Latent Heterogeneity in High School Academic Growth: A Comparison of the Performance of Growth Mixture Model, Structural Equation Modeling Tree, and Forest

Abstract

The Growth Mixture Model (GMM) is associated with several class enumeration issues. The contemporary advancement of automated algorithms presents two promising alternatives that merge confirmatory Structural Equation Modeling (SEM) with exploratory data-mining algorithms: SEM Tree and SEM Forest. This study investigated the performance of the aforementioned three methods (i.e., the GMM, SEM Tree, and SEM Forest) to detect latent heterogeneity in academic growth across four high school grades using an illustrative subsample of the Longitudinal Study of High School of 2009. The findings showed remarkable differences in detecting latent heterogeneity across the three methods as indicated by a parsimonious number of classes, with more unique growth trajectories, capturing the latent heterogeneity in the growth factors. In contrast, SEM Tree and SEM Forest were better at tracking the influences of covariates in the model parameters’ heterogeneity, as indicated by providing more accurate measures of covariate importance and a detailed description of the role of covariates at each level of the tree or the forest. These findings imply the complementary use of these methods to obtain a clear separation between growth trajectories, as estimated by GMM; and the inclusion of most influential covariates, as identified by SEM Tree and Forest (208 words).