Subgroup detection in linear growth curve models with generalized linear mixed model (GLMM) trees

Universität Innsbruck Abstract Growth curve models are popular tools for studying the development of a response variable within subjects over time. Heterogeneity between subjects is common in such models, and researchers are typically interested in explaining or predicting this heterogeneity. We show how generalized linear mixed effects model (GLMM) trees can be used to identify subgroups with differently shaped trajectories in linear growth curve models. Originally developed for clustered cross-sectional data, GLMM trees are extended here to longitudinal data. The resulting extended GLMM trees are directly applicable to growth curve models as an important special case. In simulated and real-world data, we assess the performance of the extensions and compare against other partitioning methods for growth curve models. Extended GLMM trees perform more accurately than the original algorithm and LongCART, and similarly accurate as structural equation model (SEM) trees. In addition, GLMM trees allow for modeling both discrete and continuous time series, are less sensitive to (mis-)specification of the random-effects structure and are much faster to compute. Introduction Development over time is of prime interest in psychological research. For example, in educational studies researchers may want to model student's academic development over time; in clinical studies researchers may want to model patients' symptoms over time. Mixed-effects or latent-variable models can be used to model such trajectories and allow for explaining heterogeneity with covariates of a-priori known relevance (e.g., McNeish However, when these covariates are not known in advance, methods for identifying them are needed.