Continuous-time structural equation model forests

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 (DT) models. The problem of DT 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 continuous-time SEM forests feasible for empirical practice. In this paper, 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 trough 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.