Fitting Structural Equation Model Trees and Latent Growth Curve Mixture Models in Longitudinal Designs: The Influence of Model Misspecification

Abstract

When conducting longitudinal research, the investigation of between-individual differences in patterns of within-individual change can provide important insights. In this article, we use simulation methods to investigate the performance of a model-based exploratory data mining technique—structural equation model trees (SEM trees; Brandmaier, Oertzen, McArdle, & Lindenberger, 2013)—as a tool for detecting population heterogeneity. We use a latent-change score model as a data generation model and manipulate the precision of the information provided by a covariate about the true latent profile as well as other factors, including sample size, under the possible influences of model misspecifications. Simulation results show that, compared with latent growth curve mixture models, SEM trees might be very sensitive to model misspecification in estimating the number of classes. This can be attributed to the lower statistical power in identifying classes, resulting from smaller differences of parameters prescribed by the template model between classes.

Keywords:

• classification
• decision trees
• latent growth curve mixture models
• longitudinal data
• structural equation model trees

Notes

¹ In McArdle et al. (2004), residual variances are fixed to zero, so we also specify these values as zero in this simulation.

² We specified these levels of the factors to range from small to large values so that the simulation could cover various kinds of developmental trajectories that appear in actual longitudinal data. Although the difference in results from the N = 5,000 and N = 3,000 conditions might not be clear, we considered these conditions useful because it was empirically expected that many sample sizes would be required for precise estimation of the coupling parameters () in LCS models due to possible multicollinearity between factor scores (see Usami et al., 2015b for more details). For the degree of separation , values such as and were not considered to be large enough for detecting population heterogeneity in LGCMMs based on previous research results (e.g., Henson et al., 2007; Todo & Usami, 2016), so larger values, such as 4.0 and 5.0, are also specified here.