Continuous-Time SEMs Are Like a Box of Predictors!

Understanding how individuals change over time—and how these changes differ across groups—is a central challenge in the behavioral and social sciences. Structural equation model (SEM) trees and forests offer powerful tools for uncovering heterogeneity in SEM parameters, particularly in longitudinal data. While these methods have traditionally relied on discrete-time models, such models can produce biased estimates when measurement intervals vary, a common occurrence in real-world longitudinal studies. Recent advances have enabled SEM trees based on continuous-time (CT) models, which are more flexible with irregular measurement occasions. However, early implementations were limited by computational demands and biased results, especially for forest estimation. The Psychological Research Methods Group (Manuel Völkle)has developed a novel implementation of CT-SEM forests that overcomes these limitation and demonstrated its application using empirical data from the Survey of Health, Ageing, and Retirement in Europe. Learn more about this brand new method and how CT-SEM forests can be used in practice and reflect on their advantages and limitations in their Psychological Methods Article!

Abstract

Structural equation model (SEM) trees and forests are valuable tools for exploring predictors of group differences in SEM parameters. In longitudinal studies, in particular, they hold significant potential for investigating heterogeneity in change and dynamics. In past research, longitudinal SEM trees and forests have been predominantly estimated with the R package semtree, which, until recently, only allowed the estimation of discrete-time models. The problem of discrete-time models is that they may lead to biased estimates when measurement intervals are unevenly spaced, which is frequent in longitudinal studies. As a solution to this problem, recent updates in the semtree package included SEM trees based on continuous-time (CT) models, which do not require constant intervals and can easily adapt to irregular sampling schemes. This implementation, however, yielded biased results and involved a computational burden that was prohibitive for forests. Only very recent work on score-guided algorithms, along with corresponding software implementations, have made CT-SEM forests feasible for empirical practice. In this article, we present a novel implementation of CT-SEM forests that combines the ctsemOMX package for CT modeling, the recursive partitioning infrastructure of the semtree package, and the score-guided covariate testing procedures of the strucchange package. Next, we systematically examine the performance of CT-SEM forests through a Monte Carlo study and illustrate the approach on empirical data from the Survey of Health, Ageing, and Retirement in Europe. Finally, we explore various alternatives for using the information provided by CT-SEM forests and discuss the benefits and limitations of the approach. (PsycInfo Database Record (c) 2025 APA, all rights reserved)