Extending Growth Mixture Model to Assess Heterogeneity in Joint Development with Piecewise Linear Trajectories in the Framework of Individual Measurement Occasions

Researchers continue to be interested in exploring the effects that covariates have on the heterogeneity in trajectories. The inclusion of covariates associated with latent classes allows for a more clear understanding of individual differences and a more meaningful interpretation of latent class membership. Many theoretical and empirical studies have focused on investigating heterogeneity in change patterns of a univariate repeated outcome and examining the effects on baseline covariates that inform the cluster formation. However, developmental processes rarely unfold in isolation; therefore, empirical researchers often desire to examine two or more outcomes over time, hoping to understand their joint development where these outcomes and their change patterns are correlated. This study examines the heterogeneity in parallel nonlinear trajectories and identifies baseline characteristics as predictors of latent classes. Our simulation studies show that the proposed model can tell the clusters of parallel trajectories apart and provide unbiased and accurate point estimates with target coverage probabilities for the parameters of interest in general. We illustrate how to apply the model to investigate the heterogeneity in the joint development of reading and mathematics ability from Grade K to 5. In this real-world example, we also demonstrate how to select covariates that contribute the most to the latent classes and transform candidate covariates from a large set into a more manageable set with retaining the meaningful properties of the original set in the structural equation modeling framework.