flexmix(. ~ x, data = NPreg, k = 2, model = list(Model_n, Model_p), cluster = posterior(m2), concomitant = MyConcomitant) ################################################### ### code chunk number 37: mixture-regressions.Rnw:1451-1453 ################################################### summary(m2) summary(m3) ################################################### ### code chunk number 38: mixture-regressions.Rnw:1458-1462 ################################################### determinePrior <- function(object) { object@concomitant@fit(object@concomitant@x, posterior(object))[!duplicated(object@concomitant@x), ] } ################################################### ### code chunk number 39: mixture-regressions.Rnw:1465-1467 ################################################### determinePrior(m2) determinePrior(m3) ################################################### ### code chunk number 40: mixture-regressions.Rnw:1509-1513 ################################################### SI <- sessionInfo() pkgs <- paste(sapply(c(SI$otherPkgs, SI$loadedOnly), function(x) paste("\\\\pkg{", x$Package, "} ", x$Version, sep = "")), collapse = ", ") flexmix/inst/doc/bootstrapping.R0000644000176200001440000001652714757625302016514 0ustar liggesusers### R code from vignette source 'bootstrapping.Rnw' ################################################### ### code chunk number 1: bootstrapping.Rnw:11-34 ################################################### options(useFancyQuotes = FALSE) digits <- 3 Colors <- c("#E495A5", "#39BEB1") critical_values <- function(n, p = "0.95") { data("qDiptab", package = "diptest") if (n %in% rownames(qDiptab)) { return(qDiptab[as.character(n), p]) }else { n.approx <- as.numeric(rownames(qDiptab)[which.min(abs(n - as.numeric(rownames(qDiptab))))]) return(sqrt(n.approx)/sqrt(n) * qDiptab[as.character(n.approx), p]) } } library("graphics") library("flexmix") combine <- function(x, sep, width) { cs <- cumsum(nchar(x)) remaining <- if (any(cs[-1] > width)) combine(x[c(FALSE, cs[-1] > width)], sep, width) c(paste(x[c(TRUE, cs[-1] <= width)], collapse= sep), remaining) } prettyPrint <- function(x, sep = " ", linebreak = "\n\t", width = getOption("width")) { x <- strsplit(x, sep)[[1]] paste(combine(x, sep, width), collapse = paste(sep, linebreak, collapse = "")) } ################################################### ### code chunk number 2: bootstrapping.Rnw:94-99 ################################################### cat(prettyPrint(gsub("boot_flexmix", "boot", prompt(flexmix:::boot_flexmix, filename = NA)$usage[[2]]), sep = ", ", linebreak = paste("\n", paste(rep(" ", 2), collapse = ""), sep= ""), width = 70)) ################################################### ### code chunk number 3: bootstrapping.Rnw:194-199 ################################################### library("flexmix") Component_1 <- list(Model_1 = list(coef = c(1, -2), sigma = sqrt(0.1))) Component_2 <- list(Model_1 = list(coef = c(2, 2), sigma = sqrt(0.1))) ArtEx.mix <- FLXdist(y ~ x, k = rep(0.5, 2), components = list(Component_1, Component_2)) ################################################### ### code chunk number 4: bootstrapping.Rnw:210-216 ################################################### ArtEx.data <- data.frame(x = rep(0:1, each = 100/2)) suppressWarnings(RNGversion("3.5.0")) set.seed(123) ArtEx.sim <- rflexmix(ArtEx.mix, newdata = ArtEx.data) ArtEx.data$y <- ArtEx.sim$y[[1]] ArtEx.data$class <- ArtEx.sim$class ################################################### ### code chunk number 5: bootstrapping.Rnw:225-230 ################################################### par(mar = c(5, 4, 2, 0) + 0.1) plot(y ~ x, data = ArtEx.data, pch = with(ArtEx.data, 2*class + x)) pars <- list(matrix(c(1, -2, 2, 2), ncol = 2), matrix(c(1, 3, 2, -3), ncol = 2)) for (i in 1:2) apply(pars[[i]], 2, abline, col = Colors[i]) ################################################### ### code chunk number 6: bootstrapping.Rnw:238-241 ################################################### set.seed(123) ArtEx.fit <- stepFlexmix(y ~ x, data = ArtEx.data, k = 2, nrep = 5, control = list(iter = 1000, tol = 1e-8, verbose = 0)) ################################################### ### code chunk number 7: bootstrapping.Rnw:246-248 ################################################### summary(ArtEx.fit) parameters(ArtEx.fit) ################################################### ### code chunk number 8: bootstrapping.Rnw:256-258 ################################################### ArtEx.refit <- refit(ArtEx.fit) summary(ArtEx.refit) ################################################### ### code chunk number 9: bootstrapping.Rnw:274-277 (eval = FALSE) ################################################### ## set.seed(123) ## ArtEx.bs <- boot(ArtEx.fit, R = 200, sim = "parametric") ## ArtEx.bs ################################################### ### code chunk number 10: bootstrapping.Rnw:279-287 ################################################### if (file.exists("ArtEx.bs.rda")) { load("ArtEx.bs.rda") } else { set.seed(123) ArtEx.bs <- boot(ArtEx.fit, R = 200, sim = "parametric") save(ArtEx.bs, file = "ArtEx.bs.rda") } ArtEx.bs ################################################### ### code chunk number 11: bootstrapping.Rnw:303-304 ################################################### print(plot(ArtEx.bs, ordering = "coef.x", col = Colors)) ################################################### ### code chunk number 12: bootstrapping.Rnw:321-334 ################################################### require("diptest") parameters <- parameters(ArtEx.bs) Ordering <- factor(as.vector(apply(matrix(parameters[,"coef.x"], nrow = 2), 2, order))) Comp1 <- parameters[Ordering == 1,] Comp2 <- parameters[Ordering == 2,] dip.values.art <- matrix(nrow = ncol(parameters), ncol = 3, dimnames=list(colnames(parameters), c("Aggregated", "Comp 1", "Comp 2"))) dip.values.art[,"Aggregated"] <- apply(parameters, 2, dip) dip.values.art[,"Comp 1"] <- apply(Comp1, 2, dip) dip.values.art[,"Comp 2"] <- apply(Comp2, 2, dip) dip.values.art ################################################### ### code chunk number 13: bootstrapping.Rnw:376-382 ################################################### data("seizure", package = "flexmix") model <- FLXMRglm(family = "poisson", offset = log(seizure$Hours)) control <- list(iter = 1000, tol = 1e-10, verbose = 0) set.seed(123) seizMix <- stepFlexmix(Seizures ~ Treatment * log(Day), data = seizure, k = 2, nrep = 5, model = model, control = control) ################################################### ### code chunk number 14: bootstrapping.Rnw:390-395 ################################################### par(mar = c(5, 4, 2, 0) + 0.1) plot(Seizures/Hours~Day, data=seizure, pch = as.integer(seizure$Treatment)) abline(v = 27.5, lty = 2, col = "grey") matplot(seizure$Day, fitted(seizMix)/seizure$Hours, type="l", add = TRUE, col = 1, lty = 1, lwd = 2) ################################################### ### code chunk number 15: bootstrapping.Rnw:415-418 (eval = FALSE) ################################################### ## set.seed(123) ## seizMix.bs <- boot(seizMix, R = 200, sim = "parametric") ## seizMix.bs ################################################### ### code chunk number 16: bootstrapping.Rnw:420-428 ################################################### if (file.exists("seizMix.bs.rda")) { load("seizMix.bs.rda") } else { set.seed(123) seizMix.bs <- boot(seizMix, R = 200, sim = "parametric") save(seizMix.bs, file = "seizMix.bs.rda") } seizMix.bs ################################################### ### code chunk number 17: bootstrapping.Rnw:433-434 ################################################### print(plot(seizMix.bs, ordering = "coef.(Intercept)", col = Colors)) ################################################### ### code chunk number 18: bootstrapping.Rnw:441-446 ################################################### parameters <- parameters(seizMix.bs) Ordering <- factor(as.vector(apply(matrix(parameters[,"coef.(Intercept)"], nrow = 2), 2, order))) Comp1 <- parameters[Ordering == 1,] Comp2 <- parameters[Ordering == 2,] ################################################### ### code chunk number 19: bootstrapping.Rnw:455-462 ################################################### dip.values.art <- matrix(nrow = ncol(parameters), ncol = 3, dimnames = list(colnames(parameters), c("Aggregated", "Comp 1", "Comp 2"))) dip.values.art[,"Aggregated"] <- apply(parameters, 2, dip) dip.values.art[,"Comp 1"] <- apply(Comp1, 2, dip) dip.values.art[,"Comp 2"] <- apply(Comp2, 2, dip) dip.values.art flexmix/inst/doc/flexmix-intro.Rnw0000644000176200001440000010256514404637307016766 0ustar liggesusers% % Copyright (C) 2004-2005 Friedrich Leisch % $Id: flexmix-intro.Rnw 5187 2020-06-25 17:59:39Z gruen $ % \documentclass[nojss]{jss} \title{FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in \proglang{R}} \Plaintitle{FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R} \Shorttitle{FlexMix: Finite Mixture Models in \proglang{R}} \author{Friedrich Leisch\\Universit\"at f\"ur Bodenkultur Wien} \Plainauthor{Friedrich Leisch} \Address{ Friedrich Leisch\\ Institut f\"ur Angewandte Statistik und EDV\\ Universit\"at f\"ur Bodenkultur Wien\\ Peter Jordan Stra\ss{}e 82\\ 1190 Wien, Austria\\ E-mail: \email{Friedrich.Leisch@boku.ac.at} } \usepackage[utf8]{inputenc} \usepackage{listings} \newcommand{\R}{\proglang{R}} <>= suppressWarnings(RNGversion("3.5.0")) set.seed(1504) options(width=70, prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE) grDevices::ps.options(family="Times") library("graphics") library("flexmix") data("NPreg") @ \Abstract{ This article was originally published as \cite{flexmix:Leisch:2004a} in the \emph{Journal of Statistical Software}. FlexMix implements a general framework for fitting discrete mixtures of regression models in the \R{} statistical computing environment: three variants of the EM algorithm can be used for parameter estimation, regressors and responses may be multivariate with arbitrary dimension, data may be grouped, e.g., to account for multiple observations per individual, the usual formula interface of the \proglang{S} language is used for convenient model specification, and a modular concept of driver functions allows to interface many different types of regression models. Existing drivers implement mixtures of standard linear models, generalized linear models and model-based clustering. FlexMix provides the E-step and all data handling, while the M-step can be supplied by the user to easily define new models. } \Keywords{\proglang{R}, finite mixture models, model based clustering, latent class regression} \Plainkeywords{R, finite mixture models, model based clustering, latent class regression} \Volume{11} \Issue{8} \Month{October} \Year{2004} \Submitdate{2004-04-19} \Acceptdate{2004-10-18} %%\usepackage{Sweave} %% already provided by jss.cls %%\VignetteIndexEntry{FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R} %%\VignetteDepends{flexmix} %%\VignetteKeywords{R, finite mixture models, model based clustering, latent class regression} %%\VignettePackage{flexmix} \begin{document} \section{Introduction} \label{sec:introduction} Finite mixture models have been used for more than 100 years, but have seen a real boost in popularity over the last decade due to the tremendous increase in available computing power. The areas of application of mixture models range from biology and medicine to physics, economics and marketing. On the one hand these models can be applied to data where observations originate from various groups and the group affiliations are not known, and on the other hand to provide approximations for multi-modal distributions \citep{flexmix:Everitt+Hand:1981,flexmix:Titterington+Smith+Makov:1985,flexmix:McLachlan+Peel:2000}. In the 1990s finite mixture models have been extended by mixing standard linear regression models as well as generalized linear models \citep{flexmix:Wedel+DeSarbo:1995}. An important area of application of mixture models is market segmentation \citep{flexmix:Wedel+Kamakura:2001}, where finite mixture models replace more traditional cluster analysis and cluster-wise regression techniques as state of the art. Finite mixture models with a fixed number of components are usually estimated with the expectation-maximization (EM) algorithm within a maximum likelihood framework \citep{flexmix:Dempster+Laird+Rubin:1977} and with MCMC sampling \citep{flexmix:Diebolt+Robert:1994} within a Bayesian framework. \newpage The \R{} environment for statistical computing \citep{flexmix:R-Core:2004} features several packages for finite mixture models, including \pkg{mclust} for mixtures of multivariate Gaussian distributions \citep{flexmix:Fraley+Raftery:2002,flexmix:Fraley+Raftery:2002a}, \pkg{fpc} for mixtures of linear regression models \citep{flexmix:Hennig:2000} and \pkg{mmlcr} for mixed-mode latent class regression \citep{flexmix:Buyske:2003}. There are three main reasons why we have chosen to write yet another software package for EM estimation of mixture models: \begin{itemize} \item The existing implementations did not cover all cases we needed for our own research (mainly marketing applications). \item While all \R{} packages mentioned above are open source and hence can be extended by the user by modifying the source code, we wanted an implementation where extensibility is a main design principle to enable rapid prototyping of new mixture models. \item We include a sampling-based variant of the EM-algorithm for models where weighted maximum likelihood estimation is not available. FlexMix has a clean interface between E- and M-step such that variations of both are easy to combine. \end{itemize} This paper is organized as follows: First we introduce the mathematical models for latent class regression in Section~\ref{sec:latent-class-regr} and shortly discuss parameter estimation and identifiability. Section~\ref{sec:using-flexmix} demonstrates how to use FlexMix to fit models with the standard driver for generalized linear models. Finally, Section~\ref{sec:extending-flexmix} shows how to extend FlexMix by writing new drivers using the well-known model-based clustering procedure as an example. \section{Latent class regression} \label{sec:latent-class-regr} Consider finite mixture models with $K$ components of form \begin{equation}\label{eq:1} h(y|x,\psi) = \sum_{k = 1}^K \pi_k f(y|x,\theta_k) \end{equation} \begin{displaymath} \pi_k \geq 0, \quad \sum_{k = 1}^K \pi_k = 1 \end{displaymath} where $y$ is a (possibly multivariate) dependent variable with conditional density $h$, $x$ is a vector of independent variables, $\pi_k$ is the prior probability of component $k$, $\theta_k$ is the component specific parameter vector for the density function $f$, and $\psi=(\pi_1,,\ldots,\pi_K,\theta_1',\ldots,\theta_K')'$ is the vector of all parameters. If $f$ is a univariate normal density with component-specific mean $\beta_k'x$ and variance $\sigma^2_k$, we have $\theta_k = (\beta_k', \sigma_k^2)'$ and Equation~(\ref{eq:1}) describes a mixture of standard linear regression models, also called \emph{latent class regression} or \emph{cluster-wise regression} \citep{flexmix:DeSarbo+Cron:1988}. If $f$ is a member of the exponential family, we get a mixture of generalized linear models \citep{flexmix:Wedel+DeSarbo:1995}, known as \emph{GLIMMIX} models in the marketing literature \citep{flexmix:Wedel+Kamakura:2001}. For multivariate normal $f$ and $x\equiv1$ we get a mixture of Gaussians without a regression part, also known as \emph{model-based clustering}. The posterior probability that observation $(x,y)$ belongs to class $j$ is given by \begin{equation}\label{eq:3} \Prob(j|x, y, \psi) = \frac{\pi_j f(y | x, \theta_j)}{\sum_k \pi_k f(y | x, \theta_k)} \end{equation} The posterior probabilities can be used to segment data by assigning each observation to the class with maximum posterior probability. In the following we will refer to $f(\cdot|\cdot, \theta_k)$ as \emph{mixture components} or \emph{classes}, and the groups in the data induced by these components as \emph{clusters}. \subsection{Parameter estimation} \label{sec:parameter-estimation} The log-likelihood of a sample of $N$ observations $\{(x_1,y_1),\ldots,(x_N,y_N)\}$ is given by \begin{equation}\label{eq:4} \log L = \sum_{n=1}^N \log h(y_n|x_n,\psi) = \sum_{n=1}^N \log\left(\sum_{k = 1}^K \pi_kf(y_n|x_n,\theta_k) \right) \end{equation} and can usually not be maximized directly. The most popular method for maximum likelihood estimation of the parameter vector $\psi$ is the iterative EM algorithm \citep{flexmix:Dempster+Laird+Rubin:1977}: \begin{description} \item[Estimate] the posterior class probabilities for each observation \begin{displaymath} \hat p_{nk} = \Prob(k|x_n, y_n, \hat \psi) \end{displaymath} using Equation~(\ref{eq:3}) and derive the prior class probabilities as \begin{displaymath} \hat\pi_k = \frac1N \sum_{n=1}^N \hat p_{nk} \end{displaymath} \item[Maximize] the log-likelihood for each component separately using the posterior probabilities as weights \begin{equation}\label{eq:2} \max_{\theta_k} \sum_{n=1}^N \hat p_{nk} \log f(y_n | x_n, \theta_k) \end{equation} \end{description} The E- and M-steps are repeated until the likelihood improvement falls under a pre-specified threshold or a maximum number of iterations is reached. The EM algorithm cannot be used for mixture models only, but rather provides a general framework for fitting models on incomplete data. Suppose we augment each observation $(x_n,y_n)$ with an unobserved multinomial variable $z_n = (z_{n1},\ldots,z_{nK})$, where $z_{nk}=1$ if $(x_n,y_n)$ belongs to class $k$ and $z_{nk}=0$ otherwise. The EM algorithm can be shown to maximize the likelihood on the ``complete data'' $(x_n,y_n,z_n)$; the $z_n$ encode the missing class information. If the $z_n$ were known, maximum likelihood estimation of all parameters would be easy, as we could separate the data set into the $K$ classes and estimate the parameters $\theta_k$ for each class independently from the other classes. If the weighted likelihood estimation in Equation~(\ref{eq:2}) is infeasible for analytical, computational, or other reasons, then we have to resort to approximations of the true EM procedure by assigning the observations to disjoint classes and do unweighted estimation within the groups: \begin{displaymath} \max_{\theta_k} \sum_{n: z_{nk=1}} \log f(y_n | x_n, \theta_k) \end{displaymath} This corresponds to allow only 0 and 1 as weights. Possible ways of assigning the data into the $K$ classes are \begin{itemize} \item \textbf{hard} \label{hard} assignment to the class with maximum posterior probability $p_{nk}$, the resulting procedure is called maximizing the \emph{classification likelihood} by \cite{flexmix:Fraley+Raftery:2002}. Another idea is to do \item \textbf{random} assignment to classes with probabilities $p_{nk}$, which is similar to the sampling techniques used in Bayesian estimation (although for the $z_n$ only). \end{itemize} Well known limitations of the EM algorithm include that convergence can be slow and is to a local maximum of the likelihood surface only. There can also be numerical instabilities at the margin of parameter space, and if a component gets to contain only a few observations during the iterations, parameter estimation in the respective component may be problematic. E.g., the likelihood of Gaussians increases without bounds for $\sigma^2\to 0$. As a result, numerous variations of the basic EM algorithm described above exist, most of them exploiting features of special cases for $f$. \subsection{Identifiability} \label{sec:identifiability} An open question is still identifiability of many mixture models. A comprehensive overview of this topic is beyond the scope of this paper, however, users of mixture models should be aware of the problem: \begin{description} \item[Relabelling of components:] Mixture models are only identifiable up to a permutation of the component labels. For EM-based approaches this only affects interpretation of results, but is no problem for parameter estimation itself. \item[Overfitting:] If a component is empty or two or more components have the same parameters, the data generating process can be represented by a smaller model with fewer components. This kind of unidentifiability can be avoided by requiring that the prior weights $\pi_k$ are not equal to zero and that the component specific parameters are different. \item[Generic unidentifiability:] It has been shown that mixtures of univariate normal, gamma, exponential, Cauchy and Poisson distributions are identifiable, while mixtures of discrete or continuous uniform distributions are not identifiable. A special case is the class of mixtures of binomial and multinomial distributions which are only identifiable if the number of components is limited with respect to, e.g., the number of observations per person. See \cite{flexmix:Everitt+Hand:1981}, \cite{flexmix:Titterington+Smith+Makov:1985}, \cite{flexmix:Grun:2002} and references therein for details. \end{description} FlexMix tries to avoid overfitting because of vanishing prior probabilities by automatically removing components where the prior $\pi_k$ falls below a user-specified threshold. Automated diagnostics for generic identifiability are currently under investigation. Relabelling of components is in some cases more of a nuisance than a real problem (``component 2 of the first run may be component 3 in the second run''), more serious are interactions of component relabelling and categorical predictor variables, see \cite{flexmix:Grun+Leisch:2004} for a discussion and how bootstrapping can be used to assess identifiability of mixture models. \pagebreak[4] \section{Using FlexMix} \label{sec:using-flexmix} \SweaveOpts{width=12,height=8,eps=FALSE,keep.source=TRUE} The standard M-step \texttt{FLXMRglm()} of FlexMix is an interface to R's generalized linear modelling facilities (the \texttt{glm()} function). As a simple example we use artificial data with two latent classes of size \Sexpr{nrow(NPreg)/2} each: \begin{center} \begin{tabular}{ll} Class~1: & $ y = 5x+\epsilon$\\ Class~2: & $ y = 15+10x-x^2+\epsilon$\\ \end{tabular} \end{center} with $\epsilon\sim N(0,9)$ and prior class probabilities $\pi_1=\pi_2=0.5$, see the left panel of Figure~\ref{fig:npreg}. We can fit this model in \R{} using the commands <<>>= library("flexmix") data("NPreg") m1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2) m1 @ and get a first look at the estimated parameters of mixture component~1 by <<>>= parameters(m1, component = 1) @ and <<>>= parameters(m1, component = 2) @ for component~2. The paramter estimates of both components are close to the true values. A cross-tabulation of true classes and cluster memberships can be obtained by <<>>= table(NPreg$class, clusters(m1)) @ The summary method <<>>= summary(m1) @ gives the estimated prior probabilities $\hat\pi_k$, the number of observations assigned to the corresponding clusters, the number of observations where $p_{nk}>\delta$ (with a default of $\delta=10^{-4}$), and the ratio of the latter two numbers. For well-seperated components, a large proportion of observations with non-vanishing posteriors $p_{nk}$ should also be assigned to the corresponding cluster, giving a ratio close to 1. For our example data the ratios of both components are approximately 0.7, indicating the overlap of the classes at the cross-section of line and parabola. \begin{figure}[htbp] \centering <>= par(mfrow=c(1,2)) plot(yn~x, col=class, pch=class, data=NPreg) plot(yp~x, col=class, pch=class, data=NPreg) @ \caption{Standard regression example (left) and Poisson regression (right).} \label{fig:npreg} \end{figure} Histograms or rootograms of the posterior class probabilities can be used to visually assess the cluster structure \citep{flexmix:Tantrum+Murua+Stuetzle:2003}, this is now the default plot method for \texttt{"flexmix"} objects \citep{flexmix:Leisch:2004}. Rootograms are very similar to histograms, the only difference is that the height of the bars correspond to square roots of counts rather than the counts themselves, hence low counts are more visible and peaks less emphasized. \begin{figure}[htbp] \centering <>= print(plot(m1)) @ \caption{The plot method for \texttt{"flexmix"} objects, here obtained by \texttt{plot(m1)}, shows rootograms of the posterior class probabilities.} \label{fig:root1} \end{figure} Usually in each component a lot of observations have posteriors close to zero, resulting in a high count for the corresponing bin in the rootogram which obscures the information in the other bins. To avoid this problem, all probabilities with a posterior below a threshold are ignored (we again use $10^{-4}$). A peak at probability 1 indicates that a mixture component is well seperated from the other components, while no peak at 1 and/or significant mass in the middle of the unit interval indicates overlap with other components. In our simple example the components are medium well separated, see Figure~\ref{fig:root1}. Tests for significance of regression coefficients can be obtained by <<>>= rm1 <- refit(m1) summary(rm1) @ Function \texttt{refit()} fits weighted generalized linear models to each component using the standard \R{} function \texttt{glm()} and the posterior probabilities as weights, see \texttt{help("refit")} for details. The data set \texttt{NPreg} also includes a response from a generalized linear model with a Poisson distribution and exponential link function. The two classes of size \Sexpr{nrow(NPreg)/2} each have parameters \begin{center} \begin{tabular}{ll} Class~1: & $ \mu_1 = 2 - 0.2x$\\ Class~2: & $ \mu_2 = 1 + 0.1x$\\ \end{tabular} \end{center} and given $x$ the response $y$ in group $k$ has a Poisson distribution with mean $e^{\mu_k}$, see the right panel of Figure~\ref{fig:npreg}. The model can be estimated using <>= options(width=55) @ <<>>= m2 <- flexmix(yp ~ x, data = NPreg, k = 2, model = FLXMRglm(family = "poisson")) summary(m2) @ <>= options(width=65) @ \begin{figure}[htbp] \centering <>= print(plot(m2)) @ \caption{\texttt{plot(m2)}} \label{fig:root2} \end{figure} Both the summary table and the rootograms in Figure~\ref{fig:root2} clearly show that the clusters of the Poisson response have much more overlap. For our simple low-dimensional example data the overlap of the classes is obvious by looking at scatterplots of the data. For data in higher dimensions this is not an option. The rootograms and summary tables for \texttt{"flexmix"} objects work off the densities or posterior probabilities of the observations and thus do not depend on the dimensionality of the input space. While we use simple 2-dimensional examples to demonstrate the techniques, they can easily be used on high-dimensional data sets or models with complicated covariate structures. \subsection{Multiple independent responses} \label{sec:mult-indep-resp} If the response $y=(y_1,\ldots,y_D)'$ is $D$-dimensional and the $y_d$ are mutually independent the mixture density in Equation~(\ref{eq:1}) can be written as \begin{eqnarray*} h(y|x,\psi) &=& \sum_{k = 1}^K \pi_k f(y|x,\theta_k)\\ &=& \sum_{k = 1}^K \pi_k \prod_{d=1}^D f_d(y|x,\theta_{kd}) \end{eqnarray*} To specify such models in FlexMix we pass it a list of models, where each list element corresponds to one $f_d$, and each can have a different set of dependent and independent variables. To use the Gaussian and Poisson responses of data \texttt{NPreg} simultaneously, we use the model specification \begin{Sinput} > m3 = flexmix(~x, data=NPreg, k=2, + model=list(FLXMRglm(yn~.+I(x^2)), + FLXMRglm(yp~., family="poisson"))) \end{Sinput} <>= m3 <- flexmix(~ x, data = NPreg, k = 2, model=list(FLXMRglm(yn ~ . + I(x^2)), FLXMRglm(yp ~ ., family = "poisson"))) @ Note that now three model formulas are involved: An overall formula as first argument to function \texttt{flexmix()} and one formula per response. The latter ones are interpreted relative to the overall formula such that common predictors have to be specified only once, see \texttt{help("update.formula")} for details on the syntax. The basic principle is that the dots get replaced by the respective terms from the overall formula. The rootograms show that the posteriors of the two-response model are shifted towards 0 and 1 (compared with either of the two univariate models), the clusters are now well-separated. \begin{figure}[htbp] \centering <>= print(plot(m3)) @ \caption{\texttt{plot(m3)}} \label{fig:root3} \end{figure} \subsection{Repeated measurements} \label{sec:repe-meas} If the data are repeated measurements on $M$ individuals, and we have $N_m$ observations from individual $m$, then the log-likelihood in Equation~(\ref{eq:4}) can be written as \begin{displaymath} \log L = \sum_{m=1}^M \sum_{n=1}^{N_m} \log h(y_{mn}|x_{mn},\psi), \qquad \sum_{m=1}^M N_m = N \end{displaymath} and the posterior probability that individual $m$ belongs to class $j$ is given by \begin{displaymath} \Prob(j|m) = \frac{\pi_j \prod_{n=1}^{N_m} f(y_{mn} | x_{mn}, \theta_j)}{\sum_k \pi_k \prod_{n=1}^{N_m} f(y_{mn} | x_{mn}, \theta_k)} \end{displaymath} where $(x_{mn}, y_{mn})$ is the $n$-th observation from individual $m$. As an example, assume that the data in \texttt{NPreg} are not 200 independent observations, but 4 measurements each from 50 persons such that $\forall m: N_m=4$. Column \texttt{id2} of the data frame encodes such a grouping and can easily be used in FlexMix: <<>>= m4 <- flexmix(yn ~ x + I(x^2) | id2, data = NPreg, k = 2) summary(m4) @ Note that convergence of the EM algorithm is much faster with grouping and the two clusters are now perfectly separated. \subsection{Control of the EM algorithm} \label{sec:control-em-algorithm} Details of the EM algorithm can be tuned using the \texttt{control} argument of function \texttt{flexmix()}. E.g., to use a maximum number of 15 iterations, report the log-likelihood at every 3rd step and use hard assignment of observations to clusters (cf. page~\pageref{hard}) the call is <<>>= m5 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2, control = list(iter.max = 15, verbose = 3, classify = "hard")) @ Another control parameter (\texttt{minprior}, see below for an example) is the minimum prior probability components are enforced to have, components falling below this threshold (the current default is 0.05) are removed during EM iteration to avoid numerical instabilities for components containing only a few observations. Using a minimum prior of 0 disables component removal. \subsection{Automated model search} In real applications the number of components is unknown and has to be estimated. Tuning the minimum prior parameter allows for simplistic model selection, which works surprisingly well in some situations: <<>>= m6 <- flexmix(yp ~ x + I(x^2), data = NPreg, k = 4, control = list(minprior = 0.2)) m6 @ Although we started with four components, the algorithm converged at the correct two component solution. A better approach is to fit models with an increasing number of components and compare them using AIC or BIC. As the EM algorithm converges only to the next local maximum of the likelihood, it should be run repeatedly using different starting values. The function \texttt{stepFlexmix()} can be used to repeatedly fit models, e.g., <<>>= m7 <- stepFlexmix(yp ~ x + I(x^2), data = NPreg, control = list(verbose = 0), k = 1:5, nrep = 5) @ runs \texttt{flexmix()} 5 times for $k=1,2,\ldots,5$ components, totalling in 25 runs. It returns a list with the best solution found for each number of components, each list element is simply an object of class \texttt{"flexmix"}. To find the best model we can use <<>>= getModel(m7, "BIC") @ and choose the number of components minimizing the BIC. \section{Extending FlexMix} \label{sec:extending-flexmix} One of the main design principles of FlexMix was extensibility, users can provide their own M-step for rapid prototyping of new mixture models. FlexMix was written using S4 classes and methods \citep{flexmix:Chambers:1998} as implemented in \R{} package \pkg{methods}. The central classes for writing M-steps are \texttt{"FLXM"} and \texttt{"FLXcomponent"}. Class \texttt{"FLXM"} specifies how the model is fitted using the following slots: \begin{description} \item[fit:] A \texttt{function(x,y,w)} returning an object of class \texttt{"FLXcomponent"}. \item[defineComponent:] Expression or function constructing the object of class \texttt{"FLXcomponent"}. \item[weighted:] Logical, specifies if the model may be fitted using weighted likelihoods. If \texttt{FALSE}, only hard and random classification are allowed (and hard classification becomes the default). \item[formula:] Formula relative to the overall model formula, default is \verb|.~.| \item[name:] A character string describing the model, this is only used for print output. \end{description} The remaining slots of class \texttt{"FLXM"} are used internally by FlexMix to hold data, etc. and omitted here, because they are not needed to write an M-step driver. The most important slot doing all the work is \texttt{fit} holding a function performing the maximum likelihood estimation described in Equation~(\ref{eq:2}). The \texttt{fit()} function returns an object of class \texttt{"FLXcomponent"} which holds a fitted component using the slots: \begin{description} \item[logLik:] A \texttt{function(x,y)} returning the log-likelihood for observations in matrices \texttt{x} and \texttt{y}. \item[predict:] A \texttt{function(x)} predicting \texttt{y} given \texttt{x}. \item[df:] The degrees of freedom used by the component, i.e., the number of estimated parameters. \item[parameters:] An optional list containing model parameters. \end{description} In a nutshell class \texttt{"FLXM"} describes an \emph{unfitted} model, whereas class \texttt{"FLXcomponent"} holds a \emph{fitted} model. \lstset{frame=trbl,basicstyle=\small\tt,stepnumber=5,numbers=left} \begin{figure}[tb] \centering \begin{minipage}{0.94\textwidth} \lstinputlisting{mymclust.R} \end{minipage} \caption{M-step for model-based clustering: \texttt{mymclust} is a simplified version of the standard FlexMix driver \texttt{FLXmclust}.} \label{fig:mymclust.R} \end{figure} \subsection{Writing an M-step driver} \label{sec:writing-an-m} Figure~\ref{fig:mymclust.R} shows an example driver for model-based clustering. We use function \texttt{dmvnorm()} from package \pkg{mvtnorm} for calculation of multivariate Gaussian densities. In line~5 we create a new \texttt{"FLXMC"} object named \texttt{retval}, which is also the return value of the driver. Class \texttt{"FLXMC"} extends \texttt{"FLXM"} and is used for model-based clustering. It contains an additional slot with the name of the distribution used. All drivers should take a formula as their first argument, this formula is directly passed on to \texttt{retval}. In most cases authors of new FlexMix drivers need not worry about formula parsing etc., this is done by \texttt{flexmix} itself. In addition we have to declare whether the driver can do weighted ML estimation (\texttt{weighted=TRUE}) and give a name to our model. The remainder of the driver creates a \texttt{fit()} function, which takes regressors \texttt{x}, response \texttt{y} and weights \texttt{w}. For multivariate Gaussians the maximum likelihood estimates correspond to mean and covariance matrix, the standard R function \texttt{cov.wt()} returns a list containing estimates of the weighted covariance matrix and the mean for given data. Our simple example performs clustering without a regression part, hence $x$ is ignored. If \texttt{y} has $D$ columns, we estimate $D$ parameters for the mean and $D(D-1)/2$ parameters for the covariance matrix, giving a total of $(3D+D^2)/2$ parameters (line~11). As an additional feature we allow the user to specify whether the covariance matrix is assumed to be diagonal or a full matrix. For \texttt{diagonal=TRUE} we use only the main diagonal of the covariance matrix (line~14) and the number of parameters is reduced to $2D$. In addition to parameter estimates, \texttt{flexmix()} needs a function calculating the log-likelihood of given data $x$ and $y$, which in our example is the log-density of a multivariate Gaussian. In addition we have to provide a function predicting $y$ given $x$, in our example simply the mean of the Gaussian. Finally we create a new \texttt{"FLXcomponent"} as return value of function \texttt{fit()}. Note that our internal functions \texttt{fit()}, \texttt{logLik()} and \texttt{predict()} take only \texttt{x}, \texttt{y} and \texttt{w} as arguments, but none of the model-specific parameters like means and covariances, although they use them of course. \R{} uses \emph{lexical scoping} rules for finding free variables \citep{flexmix:Gentleman+Ihaka:2000}, hence it searches for them first in the environment where a function is defined. E.g., the \texttt{fit()} function uses the variable \texttt{diagonal} in line~24, and finds it in the environment where the function itself was defined, which is the body of function \texttt{mymclust()}. Function \texttt{logLik()} uses the list \texttt{para} in lines~8 and 9, and uses the one found in the body of \texttt{defineComponent()}. Function \texttt{flexmix()} on the other hand never sees the model parameters, all it uses are function calls of form \texttt{fit(x,y,w)} or \texttt{logLik(x,y)}, which are exactly the same for all kinds of mixture models. In fact, it would not be necessary to even store the component parameters in the \texttt{"FLXcomponent"} object, they are there only for convenience such that users can easily extract and use them after \texttt{flexmix()} has finished. Lexical scope allows to write clean interfaces in a very elegant way, the driver abstracts all model details from the FlexMix main engine. \subsection{Example: Using the driver} \label{sec:example:-model-based} \SweaveOpts{width=12,height=6,eps=FALSE} <>= library("flexmix") set.seed(1504) options(width=60) grDevices::ps.options(family="Times") suppressMessages(require("ellipse")) suppressMessages(require("mvtnorm")) source("mymclust.R") @ As a simple example we use the four 2-dimensional Gaussian clusters from data set \texttt{Nclus}. Fitting a wrong model with diagonal covariance matrix is done by <<>>= data("Nclus") m1 <- flexmix(Nclus ~ 1, k = 4, model = mymclust()) summary(m1) @ The result can be seen in the left panel of Figure~\ref{fig:ell}, the result is ``wrong'' because we forced the ellipses to be parallel to the axes. The overlap between three of the four clusters can also be inferred from the low ratio statistics in the summary table (around 0.5 for components 1, 3 and 4), while the much better separated upper left cluster has a much higher ratio of 0.85. Using the correct model with a full covariance matrix can be done by setting \texttt{diagonal=FALSE} in the call to our driver \texttt{mymclust()}: <<>>= m2 <- flexmix(Nclus ~ 1, k = 4, model = mymclust(diagonal = FALSE)) summary(m2) @ \begin{figure}[htbp] \centering <>= par(mfrow=1:2) plotEll(m1, Nclus) plotEll(m2, Nclus) @ \caption{Fitting a mixture model with diagonal covariance matrix (left) and full covariance matrix (right).} \label{fig:ell} \end{figure} \pagebreak[4] \section{Summary and outlook} \label{sec:summary} The primary goal of FlexMix is extensibility, this makes the package ideal for rapid development of new mixture models. There is no intent to replace packages implementing more specialized mixture models like \pkg{mclust} for mixtures of Gaussians, FlexMix should rather be seen as a complement to those. By interfacing R's facilities for generalized linear models, FlexMix allows the user to estimate complex latent class regression models. Using lexical scope to resolve model-specific parameters hides all model details from the programming interface, FlexMix can in principle fit almost arbitrary finite mixture models for which the EM algorithm is applicable. The downside of this is that FlexMix can in principle fit almost arbitrary finite mixture models, even models where no proper theoretical results for model identification etc.\ are available. We are currently working on a toolset for diagnostic checks on mixture models to test necessary identifiability conditions for those cases where results are available. We also want to implement newer variations of the classic EM algorithm, especially for faster convergence. Another plan is to have an interactive version of the rootograms using \texttt{iPlots} \citep{flexmix:Urbanek+Theus:2003} such that the user can explore the relations between mixture components, possibly linked to background variables. Other planned extensions include covariates for the prior probabilities and to allow to mix different distributions for components, e.g., to include a Poisson point process for background noise. \section*{Computational details} <>= SI <- sessionInfo() pkgs <- paste(sapply(c(SI$otherPkgs, SI$loadedOnly), function(x) paste("\\\\pkg{", x$Package, "} ", x$Version, sep = "")), collapse = ", ") @ All computations and graphics in this paper have been done using \proglang{R} version \Sexpr{getRversion()} with the packages \Sexpr{pkgs}. \section*{Acknowledgments} This research was supported by the Austrian Science Foundation (FWF) under grant SFB\#010 (`Adaptive Information Systems and Modeling in Economics and Management Science'). 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¦:HÛã„ÚÅùd—cV¾ÂQ2ÅðšßcìžÓ|Óy±a‰õ—Ü´…äœan·Jf§œEC'Õã8“8 ÿ=ÚÐ_ädÐ4Ssˆ~ÿC›¿6¬¦oé‡" ßËInð|fý'_¯x×å]‡ënÓ- Çg8[™ÌnnÁC%4OÃ1:<¢“ ó ”yF endstream endobj startxref 314347 %%EOF flexmix/inst/doc/ziglm.R0000644000176200001440000000220514404637307014724 0ustar liggesuserssetClass("FLXMRziglm", contains = "FLXMRglm") FLXMRziglm <- function(formula = . ~ ., family = c("binomial", "poisson"), ...) { family <- match.arg(family) new("FLXMRziglm", FLXMRglm(formula, family, ...), name = paste("FLXMRziglm", family, sep=":")) } setMethod("FLXgetModelmatrix", signature(model="FLXMRziglm"), function(model, data, formula, lhs=TRUE, ...) { model <- callNextMethod(model, data, formula, lhs) if (attr(terms(model@fullformula), "intercept") == 0) stop("please include an intercept") model }) setMethod("FLXremoveComponent", signature(model = "FLXMRziglm"), function(model, nok, ...) { if (1 %in% nok) as(model, "FLXMRglm") else model }) setMethod("FLXmstep", signature(model = "FLXMRziglm"), function(model, weights, components, ...) { coef <- c(-Inf, rep(0, ncol(model@x)-1)) names(coef) <- colnames(model@x) comp.1 <- with(list(coef = coef, df = 0, offset = NULL, family = model@family), eval(model@defineComponent)) c(list(comp.1), FLXmstep(as(model, "FLXMRglm"), weights[, -1, drop=FALSE], components[-1])) }) flexmix/inst/doc/regression-examples.R0000644000176200001440000004066314757625370017620 0ustar liggesusers### R code from vignette source 'regression-examples.Rnw' ################################################### ### code chunk number 1: regression-examples.Rnw:11-14 ################################################### library("stats") library("graphics") library("flexmix") ################################################### ### code chunk number 2: start ################################################### options(width=70, prompt = "R> ", continue = "+ ", useFancyQuotes = FALSE) suppressWarnings(RNGversion("3.5.0")) set.seed(1802) library("lattice") ltheme <- canonical.theme("postscript", FALSE) lattice.options(default.theme=ltheme) ################################################### ### code chunk number 3: NregFix ################################################### set.seed(2807) library("flexmix") data("NregFix", package = "flexmix") Model <- FLXMRglm(~ x2 + x1) fittedModel <- stepFlexmix(y ~ 1, model = Model, nrep = 3, k = 3, data = NregFix, concomitant = FLXPmultinom(~ w)) fittedModel <- relabel(fittedModel, "model", "x1") summary(refit(fittedModel)) ################################################### ### code chunk number 4: diffModel ################################################### Model2 <- FLXMRglmfix(fixed = ~ x2, nested = list(k = c(1, 2), formula = c(~ 0, ~ x1)), varFix = TRUE) fittedModel2 <- flexmix(y ~ 1, model = Model2, cluster = posterior(fittedModel), data = NregFix, concomitant = FLXPmultinom(~ w)) BIC(fittedModel) BIC(fittedModel2) ################################################### ### code chunk number 5: artificial-example ################################################### plotNregFix <- NregFix plotNregFix$w <- factor(NregFix$w, levels = 0:1, labels = paste("w =", 0:1)) plotNregFix$x2 <- factor(NregFix$x2, levels = 0:1, labels = paste("x2 =", 0:1)) plotNregFix$class <- factor(NregFix$class, levels = 1:3, labels = paste("Class", 1:3)) print(xyplot(y ~ x1 | x2*w, groups = class, data = plotNregFix, cex = 0.6, auto.key = list(space="right"), layout = c(2,2))) ################################################### ### code chunk number 6: refit ################################################### summary(refit(fittedModel2)) ################################################### ### code chunk number 7: beta-glm ################################################### data("betablocker", package = "flexmix") betaGlm <- glm(cbind(Deaths, Total - Deaths) ~ Treatment, family = "binomial", data = betablocker) betaGlm ################################################### ### code chunk number 8: beta-fix ################################################### betaMixFix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, model = FLXMRglmfix(family = "binomial", fixed = ~ Treatment), k = 2:4, nrep = 3, data = betablocker) betaMixFix ################################################### ### code chunk number 9: beta-fig ################################################### library("grid") betaMixFix_3 <- getModel(betaMixFix, "3") betaMixFix_3 <- relabel(betaMixFix_3, "model", "Intercept") betablocker$Center <- with(betablocker, factor(Center, levels = Center[order((Deaths/Total)[1:22])])) clusters <- factor(clusters(betaMixFix_3), labels = paste("Cluster", 1:3)) print(dotplot(Deaths/Total ~ Center | clusters, groups = Treatment, as.table = TRUE, data = betablocker, xlab = "Center", layout = c(3, 1), scales = list(x = list(draw = FALSE)), key = simpleKey(levels(betablocker$Treatment), lines = TRUE, corner = c(1,0)))) betaMixFix.fitted <- fitted(betaMixFix_3) for (i in 1:3) { seekViewport(trellis.vpname("panel", i, 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[1:22, i], "native"), gp = gpar(lty = 1)) grid.lines(unit(1:22, "native"), unit(betaMixFix.fitted[23:44, i], "native"), gp = gpar(lty = 2)) } ################################################### ### code chunk number 10: beta-full ################################################### betaMix <- stepFlexmix(cbind(Deaths, Total - Deaths) ~ Treatment | Center, model = FLXMRglm(family = "binomial"), k = 3, nrep = 3, data = betablocker) summary(betaMix) ################################################### ### code chunk number 11: default-plot ################################################### print(plot(betaMixFix_3, mark = 1, col = "grey", markcol = 1)) ################################################### ### code chunk number 12: parameters ################################################### parameters(betaMix) ################################################### ### code chunk number 13: cluster ################################################### table(clusters(betaMix)) ################################################### ### code chunk number 14: predict ################################################### predict(betaMix, newdata = data.frame(Treatment = c("Control", "Treated"))) ################################################### ### code chunk number 15: fitted ################################################### fitted(betaMix)[c(1, 23), ] ################################################### ### code chunk number 16: refit ################################################### summary(refit(getModel(betaMixFix, "3"))) ################################################### ### code chunk number 17: mehta-fix ################################################### data("Mehta", package = "flexmix") mehtaMix <- stepFlexmix(cbind(Response, Total - Response)~ 1 | Site, model = FLXMRglmfix(family = "binomial", fixed = ~ Drug), control = list(minprior = 0.04), nrep = 3, k = 3, data = Mehta) summary(mehtaMix) ################################################### ### code chunk number 18: mehta-fig ################################################### Mehta$Site <- with(Mehta, factor(Site, levels = Site[order((Response/Total)[1:22])])) clusters <- factor(clusters(mehtaMix), labels = paste("Cluster", 1:3)) print(dotplot(Response/Total ~ Site | clusters, groups = Drug, layout = c(3,1), data = Mehta, xlab = "Site", scales = list(x = list(draw = FALSE)), key = simpleKey(levels(Mehta$Drug), lines = TRUE, corner = c(1,0)))) mehtaMix.fitted <- fitted(mehtaMix) for (i in 1:3) { seekViewport(trellis.vpname("panel", i, 1)) sapply(1:nlevels(Mehta$Drug), function(j) grid.lines(unit(1:22, "native"), unit(mehtaMix.fitted[Mehta$Drug == levels(Mehta$Drug)[j], i], "native"), gp = gpar(lty = j))) } ################################################### ### code chunk number 19: mehta-full ################################################### mehtaMix <- stepFlexmix(cbind(Response, Total - Response) ~ Drug | Site, model = FLXMRglm(family = "binomial"), k = 3, data = Mehta, nrep = 3, control = list(minprior = 0.04)) summary(mehtaMix) ################################################### ### code chunk number 20: mehta-sub ################################################### Mehta.sub <- subset(Mehta, Site != 15) mehtaMix <- stepFlexmix(cbind(Response, Total - Response) ~ 1 | Site, model = FLXMRglmfix(family = "binomial", fixed = ~ Drug), data = Mehta.sub, k = 2, nrep = 3) summary(mehtaMix) ################################################### ### code chunk number 21: tribolium ################################################### data("tribolium", package = "flexmix") TribMix <- stepFlexmix(cbind(Remaining, Total - Remaining) ~ 1, k = 2:3, model = FLXMRglmfix(fixed = ~ Species, family = "binomial"), concomitant = FLXPmultinom(~ Replicate), data = tribolium) ################################################### ### code chunk number 22: wang-model ################################################### modelWang <- FLXMRglmfix(fixed = ~ I(Species == "Confusum"), family = "binomial") concomitantWang <- FLXPmultinom(~ I(Replicate == 3)) TribMixWang <- stepFlexmix(cbind(Remaining, Total - Remaining) ~ 1, data = tribolium, model = modelWang, concomitant = concomitantWang, k = 2) summary(refit(TribMixWang)) ################################################### ### code chunk number 23: tribolium ################################################### clusters <- factor(clusters(TribMixWang), labels = paste("Cluster", 1:TribMixWang@k)) print(dotplot(Remaining/Total ~ factor(Replicate) | clusters, groups = Species, data = tribolium[rep(1:9, each = 3) + c(0:2)*9,], xlab = "Replicate", auto.key = list(corner = c(1,0)))) ################################################### ### code chunk number 24: subset ################################################### TribMixWangSub <- stepFlexmix(cbind(Remaining, Total - Remaining) ~ 1, k = 2, data = tribolium[-7,], model = modelWang, concomitant = concomitantWang) ################################################### ### code chunk number 25: trypanosome ################################################### data("trypanosome", package = "flexmix") TrypMix <- stepFlexmix(cbind(Dead, 1-Dead) ~ 1, k = 2, nrep = 3, data = trypanosome, model = FLXMRglmfix(family = "binomial", fixed = ~ log(Dose))) summary(refit(TrypMix)) ################################################### ### code chunk number 26: trypanosome ################################################### tab <- with(trypanosome, table(Dead, Dose)) Tryp.dat <- data.frame(Dead = tab["1",], Alive = tab["0",], Dose = as.numeric(colnames(tab))) plot(Dead/(Dead+Alive) ~ Dose, data = Tryp.dat) Tryp.pred <- predict(glm(cbind(Dead, 1-Dead) ~ log(Dose), family = "binomial", data = trypanosome), newdata=Tryp.dat, type = "response") TrypMix.pred <- predict(TrypMix, newdata = Tryp.dat, aggregate = TRUE)[[1]] lines(Tryp.dat$Dose, Tryp.pred, lty = 2) lines(Tryp.dat$Dose, TrypMix.pred, lty = 3) legend(4.7, 1, c("GLM", "Mixture model"), lty=c(2, 3), xjust=0, yjust=1) ################################################### ### code chunk number 27: fabric-fix ################################################### data("fabricfault", package = "flexmix") fabricMix <- stepFlexmix(Faults ~ 1, model = FLXMRglmfix(family="poisson", fixed = ~ log(Length)), data = fabricfault, k = 2, nrep = 3) summary(fabricMix) summary(refit(fabricMix)) Lnew <- seq(0, 1000, by = 50) fabricMix.pred <- predict(fabricMix, newdata = data.frame(Length = Lnew)) ################################################### ### code chunk number 28: fabric-fix-nested ################################################### fabricMix2 <- flexmix(Faults ~ 0, data = fabricfault, cluster = posterior(fabricMix), model = FLXMRglmfix(family = "poisson", fixed = ~ log(Length), nested = list(k=c(1,1), formula=list(~0,~1)))) summary(refit(fabricMix2)) fabricMix2.pred <- predict(fabricMix2, newdata = data.frame(Length = Lnew)) ################################################### ### code chunk number 29: fabric-fig ################################################### plot(Faults ~ Length, data = fabricfault) sapply(fabricMix.pred, function(y) lines(Lnew, y, lty = 1)) sapply(fabricMix2.pred, function(y) lines(Lnew, y, lty = 2)) legend(190, 25, paste("Model", 1:2), lty=c(1, 2), xjust=0, yjust=1) ################################################### ### code chunk number 30: patent ################################################### data("patent", package = "flexmix") ModelPat <- FLXMRglm(family = "poisson") FittedPat <- stepFlexmix(Patents ~ lgRD, k = 3, nrep = 3, model = ModelPat, data = patent, concomitant = FLXPmultinom(~ RDS)) summary(FittedPat) ################################################### ### code chunk number 31: patent-fixed ################################################### ModelFixed <- FLXMRglmfix(family = "poisson", fixed = ~ lgRD) FittedPatFixed <- flexmix(Patents ~ 1, model = ModelFixed, cluster = posterior(FittedPat), concomitant = FLXPmultinom(~ RDS), data = patent) summary(FittedPatFixed) ################################################### ### code chunk number 32: Poisson ################################################### lgRDv <- seq(-3, 5, by = 0.05) newdata <- data.frame(lgRD = lgRDv) plotData <- function(fitted) { with(patent, data.frame(Patents = c(Patents, unlist(predict(fitted, newdata = newdata))), lgRD = c(lgRD, rep(lgRDv, 3)), class = c(clusters(fitted), rep(1:3, each = nrow(newdata))), type = rep(c("data", "fit"), c(nrow(patent), nrow(newdata)*3)))) } plotPatents <- cbind(plotData(FittedPat), which = "Wang et al.") plotPatentsFixed <- cbind(plotData(FittedPatFixed), which = "Fixed effects") plotP <- rbind(plotPatents, plotPatentsFixed) rds <- seq(0, 3, by = 0.02) x <- model.matrix(FittedPat@concomitant@formula, data = data.frame(RDS = rds)) plotConc <- function(fitted) { E <- exp(x%*%fitted@concomitant@coef) data.frame(Probability = as.vector(E/rowSums(E)), class = rep(1:3, each = nrow(x)), RDS = rep(rds, 3)) } plotConc1 <- cbind(plotConc(FittedPat), which = "Wang et al.") plotConc2 <- cbind(plotConc(FittedPatFixed), which = "Fixed effects") plotC <- rbind(plotConc1, plotConc2) print(xyplot(Patents ~ lgRD | which, data = plotP, groups=class, xlab = "log(R&D)", panel = "panel.superpose", type = plotP$type, panel.groups = function(x, y, type = "p", subscripts, ...) { ind <- plotP$type[subscripts] == "data" panel.xyplot(x[ind], y[ind], ...) panel.xyplot(x[!ind], y[!ind], type = "l", ...) }, scales = list(alternating=FALSE), layout=c(1,2), as.table=TRUE), more=TRUE, position=c(0,0,0.6, 1)) print(xyplot(Probability ~ RDS | which, groups = class, data = plotC, type = "l", scales = list(alternating=FALSE), layout=c(1,2), as.table=TRUE), position=c(0.6, 0.01, 1, 0.99)) ################################################### ### code chunk number 33: seizure ################################################### data("seizure", package = "flexmix") seizMix <- stepFlexmix(Seizures ~ Treatment * log(Day), data = seizure, k = 2, nrep = 3, model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix) summary(refit(seizMix)) ################################################### ### code chunk number 34: seizure ################################################### seizMix2 <- flexmix(Seizures ~ Treatment * log(Day/27), data = seizure, cluster = posterior(seizMix), model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix2) summary(refit(seizMix2)) ################################################### ### code chunk number 35: seizure ################################################### seizMix3 <- flexmix(Seizures ~ log(Day/27)/Treatment, data = seizure, cluster = posterior(seizMix), model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix3) summary(refit(seizMix3)) ################################################### ### code chunk number 36: seizure ################################################### plot(Seizures/Hours~Day, pch = c(1,3)[as.integer(Treatment)], data=seizure) abline(v=27.5, lty=2, col="grey") legend(140, 9, c("Baseline", "Treatment"), pch=c(1, 3), xjust=1, yjust=1) matplot(seizure$Day, fitted(seizMix)/seizure$Hours, type="l", add=TRUE, lty = 1, col = 1) matplot(seizure$Day, fitted(seizMix3)/seizure$Hours, type="l", add=TRUE, lty = 3, col = 1) legend(140, 7, paste("Model", c(1,3)), lty=c(1, 3), xjust=1, yjust=1) ################################################### ### code chunk number 37: salmonella ################################################### data("salmonellaTA98", package = "flexmix") salmonMix <- stepFlexmix(y ~ 1, data = salmonellaTA98, k = 2, nrep = 3, model = FLXMRglmfix(family = "poisson", fixed = ~ x + log(x + 10))) ################################################### ### code chunk number 38: salmonella ################################################### salmonMix.pr <- predict(salmonMix, newdata=salmonellaTA98) plot(y~x, data=salmonellaTA98, pch=as.character(clusters(salmonMix)), xlab="Dose of quinoline", ylab="Number of revertant colonies of salmonella", ylim=range(c(salmonellaTA98$y, unlist(salmonMix.pr)))) for (i in 1:2) lines(salmonellaTA98$x, salmonMix.pr[[i]], lty=i) ################################################### ### code chunk number 39: regression-examples.Rnw:923-927 ################################################### SI <- sessionInfo() pkgs <- paste(sapply(c(SI$otherPkgs, SI$loadedOnly), function(x) paste("\\\\pkg{", x$Package, "} ", x$Version, sep = "")), collapse = ", ") flexmix/inst/doc/bootstrapping.Rnw0000644000176200001440000004660014404637307017051 0ustar liggesusers\documentclass[nojss]{jss} \usepackage{amsfonts,bm,amsmath,amssymb} %%\usepackage{Sweave} %% already provided by jss.cls %%%\VignetteIndexEntry{Finite Mixture Model Diagnostics Using Resampling Methods} %%\VignetteDepends{flexmix} %%\VignetteKeywords{R, finite mixture model, resampling, bootstrap} %%\VignettePackage{flexmix} \title{Finite Mixture Model Diagnostics Using Resampling Methods} <>= options(useFancyQuotes = FALSE) digits <- 3 Colors <- c("#E495A5", "#39BEB1") critical_values <- function(n, p = "0.95") { data("qDiptab", package = "diptest") if (n %in% rownames(qDiptab)) { return(qDiptab[as.character(n), p]) }else { n.approx <- as.numeric(rownames(qDiptab)[which.min(abs(n - as.numeric(rownames(qDiptab))))]) return(sqrt(n.approx)/sqrt(n) * qDiptab[as.character(n.approx), p]) } } library("graphics") library("flexmix") combine <- function(x, sep, width) { cs <- cumsum(nchar(x)) remaining <- if (any(cs[-1] > width)) combine(x[c(FALSE, cs[-1] > width)], sep, width) c(paste(x[c(TRUE, cs[-1] <= width)], collapse= sep), remaining) } prettyPrint <- function(x, sep = " ", linebreak = "\n\t", width = getOption("width")) { x <- strsplit(x, sep)[[1]] paste(combine(x, sep, width), collapse = paste(sep, linebreak, collapse = "")) } @ \author{Bettina Gr{\"u}n\\ Wirtschaftsuniversit{\"a}t Wien \And Friedrich Leisch\\ Universit\"at f\"ur Bodenkultur Wien} \Plainauthor{Bettina Gr{\"u}n, Friedrich Leisch} \Address{ Bettina Gr\"un\\ Institute for Statistics and Mathematics\\ Wirtschaftsuniversit{\"a}t Wien\\ Welthandelsplatz 1\\ 1020 Wien, Austria\\ E-mail: \email{Bettina.Gruen@R-project.org}\\ Friedrich Leisch\\ Institut f\"ur Angewandte Statistik und EDV\\ Universit\"at f\"ur Bodenkultur Wien\\ Peter Jordan Stra\ss{}e 82\\ 1190 Wien, Austria\\ E-mail: \email{Friedrich.Leisch@boku.ac.at} } \Abstract{ This paper illustrates the implementation of resampling methods in \pkg{flexmix} as well as the application of resampling methods for model diagnostics of fitted finite mixture models. Convenience functions to perform these methods are available in package \pkg{flexmix}. The use of the methods is illustrated with an artificial example and the \code{seizure} data set. } \Keywords{\proglang{R}, finite mixture models, resampling, bootstrap} \Plainkeywords{R, finite mixture models, resampling, bootstrap} %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \begin{document} \SweaveOpts{engine=R, echo=true, height=5, width=8, eps=FALSE, keep.source=TRUE} \setkeys{Gin}{width=0.95\textwidth} \section{Implementation of resampling methods}\label{sec:implementation} The proposed framework for model diagnostics using resampling \citep{mixtures:gruen+leisch:2004} equally allows to investigate model fit for all kinds of mixture models. The procedure is applicable to mixture models with different component specific models and does not impose any limitation such as for example on the dimension of the parameter space of the component specific model. In addition to the fitting step different component specific models only require different random number generators for the parametric bootstrap. The \code{boot()} function in \pkg{flexmix} is a generic \proglang{S4} function with a method for fitted finite mixtures of class \code{"flexmix"} and is applicable to general finite mixture models. The function with arguments and their defaults is given by: <>= cat(prettyPrint(gsub("boot_flexmix", "boot", prompt(flexmix:::boot_flexmix, filename = NA)$usage[[2]]), sep = ", ", linebreak = paste("\n", paste(rep(" ", 2), collapse = ""), sep= ""), width = 70)) @ The interface is similar to the \code{boot()} function in package \pkg{boot} \citep{mixtures:Davison+Hinkley:1997, mixtures:Canty+Ripley:2010}. The \code{object} is a fitted finite mixture of class \code{"flexmix"} and \code{R} denotes the number of resamples. The possible bootstrapping method are \code{"empirical"} (also available as \code{"ordinary"}) and \code{"parametric"}. For the parametric bootstrap sampling from the fitted mixture is performed using \code{rflexmix()}. For mixture models with different component specific models \code{rflexmix()} requires a sampling method for the component specific model. Argument \code{initialize\_solution} allows to select if the EM algorithm is started in the original finite mixture solution or if random initialization is performed. The fitted mixture model might contain weights and group indicators. The weights are case weights and allow to reduce the amount of data if observations are identical. This is useful for example for latent class analysis of multivariate binary data. The argument \code{keep\_weights} allows to indicate if they should be kept for the bootstrapping. Group indicators allow to specify that the component membership is identical over several observations, e.g., for repeated measurements of the same individual. Argument \code{keep\_groups} allows to indicate if the grouping information should also be used in the bootstrapping. \code{verbose} indicates if information on the progress should be printed. The \code{control} argument allows to control the EM algorithm for fitting the model to each of the bootstrap samples. By default the \code{control} argument is extracted from the fitted model provided by \code{object}. \code{k} allows to specify the number of components and by default this is also taken from the fitted model provided. The \code{model} argument determines if also the model and the weights slot for each sample are stored and returned. The returned object is of class \code{"FLXboot"} and otherwise only contains the fitted parameters, the fitted priors, the log likelihoods, the number of components of the fitted mixtures and the information if the EM algorithm has converged. The likelihood ratio test is implemented based on \code{boot()} in function \code{LR\_test()} and returns an object of class \code{"htest"} containing the number of valid bootstrap replicates, the p-value, the double negative log likelihood ratio test statistics for the original data and the bootstrap replicates. The \code{plot} method for \code{"FLXboot"} objects returns a parallel coordinate plot with the fitted parameters separately for each of the components. \section{Artificial data set} In the following a finite mixture model is used as the underlying data generating process which is theoretically not identifiable. We are assuming a finite mixture of linear regression models with two components of equal size where the coverage condition is not fulfilled \citep{mixtures:Hennig:2000}. Hence, intra-component label switching is possible, i.e., there exist two parameterizations implying the same mixture distribution which differ how the components between the covariate points are combined. We assume that one measurement per object and a single categorical regressor with two levels are given. The usual design matrix for a model with intercept uses the two covariate points $\mathbf{x}_1 = (1, 0)'$ and $\mathbf{x}_2 = (1, 1)'$. The mixture distribution is given by \begin{eqnarray*} H(y|\mathbf{x}, \Theta) &=& \frac{1}{2} N(\mu_1, 0.1) + \frac{1}{2} N(\mu_2, 0.1), \end{eqnarray*} where $\mu_k(\mathbf{x}) = \mathbf{x}'\bm{\alpha}_k$ and $N(\mu, \sigma^2)$ is the normal distribution. Now let $\mu_1(\mathbf{x}_1) = 1$, $\mu_2(\mathbf{x}_1) = 2$, $\mu_1(\mathbf{x}_2) = -1$ and $\mu_2(\mathbf{x}_2) = 4$. As Gaussian mixture distributions are generically identifiable the means, variances and component weights are uniquely determined in each covariate point given the mixture distribution. However, as the coverage condition is not fulfilled, the two possible solutions for $\bm{\alpha}$ are: \begin{description} \item[Solution 1:] $\bm{\alpha}_1^{(1)} = (2,\phantom{-}2)'$, $\bm{\alpha}_2^{(1)} = (1,-2)'$, \item[Solution 2:] $\bm{\alpha}_1^{(2)} = (2,-3)'$, $\bm{\alpha}_2^{(2)} = (1,\phantom{-}3)'$. \end{description} We specify this artificial mixture distribution using \code{FLXdist()}. \code{FLXdist()} returns an unfitted finite mixture of class \code{"FLXdist"}. The class of fitted finite mixture models \code{"flexmix"} extends class \code{"FLXdist"}. Each component follows a normal distribution. The parameters specified in a named list therefore consist of the regression coefficients and the standard deviation. Function \code{FLXdist()} has an argument \code{formula} for specifying the regression in each of the components, an argument \code{k} for the component weights and \code{components} for the parameters of each of the components. <<>>= library("flexmix") Component_1 <- list(Model_1 = list(coef = c(1, -2), sigma = sqrt(0.1))) Component_2 <- list(Model_1 = list(coef = c(2, 2), sigma = sqrt(0.1))) ArtEx.mix <- FLXdist(y ~ x, k = rep(0.5, 2), components = list(Component_1, Component_2)) @ We draw a balanced sample with 50 observations in each covariate point from the mixture model using \code{rflexmix()} after defining the data points for the covariates. \code{rflexmix()} can either have an unfitted or a fitted finite mixture as input. For unfitted mixtures data has to be provided using the \code{newdata} argument. For already fitted mixtures data can be optionally provided, otherwise the data used for fitting the mixture is used. <<>>= ArtEx.data <- data.frame(x = rep(0:1, each = 100/2)) suppressWarnings(RNGversion("3.5.0")) set.seed(123) ArtEx.sim <- rflexmix(ArtEx.mix, newdata = ArtEx.data) ArtEx.data$y <- ArtEx.sim$y[[1]] ArtEx.data$class <- ArtEx.sim$class @ In Figure~\ref{fig:art} the sample is plotted together with the two solutions for combining $x_1$ and $x_2$, i.e., this illustrates intra-component label switching. \begin{figure} \centering <>= par(mar = c(5, 4, 2, 0) + 0.1) plot(y ~ x, data = ArtEx.data, pch = with(ArtEx.data, 2*class + x)) pars <- list(matrix(c(1, -2, 2, 2), ncol = 2), matrix(c(1, 3, 2, -3), ncol = 2)) for (i in 1:2) apply(pars[[i]], 2, abline, col = Colors[i]) @ \caption{Balanced sample from the artificial example with the two theoretical solutions.} \label{fig:art} \end{figure} We fit a finite mixture to the sample using \code{stepFlexmix()}. <<>>= set.seed(123) ArtEx.fit <- stepFlexmix(y ~ x, data = ArtEx.data, k = 2, nrep = 5, control = list(iter = 1000, tol = 1e-8, verbose = 0)) @ The fitted mixture can be inspected using \code{summary()} and \code{parameters()}. <<>>= summary(ArtEx.fit) parameters(ArtEx.fit) @ Obviously the fitted mixture parameters correspond to the parameterization we used to specify the mixture distribution. Using standard asymptotic theory to analyze the fitted mixture model gives the following estimates for the standard deviations. <<>>= ArtEx.refit <- refit(ArtEx.fit) summary(ArtEx.refit) @ The fitted mixture can also be analyzed using resampling techniques. For analyzing the stability of the parameter estimates where the possibility of identifiability problems is also taken into account the parametric bootstrap is used with random initialization. Function \code{boot()} can be used for empirical or parametric bootstrap (specified by the argument \code{sim}). The logical argument \code{initialize_solution} specifies if the initialization is in the original solution or random. By default random initialization is made. The number of bootstrap samples is set by the argument \code{R}. Please note that the arguments are chosen to correspond to those for function \code{boot} in package \pkg{boot} \citep{mixtures:Davison+Hinkley:1997}. <>= set.seed(123) ArtEx.bs <- boot(ArtEx.fit, R = 200, sim = "parametric") ArtEx.bs @ <>= if (file.exists("ArtEx.bs.rda")) { load("ArtEx.bs.rda") } else { set.seed(123) ArtEx.bs <- boot(ArtEx.fit, R = 200, sim = "parametric") save(ArtEx.bs, file = "ArtEx.bs.rda") } ArtEx.bs @ Function \code{boot()} returns an object of class \code{"\Sexpr{class(ArtEx.bs)}"}. The default plot compares the bootstrap parameter estimates to the confidence intervals derived using standard asymptotic theory in a parallel coordinate plot (see Figure~\ref{fig:plot.FLXboot-art}). Clearly two groups of parameter estimates can be distinguished which are about of equal size. One subset of the parameter estimates stays within the confidence intervals induced by standard asymptotic theory, while the second group corresponds to the second solution and clusters around these parameter values. \begin{figure}[h!] \centering <>= print(plot(ArtEx.bs, ordering = "coef.x", col = Colors)) @ \caption{Diagnostic plot of the bootstrap results for the artificial example.} \label{fig:plot.FLXboot-art} \end{figure} In the following the DIP-test is applied to check if the parameter estimates follow a unimodal distribution. This is done for the aggregated parameter esimates where unimodality implies that this parameter is not suitable for imposing an ordering constraint which induces a unique labelling. For the separate component analysis which is made after imposing an ordering constraint on the coefficient of $x$ rejection the null hypothesis of unimodality implies that identifiability problems are present, e.g.~due to intra-component label switching. <<>>= require("diptest") parameters <- parameters(ArtEx.bs) Ordering <- factor(as.vector(apply(matrix(parameters[,"coef.x"], nrow = 2), 2, order))) Comp1 <- parameters[Ordering == 1,] Comp2 <- parameters[Ordering == 2,] dip.values.art <- matrix(nrow = ncol(parameters), ncol = 3, dimnames=list(colnames(parameters), c("Aggregated", "Comp 1", "Comp 2"))) dip.values.art[,"Aggregated"] <- apply(parameters, 2, dip) dip.values.art[,"Comp 1"] <- apply(Comp1, 2, dip) dip.values.art[,"Comp 2"] <- apply(Comp2, 2, dip) dip.values.art @ The critical value for column \code{Aggregated} is \Sexpr{round(critical_values(nrow(parameters)), digits = digits)} and for the columns of the separate components \Sexpr{round(critical_values(nrow(Comp1)), digits = digits)}. The component sizes as well as the standard deviations follow a unimodal distribution for the aggregated data as well as for each of the components. The regression coefficients are multimodal for the aggregate data as well as for each of the components. While from the aggregated case it might be concluded that imposing an ordering constraint on the intercept or the coefficient of $x$ is suitable, the component-specific analyses reveal that a unique labelling was not achieved. \section{Seizure} In \cite{mixtures:Wang+Puterman+Cockburn:1996} a Poisson mixture regression is fitted to data from a clinical trial where the effect of intravenous gammaglobulin on suppression of epileptic seizures is investigated. The data used were 140 observations from one treated patient, where treatment started on the $28^\textrm{th}$ day. In the regression model three independent variables were included: treatment, trend and interaction treatment-trend. Treatment is a dummy variable indicating if the treatment period has already started. Furthermore, the number of parental observation hours per day were available and it is assumed that the number of epileptic seizures per observation hour follows a Poisson mixture distribution. The number of epileptic seizures per parental observation hour for each day are plotted in Figure~\ref{fig:seizure}. The fitted mixture distribution consists of two components which can be interpreted as representing 'good' and 'bad' days of the patients. The mixture model can be formulated by \begin{equation*} H(y|\mathbf{x}, \Theta) = \pi_1 P(\lambda_1) + \pi_2 P(\lambda_2), \end{equation*} where $\lambda_k = e^{\mathbf{x}'\bm{\alpha}_k}$ for $k = 1,2$ and $P(\lambda)$ is the Poisson distribution. The data is loaded and the mixture fitted with two components. <<>>= data("seizure", package = "flexmix") model <- FLXMRglm(family = "poisson", offset = log(seizure$Hours)) control <- list(iter = 1000, tol = 1e-10, verbose = 0) set.seed(123) seizMix <- stepFlexmix(Seizures ~ Treatment * log(Day), data = seizure, k = 2, nrep = 5, model = model, control = control) @ The fitted regression lines for each of the two components are shown in Figure~\ref{fig:seizure}. \begin{figure}[h!] \begin{center} <>= par(mar = c(5, 4, 2, 0) + 0.1) plot(Seizures/Hours~Day, data=seizure, pch = as.integer(seizure$Treatment)) abline(v = 27.5, lty = 2, col = "grey") matplot(seizure$Day, fitted(seizMix)/seizure$Hours, type="l", add = TRUE, col = 1, lty = 1, lwd = 2) @ \caption{Seizure data with the fitted values for the \citeauthor{mixtures:Wang+Puterman+Cockburn:1996} model. The plotting character for the observed values in the base period is a circle and for those in the treatment period a triangle.} \label{fig:seizure} \end{center} \end{figure} The parameteric bootstrap with random initialization is used to investigate identifiability problems and parameter stability. The diagnostic plot is given in Figure~\ref{fig:plot.FLXboot-seiz}. The coloring is according to an ordering constraint on the intercept. Clearly the parameter estimates corresponding to the solution where the bad days from the base period are combined with the good days from the treatement period and vice versa for the good days of the base period can be distinguished and indicate the slight identifiability problems of the fitted mixture. <>= set.seed(123) seizMix.bs <- boot(seizMix, R = 200, sim = "parametric") seizMix.bs @ <>= if (file.exists("seizMix.bs.rda")) { load("seizMix.bs.rda") } else { set.seed(123) seizMix.bs <- boot(seizMix, R = 200, sim = "parametric") save(seizMix.bs, file = "seizMix.bs.rda") } seizMix.bs @ \begin{figure}[h!] \centering <>= print(plot(seizMix.bs, ordering = "coef.(Intercept)", col = Colors)) @ \label{fig:plot.FLXboot-seiz} \caption{Diagnostic plot of the bootstrap results for the \code{seizure} data.} \end{figure} <<>>= parameters <- parameters(seizMix.bs) Ordering <- factor(as.vector(apply(matrix(parameters[,"coef.(Intercept)"], nrow = 2), 2, order))) Comp1 <- parameters[Ordering == 1,] Comp2 <- parameters[Ordering == 2,] @ For applying the DIP test also an ordering constraint on the intercept is used. The critical value for column \code{Aggregated} is \Sexpr{round(critical_values(nrow(parameters)), digits = digits)} and for the columns of the separate components \Sexpr{round(critical_values(nrow(Comp1)), digits = digits)}. <<>>= dip.values.art <- matrix(nrow = ncol(parameters), ncol = 3, dimnames = list(colnames(parameters), c("Aggregated", "Comp 1", "Comp 2"))) dip.values.art[,"Aggregated"] <- apply(parameters, 2, dip) dip.values.art[,"Comp 1"] <- apply(Comp1, 2, dip) dip.values.art[,"Comp 2"] <- apply(Comp2, 2, dip) dip.values.art @ For the aggregate results the hypothesis of unimodality cannot be rejected for the trend. For the component-specific analyses unimodality cannot be rejected only for the intercept (where the ordering condition was imposed on) and again the trend. For all other parameter estimates unimodality is rejected which indicates that the ordering constraint was able to impose a unique labelling only for the own parameter and not for the other parameters. This suggests identifiability problems. %%------------------------------------------------------------------------- %%------------------------------------------------------------------------- \bibliography{mixture} \end{document} flexmix/inst/doc/myConcomitant.R0000644000176200001440000000130314404637307016424 0ustar liggesusersmyConcomitant <- function(formula = ~ 1) { z <- new("FLXP", name = "myConcomitant", formula = formula) z@fit <- function(x, y, w, ...) { if (missing(w) || is.null(w)) w <- rep(1, length(x)) f <- as.integer(factor(apply(x, 1, paste, collapse = ""))) AVG <- apply(w*y, 2, tapply, f, mean) (AVG/rowSums(AVG))[f,,drop=FALSE] } z@refit <- function(x, y, w, ...) { if (missing(w) || is.null(w)) w <- rep(1, length(x)) f <- as.integer(factor(apply(x, 1, paste, collapse = ""))) AVG <- apply(w*y, 2, tapply, f, mean) (AVG/rowSums(AVG)) } z } flexmix/inst/doc/bootstrapping.pdf0000644000176200001440000036457714757625371017105 0ustar liggesusers%PDF-1.5 %¿÷¢þ 1 0 obj << /Type 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˜­VsÌ6‘³@¦±ªƒEÀf2?§apÁ´É´F0û'X˜ QsÌžv[<Ž/R endstream endobj startxref 205064 %%EOF flexmix/inst/NEWS.Rd0000644000176200001440000004760514757625043013777 0ustar liggesusers\name{NEWS} \title{News for Package 'flexmix'} \section{Changes in flexmix version 2.3-20}{ \itemize{ \item Function \code{flxglht} added which allows to perform simultaneous inference in finite mixtures of regression models to assess zero coefficients or constant effects. } } \section{Changes in flexmix version 2.3-19}{ \itemize{ \item Internal function names were changed to avoid having them look like S3 methods. \item Updated CITATION to use \code{bibentry()}. } } \section{Changes in flexmix version 2.3-18}{ \itemize{ \item The man page improved for the different general model classes such as `\code{FLXM}', `\code{FLXMC}', `\code{FLXMR}' and `\code{FLXMCsparse}'. Thanks to Jonas Hagenberg for pointing out that the class structure is not well documented. \item An issue fixed for `\code{FLXMRlmmc}' models. } } \section{Changes in flexmix version 2.3-17}{ \itemize{ \item A model class for sparse model-based clustering added with a suitable method to resolve the formula and extract the data. \item There was a bug with dimensions being dropped if only a single individual was used for grouping. Thanks to Adam Hulman for pointing this issue out. \item The \code{FLXgetModelmatrix} method for `\code{FLXMRlmm}' objects has been improved. Thanks to Adam Hulman for pointing out that this might be unnecessarily slow. } } \section{Changes in flexmix version 2.3-16}{ \itemize{ \item The vignette explaining model diagnostics using resampling methods was modified to use more replications. Thanks to Eric Book for pointing this issue out. } } \section{Changes in flexmix version 2.3-15}{ \itemize{ \item Modified the internal function \code{groupPosteriors} to be more efficient for a large number of groups. Thanks to Marnix Koops for pointing the problem out. \item Model driver \code{FLXMRlmer()} adapted for \pkg{lme4} (>= 1.1). Thanks to Mark Senior for pointing the problem out. \item Model driver \code{FLXMRmgcv()} adapted for \pkg{mgcv} (>= 1.8-27). \item Data set \code{Catsup} is now loaded from package \pkg{Ecdat} instead of \pkg{mlogit}. } } \section{Changes in flexmix version 2.3-14}{ \itemize{ \item A bug fixed for \code{FLXMRcondlogit()} to ensure that the formula for the strata is also stored and can be used for predicting, etc. new data. Thanks to Peter Fraser-Mackenziefor for pointing the problem out. \item A bug fixed for \code{FLXMRglmfix()} which occurred if several components were simultaneously omitted. Thanks to Moritz Berger for pointing the problem out. \item For mixtures of mixed effects models and with censored data only weighted ML estimation is implemented. This is now checked and an error is given if a different estimation method is requested. \item A generic function \code{sigma()} is available for R >= 3.3.0 and thus different versions of \code{sigma()} need to be called depending on the R version. Thanks also to Stephen Martin for pointing the issue out. \item Components are now generated using functions instead of expressions. \item Functions from the base packages \pkg{stats}, \pkg{graphics} and \pkg{grDevices} are now correctly imported before being used. \item Function \code{FLXMCdist1} implements model drivers for univariate mixtures of different distributions. } } \section{Changes in flexmix version 2.3-13}{ \itemize{ \item A model driver for mixtures of regression models with (adaptive) lasso and elastic net penalizations for the coefficients building on \pkg{glmnet} was provided by Frederic Mortier and Nicolas Picard. \item A bug in a coerce method to class \code{"FLXnested"} fixed. } } \section{Changes in flexmix version 2.3-12}{ \itemize{ \item Construction of model matrices changed to re-use levels of factors while fitting for prediction. Thanks to Robert Poos for pointing the problem out. \item Package mgcv of version at least 1.8-0 is required in order to avoid loading of the package for formula evaluation. } } \section{Changes in flexmix version 2.3-11}{ \itemize{ \item Examples changed to be less time consuming. \item Bug fixed in ungroupPriors() and getPriors() to work with a grouping where only one unique value is contained. Thanks to Christine Koehler for pointing the problem out. \item The \code{logLik()} method for \code{"flexmix"} objects now also has a \code{newdata} argument. \item In the M-step only the parameters of the previously fitted components are passed over to avoid nesting of environments. Thanks to Dominik Ernst for pointing the problem out. \item Function \code{boot()} was fixed to work correctly with grouped data if the groups are kept and if fixed effects are fitted. \item Authors@R used in DESCRIPTION. Deepayan Sarkar listed as contributor due to internal code copied from package lattice used for the plots in flexmix. \item Model driver \code{FLXMRlmer()} adapted for \pkg{lme4} (>= 1.0). } } \section{Changes in flexmix version 2.3-10}{ \itemize{ \item Parallel processing disabled in \code{stepFlexmix()}. } } \section{Changes in flexmix version 2.3-9}{ \itemize{ \item Package dependencies, imports and suggests modified suitably for R >= 2.15.0. \item NEWS file adapted to a NEWS.Rd file. \item Parallel processing is enabled in \code{stepFlexmix()}. See \pkg{flexclust} for details. \item New model drivers \code{FLXMRmultinom()} and \code{FLXMRcondlogit()} are included which allow to fit finite mixtures of multinomial logit and conditional logit models. Identifiability problems might arise for this model class. Details on sufficient identifiability conditions are given in Gruen and Leisch (2008). \item A bug in \code{FLXMRlmm()} was fixed which did not allow to specify restrictions on the variances of the random effects and / or the residuals. Thanks to Gregory Matthews for pointing the problem out. } } \section{Changes in flexmix version 2.3-8}{ \itemize{ \item The fit function in the M-step by default now is called with an argument containing the fitted component. This allows to use the parameter estimates from the previous step for initialization. Fit functions which do not require this now need a \code{...} argument. Thanks to Hannah Frick and Achim Zeileis for requesting this feature. \item Function \code{initFlexmix()} was added which is an alternative to \code{stepFlexmix()} where first several short runs of EM, SEM or CEM are performed followed by a long run of EM. } } \section{Changes in flexmix version 2.3-7}{ \itemize{ \item A bug fixed in \code{predict()} and \code{fitted()} if a concomitant variable model is specified and \code{aggregate = TRUE}. Thanks to Julia Schiffner for pointing this out. \item A bug fixed in \code{FLXMRmgcv()} if observations were removed in the M-step because their a-posterior probabilities were smaller than eps. Thanks to Ghislain Geniaux for pointing the problem out. } } \section{Changes in flexmix version 2.3-6}{ \itemize{ \item Vignettes moved from /inst/doc to /vignettes. \item \code{stepFlexmix()} can now be called with a concomitant variable model \code{FLXPmultinom()} for \code{k} starting with 1 without getting an error. The concomitant variable model is internally replaced by \code{FLXPconstant()}. \item The \code{boot()} method for \code{"flexmix"} objects is extended to mixture models with concomitant variables and mixtures of linear mixed models. \item A bug fixed in the \code{summary()} method for \code{"flexmix"} objects. The column post > 0 did not give the correct results if weights were used for fitting the mixture. \item A bug fixed in the \code{unique()} method for \code{"stepFlexmix"} objects. This only occurred if components were dropped as well as if the EM algorithm did not converge for all repetitions. Thanks to Sebastian Meyer for pointing this out. } } \section{Changes in flexmix version 2.3-5}{ \itemize{ \item A bug fixed in \code{posterior()}. Fixed priors were always used, also if a concomitant variable model was present. \item A method added for \code{prior()} such that if newdata is supplied and the object is of class \code{"flexmix"} the prior class probabilities for each observation are returned. } } \section{Changes in flexmix version 2.3-4}{ \itemize{ \item A generic method for \code{nobs()} is introduced in \pkg{stats4} for \R 2.13.0. \pkg{flexmix} now does not define this generic function and \code{logLik()}, \code{AIC()} and \code{BIC()} methods were modified to better exploit already available methods. Thanks to Prof. Brian D. Ripley for suggesting the modification. } } \section{Changes in flexmix version 2.3-3}{ \itemize{ \item A bug for \code{boot()} fixed for \code{"flexmix"} objects with an unbalanced grouping variable. Thanks to Laszlo Sandor for pointing this out. } } \section{Changes in flexmix version 2.3-2}{ \itemize{ \item A bug for \code{rflexmix()} fixed for \code{"flexmix"} objects with a concomitant variable model. Thanks to Greg Petroski for pointing this out. } } \section{Changes in flexmix version 2.3-1}{ \itemize{ \item Functionality for bootstrapping finite mixture models added. } } \section{Changes in flexmix version 2.2-11}{ \itemize{ \item More generics and methods exported to use the \code{refit()} method when extending \pkg{flexmix} in other packages. } } \section{Changes in flexmix version 2.2-10}{ \itemize{ \item For long formulas \code{FLXMRglmfix()} did not work properly due to the splitting of the formula into several parts by \code{deparse()}. This is fixed by pasting them together again. Thanks to Dustin Tingley for the bug report. } } \section{Changes in flexmix version 2.2-9}{ \itemize{ \item A new model driver \code{FLXMRmgcv()} is added which allows to fit regularized linear models in the components. \item More generics and methods exported to allow extending \pkg{flexmix} in other packages. } } \section{Changes in flexmix version 2.2-8}{ \itemize{ \item The a-posteriori probabilities are now also determined as changed for \code{FLXfit()} for version 2.2-6 for \code{refit()}. \item Bug fixed for FLXfillconcomitant and refit when weights and grouping are present. A check was added that weights are identical within groups. \item Function \code{group()} is now exported. } } \section{Changes in flexmix version 2.2-7}{ \itemize{ \item Bug in the \code{FLXgetModelmatrix()} method for the \code{"FLXMRlmm"} class fixed when determining identical random effects covariates for the grouping. \item A new model driver for finite mixtures of linear mixed effects models with left-censored observations is added. } } \section{Changes in flexmix version 2.2-6}{ \itemize{ \item Determination of the a-posteriori probabilities made numerically more stable for small likelihoods. Thanks to Nicolas Picard for the code patch. \item \code{summary()} for \code{"FLXMRmstep"} objects now returns similar output for \code{which = "concomitant"} as for \pkg{flexmix} version 2.0-1. \item New demo driver \code{FLXMCnorm1()} for univariate Gaussian clustering. \item Non-postive values for the maximum number of iterations for the \code{"FLXcontrol"} object are not valid. A validity check for this is now included. } } \section{Changes in flexmix version 2.2-5}{ \itemize{ \item Model class \code{"FLXMRfix"} introduced which is a subclass of \code{"FLXMR"} and a superclass for \code{"FLXMRglmfix"} which also extends \code{"FLXMRglm"}. \item Model driver \code{FLXMCfactanal()} added which allows to fit finite mixtures of Gaussian distributions where the variance-covariance matrix is estimated using factor analyzers. \item Comparison of formulas now done using \code{identical()}. } } \section{Changes in flexmix version 2.2-4}{ \itemize{ \item Model drivers \code{FLXMRlmer()} and \code{FLXMRlmm()} added for fitting finite mixtures of linear mixed effects models. \item \code{EIC()} added as additional information criterion for assessing model fit. \item Bug fixed in \code{plot()} method for \code{"flexmix"} objects introduced in version 2.2-3. } } \section{Changes in flexmix version 2.2-3}{ \itemize{ \item New model driver \code{FLXMCmvcombi()} which is a combination of Gaussian and binary. \item \code{parameters()} now also has a which argument in order to allow to access the parameters of the concomitant variable model. \item Bug fixed in \code{refit()}. \item \code{nobs()} now returns the number of rows in the data.frame and not the number of individuals (similar as for example by lme). } } \section{Changes in flexmix version 2.2-0}{ \itemize{ \item vignette describing Version 2 added \item isTRUE(\code{all.equal()}) replaced with \code{identical()}. \item Bug fixed for prior in \code{flexmix()}. \item New function \code{relabel()} to sort components (generic is in modeltools). \item New example data generator \code{ExLinear()}. \item Fixed a bug in handling groups (gave an error for empty design matrices). \item Added new model \code{FLXMRrobglm()} for robust estimation of GLMs. } } \section{Changes in flexmix version 2.1-0}{ \itemize{ \item Renamed \code{cluster()} to \code{clusters()} to avoid conflict with \code{cluster()} from package survival \item Bug fixed in internal functions using S4 generics and methods. } } \section{Changes in flexmix version 2.0-2}{ \itemize{ \item \code{refit()} now has a method argument. For method \code{"optim"} the variance-covariance matrix is determined using \code{optim()} to maximize the likelihood initialized in the solution found by the EM algorithm. Method \code{"mstep"} refits the component specific and concomitant models treating the posterior probabilities as given, i.e. performs an M-step of the EM algorithm. } } \section{Changes in flexmix version 2.0-1}{ \itemize{ \item \code{Lapply()} added which allows to apply a function to each component of a finite mixture \item \code{KLdiv()} modified to allow for determination with a discrete and a continuous version of the KL divergence } } \section{Changes in flexmix version 2.0-0}{ \itemize{ \item Model driver for zero-inflated component specific models. \item Latent class analysis for binary multivariate data is now possible to estimate for truncated data where the number of observations with pattern only zeros is missing. \item new argument newdata for \code{cluster()} \item new \code{unique()} method for \code{"stepFlexmix"} objects } } \section{Changes in flexmix version 1.9-0}{ \itemize{ \item New class definitions for component specific models and concomitant variable models. \item \code{fitted()} and \code{predict()} now have an aggregate argument in order to be able to determine the aggregated values over all components. \item The package has now a vignette presenting several applications of finite mixtures of regression models with varying and fixed effects on artificial and real data which can be a accessed using the command vignette("regression-examples"). \item The vignette "flexmix-intro" was adapted to reflect the changes made in the package. \item \code{stepFlexmix()} now returns an object of class \code{"stepFlexmix"} which has a \code{print()} and \code{plot()} method. In addition \code{getModel()} can be used to select an appropriate model. \item \code{flexmix()} now has a weights argument for multiple identical observations. \item New model drivers for latent class analysis with Bernoulli and Poisson distributed multivariate observations. \item Variants of the EM algorithm have been modified to correspond to CEM and SEM. These names can now also be used for specifying the classify slot of the \code{"FLXcontrol"} object. } } \section{Changes in flexmix version 1.8-1}{ \itemize{ \item The package can now fit concomitant variable models. \item New M-step driver for regression models with varying and fixed effects. \item ICL information criterion added. } } \section{Changes in flexmix version 1.1-2}{ \itemize{ \item Fixed a bug that made the log-likelihood infinity for observations where all posteriors are numerically zero. \item Fixed a bug for formulae with dots. \item \code{posterior()} now has a newdata argument. \item New demo driver for model-based clustering of binary data. \item Adapted to changes in \code{summary.glm()} of \R version 2.3.0. } } \section{Changes in flexmix version 1.1-1}{ \itemize{ \item The \code{cluster} argument of \code{flexmix()} may now also be a matrix of posterior probabilities. \item Fixed a bug to make size table work in case of empty clusters. \item Fixed a bug in likelihood computation for grouped observations. \item The artificial NPreg data now also have a binomial response, added example to help(\code{"flexmix"}). } } \section{Changes in flexmix version 1.1-0}{ \itemize{ \item The \code{FLXglm()} driver now has an offset argument. \item New data set seizure as example for a Poisson GLM with an offset. \item \code{fitted()} can be used to extract fitted values from \code{"flexmix"} and \code{"FLXrefit"} objects. \item New accessor methods \code{cluster()} and \code{posterior()}. \item The package now uses lazy loading and has a namespace. } } \section{Changes in flexmix version 1.0-0}{ \itemize{ \item The package has now an introductionary vignette which can be accessed using the command vignette("flexmix-intro"). The vignette has been published in the Journal of Statistical Software, Volume 11, Issue 8 (\doi{10.18637/jss.v011.i08}), and the paper should be used as citation for \pkg{flexmix}, run \code{citation("flexmix")} in \R 2.0.0 or newer for details. \item Several typos in help pages have been fixed. } } \section{Changes in flexmix version 0.9-1}{ \itemize{ \item Adjusted for \R 2.0.0. \item Fixed a bug in the \code{summary()} and \code{plot()} methods of \code{"flexmix"} objects in case of empty clusters. \item \code{stepFlexmix()} takes two new arguments: \code{compare} allows fo find minimum AIC/BIC solutions in addition to maximum likelihood, \code{verbose} gives some information about progress. \item Use a default of \code{verbose = 0} in \code{FLXcontrol()} (better in combination with \code{stepFlexmix()}). } } \section{Changes in flexmix version 0.9-0}{ \itemize{ \item New \code{summary()} and \code{plot()} methods for \code{"flexmix"} objects. \item \code{"FLXglm"} objects can now be automatically \code{refit()}ted to get table of significance tests for coefficients. \item New function \code{stepFlexmix()} for more automated model search. \item The artificial example data now have functions to create them and a pre-stored data sets, new function \code{plotEll()} to plot 2d Gaussians with confidence ellipses. \item New function \code{KLdiv()} to compute Kullback-Leibler divergence of components. \item The calculation of the degrees of freedom for \code{FLXmclust()} was wrong } } \section{Changes in flexmix version 0.7-1}{ \itemize{ \item Fixed some codoc problems (missing aliases). \item First version released on CRAN: 0.7-0 } } flexmix/build/0000755000176200001440000000000014757625370013045 5ustar liggesusersflexmix/build/vignette.rds0000644000176200001440000000077214757625370015412 0ustar liggesusers‹ÍTAoÓ0ÎÚ²ÑJÐãøþ@{@\ØmZPiª`p}M^:‹ÄŽlOívâ‡#Êsb7M”íÄUIì÷¹ß÷üÞgÿ˜DQ4ˆF£A4òpxʯc~^ñ3âߘ¿¯WJYc5–¥ëÙRnå´-Äv*¤Õê8ç ½Ó4Õ´ÖdŒPÒÂMxJ[,Êœj¸­û1RX‚EM •Rsk©Œ‰o†‚%Çᆠ²·*5žà{Ìùñ¿/à>‘$9Ä Ú(ý2¥¡OÁʾ %iá*GcX!ä BÂÒÓ£§‡Òöþ¢Ch`#ì-\)™¨BXdÂÔW¼áJ…g÷.o7æU¦Zr.Gˤ^èÃeÉÛKк:‚Ê «UŠ Â¡¦¤PT»xº‰ešõ7±z›x÷5ÑÁmÝ—ó„pÇ:>|ÖkœöÚ†ÓJ¯Ö=ò‹O¼À¿ j„½…ÌÞ´RwÀc½·§Œ÷%yŒï¬/¸ám5ƒJ!Éï ;¥!?Ïkã&•q›ŠýROUéݺ>Ÿâ•¸V„º…?®ÅWWÓ°g’ON°þ±Žb‘SXðUØýdx=»IžÌ©$¹¿Bž¦{¾-xÞkµ™±îýůÝn÷»›Q•qÇW“-Î2wÌyöç/ g†flexmix/man/0000755000176200001440000000000014757625043012516 5ustar liggesusersflexmix/man/logLik-methods.Rd0000644000176200001440000000105414404637306015661 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: logLik-methods.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{logLik-methods} \docType{methods} \title{Methods for Function logLik in Package \pkg{flexmix}} \alias{logLik,flexmix-method} \alias{logLik,stepFlexmix-method} \description{Evaluate the log-likelihood. This function is defined as an S4 generic in the \code{stats4} package.} \section{Methods}{ \describe{ \item{object = flexmix}{Evaluate the log-likelihood of an \code{flexmix} object} } } \keyword{methods} flexmix/man/FLXdist-class.Rd0000644000176200001440000000464314404637306015426 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXdist-class.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXdist-class} \docType{class} \alias{FLXdist-class} \alias{predict,FLXdist-method} \alias{predict,FLXM-method} \alias{predict,FLXMRglm-method} \alias{predict,FLXMRmgcv-method} \alias{parameters,FLXdist-method} \alias{prior} \alias{prior,FLXdist-method} \title{Class "FLXdist"} \description{ Objects of class \code{FLXdist} represent unfitted finite mixture models. } \usage{ \S4method{parameters}{FLXdist}(object, component = NULL, model = NULL, which = c("model", "concomitant"), simplify = TRUE, drop = TRUE) \S4method{predict}{FLXdist}(object, newdata = list(), aggregate = FALSE, ...) } \arguments{ \item{object}{An object of class "FLXdist".} \item{component}{Number of component(s), if \code{NULL} all components are returned.} \item{model}{Number of model(s), if \code{NULL} all models are returned.} \item{which}{Specifies if the parameters of the component specific model or the concomitant variable model are returned.} \item{simplify}{Logical, if \code{TRUE} the returned values are simplified to a vector or matrix if possible.} \item{drop}{Logical, if \code{TRUE} the function tries to simplify the return object by omitting lists of length one.} \item{newdata}{Dataframe containing new data.} \item{aggregate}{Logical, if \code{TRUE} then the predicted values for each model aggregated over the components are returned.} \item{\dots}{Passed to the method of the model class.} } \section{Slots}{ \describe{ \item{model}{List of \code{FLXM} objects.} \item{prior}{Numeric vector with prior probabilities of clusters.} \item{components}{List describing the components using \code{FLXcomponent} objects.} \item{\code{concomitant}:}{Object of class \code{"FLXP"}.} \item{formula}{Object of class \code{"formula"}.} \item{call}{The function call used to create the object.} \item{k}{Number of clusters.} } } \section{Accessor Functions}{ The following functions should be used for accessing the corresponding slots: \describe{ \item{\code{parameters}:}{The parameters for each model and component, return value depends on the model.} \item{\code{prior}:}{Numeric vector of prior class probabilities/component weights} } } \author{Friedrich Leisch and Bettina Gruen} \seealso{\code{FLXdist}} \keyword{classes} flexmix/man/FLXMCfactanal.Rd0000644000176200001440000000452614404637306015351 0ustar liggesusers\name{FLXMCfactanal} \alias{FLXMCfactanal} \alias{rFLXM,FLXMCfactanal,FLXcomponent-method} \title{Driver for Mixtures of Factor Analyzers} \description{ This driver for \code{\link{flexmix}} implements estimation of mixtures of factor analyzers using ML estimation of factor analysis implemented in \code{factanal} in each M-step. } \usage{ FLXMCfactanal(formula = . ~ ., factors = 1, ...) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Only the left-hand side (response) of the formula is used. Default is to use the original \code{\link{flexmix}} model formula.} \item{factors}{Integer specifying the number of factors in each component.} \item{\dots}{Passed to \code{factanal}} } \value{ \code{FLXMCfactanal} returns an object of class \code{FLXM}. } \references{ G. McLachlan and D. Peel. \emph{Finite Mixture Models}, 2000. John Wiley and Sons Inc. } \author{Bettina Gruen} \section{Warning}{ This does not implement the AECM framework presented in McLachlan and Peel (2000, p.245), but uses the available functionality in R for ML estimation of factor analyzers. The implementation therefore is only experimental and has not been well tested. Please note that in general a good initialization is crucial for the EM algorithm to converge to a suitable solution for this model class. } \seealso{\code{\link{flexmix}}} \examples{ ## Reproduce (partly) Table 8.1. p.255 (McLachlan and Peel, 2000) if (require("gclus")) { data("wine", package = "gclus") wine_data <- as.matrix(wine[,-1]) set.seed(123) wine_fl_diag <- initFlexmix(wine_data ~ 1, k = 3, nrep = 10, model = FLXMCmvnorm(diagonal = TRUE)) wine_fl_fact <- lapply(1:4, function(q) flexmix(wine_data ~ 1, model = FLXMCfactanal(factors = q, nstart = 3), cluster = posterior(wine_fl_diag))) sapply(wine_fl_fact, logLik) ## FULL set.seed(123) wine_full <- initFlexmix(wine_data ~ 1, k = 3, nrep = 10, model = FLXMCmvnorm(diagonal = FALSE)) logLik(wine_full) ## TRUE wine_true <- flexmix(wine_data ~ 1, cluster = wine$Class, model = FLXMCmvnorm(diagonal = FALSE)) logLik(wine_true) } } \keyword{models} flexmix/man/fabricfault.Rd0000644000176200001440000000227314404637306015265 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: fabricfault.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{fabricfault} \alias{fabricfault} \docType{data} \title{Fabric Faults} \description{ Number of faults in rolls of a textile fabric. } \usage{data("fabricfault")} \format{ A data frame with 32 observations on the following 2 variables. \describe{ \item{Length}{Length of role (m).} \item{Faults}{Number of faults.} } } \source{ G. McLachlan and D. Peel. \emph{Finite Mixture Models}, 2000, John Wiley and Sons Inc. \url{http://www.maths.uq.edu.au/~gjm/DATA/mmdata.html} } \references{ A. F. Bissell. A Negative Binomial Model with Varying Element Sizes \emph{Biometrika}, \bold{59}, 435--441, 1972. M. Aitkin. A general maximum likelihood analysis of overdispersion in generalized linear models. \emph{Statistics and Computing}, \bold{6}, 251--262, 1996. } \examples{ data("fabricfault", package = "flexmix") fabricMix <- initFlexmix(Faults ~ 1, data = fabricfault, k = 2, model = FLXMRglmfix(family = "poisson", fixed = ~ log(Length)), nrep = 5) } \keyword{datasets} flexmix/man/KLdiv.Rd0000644000176200001440000000532414404637306014014 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: KLdiv.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{KLdiv} \alias{KLdiv,matrix-method} \alias{KLdiv,flexmix-method} \alias{KLdiv,FLXMRglm-method} \alias{KLdiv,FLXMC-method} \title{Kullback-Leibler Divergence} \description{ Estimate the Kullback-Leibler divergence of several distributions.} \usage{ \S4method{KLdiv}{matrix}(object, eps = 10^-4, overlap = TRUE,...) \S4method{KLdiv}{flexmix}(object, method = c("continuous", "discrete"), ...) } \arguments{ \item{object}{See Methods section below.} \item{method}{The method to be used; "continuous" determines the Kullback-Leibler divergence between the unweighted theoretical component distributions and the unweighted posterior probabilities at the observed points are used by "discrete".} \item{eps}{Probabilities below this threshold are replaced by this threshold for numerical stability.} \item{overlap}{Logical, do not determine the KL divergence for those pairs where for each point at least one of the densities has a value smaller than \code{eps}.} \item{...}{Passed to the matrix method.} } \section{Methods}{ \describe{ \item{object = "matrix":}{Takes as input a matrix of density values with one row per observation and one column per distribution.} \item{object = "flexmix":}{Returns the Kullback-Leibler divergence of the mixture components.} }} \details{ Estimates \deqn{\int f(x) (\log f(x) - \log g(x)) dx} for distributions with densities \eqn{f()} and \eqn{g()}. } \value{ A matrix of KL divergences where the rows correspond to using the respective distribution as \eqn{f()} in the formula above. } \note{ The density functions are modified to have equal support. A weight of at least \code{eps} is given to each observation point for the modified densities. } \keyword{methods} \author{Friedrich Leisch and Bettina Gruen} \references{ S. Kullback and R. A. Leibler. On information and sufficiency.\emph{The Annals of Mathematical Statistics}, \bold{22}(1), 79--86, 1951. Friedrich Leisch. Exploring the structure of mixture model components. In Jaromir Antoch, editor, Compstat 2004--Proceedings in Computational Statistics, 1405--1412. Physika Verlag, Heidelberg, Germany, 2004. ISBN 3-7908-1554-3. } \examples{ ## Gaussian and Student t are much closer to each other than ## to the uniform: x <- seq(-3, 3, length = 200) y <- cbind(u = dunif(x), n = dnorm(x), t = dt(x, df = 10)) matplot(x, y, type = "l") KLdiv(y) if (require("mlbench")) { set.seed(2606) x <- mlbench.smiley()$x model1 <- flexmix(x ~ 1, k = 9, model = FLXmclust(diag = FALSE), control = list(minprior = 0)) plotEll(model1, x) KLdiv(model1) } }flexmix/man/FLXnested-class.Rd0000644000176200001440000000200214404637306015730 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXnested-class.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXnested-class} \docType{class} \alias{FLXnested-class} \alias{coerce,list,FLXnested-method} \alias{coerce,NULL,FLXnested-method} \alias{coerce,numeric,FLXnested-method} \alias{initialize,FLXnested-method} \title{Class "FLXnested"} \description{Specification of nesting structure for regression coefficients.} \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("FLXnested", formula, k, ...)}. In addition, named lists can be coerced to \code{FLXnested} objects, names are completed if unique. } \section{Slots}{ \describe{ \item{\code{formula}:}{Object of class \code{"list"} containing the formula for determining the model matrix for each nested parameter.} \item{\code{k}:}{Object of class \code{"numeric"} specifying the number of components in each group.} } } \author{Friedrich Leisch and Bettina Gruen} \keyword{classes} flexmix/man/Lapply-methods.Rd0000644000176200001440000000313014404637306015676 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: Lapply-methods.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{Lapply-methods} \docType{methods} \title{Methods for Function Lapply} \alias{Lapply,FLXRmstep-method} \description{Apply a function to each component of a finite mixture} \usage{ \S4method{Lapply}{FLXRmstep}(object, FUN, model = 1, component = TRUE, ...) } \arguments{ \item{object}{S4 class object.} \item{FUN}{The function to be applied.} \item{model}{The model (for a multivariate response) that shall be used.} \item{component}{Index vector for selecting the components.} \item{\dots}{Optional arguments to \code{FUN}.} } \section{Methods}{ \describe{ \item{object = FLXRmstep:}{Apply a function to each component of a refitted \code{flexmix} object using method = \code{"mstep"}.} } } \details{ \code{FUN} is found by a call to \code{match.fun} and typically is specified as a function or a symbol (e.g. a backquoted name) or a character string specifying a function to be searched for from the environment of the call to \code{Lapply}. } \value{ A list of the length equal to the number of components specified is returned, each element of which is the result of applying \code{FUN} to the specified component of the refitted mixture model. } \keyword{methods} \author{Friedrich Leisch and Bettina Gruen} \examples{ data("NPreg", package = "flexmix") ex2 <- flexmix(yn ~ x, data = NPreg, k = 2, model = list(FLXMRglm(yn ~ . + I(x^2)), FLXMRglm(yp ~ ., family = "poisson"))) ex2r <- refit(ex2, method = "mstep") Lapply(ex2r, "vcov", 2) } flexmix/man/FLXMCmvcombi.Rd0000644000176200001440000000407614404637306015234 0ustar liggesusers% % Copyright (C) 2009 Friedrich Leisch and Bettina Gruen % $Id: FLXMCmvcombi.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXMCmvcombi} \alias{FLXMCmvcombi} \title{FlexMix Binary and Gaussian Clustering Driver} \description{ This is a model driver for \code{\link{flexmix}} implementing model-based clustering of a combination of binary and Gaussian data. } \usage{ FLXMCmvcombi(formula = . ~ .) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Only the left-hand side (response) of the formula is used. Default is to use the original \code{\link{flexmix}} model formula.} } \details{ This model driver can be used to cluster mixed-mode binary and Gaussian data. It checks which columns of a matrix contain only zero and ones, and does the same as \code{\link{FLXMCmvbinary}} for them. For the remaining columns of the data matrix independent Gaussian distributions are used (same as \code{\link{FLXMCmvnorm}} with \code{diagonal = FALSE}. The same could be obtained by creating a corresponding list of two models for the respective columns, but \code{FLXMCmvcombi} does a better job in reporting parameters. } \value{ \code{FLXMCmvcombi} returns an object of class \code{FLXMC}. } \author{Friedrich Leisch} \seealso{\code{\link{flexmix}}, \code{\link{FLXMCmvbinary}}, \code{\link{FLXMCmvnorm}}} \keyword{cluster} \examples{ ## create some artificial data x1 <- cbind(rnorm(300), sample(0:1, 300, replace = TRUE, prob = c(0.25, 0.75))) x2 <- cbind(rnorm(300, mean = 2, sd = 0.5), sample(0:1, 300, replace = TRUE, prob = c(0.75, 0.25))) x <- rbind(x1, x2) ## fit the model f1 <- flexmix(x ~ 1, k = 2, model = FLXMCmvcombi()) ## should be similar to the original parameters parameters(f1) table(clusters(f1), rep(1:2, c(300,300))) ## a column with noise should not hurt too much x <- cbind(x, rnorm(600)) f2 <- flexmix(x ~ 1, k = 2, model = FLXMCmvcombi()) parameters(f2) table(clusters(f2), rep(1:2, c(300,300))) } flexmix/man/FLXglmFix.Rd0000644000176200001440000000432514404637306014603 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXglmFix.Rd 5229 2022-06-02 14:47:26Z gruen $ % \name{FLXMRglmfix} \alias{FLXMRglmfix} \alias{FLXglmFix} \title{FlexMix Interface to GLMs with Fixed Coefficients} \description{ This implements a driver for FlexMix which interfaces the \code{glm} family of models and where it is possible to specify fixed (constant) or nested varying coefficients or to ensure that in the Gaussian case the variance estimate is equal for all components. } \usage{ FLXMRglmfix(formula = . ~ ., fixed = ~0, varFix = FALSE, nested = NULL, family = c("gaussian", "binomial", "poisson", "Gamma"), offset = NULL) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{flexmix} using \code{update.formula}. Default is to use the original \code{flexmix} model formula.} \item{fixed}{A formula which specifies the additional regressors for the fixed (constant) coefficients.} \item{varFix}{A logical indicating if the variance estimate for Gaussian components should be constrained to be equal for all components. It can be also a vector specifying the number of components with equal variance.} \item{nested}{An object of class \code{FLXnested} or a list specifying the nested structure.} \item{family}{A character string naming a \code{glm} family function.} \item{offset}{This can be used to specify an \emph{a priori} known component to be included in the linear predictor during fitting.} } \value{ Returns an object of class \code{FLXMRglmfix} inheriting from \code{FLXMRglm} and \code{FLXMRfix}. } \author{Friedrich Leisch and Bettina Gruen} \seealso{\code{FLXMRglm}} \examples{ data("NPreg", package = "flexmix") ex <- flexmix(yn ~ x | id2, data = NPreg, k = 2, cluster = NPreg$class, model = FLXMRglm(yn ~ . + I(x^2))) ex.fix <- flexmix(yn ~ x | id2, data = NPreg, cluster = posterior(ex), model = FLXMRglmfix(nested = list(k = c(1, 1), formula = c(~0, ~I(x^2))))) summary(refit(ex)) \dontrun{ summary(refit(ex.fix)) } } \keyword{regression} \keyword{models} flexmix/man/salmonellaTA98.Rd0000644000176200001440000000342414404637306015537 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: salmonellaTA98.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{salmonellaTA98} \alias{salmonellaTA98} \title{Salmonella Reverse Mutagenicity Assay} \usage{data("salmonellaTA98")} \description{ Data on Ames Salmonella reverse mutagenicity assay. } \format{ This data frame contains the following columns: \describe{ \item{x}{Dose levels of quinoline.} \item{y}{Numbers of revertant colonies of TA98 Salmonella observed on each of three replicate plates tested at each of six dose levels of quinoline diameter.} } } \details{ This data set is taken from package \pkg{dispmod} provided by Luca Scrucca. } \source{ Margolin, B.J., Kaplan, N. and Zeiger, E. Statistical analysis of the Ames Salmonella/microsome test, \emph{Proc. Natl. Acad. Sci. USA}, \bold{76}, 3779--3783, 1981. } \references{ Breslow, N.E. Extra-Poisson variation in log-linear models, \emph{Applied Statistics}, \bold{33}, 38--44, 1984. Wang, P., Puterman, M.L., Cockburn, I.M., and Le, N.D. Mixed Poisson regression models with covariate dependent rates, \emph{Biometrics}, \bold{52}, 381--400, 1996. } \examples{ data("salmonellaTA98", package = "flexmix") salmonMix <- initFlexmix(y ~ 1, data = salmonellaTA98, model = FLXMRglmfix(family = "poisson", fixed = ~ x + log(x + 10)), k = 2, nrep = 5) salmonMix.pr <- predict(salmonMix, newdata = salmonellaTA98) plot(y ~ x, data = salmonellaTA98, pch = as.character(clusters(salmonMix)), ylim = range(c(salmonellaTA98$y, unlist(salmonMix.pr)))) for (i in 1:2) lines(salmonellaTA98$x, salmonMix.pr[[i]], lty = i) } \keyword{datasets} flexmix/man/FLXMRmultinom.Rd0000644000176200001440000000222614404637306015456 0ustar liggesusers\name{FLXMRmultinom} \alias{FLXMRmultinom} \title{FlexMix Interface to Multiomial Logit Models} \description{ Model driver for fitting mixtures of multinomial logit models. } \usage{ FLXMRmultinom(formula = . ~ ., ...) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Default is to use the original \code{\link{flexmix}} model formula.} \item{\dots}{Additional arguments to be passed to \code{nnet.default}.} } \details{ The M-step is performed using \code{nnet.default}. } \value{ Returns an object of class \code{FLXMRmultinom} inheriting from \code{FLXMRglm}. } \references{ Bettina Gruen and Friedrich Leisch. Identifiability of finite mixtures of multinomial logit models with varying and fixed effects. \emph{Journal of Classification}, \bold{25}, 225--247. 2008. } \author{ Bettina Gruen } \section{Warning}{ To ensure identifiability repeated measurements are necessary. Sufficient conditions are given in Gruen and Leisch (2008). } \seealso{\code{\link{FLXMRcondlogit}}} \keyword{regression} \keyword{models} flexmix/man/FLXMRrobglm.Rd0000644000176200001440000000531014404637306015071 0ustar liggesusers% % Copyright (C) 2008 Friedrich Leisch and Bettina Gruen % $Id: FLXMRrobglm.Rd 5229 2022-06-02 14:47:26Z gruen $ % \name{FLXMRrobglm} \alias{FLXMRrobglm} \alias{FLXMRrobglm-class} \title{FlexMix Driver for Robust Estimation of Generalized Linear Models} \description{ This driver adds a noise component to the mixture model which can be used to model background noise in the data. See the Compstat paper Leisch (2008) cited below for details. } \usage{ FLXMRrobglm(formula = . ~ ., family = c("gaussian", "poisson"), bgw = FALSE, ...) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{flexmix} using \code{\link{update.formula}}. Default is to use the original \code{flexmix} model formula.} \item{family}{A character string naming a \code{\link{glm}} family function.} \item{bgw}{Logical, controls whether the parameters of the background component are fixed to multiples of location and scale of the complete data (the default), or estimated by EM with normal weights for the background (\code{bgw = TRUE}).} \item{\dots}{passed to \code{FLXMRglm}} } \value{ Returns an object of class \code{FLXMRrobglm} inheriting from \code{FLXMRglm}. } \author{Friedrich Leisch and Bettina Gruen} \note{ The implementation of this model class is currently under development, and some methods like \code{refit} are still missing. } \references{ Friedrich Leisch. Modelling background noise in finite mixtures of generalized linear regression models. In Paula Brito, editor, Compstat 2008--Proceedings in Computational Statistics, 385--396. Physica Verlag, Heidelberg, Germany, 2008.\cr Preprint available at http://epub.ub.uni-muenchen.de/6332/. } \examples{ ## Example from Compstat paper, see paper for detailed explanation: data("NPreg", package = "flexmix") DATA <- NPreg[, 1:2] set.seed(3) DATA2 <- rbind(DATA, cbind(x = -runif(3), yn = 50 + runif(3))) ## Estimation without (f2) and with (f3) background component f2 <- flexmix(yn ~ x + I(x^2), data = DATA2, k = 2) f3 <- flexmix(yn ~ x + I(x^2), data = DATA2, k = 3, model = FLXMRrobglm(), control = list(minprior = 0)) ## Predict on new data for plots x <- seq(-5,15, by = .1) y2 <- predict(f2, newdata = data.frame(x = x)) y3 <- predict(f3, newdata = data.frame(x = x)) ## f2 was estimated without background component: plot(yn ~ x, data = DATA2, pch = clusters(f2), col = clusters(f2)) lines(x, y2$Comp.1, col = 1) lines(x, y2$Comp.2, col = 2) ## f3 is with background component: plot(yn ~ x, data = DATA2, pch = 4 - clusters(f3), col = 4 - clusters(f3)) lines(x, y3$Comp.2, col = 2) lines(x, y3$Comp.3, col = 1) } \keyword{models} flexmix/man/flexmix-internal.Rd0000644000176200001440000000732214404637306016271 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: flexmix-internal.Rd 5184 2020-06-20 18:27:29Z gruen $ % \name{flexmix-internal} \alias{FLXgetModelmatrix} \alias{FLXcheckComponent} \alias{FLXcheckComponent,FLXM-method} \alias{FLXcheckComponent,FLXMRfix-method} \alias{FLXdeterminePostunscaled} \alias{FLXdeterminePostunscaled,FLXM-method} \alias{FLXdeterminePostunscaled,FLXMRfix-method} \alias{FLXdeterminePostunscaled,FLXMRlmc-method} \alias{FLXdeterminePostunscaled,FLXMRlmmc-method} \alias{FLXdeterminePostunscaled,FLXMRcondlogit-method} \alias{FLXgetK} \alias{FLXgetK,FLXM-method} \alias{FLXgetK,FLXMRfix-method} \alias{FLXgetModelmatrix} \alias{FLXgetModelmatrix,FLXM-method} \alias{FLXgetModelmatrix,FLXMCsparse-method} \alias{FLXgetModelmatrix,FLXMCmvcombi-method} \alias{FLXgetModelmatrix,FLXMRcondlogit-method} \alias{FLXgetModelmatrix,FLXMRfix-method} \alias{FLXgetModelmatrix,FLXMRlmc-method} \alias{FLXgetModelmatrix,FLXMRlmmc-method} \alias{FLXgetModelmatrix,FLXMRmgcv-method} \alias{FLXgetModelmatrix,FLXMRrobglm-method} \alias{FLXgetModelmatrix,FLXMRziglm-method} \alias{FLXgetModelmatrix,FLXP-method} \alias{FLXgetObs} \alias{FLXgetObs,FLXM-method} \alias{FLXgetObs,FLXMRfix-method} \alias{FLXgetObs,FLXMRlmc-method} \alias{FLXmstep} \alias{FLXmstep,FLXM-method} \alias{FLXmstep,FLXMCmvcombi-method} \alias{FLXmstep,FLXMRcondlogit-method} \alias{FLXmstep,FLXMRfix-method} \alias{FLXmstep,FLXMRlmc-method} \alias{FLXmstep,FLXMRlmcfix-method} \alias{FLXmstep,FLXMRlmmc-method} \alias{FLXmstep,FLXMRlmmcfix-method} \alias{FLXmstep,FLXMRmgcv-method} \alias{FLXmstep,FLXMRrobglm-method} \alias{FLXmstep,FLXMRziglm-method} \alias{FLXremoveComponent} \alias{FLXremoveComponent,FLXM-method} \alias{FLXremoveComponent,FLXMRfix-method} \alias{FLXremoveComponent,FLXMRrobglm-method} \alias{FLXremoveComponent,FLXMRziglm-method} \alias{FLXMRglm-class} \alias{FLXR-class} \alias{FLXRMRglm-class} \alias{FLXRPmultinom-class} \alias{summary.flexmix-class} \alias{posterior,FLXM,listOrdata.frame-method} \alias{FLXMRfix-class} \alias{FLXMRglmfix-class} \alias{FLXRMRglmfix-class} \alias{predict,FLXMRglmfix-method} \alias{fitted,FLXMRglmfix-method} \alias{summary,FLXRMRglmfix-method} \alias{listOrdata.frame-class} \alias{refit_optim} \alias{refit_optim,FLXM-method} \alias{refit_optim,FLXMC-method} \alias{refit_optim,FLXMRglm-method} \alias{refit_optim,FLXMRziglm-method} \alias{refit_optim,FLXP-method} \alias{FLXgetDesign} \alias{FLXgetDesign,FLXM-method} \alias{FLXgetDesign,FLXMRglmfix-method} \alias{FLXgetDesign,FLXMRziglm-method} \alias{FLXgetParameters} \alias{FLXgetParameters,FLXdist-method} \alias{FLXgetParameters,FLXM-method} \alias{FLXgetParameters,FLXMC-method} \alias{FLXgetParameters,FLXMRglm-method} \alias{FLXgetParameters,FLXP-method} \alias{FLXgetParameters,FLXPmultinom-method} \alias{FLXreplaceParameters} \alias{FLXreplaceParameters,FLXdist-method} \alias{FLXreplaceParameters,FLXM-method} \alias{FLXreplaceParameters,FLXMC-method} \alias{FLXreplaceParameters,FLXMRglm-method} \alias{FLXreplaceParameters,FLXP-method} \alias{FLXreplaceParameters,FLXPmultinom-method} \alias{FLXlogLikfun} \alias{FLXlogLikfun,flexmix-method} \alias{FLXgradlogLikfun} \alias{FLXgradlogLikfun,flexmix-method} \alias{FLXgradlogLikfun,FLXM-method} \alias{FLXgradlogLikfun,FLXMRglm-method} \alias{FLXgradlogLikfun,FLXP-method} \alias{existGradient} \alias{existGradient,FLXM-method} \alias{existGradient,FLXMRglm-method} \alias{existGradient,FLXMRcondlogit-method} \alias{existGradient,FLXMRglmfix-method} \alias{existGradient,FLXMRmultinom-method} \alias{existGradient,FLXP-method} \title{Internal FlexMix Functions} \description{ Internal flexmix functions, methods and classes. } \details{ These are not to be called by the user. } \keyword{internal} flexmix/man/FLXMRglmnet.Rd0000644000176200001440000000657214404637306015110 0ustar liggesusers\name{FLXMRglmnet} \alias{FLXMRglmnet} \alias{FLXMRglmnet-class} \title{FlexMix Interface for Adaptive Lasso / Elastic Net with GLMs} \description{ This is a driver which allows fitting of mixtures of GLMs where the coefficients are penalized using the (adaptive) lasso or the elastic net by reusing functionality from package \pkg{glmnet}. } \usage{ FLXMRglmnet(formula = . ~ ., family = c("gaussian", "binomial", "poisson"), adaptive = TRUE, select = TRUE, offset = NULL, ...) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Default is to use the original \code{\link{flexmix}} model formula.} \item{family}{A character string naming a \code{\link{glm}} family function.} \item{adaptive}{A logical indicating if the adaptive lasso should be used. By default equal to \code{TRUE}.} \item{select}{A logical vector indicating which variables in the model matrix should be included in the penalized part. By default equal to \code{TRUE} implying that all variables are penalized.} \item{offset}{This can be used to specify an \emph{a priori} known component to be included in the linear predictor during fitting.} \item{\dots}{Additional arguments to be passed to \code{\link[glmnet]{cv.glmnet}} fitter.} } \details{ Some care is needed to ensure convergence of the algorithm, which is computationally more challenging than a standard EM. In the proposed method, not only are cluster allocations identified and component parameters estimated as commonly done in mixture models, but there is also variable selection via penalized regression using $k$-fold cross-validation to choose the penalty parameter. For the algorithm to converge, it is necessary that the same cross-validation partitioning be used across the EM iterations, i.e., the subsamples for cross-validation must be defined at the beginning This is accomplished using the \code{foldid} option as an additional parameter to be passed to \code{\link[glmnet]{cv.glmnet}} (see \pkg{glmnet} package documentation). } \value{ Returns an object of class \code{FLXMRglm}. } \author{ Frederic Mortier and Nicolas Picard. } \seealso{ \code{\link{FLXMRglm}} } \references{ Frederic Mortier, Dakis-Yaoba Ouedraogo, Florian Claeys, Mahlet G. Tadesse, Guillaume Cornu, Fidele Baya, Fabrice Benedet, Vincent Freycon, Sylvie Gourlet-Fleury and Nicolas Picard. Mixture of inhomogeneous matrix models for species-rich ecosystems. \emph{Environmetrics}, \bold{26}(1), 39-51, 2015. doi:10.1002/env.2320 } \examples{ set.seed(12) p <- 10 beta <- matrix(0, nrow = p + 1, ncol = 2) beta[1,] <- c(-1, 1) beta[cbind(c(5, 10), c(1, 2))] <- 1 nobs <- 100 X <- matrix(rnorm(nobs * p), nobs, p) mu <- cbind(1, X) \%*\% beta z <- sample(1:ncol(beta), nobs, replace = TRUE) y <- mu[cbind(1:nobs, z)] + rnorm(nobs) data <- data.frame(y, X) ## The maximum number of iterations is reduced to ## avoid a long running time. fo <- sample(rep(seq(10), length = nrow(data))) ex1 <- flexmix(y ~ ., data = data, k = 2, cluster = z, model = FLXMRglmnet(foldid = fo), control = list(iter.max = 2)) parameters(ex1) } \keyword{regression} \keyword{cluster} flexmix/man/patent.Rd0000644000176200001440000000312614404637306014274 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: patent.Rd 5220 2022-04-18 18:05:04Z gruen $ % \name{patent} \alias{patent} \docType{data} \title{Patents and R&D Spending} \description{ Number of patents, R&D spending and sales in millions of dollar for 70 pharmaceutical and biomedical companies in 1976. } \usage{data("patent")} \format{ A data frame with 70 observations on the following 4 variables. \describe{ \item{Company}{Name of company.} \item{Patents}{Number of patents.} \item{RDS}{R&D spending per sales.} \item{lgRD}{Logarithmized R&D spendings (in millions of dollars).} } } \details{ The data is taken from the National Bureau of Economic Research R&D Masterfile. } \source{ P. Wang, I.M. Cockburn and M.L. Puterman. Analysis of Patent Data -- A Mixed-Poisson-Regression-Model Approach. \emph{Journal of Business & Economic Statistics}, \bold{16}(1), 27--41, 1998. } \references{ B.H. Hall, C. Cummins, E. Laderman and J. Mundy. The R&D Master File Documentation. Technical Working Paper 72, National Bureau of Economic Research, 1988. Cambridge, MA. } \examples{ data("patent", package = "flexmix") patentMix <- initFlexmix(Patents ~ lgRD, k = 3, model = FLXMRglm(family = "poisson"), concomitant = FLXPmultinom(~RDS), nrep = 5, data = patent) plot(Patents ~ lgRD, data = patent, pch = as.character(clusters(patentMix))) ordering <- order(patent$lgRD) apply(fitted(patentMix), 2, function(y) lines(sort(patent$lgRD), y[ordering])) } \keyword{datasets} flexmix/man/dmft.Rd0000644000176200001440000000370214404637306013733 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: dmft.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{dmft} \alias{dmft} \docType{data} \title{Dental Data} \description{ Count data from a dental epidemiological study for evaluation of various programs for reducing caries collected among school children from an urban area of Belo Horizonte (Brazil). } \usage{data("dmft")} \format{ A data frame with 797 observations on the following 5 variables. \describe{ \item{End}{Number of decayed, missing or filled teeth at the end of the study.} \item{Begin}{Number of decayed, missing or filled teeth at the beginning of the study.} \item{Gender}{A factor with levels \code{male} and \code{female}.} \item{Ethnic}{A factor with levels \code{brown}, \code{white} and \code{black}.} \item{Treatment}{A factor with levels \code{control}, \code{educ}, \code{enrich}, \code{rinse}, \code{hygiene} and \code{all}.} } } \details{ The aim of the caries prevention study was to compare four methods to prevent dental caries. Interventions were carried out according to the following scheme: \describe{ \item{control}{Control group} \item{educ}{Oral health education} \item{enrich}{Enrichment of the school diet with rice bran} \item{rinse}{Mouthwash with 0.2\% sodium floride (NaF) solution} \item{hygiene}{Oral hygiene} \item{all}{All four methods together} } } \source{ D. Boehning, E. Dietz, P. Schlattmann, L. Mendonca and U. Kirchner. The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology. \emph{Journal of the Royal Statistical Society A}, \bold{162}(2), 195--209, 1999. } \examples{ data("dmft", package = "flexmix") dmft_flx <- initFlexmix(End ~ 1, data = dmft, k = 2, model = FLXMRglmfix(family = "poisson", fixed = ~ Gender + Ethnic + Treatment)) } \keyword{datasets} flexmix/man/ICL.Rd0000644000176200001440000000245414404637306013413 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: ICL.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{ICL} \alias{ICL,flexmix-method} \alias{ICL,stepFlexmix-method} \title{Integrated Completed Likelihood Criterion} \description{ Compute the Integrated Completed Likelihood criterion for model selection. } \usage{ \S4method{ICL}{flexmix}(object, \dots) \S4method{ICL}{stepFlexmix}(object, \dots) } \arguments{ \item{object}{see Methods section below} \item{\dots}{Some methods for this generic function may take additional, optional arguments. At present none do.} } \section{Methods}{ \describe{ \item{object = "flexmix":}{Compute the ICL of a \code{flexmix} object.} \item{object = "stepFlexmix":}{Compute the ICL of all models contained in the \code{stepFlexmix} object.} }} \value{ Returns a numeric vector with the corresponding ICL value(s). } \keyword{methods} \author{Friedrich Leisch and Bettina Gruen} \references{ C. Biernacki, G. Celeux, and G. Govaert. Assessing a mixture model for clustering with the integrated completed likelihood. \emph{IEEE Transactions on Pattern Analysis and Machine Intelligence}, \emph{22}(7), 719--725, 2000. } \examples{ data("NPreg", package = "flexmix") ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2) ICL(ex1) } flexmix/man/FLXfit.Rd0000644000176200001440000000227014404637306014134 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXfit.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXfit} \alias{FLXfit} \alias{FLXfit,list-method} \title{Fitter Function for FlexMix Models} \description{ This is the basic computing engine called by \code{\link{flexmix}}, it should usually not be used directly. } \usage{ FLXfit(model, concomitant, control, postunscaled = NULL, groups, weights) } \arguments{ \item{model}{List of \code{FLXM} objects.} \item{concomitant}{Object of class \code{FLXP}.} \item{control}{Object of class \code{FLXcontrol}.} \item{weights}{A numeric vector of weights to be used in the fitting process.} \item{postunscaled}{Initial a-posteriori probabilities of the observations at the start of the EM algorithm.} \item{groups}{List with components \code{group} which is a factor with optional grouping of observations and \code{groupfirst} which is a logical vector for the first observation of each group.} } \value{ Returns an object of class \code{flexmix}. } \author{Friedrich Leisch and Bettina Gruen} \seealso{\code{\link{flexmix}}, \code{\link{flexmix-class}}} \keyword{regression} \keyword{cluster} flexmix/man/FLXMRlmer.Rd0000644000176200001440000000767614404637306014567 0ustar liggesusers\name{FLXMRlmer} \alias{FLXMRlmer} \alias{FLXMRlmer-class} \alias{FLXMRlmm-class} \alias{FLXMRlmmfix-class} \alias{FLXdeterminePostunscaled,FLXMRlmer-method} \alias{FLXdeterminePostunscaled,FLXMRlmm-method} \alias{FLXmstep,FLXMRlmer-method} \alias{FLXmstep,FLXMRlmm-method} \alias{FLXgetModelmatrix,FLXMRlmer-method} \alias{FLXgetModelmatrix,FLXMRlmm-method} \alias{FLXMRlmm} \alias{FLXgetObs,FLXMRlmm-method} \alias{FLXmstep,FLXMRlmmfix-method} \alias{predict,FLXMRlmm-method} \alias{rFLXM,FLXMRlmm,FLXcomponent-method} \alias{rFLXM,FLXMRlmm,list-method} \alias{rFLXM,FLXMRlmc,FLXcomponent-method} \alias{rFLXM,FLXMRlmer,FLXcomponent-method} \title{FlexMix Interface to Linear Mixed Models} \description{ This is a driver which allows fitting of mixtures of linear models with random effects. } \usage{ FLXMRlmm(formula = . ~ ., random, lm.fit = c("lm.wfit", "smooth.spline"), varFix = c(Random = FALSE, Residual = FALSE), \dots) FLXMRlmer(formula = . ~ ., random, weighted = TRUE, control = list(), eps = .Machine$double.eps) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{flexmix} using \code{\link{update.formula}}. Default is to use the original \code{flexmix} model formula.} \item{random}{A formula for specifying the random effects.} \item{weighted}{A logical indicating if the model should be estimated with weighted ML.} \item{control}{A list of control parameters. See \code{\link[lme4]{lmer}} for details.} \item{eps}{Observations with a component-specific posterior smaller than \code{eps} are omitted in the M-step for this component.} \item{lm.fit}{A character string indicating if the coefficients should be fitted using either a linear model or the function \code{smooth.spline}} \item{varFix}{Named logical vector of length 2 indicating if the variance of the random effects and the residuals are fixed over the components.} \item{\dots}{Additional arguments to be passed to \code{smooth.spline}.} } \details{ \code{FLXMRlmm} allows only one random effect. \code{FLXMRlmer} allows an arbitrary number of random effects if \code{weighted = FALSE}; a certain structure of the model matrix of the random effects has to be given for weighted ML estimation, i.e. where \code{weighted = TRUE}. } \value{ Returns an object of class \code{FLXMRlmer} and \code{FLXMRlmm} inheriting from \code{FLXMRglm} and \code{FLXMR}, respectively. } \section{Warning}{ For \code{FLXMRlmer} the weighted ML estimation is only correct if the covariate matrix of the random effects is the same for each observation. By default weighted ML estimation is made and the condition on the covariate matrix of the random effects is checked. If this fails, only estimation with \code{weighted = FALSE} is possible which will maximize the classification likelihood. } \author{Bettina Gruen} \examples{ id <- rep(1:50, each = 10) x <- rep(1:10, 50) sample <- data.frame(y = rep(rnorm(unique(id)/2, 0, c(5, 2)), each = 10) + rnorm(length(id), rep(c(3, 8), each = 10)) + rep(c(0, 3), each = 10) * x, x = x, id = factor(id)) fitted <- flexmix(.~.|id, k = 2, model = FLXMRlmm(y ~ x, random = ~ 1), data = sample, control = list(tolerance = 10^-3), cluster = rep(rep(1:2, each = 10), 25)) parameters(fitted) fitted1 <- flexmix(.~.|id, k = 2, model = FLXMRlmer(y ~ x, random = ~ 1), data = sample, control = list(tolerance = 10^-3), cluster = rep(rep(1:2, each = 10), 25)) parameters(fitted1) fitted2 <- flexmix(.~.|id, k = 2, model = FLXMRlmm(y ~ 0 + x, random = ~ 1, lm.fit = "smooth.spline"), data = sample, control = list(tolerance = 10^-3), cluster = rep(rep(1:2, each = 10), 25)) parameters(fitted2) } \keyword{models} flexmix/man/plotEll.Rd0000644000176200001440000000253514404637306014417 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: plotEll.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{plotEll} \alias{plotEll} \title{Plot Confidence Ellipses for FLXMCmvnorm Results} \description{ Plot 50\% and 95\% confidence ellipses for mixtures of Gaussians fitted using \code{\link{FLXMCmvnorm}}. } \usage{ plotEll(object, data, which = 1:2, model = 1, project = NULL, points = TRUE, eqscale = TRUE, col = NULL, number = TRUE, cex = 1.5, numcol = "black", pch = NULL, ...) } \arguments{ \item{object}{An object of class \code{flexmix} with a fitted \code{FLXMCmvnorm} model.} \item{data}{The response variable in a data frame or as a matrix.} \item{which}{Index numbers of dimensions of (projected) input space to plot.} \item{model}{The model (for a multivariate response) that shall be plotted.} \item{project}{Projection object, currently only the result of \code{\link[stats]{prcomp}} is supported.} \item{points}{Logical, shall data points be plotted?} \item{eqscale}{Logical, plot using \code{\link[MASS]{eqscplot}}?} \item{number}{Logical, plot number labels at cluster centers?} \item{cex, numcol}{Size and color of number labels.} \item{pch, col, \dots}{Graphical parameters.} } \author{Friedrich Leisch and Bettina Gruen} \seealso{\code{\link{FLXMCmvnorm}}} \keyword{cluster} flexmix/man/boot.Rd0000644000176200001440000000607314404637306013750 0ustar liggesusers\name{boot} \alias{boot} \alias{boot,flexmix-method} \alias{LR_test} \alias{LR_test,flexmix-method} \alias{boot,flexmix-method} \alias{show,FLXboot-method} \alias{FLXboot-class} \alias{plot,FLXboot,missing-method} \alias{parameters,FLXboot-method} \alias{clusters,FLXboot,listOrdata.frame-method} \alias{predict,FLXboot-method} \alias{posterior,FLXboot,listOrdata.frame-method} \title{Bootstrap a flexmix Object} \description{ Given a \code{flexmix} object perform parametric or empirical bootstrap. } \usage{ boot(object, ...) \S4method{boot}{flexmix}(object, R, sim = c("ordinary", "empirical", "parametric"), initialize_solution = FALSE, keep_weights = FALSE, keep_groups = TRUE, verbose = 0, control, k, model = FALSE, ...) LR_test(object, ...) \S4method{LR_test}{flexmix}(object, R, alternative = c("greater", "less"), control, ...) } \arguments{ \item{object}{A fitted finite mixture model of class \code{flexmix}.} \item{R}{The number of bootstrap replicates.} \item{sim}{A character string indicating the type of simulation required. Possible values are \code{"ordinary"} (the default), \code{"parametric"}, or \code{"empirical"}.} \item{initialize_solution}{A logical. If \code{TRUE} the EM algorithm is initialized in the given solution.} \item{keep_weights}{A logical. If \code{TRUE} the weights are kept.} \item{keep_groups}{A logical. If \code{TRUE} the groups are kept.} \item{verbose}{If a positive integer, then progress information is reported every \code{verbose} iterations. If 0, no output is generated during the bootstrap replications.} \item{control}{Object of class \code{FLXcontrol} or a named list. If missing the control of the fitted \code{object} is taken.} \item{k}{Vector of integers specifying for which number of components finite mixtures are fitted to the bootstrap samples. If missing the number of components of the fitted \code{object} are taken.} \item{alternative}{A character string specifying the alternative hypothesis, must be either \code{"greater"} (default) or \code{"less"} indicating if the alternative hypothesis is that the mixture has one more component or one less.} \item{model}{A logical. If \code{TRUE} the model and the weights slot for each sample are stored and returned.} \item{\dots}{Further arguments to be passed to or from methods.} } \value{ \code{boot} returns an object of class \code{FLXboot} which contains the fitted parameters, the fitted priors, the log likelihoods, the number of components of the fitted mixtures and the information if the EM algorithm has converged. \code{LR_test} returns an object of class \code{htest} containing the number of valid bootstrap replicates, the p-value, the - twice log likelihood ratio test statistics for the original data and the bootstrap replicates. } \author{Bettina Gruen} \examples{ data("NPreg", package = "flexmix") fitted <- initFlexmix(yn ~ x + I(x^2) | id2, data = NPreg, k = 2) \dontrun{ lrtest <- LR_test(fitted, alternative = "greater", R = 20, verbose = 1) } } \keyword{methods} flexmix/man/rflexmix.Rd0000644000176200001440000000315614404637306014642 0ustar liggesusers\name{rflexmix} \alias{rflexmix} \alias{rflexmix,flexmix,missing-method} \alias{rflexmix,FLXdist,numeric-method} \alias{rflexmix,FLXdist,listOrdata.frame-method} \alias{rFLXM} \alias{rFLXM,FLXM,list-method} \alias{rFLXM,FLXMC,FLXcomponent-method} \alias{rFLXM,FLXMCmultinom,FLXcomponent-method} \alias{rFLXM,FLXMCbinom,FLXcomponent-method} \alias{rFLXM,FLXMRglm,list-method} \alias{rFLXM,FLXMRglmfix,list-method} \alias{rFLXM,FLXM,FLXcomponent-method} \alias{rFLXM,FLXMRglm,FLXcomponent-method} \title{Random Number Generator for Finite Mixtures} \description{ Given a finite mixture model generate random numbers from it. } \usage{ rflexmix(object, newdata, ...) } \arguments{ \item{object}{A fitted finite mixture model of class \code{flexmix} or an unfitted of class \code{FLXdist}.} \item{newdata}{Optionally, a data frame in which to look for variables with which to predict or an integer specifying the number of random draws for model-based clustering. If omitted, the data to which the model was fitted is used.} \item{\dots}{Further arguments to be passed to or from methods.} } \details{ \code{rflexmix} provides the creation of the model matrix for new data and the sampling of the cluster memberships. The sampling of the component distributions given the classification is done by calling \code{rFLXM}. This step has to be provided for the different model classes. } \value{ A list with components \item{y}{Random sample} \item{group}{Grouping factor} \item{class}{Class membership} } \author{Bettina Gruen} \examples{ example(flexmix) sample <- rflexmix(ex1) } \keyword{distribution} flexmix/man/FLXMRcondlogit.Rd0000644000176200001440000000441614404637306015577 0ustar liggesusers\name{FLXMRcondlogit} \alias{FLXMRcondlogit} \title{FlexMix Interface to Conditional Logit Models} \description{ Model driver for fitting mixtures of conditional logit models. } \usage{ FLXMRcondlogit(formula = . ~ ., strata) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Default is to use the original \code{\link{flexmix}} model formula.} \item{strata}{A formula which is interpreted such that no intercept is fitted and which allows to determine the variable indicating which observations are from the same stratum.} } \details{ The M-step is performed using \code{coxph.fit}. } \value{ Returns an object of class \code{FLXMRcondlogit} inheriting from \code{FLXMRglm}. } \references{ Bettina Gruen and Friedrich Leisch. Identifiability of finite mixtures of multinomial logit models with varying and fixed effects. \emph{Journal of Classification}, \bold{25}, 225--247. 2008. } \author{ Bettina Gruen } \section{Warning}{ To ensure identifiability repeated measurements are necessary. Sufficient conditions are given in Gruen and Leisch (2008). } \seealso{\code{\link{FLXMRmultinom}}} \examples{ if (require("Ecdat")) { data("Catsup", package = "Ecdat") ## To reduce the time needed for the example only a subset is used Catsup <- subset(Catsup, id \%in\% 1:100) Catsup$experiment <- seq_len(nrow(Catsup)) vnames <- c("display", "feature", "price") Catsup_long <- reshape(Catsup, idvar = c("id", "experiment"), times = c(paste("heinz", c(41, 32, 28), sep = ""), "hunts32"), timevar = "brand", varying = matrix(colnames(Catsup)[2:13], nrow = 3, byrow = TRUE), v.names = vnames, direction = "long") Catsup_long$selected <- with(Catsup_long, choice == brand) Catsup_long <- Catsup_long[, c("id", "selected", "experiment", vnames, "brand")] Catsup_long$brand <- relevel(factor(Catsup_long$brand), "hunts32") set.seed(0808) flx1 <- flexmix(selected ~ display + feature + price + brand | id, model = FLXMRcondlogit(strata = ~ experiment), data = Catsup_long, k = 1) } } \keyword{regression} \keyword{models} flexmix/man/plot-methods.Rd0000644000176200001440000000727614404637306015432 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: plot-methods.Rd 5115 2017-04-07 08:18:13Z gruen $ % \name{plot-methods} \docType{methods} \alias{plot-methods} \alias{plot,flexmix,missing-method} \title{Rootogram of Posterior Probabilities} \description{ The \code{plot} method for \code{\link{flexmix-class}} objects gives a rootogram or histogram of the posterior probabilities. } \usage{ \S4method{plot}{flexmix,missing}(x, y, mark = NULL, markcol = NULL, col = NULL, eps = 1e-4, root = TRUE, ylim = TRUE, main = NULL, xlab = "", ylab = "", as.table = TRUE, endpoints = c(-0.04, 1.04), ...) } \arguments{ \item{x}{An object of class \code{"flexmix"}.} \item{y}{Not used.} \item{mark}{Integer: mark posteriors of this component.} \item{markcol}{Color used for marking components.} \item{col}{Color used for the bars.} \item{eps}{Posteriors smaller than \code{eps} are ignored.} \item{root}{If \code{TRUE}, a rootogram of the posterior probabilities is drawn, otherwise a standard histogram.} \item{ylim}{A logical value or a numeric vector of length 2. If \code{TRUE}, the y axes of all rootograms are aligned to have the same limits, if \code{FALSE} each y axis is scaled separately. If a numeric vector is specified it is used as usual.} \item{main}{Main title of the plot.} \item{xlab}{Label of x-axis.} \item{ylab}{Label of y-axis.} \item{as.table}{Logical that controls the order in which panels should be plotted: if \code{FALSE} (the default), panels are drawn left to right, bottom to top (as in a graph); if \code{TRUE}, left to right, top to bottom.} \item{endpoints}{Vector of length 2 indicating the range of x-values that is to be covered by the histogram. This applies only when \code{breaks} is unspecified. In \code{do.breaks}, this specifies the interval that is to be divided up.} \item{...}{Further graphical parameters for the lattice function histogram.} } \details{ For each mixture component a rootogram or histogram of the posterior probabilities of all observations is drawn. Rootograms are very similar to histograms, the only difference is that the height of the bars correspond to square roots of counts rather than the counts themselves, hence low counts are more visible and peaks less emphasized. Please note that the y-axis denotes the number of observations in each bar in any case. Usually in each component a lot of observations have posteriors close to zero, resulting in a high count for the corresponding bin in the rootogram which obscures the information in the other bins. To avoid this problem, all probabilities with a posterior below \code{eps} are ignored. A peak at probability one indicates that a mixture component is well seperated from the other components, while no peak at one and/or significant mass in the middle of the unit interval indicates overlap with other components. } \references{ Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. \emph{Journal of Statistical Software}, \bold{11}(8), 2004. doi:10.18637/jss.v011.i08 Jeremy Tantrum, Alejandro Murua and Werner Stuetzle. Assessment and pruning of hierarchical model based clustering. Proceedings of the 9th ACM SIGKDD international conference on Knowledge Discovery and Data Mining, 197--205. ACM Press, New York, NY, USA, 2003. Friedrich Leisch. Exploring the structure of mixture model components. In Jaromir Antoch, editor, Compstat 2004--Proceedings in Computational Statistics, 1405--1412. Physika Verlag, Heidelberg, Germany, 2004. ISBN 3-7908-1554-3. } \author{Friedrich Leisch and Bettina Gruen} \keyword{methods} \keyword{hplot} flexmix/man/relabel.Rd0000644000176200001440000000357314404637306014415 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: posterior.Rd 3937 2008-03-28 14:56:01Z leisch $ % \name{relabel} \alias{relabel} \alias{relabel,FLXdist,missing-method} \alias{relabel,FLXdist,character-method} \alias{relabel,FLXdist,integer-method} \title{Relabel the Components} \description{ The components are sorted by the value of one of the parameters or according to an integer vector containing the permutation of the numbers from 1 to the number of components. } \usage{ relabel(object, by, ...) \S4method{relabel}{FLXdist,character}(object, by, which = NULL, ...) } \arguments{ \item{object}{An object of class \code{"flexmix"}.} \item{by}{If a character vector, it needs to be one of \code{"prior"}, \code{"model"}, \code{"concomitant"} indicating if the parameter should be from the component-specific or the concomitant variable model. If an integer vector it indicates how the components should be sorted. If missing, the components are sorted by component size.} \item{which}{Name (or unique substring) of a parameter if \code{by} is equal to "model" or "concomitant".} \item{\dots}{Currently not used.} } \author{Friedrich Leisch and Bettina Gruen} \keyword{methods} \examples{ set.seed(123) beta <- matrix(1:16, ncol = 4) beta df1 <- ExLinear(beta, n = 100, sd = .5) f1 <- flexmix(y~., data = df1, k = 4) ## There was label switching, parameters are not in the same order ## as in beta: round(parameters(f1)) betas <- rbind(beta, .5) betas ## This makes no sense: summary(abs(as.vector(betas-parameters(f1)))) ## We relabel the components by sorting the coefficients of x1: r1 <- relabel(f1, by = "model", which = "x1") round(parameters(r1)) ## Now we can easily compare the fit with the true parameters: summary(abs(as.vector(betas-parameters(r1)))) } flexmix/man/bioChemists.Rd0000644000176200001440000000240014404637306015244 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: bioChemists.Rd 5193 2020-10-09 18:38:20Z gruen $ % \name{bioChemists} \alias{bioChemists} \docType{data} \title{Articles by Graduate Students in Biochemistry Ph.D. Programs} \description{ A sample of 915 biochemistry graduate students. } \usage{ data("bioChemists") } \format{ \describe{ \item{art}{count of articles produced during last 3 years of Ph.D.} \item{fem}{factor indicating gender of student, with levels Men and Women} \item{mar}{factor indicating marital status of student, with levels Single and Married} \item{kid5}{number of children aged 5 or younger} \item{phd}{prestige of Ph.D. department} \item{ment}{count of articles produced by Ph.D. mentor during last 3 years} } } \details{ This data set is taken from package \pkg{pscl} provided by Simon Jackman. } \source{ found in Stata format at \url{https://jslsoc.sitehost.iu.edu/stata/spex_data/couart2.dta} } \references{ Long, J. Scott. The origins of sex difference in science. \emph{Social Forces}, \bold{68}, 1297--1315, 1990. Long, J. Scott. \emph{Regression Models for Categorical and Limited Dependent Variables}, 1997. Thousand Oaks, California: Sage. } \keyword{datasets} flexmix/man/tribolium.Rd0000644000176200001440000000356614404637306015017 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: tribolium.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{tribolium} \alias{tribolium} \docType{data} \title{Tribolium Beetles} \description{ The data investigates whether the adult Tribolium species Castaneum has developed an evolutionary advantage to recognize and avoid eggs of their own species while foraging. } \usage{data("tribolium")} \format{ A data frame with 27 observations on the following 4 variables. \describe{ \item{\code{Remaining}}{A numeric vector.} \item{\code{Total}}{A numeric vector.} \item{\code{Replicate}}{A factor with levels \code{1}, \code{2}, \code{3}.} \item{\code{Species}}{A factor with levels \code{Castaneum} \code{Confusum} \code{Madens}.} } } \details{ Beetles of the genus Tribolium are cannibalistic in the sense that adults eat the eggs of their own species as well as those of closely related species. The experiment isolated a number of adult beetles of the same species and presented them with a vial of 150 eggs (50 of each type), the eggs being thoroughly mixed to ensure uniformity throughout the vial. The data gives the consumption data for adult Castaneum species. It reports the number of Castaneum, Confusum and Madens eggs, respectively, that remain uneaten after two day exposure to the adult beetles. Replicates 1, 2, and 3 correspond to different occasions on which the experiment was conducted. } \source{ P. Wang and M.L. Puterman. Mixed Logistic Regression Models. \emph{Journal of Agricultural, Biological, and Environmental Statistics}, \bold{3} (2), 175--200, 1998. } \examples{ data("tribolium", package = "flexmix") tribMix <- initFlexmix(cbind(Remaining, Total - Remaining) ~ Species, k = 2, nrep = 5, data = tribolium, model = FLXMRglm(family = "binomial")) } \keyword{datasets} flexmix/man/BIC-methods.Rd0000644000176200001440000000105014404637306015031 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: BIC-methods.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{BIC-methods} \docType{methods} \title{Methods for Function BIC} \alias{BIC,flexmix-method} \alias{BIC,stepFlexmix-method} \description{Compute the Bayesian Information Criterion.} \section{Methods}{ \describe{ \item{object = flexmix:}{Compute the BIC of a \code{flexmix} object} \item{object = stepFlexmix:}{Compute the BIC of all models contained in the \code{stepFlexmix} object.} } } \keyword{methods} flexmix/man/AIC-methods.Rd0000644000176200001440000000104614404637306015035 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: AIC-methods.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{AIC-methods} \docType{methods} \title{Methods for Function AIC} \alias{AIC,flexmix-method} \alias{AIC,stepFlexmix-method} \description{Compute the Akaike Information Criterion.} \section{Methods}{ \describe{ \item{object = flexmix:}{Compute the AIC of a \code{flexmix} object} \item{object = stepFlexmix:}{Compute the AIC of all models contained in the \code{stepFlexmix} object.} } } \keyword{methods} flexmix/man/trypanosome.Rd0000644000176200001440000000321514404637306015360 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: trypanosome.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{trypanosome} \alias{trypanosome} \docType{data} \title{Trypanosome} \description{ Trypanosome data from a dosage-response analysis to assess the proportion of organisms belonging to different populations. It is assumed that organisms belonging to different populations are indistinguishable other than in terms of their reaction to the stimulus. } \usage{data("trypanosome")} \format{ A data frame with 426 observations on the following 2 variables. \describe{ \item{\code{Dead}}{A logical vector.} \item{\code{Dose}}{A numeric vector.} } } \details{ The experimental technique involved inspection under the microscope of a representative aliquot of a suspension, all organisms appearing within two fields of view being classified either alive or dead. Hence the total numbers of organisms present at each dose and the number showing the quantal response were both random variables. } \source{ R. Ashford and P.J. Walker. Quantal Response Analysis for a Mixture of Populations. \emph{Biometrics}, \bold{28}, 981--988, 1972. } \references{ D.A. Follmann and D. Lambert. Generalizing Logistic Regression by Nonparametric Mixing. \emph{Journal of the American Statistical Association}, \bold{84}(405), 195--300, 1989. } \examples{ data("trypanosome", package = "flexmix") trypMix <- initFlexmix(cbind(Dead, 1-Dead) ~ 1, k = 2, nrep = 5, data = trypanosome, model = FLXMRglmfix(family = "binomial", fixed = ~log(Dose))) } \keyword{datasets} flexmix/man/FLXMCmvpois.Rd0000644000176200001440000000175714404637306015120 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXMCmvpois.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXMCmvpois} \alias{FLXMCmvpois} \title{FlexMix Poisson Clustering Driver} \description{ This is a model driver for \code{\link{flexmix}} implementing model-based clustering of Poisson distributed data. } \usage{ FLXMCmvpois(formula = . ~ .) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Only the left-hand side (response) of the formula is used. Default is to use the original \code{\link{flexmix}} model formula.} } \details{ This can be used to cluster Poisson distributed data where given the component membership the variables are mutually independent. } \value{ \code{FLXMCmvpois} returns an object of class \code{FLXMC}. } \author{Friedrich Leisch and Bettina Gruen} \seealso{\code{\link{flexmix}}} \keyword{cluster} flexmix/man/FLXMRmgcv.Rd0000644000176200001440000000402214404637306014542 0ustar liggesusers\name{FLXMRmgcv} \alias{FLXMRmgcv} \alias{FLXMRmgcv-class} \title{FlexMix Interface to GAMs} \description{ This is a driver which allows fitting of mixtures of GAMs. } \usage{ FLXMRmgcv(formula = . ~ ., family = c("gaussian", "binomial", "poisson"), offset = NULL, control = NULL, optimizer = c("outer", "newton"), in.out = NULL, eps = .Machine$double.eps, ...) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Default is to use the original \code{\link{flexmix}} model formula.} \item{family}{A character string naming a \code{\link{glm}} family function.} \item{offset}{This can be used to specify an \emph{a priori} known component to be included in the linear predictor during fitting.} \item{control}{A list of fit control parameters returned by \code{gam.control}.} \item{optimizer}{An array specifying the numerical optimization method to use to optimize the smoothing parameter estimation criterion; for more details see \code{\link[mgcv]{gam}}.} \item{in.out}{Optional list for initializing outer iteration; for more details see \code{\link[mgcv]{gam}}.} \item{eps}{Observations with an a-posteriori probability smaller or equal to \code{eps} are omitted in the M-step.} \item{\dots}{Additional arguments to be pased to the GAM fitter.} } \value{ Returns an object of class \code{FLXMRmgcv} inheriting from \code{FLXMRglm}. } \author{ Bettina Gruen } \seealso{ \code{\link{FLXMRglm}} } \examples{ set.seed(2012) x <- seq(0, 1, length.out = 100) z <- sample(0:1, length(x), replace = TRUE) y <- rnorm(length(x), ifelse(z, 5 * sin(x * 2 * pi), 10 * x - 5)) fitted_model <- flexmix(y ~ s(x), model = FLXMRmgcv(), cluster = z + 1, control = list(tolerance = 10^-3)) plot(y ~ x, col = clusters(fitted_model)) matplot(x, fitted(fitted_model), type = "l", add = TRUE) } \keyword{regression} \keyword{cluster} flexmix/man/Mehta.Rd0000644000176200001440000000265514404637306014045 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: Mehta.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{Mehta} \alias{Mehta} \docType{data} \title{Mehta Trial} \description{ For a 22-centre trial the number of responses and the total number of patients is reported for the control group and the group receiving a new drug. } \usage{data("Mehta")} \format{ A data frame with 44 observations on the following 4 variables. \describe{ \item{Response}{Number of responses.} \item{Total}{Total number of observations.} \item{Drug}{A factor indicating treatment with levels \code{New} and \code{Control}.} \item{Site}{A factor indicating the site/centre.} } } \source{ M. Aitkin. Meta-analysis by random effect modelling in generalized linear models. \emph{Statistics in Medicine}, \bold{18}, 2343--2351, 1999. } \references{ C.R. Mehta, N.R. Patel and P. Senchaudhuri. Importance sampling for estimating exact probabilities in permutational inference. \emph{Journal of the American Statistical Association}, \emph{83}, 999--1005, 1988. } \examples{ data("Mehta", package = "flexmix") mehtaMix <- initFlexmix(cbind(Response, Total-Response) ~ 1|Site, data = Mehta, nrep = 5, k = 3, model = FLXMRglmfix(family = "binomial", fixed = ~ Drug), control = list(minprior = 0.04)) } \keyword{datasets} flexmix/man/FLXmodel-class.Rd0000644000176200001440000000402514404637306015555 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXmodel-class.Rd 5229 2022-06-02 14:47:26Z gruen $ % \name{FLXM-class} \docType{class} \alias{FLXM-class} \alias{FLXMC-class} \alias{FLXMR-class} \alias{FLXMCsparse-class} \alias{show,FLXM-method} \title{Class "FLXM"} \description{FlexMix model specification.} \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("FLXM", ...)}, typically inside driver functions like \code{\link{FLXMRglm}} or \code{\link{FLXMCmvnorm}}. } \section{Slots}{ \describe{ \item{\code{fit}:}{Function returning an \code{FLXcomponent} object.} \item{\code{defineComponent}:}{Function or expression to determine the \code{FLXcomponent} object given the parameters.} \item{\code{weighted}:}{Logical indicating whether \code{fit} can do weighted likelihood maximization.} \item{\code{name}:}{Character string used in print methods.} \item{\code{formula}:}{Formula describing the model.} \item{\code{fullformula}:}{Resulting formula from updating the model formula with the formula specified in the call to \code{flexmix}.} \item{\code{x}:}{Model matrix.} \item{\code{y}:}{Model response.} \item{\code{terms}, \code{xlevels}, \code{contrasts}:}{Additional information for model matrix.} \item{\code{preproc.x}:}{Function for preprocessing matrix \code{x} before the EM algorithm starts, by default the identity function.} \item{\code{preproc.y}:}{Function for preprocessing matrix \code{y} before the EM algorithm starts, by default the identity function.} } } \details{ The most generic class is the virtual class \code{FLXM}. The classes \code{FLXMC} for model-based clustering and \code{FLXMR} for clusterwise regression extend the virtual class. Both have further more specific model classes which inherit from them. Model class \code{FLXMCsparse} allows for model-based clustering with a sparse matrix as data input. } \author{Friedrich Leisch and Bettina Gruen} \keyword{classes} flexmix/man/FLXmclust.Rd0000644000176200001440000000465314404637306014670 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXmclust.Rd 5115 2017-04-07 08:18:13Z gruen $ % \name{FLXMCmvnorm} \alias{FLXMCmvnorm} \alias{FLXMCnorm1} \alias{FLXmclust} \title{FlexMix Clustering Demo Driver} \description{ These are demo drivers for \code{\link{flexmix}} implementing model-based clustering of Gaussian data. } \usage{ FLXMCmvnorm(formula = . ~ ., diagonal = TRUE) FLXMCnorm1(formula = . ~ .) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Only the left-hand side (response) of the formula is used. Default is to use the original \code{\link{flexmix}} model formula.} \item{diagonal}{If \code{TRUE}, then the covariance matrix of the components is restricted to diagonal matrices.} } \details{ This is mostly meant as a demo for FlexMix driver programming, you should also look at package \pkg{mclust} for real applications. \code{FLXMCmvnorm} clusters multivariate data, \code{FLXMCnorm1} univariate data. In the latter case smart initialization is important, see the example below. } \value{ \code{FLXMCmvnorm} returns an object of class \code{FLXMC}. } \author{Friedrich Leisch and Bettina Gruen} \references{ Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. \emph{Journal of Statistical Software}, \bold{11}(8), 2004. doi:10.18637/jss.v011.i08 } \seealso{\code{\link{flexmix}}} \keyword{cluster} \examples{ data("Nclus", package = "flexmix") require("MASS") eqscplot(Nclus) ## This model is wrong (one component has a non-diagonal cov matrix) ex1 <- flexmix(Nclus ~ 1, k = 4, model = FLXMCmvnorm()) print(ex1) plotEll(ex1, Nclus) ## True model, wrong number of components ex2 <- flexmix(Nclus ~ 1, k = 6, model = FLXMCmvnorm(diagonal = FALSE)) print(ex2) plotEll(ex2, Nclus) ## Get parameters of first component parameters(ex2, component = 1) ## Have a look at the posterior probabilies of 10 random observations ok <- sample(1:nrow(Nclus), 10) p <- posterior(ex2)[ok, ] p ## The following two should be the same max.col(p) clusters(ex2)[ok] \testonly{ stopifnot(all.equal(max.col(p), clusters(ex2)[ok])) } ## Now try the univariate case plot(density(Nclus[, 1])) ex3 <- flexmix(Nclus[, 1] ~ 1, cluster = cut(Nclus[, 1], 3), model = FLXMCnorm1()) ex3 parameters(ex3) } flexmix/man/stepFlexmix.Rd0000644000176200001440000001451414404637306015314 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: stepFlexmix.Rd 5115 2017-04-07 08:18:13Z gruen $ % \name{stepFlexmix} \alias{stepFlexmix} \alias{initFlexmix} \alias{initMethod} \alias{stepFlexmix-class} \alias{initMethod-class} \alias{plot,stepFlexmix,missing-method} \alias{show,stepFlexmix-method} \alias{getModel,stepFlexmix-method} \alias{unique,stepFlexmix-method} \title{Run FlexMix Repeatedly} \description{ Runs flexmix repeatedly for different numbers of components and returns the maximum likelihood solution for each. } \usage{ initFlexmix(..., k, init = list(), control = list(), nrep = 3L, verbose = TRUE, drop = TRUE, unique = FALSE) initMethod(name = c("tol.em", "cem.em", "sem.em"), step1 = list(tolerance = 10^-2), step2 = list(), control = list(), nrep = 3L) stepFlexmix(..., k = NULL, nrep = 3, verbose = TRUE, drop = TRUE, unique = FALSE) \S4method{plot}{stepFlexmix,missing}(x, y, what = c("AIC", "BIC", "ICL"), xlab = NULL, ylab = NULL, legend = "topright", ...) \S4method{getModel}{stepFlexmix}(object, which = "BIC") \S4method{unique}{stepFlexmix}(x, incomparables = FALSE, ...) } \arguments{ \item{\dots}{Passed to \code{\link{flexmix}} (or \code{\link{matplot}} in the \code{plot} method).} \item{k}{A vector of integers passed in turn to the \code{k} argument of \code{\link{flexmix}}.} \item{init}{An object of class \code{"initMethod"} or a named list where \code{initMethod} is called with it as arguments in addition to the \code{control} argument.} \item{name}{A character string indication which initialization strategy should be employed: short runs of EM followed by a long (\code{"tol.em"}), short runs of CEM followed by a long EM run (\code{"cem.em"}), short runs of SEM followed by a long EM run (\code{"sem.em"}).} \item{step1}{A named list which combined with the \code{control} argument is coercable to a \code{"FLXcontrol"} object. This control setting is used for the short runs.} \item{step2}{A named list which combined with the \code{control} argument is coercable to a \code{"FLXcontrol"} object. This control setting is used for the long run.} \item{control}{A named list which combined with the \code{step1} or the \code{step2} argument is coercable to a \code{"FLXcontrol"} object.} \item{nrep}{For each value of \code{k} run \code{\link{flexmix}} \code{nrep} times and keep only the solution with maximum likelihood. If \code{nrep} is set for the long run, it is ignored, because the EM algorithm is deterministic using the best solution discovered in the short runs for initialization.} \item{verbose}{If \code{TRUE}, show progress information during computations.} \item{drop}{If \code{TRUE} and \code{k} is of length 1, then a single flexmix object is returned instead of a \code{"stepFlexmix"} object.} \item{unique}{If \code{TRUE}, then \code{unique()} is called on the result, see below.} \item{x, object}{An object of class \code{"stepFlexmix"}.} \item{y}{Not used.} \item{what}{Character vector naming information criteria to plot. Functions of the same name must exist, which take a \code{stepFlexmix} object as input and return a numeric vector like \code{AIC,stepFlexmix-method} (see examples below).} \item{xlab,ylab}{Graphical parameters.} \item{legend}{If not \code{FALSE} and \code{what} contains more than 1 element, a legend is placed at the specified location, see \code{\link{legend}} for details.} \item{which}{Number of model to get. If character, interpreted as number of components or name of an information criterion.} \item{incomparables}{A vector of values that cannot be compared. Currently, \code{FALSE} is the only possible value, meaning that all values can be compared.} } \value{ An object of class \code{"stepFlexmix"} containing the best models with respect to the log likelihood for the different number of components in a slot if \code{length(k)>1}, else directly an object of class \code{"flexmix"}. If \code{unique = FALSE}, then the resulting object contains one model per element of \code{k} (which is the number of clusters the EM algorithm started with). If \code{unique = TRUE}, then the result is resorted according to the number of clusters contained in the fitted models (which may be less than the number with which the EM algorithm started), and only the maximum likelihood solution for each number of fitted clusters is kept. This operation can also be done manually by calling \code{unique()} on objects of class \code{"stepFlexmix"}. } \author{Friedrich Leisch and Bettina Gruen} \references{ Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. \emph{Journal of Statistical Software}, \bold{11}(8), 2004. doi:10.18637/jss.v011.i08 Christophe Biernacki, Gilles Celeux and Gerard Govaert. Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. \emph{Computational Statistics & Data Analysis}, \bold{41}(3--4), 561--575, 2003. Theresa Scharl, Bettina Gruen and Friedrch Leisch. Mixtures of regression models for time-course gene expression data: Evaluation of initialization and random effects. \emph{Bioinformatics}, \bold{26}(3), 370--377, 2010. } \examples{ data("Nclus", package = "flexmix") ## try 2 times for k = 4 set.seed(511) ex1 <- initFlexmix(Nclus~1, k = 4, model = FLXMCmvnorm(diagonal = FALSE), nrep = 2) ex1 ## now 2 times each for k = 2:5, specify control parameter ex2 <- initFlexmix(Nclus~1, k = 2:5, model = FLXMCmvnorm(diagonal = FALSE), control = list(minprior = 0), nrep = 2) ex2 plot(ex2) ## get BIC values BIC(ex2) ## get smallest model getModel(ex2, which = 1) ## get model with 3 components getModel(ex2, which = "3") ## get model with smallest ICL (here same as for AIC and BIC: true k = 4) getModel(ex2, which = "ICL") ## now 1 time each for k = 2:5, with larger minimum prior ex3 <- initFlexmix(Nclus~1, k = 2:5, model = FLXMCmvnorm(diagonal = FALSE), control = list(minprior = 0.1), nrep = 1) ex3 ## keep only maximum likelihood solution for each unique number of ## fitted clusters: unique(ex3) } \keyword{cluster} \keyword{regression} flexmix/man/BregFix.Rd0000644000176200001440000000212114404637306014321 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: BregFix.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{BregFix} \alias{BregFix} \docType{data} \title{Artificial Example for Binomial Regression} \description{ A simple artificial regression example data set with 3 latent classes, one independent variable \code{x} and a concomitant variable \code{w}. } \usage{data("BregFix")} \format{ A data frame with 200 observations on the following 5 variables. \describe{ \item{\code{yes}}{number of successes} \item{\code{no}}{number of failures} \item{\code{x}}{independent variable} \item{\code{w}}{concomitant variable, a factor with levels \code{0} \code{1}} \item{\code{class}}{latent class memberships} } } \examples{ data("BregFix", package = "flexmix") Model <- FLXMRglmfix(family="binomial", nested = list(formula = c(~x, ~0), k = c(2, 1))) Conc <- FLXPmultinom(~w) FittedBin <- initFlexmix(cbind(yes, no) ~ 1, data = BregFix, k = 3, model = Model, concomitant = Conc) summary(FittedBin) } \keyword{datasets} flexmix/man/FLXMRziglm.Rd0000644000176200001440000000302114404637306014726 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXMRziglm.Rd 5229 2022-06-02 14:47:26Z gruen $ % \name{FLXMRziglm} \alias{FLXMRziglm} \alias{FLXMRziglm-class} \alias{refit,FLXMRziglm-method} \alias{FLXreplaceParameters,FLXMRziglm-method} \alias{FLXgradlogLikfun,FLXMRziglm-method} \title{FlexMix Interface to Zero Inflated Generalized Linear Models} \description{ This is a driver which allows fitting of zero inflated poisson and binomial models. } \usage{ FLXMRziglm(formula = . ~ ., family = c("binomial", "poisson"), ...) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{flexmix} using \code{\link{update.formula}}. Default is to use the original \code{flexmix} model formula.} \item{family}{A character string naming a \code{\link{glm}} family function.} \item{\dots}{passed to \code{FLXMRglm}} } \value{ Returns an object of class \code{FLXMRziglm} inheriting from \code{FLXMRglm}. } \author{Friedrich Leisch and Bettina Gruen} \note{ In fact this only approximates zero inflated models by fixing the coefficient of the intercept at -Inf and the other coefficients at zero for the first component. } \examples{ data("dmft", package = "flexmix") Model <- FLXMRziglm(family = "poisson") Fitted <- flexmix(End ~ log(Begin + 0.5) + Gender + Ethnic + Treatment, model = Model, k = 2 , data = dmft, control = list(minprior = 0.01)) summary(refit(Fitted)) } \keyword{models} flexmix/man/FLXdist.Rd0000644000176200001440000000255614404637306014324 0ustar liggesusers\name{FLXdist} \alias{FLXdist} \alias{simulate,FLXdist-method} \alias{show,FLXdist-method} \title{Finite Mixtures of Distributions} \description{ Constructs objects of class \code{FLXdist} which represent unfitted finite mixture models. } \usage{ FLXdist(formula, k = NULL, model = FLXMRglm(), components, concomitant = FLXPconstant()) } \arguments{ \item{formula}{A symbolic description of the model to be fit. The general form is \code{~x|g} where \code{x} is the set of predictors and \code{g} an optional grouping factor for repeated measurements.} \item{k}{Integer specifying the number of cluster or a numeric vector of length equal to the length of components, specifying the prior probabilities of clusters.} \item{model}{Object of class \code{FLXM} or a list of \code{FLXM} objects. Default is the object returned by calling \code{FLXMRglm()}.} \item{components}{A list of length equal to the number of components containing a list of length equal to the number of models which again contains a list of named elements for defining the parameters of the component-specific model.} \item{concomitant}{Object of class \code{FLXconcomitant} specifying the model for concomitant variables.} } \value{ Returns an object of class \code{FLXdist}. } \author{Bettina Gruen} \seealso{\code{FLXdist-class}} \keyword{utilities} flexmix/man/FLXMRlmmc.Rd0000644000176200001440000000300314404637306014534 0ustar liggesusers\name{FLXMRlmmc} \alias{FLXMRlmmc} \alias{FLXMRlmmc-class} \alias{FLXMRlmmcfix-class} \alias{FLXMRlmc-class} \alias{FLXMRlmcfix-class} \alias{predict,FLXMRlmc-method} \title{FlexMix Interface to Linear Mixed Models with Left-Censoring} \description{ This is a driver which allows fitting of mixtures of linear models with random effects and left-censored observations. } \usage{ FLXMRlmmc(formula = . ~ ., random, censored, varFix, eps = 10^-6, ...) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{flexmix} using \code{\link{update.formula}}. Default is to use the original \code{flexmix} model formula.} \item{random}{A formula for specifying the random effects. If missing no random effects are fitted.} \item{varFix}{If random effects are specified a named logical vector of length 2 indicating if the variance of the random effects and the residuals are fixed over the components. Otherwise a logical indicating if the variance of the residuals are fixed over the components.} \item{censored}{A formula for specifying the censoring variable.} \item{eps}{Observations with an a-posteriori probability smaller or equal to \code{eps} are omitted in the M-step.} \item{\dots}{Additional arguments to be passed to \code{lm.wfit}.} } \value{ Returns an object of class \code{FLXMRlmmc}, \code{FLXMRlmmcfix}, \code{FLXMRlmc} or \code{FLXMRlmcfix} inheriting from \code{FLXMR}. } \author{Bettina Gruen} \keyword{models} flexmix/man/FLXglm.Rd0000644000176200001440000000261114404637306014130 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXglm.Rd 5229 2022-06-02 14:47:26Z gruen $ % \name{FLXMRglm} \alias{FLXMRglm} \alias{FLXglm} \title{FlexMix Interface to Generalized Linear Models} \description{ This is the main driver for FlexMix interfacing the \code{\link{glm}} family of models. } \usage{ FLXMRglm(formula = . ~ ., family = c("gaussian", "binomial", "poisson", "Gamma"), offset = NULL) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Default is to use the original \code{\link{flexmix}} model formula.} \item{family}{A character string naming a \code{\link{glm}} family function.} \item{offset}{This can be used to specify an \emph{a priori} known component to be included in the linear predictor during fitting.} } \details{ See \code{\link{flexmix}} for examples. } \value{ Returns an object of class \code{FLXMRglm} inheriting from \code{FLXMR}. } \author{Friedrich Leisch and Bettina Gruen} \references{ Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. \emph{Journal of Statistical Software}, \bold{11}(8), 2004. doi:10.18637/jss.v011.i08 } \seealso{\code{\link{flexmix}}, \code{\link{glm}}} \keyword{regression} \keyword{models} flexmix/man/posterior.Rd0000644000176200001440000000225514404637306015031 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: posterior.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{posterior} \alias{clusters,flexmix,missing-method} \alias{clusters,FLXdist,ANY-method} \alias{posterior,flexmix,missing-method} \alias{posterior,FLXdist,listOrdata.frame-method} \title{Determine Cluster Membership and Posterior Probabilities} \description{Determine posterior probabilities or cluster memberships for a fitted \code{flexmix} or unfitted \code{FLXdist} model.} \usage{ \S4method{posterior}{flexmix,missing}(object, newdata, unscaled = FALSE, ...) \S4method{posterior}{FLXdist,listOrdata.frame}(object, newdata, unscaled = FALSE, ...) \S4method{clusters}{flexmix,missing}(object, newdata, ...) \S4method{clusters}{FLXdist,ANY}(object, newdata, ...) } \arguments{ \item{object}{An object of class "flexmix" or "FLXdist".} \item{newdata}{Data frame or list containing new data. If missing the posteriors of the original observations are returned.} \item{unscaled}{Logical, if \code{TRUE} the component-specific likelihoods are returned.} \item{\dots}{Currently not used.} } \author{Friedrich Leisch and Bettina Gruen} \keyword{methods} flexmix/man/NregFix.Rd0000644000176200001440000000243214404637306014342 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: NregFix.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{NregFix} \alias{NregFix} \title{Artificial Example for Normal Regression} \description{ A simple artificial regression example with 3 latent classes, two independent variables, one concomitant variable and a dependent variable which follows a Gaussian distribution. } \usage{ data("NregFix") } \format{ A data frame with 200 observations on the following 5 variables. \describe{ \item{\code{x1}}{Independent variable: numeric variable.} \item{\code{x2}}{Independent variable: a factor with two levels: \code{0} and \code{1}.} \item{\code{w}}{Concomitant variable: a factor with two levels: \code{0} and \code{1}.} \item{\code{y}}{Dependent variable.} \item{\code{class}}{Latent class memberships.} } } \examples{ data("NregFix", package = "flexmix") library("lattice") xyplot(y ~ x1 | x2 * w, data = NregFix, groups = class) Model <- FLXMRglmfix(~ 1, fixed = ~ x2, nested = list(k = c(2, 1), formula = c(~x1, ~0))) fittedModel <- initFlexmix(y ~ 1, model = Model, data = NregFix, k = 3, concomitant = FLXPmultinom(~ w), nrep = 5) fittedModel } \keyword{datasets} flexmix/man/flexmix-class.Rd0000644000176200001440000000370214404637306015560 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: flexmix-class.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{flexmix-class} \docType{class} \alias{flexmix-class} \title{Class "flexmix"} \description{A fitted \code{\link{flexmix}} model.} \section{Slots}{ \describe{ \item{\code{model}:}{List of \code{FLXM} objects.} \item{\code{prior}:}{Numeric vector with prior probabilities of clusters.} \item{\code{posterior}:}{Named list with elements \code{scaled} and \code{unscaled}, both matrices with one row per observation and one column per cluster.} \item{\code{iter}:}{Number of EM iterations.} \item{\code{k}:}{Number of clusters after EM.} \item{\code{k0}:}{Number of clusters at start of EM.} \item{\code{cluster}:}{Cluster assignments of observations.} \item{\code{size}:}{Cluster sizes.} \item{\code{logLik}:}{Log-likelihood at EM convergence.} \item{\code{df}:}{Total number of parameters of the model.} \item{\code{components}:}{List describing the fitted components using \code{FLXcomponent} objects.} \item{\code{formula}:}{Object of class \code{"formula"}.} \item{\code{control}:}{Object of class \code{"FLXcontrol"}.} \item{\code{call}:}{The function call used to create the object.} \item{\code{group}:}{Object of class \code{"factor"}.} \item{\code{converged}:}{Logical, \code{TRUE} if EM algorithm converged.} \item{\code{concomitant}:}{Object of class \code{"FLXP"}..} \item{\code{weights}:}{Optional weights of the observations.} } } \section{Extends}{ Class \code{FLXdist}, directly. } \section{Accessor Functions}{ The following functions should be used for accessing the corresponding slots: \describe{ \item{\code{cluster}:}{Cluster assignments of observations.} \item{\code{posterior}:}{A matrix of posterior probabilities for each observation.} } } \author{Friedrich Leisch and Bettina Gruen} \keyword{classes} flexmix/man/EIC.Rd0000644000176200001440000000241414404637306013400 0ustar liggesusers% % Copyright (C) 2004-2009 Friedrich Leisch and Bettina Gruen % $Id: EIC.Rd 3912 2008-03-13 15:10:24Z gruen $ % \name{EIC} \alias{EIC} \alias{EIC,flexmix-method} \alias{EIC,stepFlexmix-method} \title{Entropic Measure Information Criterion} \description{ Compute the entropic measure information criterion for model selection. } \usage{ \S4method{EIC}{flexmix}(object, \dots) \S4method{EIC}{stepFlexmix}(object, \dots) } \arguments{ \item{object}{See Methods section below} \item{\dots}{Some methods for this generic function may take additional, optional arguments. At present none do.} } \section{Methods}{ \describe{ \item{object = "flexmix":}{Compute the EIC of a \code{flexmix} object.} \item{object = "stepFlexmix":}{Compute the EIC of all models contained in the \code{stepFlexmix} object.} }} \value{ Returns a numeric vector with the corresponding EIC value(s). } \keyword{methods} \author{Bettina Gruen} \references{ V. Ramaswamy, W. S. DeSarbo, D. J. Reibstein, and W. T. Robinson. An empirical pooling approach for estimating marketing mix elasticities with PIMS data. \emph{Marketing Science}, \bold{12}(1), 103--124, 1993. } \examples{ data("NPreg", package = "flexmix") ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2) EIC(ex1) } flexmix/man/refit.Rd0000644000176200001440000001204614404637306014113 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: refit.Rd 5115 2017-04-07 08:18:13Z gruen $ % \name{refit-methods} \alias{refit,flexmix-method} \alias{FLXRmstep-class} \alias{FLXRoptim-class} \alias{show,FLXR-method} \alias{show,Coefmat-method} \alias{summary,FLXRoptim-method} \alias{summary,FLXRmstep-method} \alias{plot,FLXRoptim,missing-method} \title{Refit a Fitted Model} \description{ Refits an estimated flexmix model to obtain additional information like coefficient significance p-values for GLM regression. } \usage{ \S4method{refit}{flexmix}(object, newdata, method = c("optim", "mstep"), ...) \S4method{summary}{FLXRoptim}(object, model = 1, which = c("model", "concomitant"), ...) \S4method{summary}{FLXRmstep}(object, model = 1, which = c("model", "concomitant"), ...) \S4method{plot}{FLXRoptim,missing}(x, y, model = 1, which = c("model", "concomitant"), bycluster = TRUE, alpha = 0.05, components, labels = NULL, significance = FALSE, xlab = NULL, ylab = NULL, ci = TRUE, scales = list(), as.table = TRUE, horizontal = TRUE, ...) } \arguments{ \item{object}{An object of class \code{"flexmix"}} \item{newdata}{Optional new data.} \item{method}{Specifies if the variance covariance matrix is determined using \code{\link{optim}} or if the posteriors are assumed as given and an M-step is performed.} \item{model}{The model (for a multivariate response) that shall be used.} \item{which}{Specifies if a component specific model or the concomitant variable model is used.} \item{x}{An object of class \code{"FLXRoptim"}} \item{y}{Missing object.} \item{bycluster}{A logical if the parameters should be group by cluster or by variable.} \item{alpha}{Numeric indicating the significance level.} \item{components}{Numeric vector specifying which components are plotted. The default is to plot all components.} \item{labels}{Character vector specifying the variable names used.} \item{significance}{A logical indicating if non-significant coefficients are shaded in a lighter grey.} \item{xlab}{String for the x-axis label.} \item{ylab}{String for the y-axis label.} \item{ci}{A logical indicating if significant and insignificant parameter estimates are shaded differently.} \item{scales}{See argument of the same name for function \code{\link[lattice]{xyplot}}.} \item{as.table}{See arguments of the same name for function \code{\link[lattice]{xyplot}}.} \item{horizontal}{See arguments of the same name for function \code{\link[lattice]{xyplot}}.} \item{\dots}{Currently not used} } \value{ An object inheriting form class \code{FLXR} is returned. For the method using \code{optim} the object has class \code{FLXRoptim} and for the M-step method it has class \code{FLXRmstep}. Both classes give similar results for their \code{summary} methods. Objects of class \code{FLXRoptim} have their own \code{plot} method. \code{Lapply} can be used to further analyse the refitted component specific models of objects of class \code{FLXRmstep}. } \details{ The \code{refit} method for \code{FLXMRglm} models in combination with the \code{summary} method can be used to obtain the usual tests for significance of coefficients. Note that the tests are valid only if \code{flexmix} returned the maximum likelihood estimator of the parameters. If \code{refit} is used with \code{method = "mstep"} for these component specific models the returned object contains a \code{glm} object for each component where the elements \code{model} which is the model frame and \code{data} which contains the original dataset are missing. } \keyword{methods} \author{Friedrich Leisch and Bettina Gruen} \references{ Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. \emph{Journal of Statistical Software}, \bold{11}(8), 2004. doi:10.18637/jss.v011.i08 } \section{Warning}{ For \code{method = "mstep"} the standard deviations are determined separately for each of the components using the a-posteriori probabilities as weights without accounting for the fact that the components have been simultaneously estimated. The derived standard deviations are hence approximative and should only be used in an exploratory way, as they are underestimating the uncertainty given that the missing information of the component memberships are replaced by the expected values. The \code{newdata} argument can only be specified when using \code{method = "mstep"} for refitting \code{FLXMRglm} components. A variant of \code{glm} for weighted ML estimation is used for fitting the components and full \code{glm} objects are returned. Please note that in this case the data and the model frame are stored for each component which can significantly increase the object size. } \examples{ data("NPreg", package = "flexmix") ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2) ex1r <- refit(ex1) ## in one component all coefficients should be highly significant, ## in the other component only the linear term summary(ex1r) } flexmix/man/flexmix.Rd0000644000176200001440000001266614404637306014466 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: flexmix.Rd 5115 2017-04-07 08:18:13Z gruen $ % \name{flexmix} \alias{flexmix} \alias{flexmix,formula,ANY,ANY,ANY,missing-method} \alias{flexmix,formula,ANY,ANY,ANY,list-method} \alias{flexmix,formula,ANY,ANY,ANY,FLXM-method} \alias{prior,flexmix-method} \alias{show,flexmix-method} \alias{summary,flexmix-method} \alias{show,summary.flexmix-method} \title{Flexible Mixture Modeling} \description{ FlexMix implements a general framework for finite mixtures of regression models. Parameter estimation is performed using the EM algorithm: the E-step is implemented by \code{flexmix}, while the user can specify the M-step. } \usage{ flexmix(formula, data = list(), k = NULL, cluster = NULL, model = NULL, concomitant = NULL, control = NULL, weights = NULL) \S4method{summary}{flexmix}(object, eps = 1e-4, ...) } \arguments{ \item{formula}{A symbolic description of the model to be fit. The general form is \code{y~x|g} where \code{y} is the response, \code{x} the set of predictors and \code{g} an optional grouping factor for repeated measurements.} \item{data}{An optional data frame containing the variables in the model.} \item{k}{Number of clusters (not needed if \code{cluster} is specified).} \item{cluster}{Either a matrix with \code{k} columns of initial cluster membership probabilities for each observation; or a factor or integer vector with the initial cluster assignments of observations at the start of the EM algorithm. Default is random assignment into \code{k} clusters.} \item{weights}{An optional vector of replication weights to be used in the fitting process. Should be \code{NULL}, an integer vector or a formula.} \item{model}{Object of class \code{FLXM} or list of \code{FLXM} objects. Default is the object returned by calling \code{\link{FLXMRglm}()}.} \item{concomitant}{Object of class \code{FLXP}. Default is the object returned by calling \code{\link{FLXPconstant}}.} \item{control}{Object of class \code{FLXcontrol} or a named list.} \item{object}{Object of class \code{flexmix}.} \item{eps}{Probabilities below this threshold are treated as zero in the summary method.} \item{\dots}{Currently not used.} } \details{ FlexMix models are described by objects of class \code{FLXM}, which in turn are created by driver functions like \code{\link{FLXMRglm}} or \code{\link{FLXMCmvnorm}}. Multivariate responses with independent components can be specified using a list of \code{FLXM} objects. The \code{summary} method lists for each component the prior probability, the number of observations assigned to the corresponding cluster, the number of observations with a posterior probability larger than \code{eps} and the ratio of the latter two numbers (which indicates how separated the cluster is from the others). } \value{ Returns an object of class \code{flexmix}. } \author{Friedrich Leisch and Bettina Gruen} \seealso{\code{\link[flexmix]{plot-methods}}} \references{ Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. \emph{Journal of Statistical Software}, \bold{11}(8), 2004. doi:10.18637/jss.v011.i08 Bettina Gruen and Friedrich Leisch. Fitting finite mixtures of generalized linear regressions in R. Computational Statistics & Data Analysis, 51(11), 5247-5252, 2007. doi:10.1016/j.csda.2006.08.014 Bettina Gruen and Friedrich Leisch. FlexMix Version 2: Finite mixtures with concomitant variables and varying and constant parameters Journal of Statistical Software, 28(4), 1-35, 2008. doi:10.18637/jss.v028.i04 } \keyword{regression} \keyword{cluster} \examples{ data("NPreg", package = "flexmix") ## mixture of two linear regression models. Note that control parameters ## can be specified as named list and abbreviated if unique. ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2, control = list(verb = 5, iter = 100)) ex1 summary(ex1) plot(ex1) ## now we fit a model with one Gaussian response and one Poisson ## response. Note that the formulas inside the call to FLXMRglm are ## relative to the overall model formula. ex2 <- flexmix(yn ~ x, data = NPreg, k = 2, model = list(FLXMRglm(yn ~ . + I(x^2)), FLXMRglm(yp ~ ., family = "poisson"))) plot(ex2) ex2 table(ex2@cluster, NPreg$class) ## for Gaussian responses we get coefficients and standard deviation parameters(ex2, component = 1, model = 1) ## for Poisson response we get only coefficients parameters(ex2, component = 1, model = 2) ## fitting a model only to the Poisson response is of course ## done like this ex3 <- flexmix(yp ~ x, data = NPreg, k = 2, model = FLXMRglm(family = "poisson")) ## if observations are grouped, i.e., we have several observations per ## individual, fitting is usually much faster: ex4 <- flexmix(yp~x|id1, data = NPreg, k = 2, model = FLXMRglm(family = "poisson")) ## And now a binomial example. Mixtures of binomials are not generically ## identified, here the grouping variable is necessary: set.seed(1234) ex5 <- initFlexmix(cbind(yb,1 - yb) ~ x, data = NPreg, k = 2, model = FLXMRglm(family = "binomial"), nrep = 5) table(NPreg$class, clusters(ex5)) ex6 <- initFlexmix(cbind(yb, 1 - yb) ~ x | id2, data = NPreg, k = 2, model = FLXMRglm(family = "binomial"), nrep = 5) table(NPreg$class, clusters(ex6)) } flexmix/man/flxglht.Rd0000644000176200001440000000310514757625043014454 0ustar liggesusers\name{flxglht} \docType{methods} \alias{flxglht} \alias{flxglht,flexmix,character-method} \alias{flxglht,FLXRoptim,character-method} \title{ Simultaneous Inference in Finite Mixtures of Regression Models } \description{ Extracts coefficient estimates and their covariance estimate to perform tests for zero coefficients or constant effects re-using functionality from package \pkg{multcomp}. } \usage{ flxglht(model, linfct, ...) \S4method{flxglht}{flexmix,character}(model, linfct, ...) \S4method{flxglht}{FLXRoptim,character}(model, linfct, ...) } \arguments{ \item{model}{ Either a fitted mixture model of class \code{"flexmix"} or a re-fitted mixture model of class \code{"FLXRoptim"}. } \item{linfct}{ A character string which can be either \code{"zero"} or \code{"tukey"}. } \item{\dots}{ Currently not used. } } \details{ Only tested for finite mixture models fitted with driver \code{\link{FLXMRglm}}. } \value{ An object of class \code{"glht"}. } \references{ Friedrich Leisch and Torsten Hothorn. Simultaneous Inference in Finite Mixtures of Regression Models. \emph{Austrian Journal of Statistics}, forthcoming. } \author{ Friedrich Leisch } \seealso{ \code{\link[multcomp]{glht}} } \examples{ data("NPreg", package = "flexmix") ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2, control = list(verb = 5, iter = 100)) zero_effect <- flxglht(ex1, "zero") zero_effect summary(zero_effect) comp_effect <- flxglht(ex1, "tukey") comp_effect summary(comp_effect) } \keyword{cluster} \keyword{regression} \keyword{methods} flexmix/man/seizure.Rd0000644000176200001440000000414514404637306014471 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: seizure.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{seizure} \alias{seizure} \docType{data} \title{Epileptic Seizure Data} \description{ Data from a clinical trial where the effect of intravenous gamma-globulin on suppression of epileptic seizures is studied. Daily observations for a period of 140 days on one patient are given, where the first 27 days are a baseline period without treatment, the remaining 113 days are the treatment period. } \usage{data("seizure")} \format{ A data frame with 140 observations on the following 4 variables. \describe{ \item{Seizures}{A numeric vector, daily counts of epileptic seizures.} \item{Hours}{A numeric vector, hours of daily parental observation.} \item{Treatment}{A factor with levels \code{No} and \code{Yes}.} \item{Day}{A numeric vector.} } } \source{ P. Wang, M. Puterman, I. Cockburn, and N. Le. Mixed poisson regression models with covariate dependent rates. \emph{Biometrics}, \bold{52}, 381--400, 1996. } \references{ B. Gruen and F. Leisch. Bootstrapping finite mixture models. In J. Antoch, editor, Compstat 2004--Proceedings in Computational Statistics, 1115--1122. Physika Verlag, Heidelberg, Germany, 2004. ISBN 3-7908-1554-3. } \examples{ data("seizure", package = "flexmix") plot(Seizures/Hours ~ Day, col = as.integer(Treatment), pch = as.integer(Treatment), data = seizure) abline(v = 27.5, lty = 2, col = "grey") legend(140, 9, c("Baseline", "Treatment"), pch = 1:2, col = 1:2, xjust = 1, yjust = 1) set.seed(123) ## The model presented in the Wang et al paper: two components for ## "good" and "bad" days, respectively, each a Poisson GLM with hours of ## parental observation as offset seizMix <- flexmix(Seizures ~ Treatment * log(Day), data = seizure, k = 2, model = FLXMRglm(family = "poisson", offset = log(seizure$Hours))) summary(seizMix) summary(refit(seizMix)) matplot(seizure$Day, fitted(seizMix)/seizure$Hours, type = "l", add = TRUE, col = 3:4) } \keyword{datasets} flexmix/man/ExNclus.Rd0000644000176200001440000000151314404637306014360 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: ExNclus.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{ExNclus} \alias{ExNclus} \alias{Nclus} \title{Artificial Example with 4 Gaussians} \description{ A simple artificial example for normal clustering with 4 latent classes, all of them having a Gaussian distribution. See the function definition for true means and covariances. } \usage{ ExNclus(n) data("Nclus") } \arguments{ \item{n}{Number of observations in the two small latent classes.} } \details{ The \code{Nclus} data set can be re-created by \code{ExNclus(100)} using \code{set.seed(2602)}, it has been saved as a data set for simplicity of examples only. } \examples{ data("Nclus", package = "flexmix") require("MASS") eqscplot(Nclus, col = rep(1:4, c(100, 100, 150, 200))) } \keyword{datasets} flexmix/man/betablocker.Rd0000644000176200001440000000276614404637306015267 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: betablocker.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{betablocker} \alias{betablocker} \docType{data} \title{Clinical Trial of Beta-Blockers} \description{ 22-centre clinical trial of beta-blockers for reducing mortality after myocardial infarction. } \usage{data("betablocker")} \format{ A data frame with 44 observations on the following 4 variables. \describe{ \item{Deaths}{Number of deaths.} \item{Total}{Total number of patients.} \item{Center}{Number of clinical centre.} \item{Treatment}{A factor with levels \code{Control} and \code{Treated}.} } } \source{ G. McLachlan and D. Peel. \emph{Finite Mixture Models}, 2000. John Wiley and Sons Inc. \url{http://www.maths.uq.edu.au/~gjm/DATA/mmdata.html} } \references{ M. Aitkin. Meta-analysis by random effect modelling in generalized linear models. \emph{Statistics in Medicine}, \bold{18}, 2343--2351, 1999. S. Yusuf, R. Peto, J. Lewis, R. Collins and P. Sleight. Beta blockade during and after myocardial infarction: an overview of the randomized trials. \emph{Progress in Cardiovascular Diseases}, \bold{27}, 335--371, 1985. } \examples{ data("betablocker", package = "flexmix") betaMix <- initFlexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center, data = betablocker, k = 3, nrep = 5, model = FLXMRglmfix(family = "binomial", fixed = ~Treatment)) } \keyword{datasets} flexmix/man/FLXMCdist1.Rd0000644000176200001440000000373614404637306014626 0ustar liggesusers% % Copyright (C) 2016 Bettina Gruen % $Id: FLXMCdist1.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXMCdist1} \alias{FLXMCdist1} \title{FlexMix Clustering of Univariate Distributions} \description{ These are drivers for \code{\link{flexmix}} implementing model-based clustering of univariate data using different distributions for the component-specific models. } \usage{ FLXMCdist1(formula = . ~ ., dist, ...) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Only the left-hand side (response) of the formula is used. Default is to use the original \code{\link{flexmix}} model formula.} \item{dist}{Character string indicating the component-specific univariate distribution.} \item{...}{Arguments for the specific model drivers.} } \details{ Currently drivers for the following distributions are available: \enumerate{ \item Lognormal (\code{"lnorm"}) \item inverse Gaussian (\code{"invGauss"} using \code{\link[SuppDists:invGauss]{dinvGauss}}) \item gamma (\code{"gamma"}) \item exponential (\code{"exp"}) \item Weibull (\code{"weibull"}) \item Burr (\code{"burr"} using \code{\link[actuar:Burr]{dburr}}) \item Inverse Burr (\code{"invburr"} using \code{\link[actuar:Burr]{dinvburr}}) } } \value{ \code{FLXMCdist1} returns an object of class \code{FLXMC}. } \author{Friedrich Leisch and Bettina Gruen} \references{ Tatjana Miljkovic and Bettina Gruen. Modeling loss data using mixtures of distributions. \emph{Insurance: Mathematics and Economics}, \bold{70}, 387-396, 2016. doi:10.1016/j.insmatheco.2016.06.019 } \seealso{\code{\link{flexmix}}} \keyword{cluster} \examples{ if (require("actuar")) { set.seed(123) y <- c(rexp(100, 10), rexp(100, 1)) ex <- flexmix(y ~ 1, cluster = rep(1:2, each = 100), model = FLXMCdist1(dist = "exp")) parameters(ex) } } flexmix/man/candy.Rd0000644000176200001440000000250314404637306014075 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: candy.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{candy} \alias{candy} \docType{data} \title{Candy Packs Purchased} \description{ The data is from a new product and concept test where the number of individual packs of hard candy purchased within the past 7 days is recorded. } \usage{data("candy")} \format{ A data frame with 21 observations on the following 2 variables. \describe{ \item{\code{Packages}}{a numeric vector} \item{\code{Freq}}{a numeric vector} } } \source{ D. Boehning, E. Dietz and P. Schlattmann. Recent Developments in Computer-Assisted Analysis of Mixtures. Biometrics 54(2), 525--536, 1998. } \references{ J. Magidson and J. K. Vermunt. Latent Class Models. In D. W. Kaplan (ed.), The Sage Handbook of Quantitative Methodology for the Social Sciences, 175--198, 2004. Thousand Oakes: Sage Publications. D. Boehning, E. Dietz and P. Schlattmann. Recent Developments in Computer-Assisted Analysis of Mixtures. \emph{Biometrics}, \bold{54}(2), 525--536, 1998. W. R. Dillon and A. Kumar. Latent structure and other mixture models in marketing: An integrative survey and overview. In R. P. Bagozzi (ed.), Advanced methods of marketing research, 352--388, 1994. Cambridge, UK: Blackwell. } \keyword{datasets} flexmix/man/FLXP-class.Rd0000644000176200001440000000211414404637306014651 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXP-class.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXP-class} \docType{class} \alias{FLXP-class} \title{Class "FLXP"} \alias{initialize,FLXP-method} \alias{FLXPconstant-class} \alias{FLXPmultinom-class} \description{ Concomitant model class. } \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("FLXP", ...)}, typically inside driver functions like \code{\link{FLXPconstant}} or \code{\link{FLXPmultinom}}. } \section{Slots}{ \describe{ \item{\code{name}:}{Character string used in print methods.} \item{\code{formula}:}{Formula describing the model.} \item{\code{x}:}{Model matrix.} \item{\code{fit}:}{Function returning the fitted prior probabilities.} \item{\code{refit}:}{Function returning the fitted concomitant model.} \item{\code{coef}:}{Matrix containing the fitted parameters.} \item{\code{df}:}{Function for determining the number of degrees of freedom used.} } } \author{Friedrich Leisch and Bettina Gruen} \keyword{classes} flexmix/man/fitted.Rd0000644000176200001440000000213514404637306014257 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: fitted.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{fitted-methods} \docType{methods} \alias{fitted,flexmix-method} \alias{fitted,FLXM-method} \alias{fitted,FLXR-method} \alias{fitted,FLXRMRglm-method} \title{Extract Model Fitted Values} \description{ Extract fitted values for each component from a flexmix object. } \usage{ \S4method{fitted}{flexmix}(object, drop = TRUE, aggregate = FALSE, ...) } \arguments{ \item{object}{an object of class \code{"flexmix"} or \code{"FLXR"}} \item{drop}{logical, if \code{TRUE} then the function tries to simplify the return object by combining lists of length 1 into matrices.} \item{aggregate}{logical, if \code{TRUE} then the fitted values for each model aggregated over the components are returned.} \item{\dots}{currently not used} } \keyword{methods} \author{Friedrich Leisch and Bettina Gruen} \examples{ data("NPreg", package = "flexmix") ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2) matplot(NPreg$x, fitted(ex1), pch = 16, type = "p") points(NPreg$x, NPreg$yn) } flexmix/man/ExNPreg.Rd0000644000176200001440000000165114404637306014312 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: ExNPreg.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{ExNPreg} \alias{ExNPreg} \alias{NPreg} \title{Artificial Example for Normal, Poisson and Binomial Regression} \description{ A simple artificial regression example with 2 latent classes, one independent variable (uniform on \eqn{[0,10]}), and three dependent variables with Gaussian, Poisson and Binomial distribution, respectively. } \usage{ ExNPreg(n) data("NPreg") } \arguments{ \item{n}{Number of observations per latent class.} } \details{ The \code{NPreg} data frame can be re-created by \code{ExNPreg(100)} using \code{set.seed(2602)}, it has been saved as a data set for simplicity of examples only. } \examples{ data("NPreg", package = "flexmix") plot(yn ~ x, data = NPreg, col = class) plot(yp ~ x, data = NPreg, col = class) plot(yb ~ x, data = NPreg, col = class) } \keyword{datasets} flexmix/man/group.Rd0000644000176200001440000000073314404637306014136 0ustar liggesusers\name{group} \docType{methods} \alias{group} \alias{group-methods} \alias{group,flexmix-method} \alias{group,FLXM-method} \alias{group,FLXMRglmfix-method} \title{Extract Grouping Variable} \description{ Extract grouping variable for all observations. } \usage{ \S4method{group}{flexmix}(object) \S4method{group}{FLXM}(object) \S4method{group}{FLXMRglmfix}(object) } \arguments{ \item{object}{an object of class \code{flexmix}.} } \keyword{methods} \author{Bettina Gruen} flexmix/man/FLXbclust.Rd0000644000176200001440000000233314404637306014646 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXbclust.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXMCmvbinary} \alias{FLXMCmvbinary} \alias{FLXbclust} \title{FlexMix Binary Clustering Driver} \description{ This is a model driver for \code{\link{flexmix}} implementing model-based clustering of binary data. } \usage{ FLXMCmvbinary(formula = . ~ ., truncated = FALSE) } \arguments{ \item{formula}{A formula which is interpreted relative to the formula specified in the call to \code{\link{flexmix}} using \code{\link{update.formula}}. Only the left-hand side (response) of the formula is used. Default is to use the original \code{\link{flexmix}} model formula.} \item{truncated}{logical, if \code{TRUE} the observations for the pattern with only zeros are missing and the truncated likelihood is optimized using an EM-algorithm.} } \details{ This model driver can be used to cluster binary data. The only parameter is the column-wise mean of the data, which equals the probability of observing a 1. } \value{ \code{FLXMCmvbinary} returns an object of class \code{FLXMC}. } \author{Friedrich Leisch and Bettina Gruen} \seealso{\code{\link{flexmix}}} \keyword{cluster} flexmix/man/ExLinear.Rd0000644000176200001440000000560514404637306014514 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: ExNclus.Rd 3912 2008-03-13 15:10:24Z gruen $ % \name{ExLinear} \alias{ExLinear} \title{Artificial Data from a Generalized Linear Regression Mixture} \description{ Generate random data mixed from k generalized linear regressions (GLMs). } \usage{ ExLinear(beta, n, xdist = "runif", xdist.args = NULL, family = c("gaussian","poisson"), sd = 1, ...) } \arguments{ \item{beta}{A matrix of regression coefficients. Each row corresponds to a variable, each column to a mixture component. The first row is used as intercept.} \item{n}{Integer, the number of observations per component.} \item{xdist}{Character, name of a random number function for the explanatory variables.} \item{xdist.args}{List, arguments for the random number functions.} \item{family}{A character string naming a GLM family.Only \code{"gaussian"} and \code{"poisson"} are implemented at the moment.} \item{sd}{Numeric, the error standard deviation for each component for Gaussian responses.} \item{\dots}{Used as default for \code{xdist.args} if that is not specified.} } \details{ First, arguments \code{n} (and \code{sd} for Gaussian response) are recycled to the number of mixture components \code{ncol(beta)}, and arguments \code{xdist} and \code{xdist.args} are recycled to the number of explanatory variables \code{nrow(beta)-1}. Then a design matrix is created for each mixture component by drawing random numbers from \code{xdist}. For each component, the design matrix is multiplied by the regression coefficients to form the linear predictor. For Gaussian responses the identity link is used, for Poisson responses the log link. The true cluster memberships are returned as attribute \code{"clusters"}. } \examples{ ## simple example in 2d beta <- matrix(c(1, 2, 3, -1), ncol = 2) sigma <- c(.5, 1) df1 <- ExLinear(beta, 100, sd = sigma, min = -1, max = 2) plot(y~x1, df1, col = attr(df1, "clusters")) ## add a second explanatory variable with exponential distribution beta2 <- rbind(beta, c(-2, 2)) df2 <- ExLinear(beta2, 100, sd = c(.5, 1), xdist = c("runif", "rexp"), xdist.args = list(list(min = -1, max = 2), list(rate = 3))) summary(df2) opar = par("mfrow") par(mfrow = 1:2) hist(df2$x1) hist(df2$x2) par(opar) f1 <- flexmix(y ~ ., data = df2, k = 2) ## sort components on Intercept f1 <- relabel(f1, "model", "Intercept") ## the parameters should be close to the true beta and sigma round(parameters(f1), 3) rbind(beta2, sigma) ### A simple Poisson GLM df3 <- ExLinear(beta/2, 100, min = -1, max = 2, family = "poisson") plot(y ~ x1, df3, col = attr(df3, "clusters")) f3 <- flexmix(y ~ ., data = df3, k = 2, model = FLXMRglm(family = "poisson")) round(parameters(relabel(f3, "model", "Intercept")), 3) beta/2 } \keyword{datasets} flexmix/man/whiskey.Rd0000644000176200001440000000300314757625043014464 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: whiskey.Rd 5298 2025-02-26 14:50:01Z gruen $ % \name{whiskey} \alias{whiskey} \alias{whiskey_brands} \docType{data} \title{Survey Data on Brands of Scotch Whiskey Consumed} \description{ The data set is from Simmons Study of Media and Markets and contains the incidence matrix for scotch brands used in last year for those households who report consuming scotch. } \usage{data("whiskey")} \format{ A data frame \code{whiskey} with 484 observations on the following 2 variables. \describe{ \item{\code{Freq}}{a numeric vector} \item{\code{Incidence}}{a matrix with 21 columns} } Additional information on the brands is contained in the data frame \code{whiskey_brands} which is simultaneously loaded. This data frame contains 21 observations on the following 3 variables. \describe{ \item{\code{Brand}}{a character vector} \item{\code{Type}}{a factor with levels \code{Blend} \code{Single Malt}} \item{\code{Bottled}}{a factor with levels \code{Domestic} \code{Foreign}} } } \details{ The dataset is taken from the \pkg{bayesm} package. } \source{ Peter Rossi and Rob McCulloch. bayesm: Bayesian Inference for Marketing/Micro-econometrics. R package version 2.0-8, 2006. http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html } \references{ Edwards, Y. and G. Allenby. Multivariate Analysis of Multiple Response Data, \emph{Journal of Marketing Research}, \bold{40}, 321--334, 2003. } \keyword{datasets} flexmix/man/FLXcontrol-class.Rd0000644000176200001440000000333414404637306016137 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXcontrol-class.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXcontrol-class} \docType{class} \alias{FLXcontrol-class} \alias{coerce,list,FLXcontrol-method} \alias{coerce,NULL,FLXcontrol-method} \title{Class "FLXcontrol"} \description{Hyperparameters for the EM algorithm.} \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("FLXcontrol", ...)}. In addition, named lists can be coerced to \code{FLXcontrol} objects, names are completed if unique (see examples). } \section{Slots}{ \describe{ \item{\code{iter.max}:}{Maximum number of iterations.} \item{\code{minprior}:}{Minimum prior probability of clusters, components falling below this threshold are removed during the iteration.} \item{\code{tolerance}:}{The EM algorithm is stopped when the (relative) change of log-likelihood is smaller than \code{tolerance}.} \item{\code{verbose}:}{If a positive integer, then the log-likelihood is reported every \code{verbose} iterations. If 0, no output is generated during model fitting.} \item{\code{classify}:}{Character string, one of \code{"auto"}, \code{"weighted"}, \code{"hard"} (or \code{"CEM"}), \code{"random"} or (\code{"SEM"}).} \item{\code{nrep}:}{Reports the number of random initializations used in \code{\link{stepFlexmix}()} to determine the mixture.} } Run \code{new("FLXcontrol")} to see the default settings of all slots. } \author{Friedrich Leisch and Bettina Gruen} \keyword{classes} \examples{ ## have a look at the defaults new("FLXcontrol") ## corce a list mycont <- list(iter = 200, tol = 0.001, class = "r") as(mycont, "FLXcontrol") } flexmix/man/FLXconcomitant.Rd0000644000176200001440000000177514404637306015701 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXconcomitant.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXP} \docType{class} \alias{FLXPconstant} \alias{FLXPmultinom} \alias{FLXconstant} \alias{FLXmultinom} \alias{show,FLXP-method} \title{Creates the Concomitant Variable Model} \description{ Creator functions for the concomitant variable model. \code{FLXPconstant} specifies constant priors and \code{FLXPmultinom} multinomial logit models for the priors. } \usage{ FLXPconstant() FLXPmultinom(formula = ~1) } \arguments{ \item{formula}{A formula for determining the model matrix of the concomitant variables.} } \details{ \code{FLXPmultinom} uses \code{nnet.default} from \pkg{nnet} to fit the multinomial logit model. } \value{ Object of class \code{FLXP}. \code{FLXPmultinom} returns an object of class \code{FLXPmultinom} which extends class \code{FLXP} directly and is used for method dispatching. } \author{Friedrich Leisch and Bettina Gruen} \keyword{models} flexmix/man/FLXcomponent-class.Rd0000644000176200001440000000147014404637306016460 0ustar liggesusers% % Copyright (C) 2004-2015 Friedrich Leisch and Bettina Gruen % $Id: FLXcomponent-class.Rd 5008 2015-01-13 20:30:25Z gruen $ % \name{FLXcomponent-class} \docType{class} \alias{FLXcomponent-class} \alias{show,FLXcomponent-method} \title{Class "FLXcomponent"} \description{A fitted component of a \code{\link{flexmix}} model.} \section{Objects from the Class}{ Objects can be created by calls of the form \code{new("FLXcomponent", ...)}. } \section{Slots}{ \describe{ \item{\code{df}:}{Number of parameters used by the component.} \item{\code{logLik}:}{Function computing the log-likelihood of observations.} \item{\code{parameters}:}{List with model parameters.} \item{\code{predict}:}{Function predicting response for new data.} } } \author{Friedrich Leisch and Bettina Gruen} \keyword{classes} flexmix/DESCRIPTION0000644000176200001440000000344214760252622013445 0ustar liggesusersPackage: flexmix Type: Package Title: Flexible Mixture Modeling Version: 2.3-20 Authors@R: c(person("Bettina", "Gruen", role = c("aut", "cre"), email = "Bettina.Gruen@R-project.org", comment = c(ORCID = "0000-0001-7265-4773")), person("Friedrich", "Leisch", role = "aut", comment = c(ORCID = "0000-0001-7278-1983")), person("Deepayan", "Sarkar", role = "ctb", comment = c(ORCID = "0000-0003-4107-1553")), person("Frederic", "Mortier", role = "ctb"), person("Nicolas", "Picard", role = "ctb", comment = c(ORCID = "0000-0001-5548-9171"))) Description: A general framework for finite mixtures of regression models using the EM algorithm is implemented. The E-step and all data handling are provided, while the M-step can be supplied by the user to easily define new models. Existing drivers implement mixtures of standard linear models, generalized linear models and model-based clustering. Depends: R (>= 2.15.0), lattice Imports: graphics, grid, grDevices, methods, modeltools (>= 0.2-16), nnet, stats, stats4, utils Suggests: actuar, codetools, diptest, Ecdat, ellipse, gclus, glmnet, lme4 (>= 1.1), MASS, mgcv (>= 1.8-0), mlbench, multcomp, mvtnorm, SuppDists, survival License: GPL (>= 2) LazyLoad: yes NeedsCompilation: no Packaged: 2025-02-26 14:53:48 UTC; gruen Author: Bettina Gruen [aut, cre] (), Friedrich Leisch [aut] (), Deepayan Sarkar [ctb] (), Frederic Mortier [ctb], Nicolas Picard [ctb] () Maintainer: Bettina Gruen Repository: CRAN Date/Publication: 2025-02-28 06:20:02 UTC