Beta Mixed-Effects Regression Trees
Model-based recursive partitioning based on mixed-effects beta regression. utf8
betamertree(formula, data, family = NULL, weights = NULL, cluster = NULL, ranefstart = NULL, offset = NULL, REML = TRUE, joint = TRUE, abstol = 0.001, maxit = 100, dfsplit = TRUE, verbose = FALSE, plot = FALSE, glmmTMB.control = glmmTMB::glmmTMBControl(), ...)
formula: formula specifying the response variable and a three-part right-hand-side describing the regressors, random effects, and partitioning variables, respectively. For details see below.data: data.frame to be used for estimating the model tree.family: currently not used. The default beta distribution parameterization of package betareg is used, see also ?glmmTMB::beta_family.weights: numeric. An optional numeric vector of weights. Can be a name of a column in data or a vector of length nrow(data).cluster: currently not used.ranefstart: currently not used.offset: optional numeric vector to be included in the linear predictor with a coeffcient of one. Note that offset can be a name of a column in data or a a numeric vector of length nrow(data).joint: currently not used. Fixed effects from the tree are always (re-)estimated jointly along with the random effects.abstol: numeric. The convergence criterion used for estimation of the model. When the difference in log-likelihoods of the random-effects model from two consecutive iterations is smaller than abstol, estimation of the model tree has converged.maxit: numeric. The maximum number of iterations to be performed in estimation of the model tree.dfsplit: logical or numeric. as.integer(dfsplit) is the degrees of freedom per selected split employed when extracting the log-likelihood.verbose: Should the log-likelihood value of the estimated random-effects model be printed for every iteration of the estimation?plot: Should the tree be plotted at every iteration of the estimation? Note that selecting this option slows down execution of the function.REML: logical scalar. Should the fixed-effects estimates be chosen to optimize the REML criterion (as opposed to the log-likelihood)? Will be passed to funtion glmmTMB(). See glmmTMB for details.glmmTMB.control: list. An optional list with control parameters to be passed to glmmTMB(). See glmmTMBControl for details....: Additional arguments to be passed to lmtree() or glmtree(). See mob_control documentation for details.Function betamertree aims to learn a tree where each terminal node is associated with different fixed-effects regression coefficients, while adjusting for global random effects (such as a random intercept). It is a generalization of the ideas underlying function glmertree, to allow for detection of subgroups with different fixed-effects parameter estimates, keeping the random effects constant throughout the tree (i.e., random effects are estimated globally). The estimation algorithm iterates between (1) estimation of the tree given an offset of random effects, and (2) estimation of the random effects given the tree structure. See Fokkema et al. (2018) for a detailed description.
Where glmertree uses function glmtree from package partykit to find the subgroups, and function glmer from package lme4 to estimate the mixed-effects model, betamertree uses function betatree from package betareg to find the subgroups, and function glmmTMB from package package glmmTMB to estimate the mixed-effects model.
The code is experimental and will change in future versions.
The function returns a list with the following objects: - tree: The final betatree.
glmmTMB: The final glmmTMB random-effects model.
ranef: The corresponding random effects of glmmTMB.
varcorr: The corresponding VarCorr(glmmTMB).
variance: The corresponding attr(VarCorr(glmmTMB), "sc")^2.
data: The dataset specified with the data argument including added auxiliary variables .ranef and .tree
from the last iteration.
loglik: The log-likelihood value of the last iteration.
iterations: The number of iterations used to estimate the betamertree.
maxit: The maximum number of iterations specified with the maxit argument.
ranefstart: The random effects used as an offset, as specified with the ranefstart argument.
formula: The formula as specified with the formula argument.
randomformula: The formula as specified with the randomformula argument.
abstol: The prespecified value for the change in log-likelihood to evaluate convergence, as specified with the abstol argument.
mob.control: A list containing control parameters passed to betatree(), as specified with ....
glmmTMB.control: A list containing control parameters passed to glmmTMB(), as specified in the control argument of function glmmTMB.
joint: Whether the fixed effects from the tree were (re-)estimated jointly along with the random effects, specified with the joint argument.
Fokkema M, Smits N, Zeileis A, Hothorn T, Kelderman H (2018). Detecting Treatment-Subgroup Interactions in Clustered Data withGeneralized Linear Mixed-Effects Model Trees . Behavior Research Methods, 50 (5), 2016--2034. tools:::Rd_expr_doi("10.3758/s13428-017-0971-x")
Fokkema M, Edbrooke-Childs J, Wolpert M (2021). Generalized Linear Mixed-Model (GLMM) Trees: A Flexible Decision-TreeMethod for Multilevel and Longitudinal Data.
Psychotherapy Research, 31 (3), 329--341. tools:::Rd_expr_doi("10.1080/10503307.2020.1785037")
Fokkema M, Zeileis A (2024). Subgroup Detection in Linear Growth Curve Models with GeneralizedLinear Mixed Model (GLMM) Trees.
Behavior Research Methods, 56 (7), 6759--6780. tools:::Rd_expr_doi("10.3758/s13428-024-02389-1")
Grün B, Kosmidis I, Zeileis A (2012). Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned. Journal of Statistical Software, 48 (11), 1--25. tools:::Rd_expr_doi("10.18637/jss.v048.i11")
glmmTMB, betatree
if (require("betareg") && require("glmmTMB")) { ## load example data data("ReadingSkills", package = "betareg") ## add random noise (not associated with reading scores) set.seed(1071) ReadingSkills$x1 <- rnorm(nrow(ReadingSkills)) ReadingSkills$x2 <- runif(nrow(ReadingSkills)) ReadingSkills$x3 <- factor(rnorm(nrow(ReadingSkills)) > 0) ReadingSkills$gr <- factor(rep(letters[1:5], length.out = nrow(ReadingSkills))) ## Fit beta mixed-effects regression tree betamer_form <- accuracy ~ iq | gr | dyslexia + x1 + x2 + x3 bmertree <- betamertree(betamer_form, data = ReadingSkills, minsize = 10) VarCorr(bmertree) ranef(bmertree) fixef(bmertree) coef(bmertree) plot(bmertree) predict(bmertree, newdata = ReadingSkills[1:5,]) predict(bmertree) ## see ?predict.glmmmTMB for other arguments that can be passed residuals(bmertree) ## see ?residuals.glmmmTMB for other arguments that can be passed }
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