Score-Guided Recursive Partitioning of Continuous-Time Structural Equation Models

Model-based recursive partitioning is a powerful approach to analyzing heterogeneity between subjects. In the past decade, the semtree software package has established itself as one of the primary tools for the recursive partitioning of structural equation models (SEM). The resulting SEM trees partition the sample into groups of similar individuals while identifying the most important predictors of group differences in the process. However, until recently, an ad hoc covariate testing procedure that was computationally demanding and favored the selection of certain covariates over others hindered the partitioning of complex SEMs. These hurdles have been overcome by selecting covariates utilizing score-based tests, which offer unbiased covariate selection and drastically reduce the runtime of trees. In this chapter, we show how semtree can be used to uncover heterogeneity in dynamic structural equation models for longitudinal data, focusing on continuous-time (CT) models. Unlike the more widely used discrete-time (DT) models, CT models do not require the time intervals between measurements to be equal and, therefore, can adapt effortlessly to irregular sampling schemes. Thus, our resulting approach, which we call score-based CTSEM trees, is well suited to deal with heterogeneity between individuals and measurement occasions. We illustrate the approach with empirical data from the Survey of Health, Ageing and Retirement in Europe.