One model may not fit all: Subgroup detection using model-based recursive partitioning

Model-based recursive partitioning (MOB; Zeileis et al., 2008) is a flexible framework for detecting subgroups of persons showing different effects in a wide range of parametric models. It provides a versatile tool for detecting and explaining heterogeneity in, for example, intervention studies. In this tutorial article, we introduce the general MOB framework. In two specific case studies, we illustrate how MOB-based methods can be used to detect and explain heterogeneity in two widely used frameworks in educational studies: (a) The generalized linear mixed model (GLMM) and (b) item response theory (IRT). In the first case study, we show how GLMM trees (Fokkema et al., 2018) can be used to detect subgroups with different parameters in mixed-effects models. We apply GLMM trees to longitudinal data from a study on the effects of the Head Start pre-school program to identify subgroups of families where children show comparatively larger or smaller gains in performance. In a second case study, we show how Rasch trees (Strobl et al., 2015) can be used to detect subgroups with different item parameters in IRT models (i.e. differential item functioning [DIF]). DIF should be investigated before using test results for group comparisons. We show how a recently developed stopping criterion (Henninger et al., 2023) can be used to guide subgroup detection based on DIF effect sizes.