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Researchers continue to be interested in exploring the effects thatcovariates have on the heterogeneity in trajectories. The inclusion ofcovariates associated with latent classes allows for a more clear understandingof individual differences and a more meaningful interpretation of latent classmembership. Many theoretical and empirical studies have focused oninvestigating heterogeneity in change patterns of a univariate repeated outcomeand examining the effects on baseline covariates that inform the clusterformation. However, developmental processes rarely unfold in isolation;therefore, empirical researchers often desire to examine two or more outcomesover time, hoping to understand their joint development where these outcomesand their change patterns are correlated. This study examines the heterogeneityin parallel nonlinear trajectories and identifies baseline characteristics aspredictors of latent classes. Our simulation studies show that the proposedmodel can tell the clusters of parallel trajectories apart and provide unbiasedand accurate point estimates with target coverage probabilities for theparameters of interest in general. We illustrate how to apply the model toinvestigate the heterogeneity in the joint development of reading andmathematics ability from Grade K to 5. In this real-world example, we alsodemonstrate how to select covariates that contribute the most to the latentclasses and transform candidate covariates from a large set into a moremanageable set with retaining the meaningful properties of the original set inthe structural equation modeling framework.

psychological methods

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