Extending Mixture of Experts Model to Investigate Heterogeneity of Trajectories: When, Where, and How to Add Which Covariates

• Published in: Psychological methods 2023-02, Vol.28 (1), p.152-178
• Main Authors: Liu, Jin, Perera, Robert A.
• Format: Article
• Language: English
• Subjects: Computer Simulation; Experience Level; Humans; Latent Class Analysis; Mathematics Achievement; Measurement; Models, Theoretical; Nonlinear Regression; Simulation; Structural Equation Modeling
• ISSN: 1082-989X; 1939-1463
• DOI: 10.1037/met0000436

Researchers are usually interested in examining the impact of covariates when separating heterogeneous samples into latent classes that are more homogeneous. The majority of theoretical and empirical studies with such aims have focused on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, the covariates only indirectly affect the sample heterogeneity. However, the covariates' influence on between-individual differences can also be direct. This article presents a mixture model that investigates covariates to explain within-cluster and between-cluster heterogeneity simultaneously, known as a mixture-of-experts (MoE) model. This study aims to extend the MoE framework to investigate heterogeneity in nonlinear trajectories: to identify latent classes, covariates as predictors to clusters, and covariates that explain within-cluster differences in change patterns over time. Our simulation studies demonstrate that the proposed model generally estimates the parameters unbiasedly, precisely, and exhibits appropriate empirical coverage for a nominal 95% confidence interval. This study also proposes implementing structural equation model forests to shrink the covariate space of the proposed mixture model. We illustrate how to select covariates and construct the proposed model with longitudinal mathematics achievement data. Additionally, we demonstrate that the proposed mixture model can be further extended in the structural equation modeling framework by allowing the covariates that have direct effects to be time-varying. Translational AbstractThe examination of person-level change or trajectories over time is a commonly used method in the social and behavioral sciences. Often, it is of interest to group or cluster individuals into a small number of classes (groups) that share similar growth trajectories. Additionally, researchers may aim to explore how covariates influence the likelihood a person belongs to a certain class as well as their effects on the person's trajectory. For example, when examining the heterogeneity in mathematics development, researchers may want to build up a model to cluster the trajectories of mathematics scores and identify covariates that inform the cluster formation and those account for within-cluster variability of the developmental process. This article presents a modeling framework that completes these aims. The model performance is evaluated via a simulation study an