A comparison of three approaches for identifying correlates of heterogeneity in change

Longitudinal research is often interested in identifying correlates of heterogeneity in change. This paper compares three approaches for doing so: the mixed-effects model (latent growth curve model), the growth mixture model, and structural equation model trees. Each method is described, with special focus given to how each structures heterogeneity, attributes that heterogeneity to covariates, and the kinds of research questions each can be used to address. Each approach is used to analyze data from the National Longitudinal Survey of Youth to understand the similarities and differences between methods in the context of empirical data. Specifically, changes in weight across adolescence are examined, as well as how differences in these change patterns can be explained by sex, race, and mother's education. Recommendations are provided for how to select which approach is most appropriate for analyzing one's own data.