Extending Mixture of Experts Model to Investigate Heterogeneity of Trajectories: When, Where and How to Add Which Covariates
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Researchers are usually interested in examining the impact of covariates when uncovering sample heterogeneity. The majority of theoretical and empirical studies with such aims focus on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, those 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). 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 estimate the parameters unbiasedly, precisely and exhibit appropriate empirical coverage for a nominal 95% confidence interval. This study also proposes implementing structural equation model forests to shrink the covariate space of MoE models and illustrates how to select covariate and construct a MoE with longitudinal mathematics achievement data.
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