Ensemble Methods to Assess Heterogeneity in Joint Development with Nonlinear Trajectories

Researchers are often interested in uncovering heterogeneity in change patterns and grouping trajectories into homogeneous latent classes. A considerable number of theoretical and empirical studies have focused on investigating heterogeneity in change patterns of a univariate repeated outcome. 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. It is also of importance to examine the impact that covariates have on the heterogeneity of joint development. 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 separate parallel change patterns and provide unbiased point estimates with small standard errors and confidence intervals with satisfactory coverage probabilities for the parameters of interest. We illustrate how to apply the model to investigate the heterogeneity of parallel nonlinear trajectories of joint development of reading and mathematics ability from Grade K to 5. In this real-world example, we demonstrate how to employ two methods, feature selection and feature reduction, to address covariate space with a large-dimension and highly correlated subsets in the structural equation modeling framework.