Extending growth mixture model to assess heterogeneity in joint development with piecewise linear trajectories in the framework of individual measurement occasions.

Almost always, developmental processes are multivariate in nature such that several outcomes and the development among these variables are correlated; therefore, empirical researchers often desire to examine two or more variables over time to understand how these outcomes and their change patterns are correlated. Multivariate growth models (MGMs) allow researchers to examine the correlations among developmental parameters. This study relaxes one population assumption of MGMs to investigate possible latent classes of joint development. The developed model enables the investigation of heterogeneity in the correlation between longitudinal outcomes and the effect of covariates on heterogeneity. More importantly, we propose using the piecewise linear functional form to estimate the stage-specific growth rates and stage-specific correlations. We demonstrate the proposed model through a simulation study and an analysis of real-world data. Our simulation study shows that the proposed model can separate joint development into multiple latent classes and provide unbiased and accurate point estimates with target coverage probabilities for the parameters of interest. Using longitudinal reading and mathematics scores from Grade K to 5, we demonstrate that the proposed model can capture heterogeneity in the correlation between joint development and estimate the stage-specific correlations. Additionally, we demonstrate how to identify the covariates that contribute the most to latent classes and transform candidate covariates from a large set to a manageable set while retaining the meaningful properties of the original covariate set for the mixture model with joint developmental processes. (PsycInfo Database Record (c) 2023 APA, all rights reserved).