Variable Selection for Explaining Inter-Individual Heterogeneity in Longitudinal Growth Trajectories

Longitudinal growth modeling enables researchers to understand how individuals change over time and which covariates explain differences in their developmental trajectories. This study examines strategies for identifying the most significant covariates that influence these differences. For these purposes, we compare Bayesian penalization with the widely used traditional approach of restricted maximum likelihood (REML). Our findings show that when the number of individuals exceeds the number of covariates considered, Bayesian penalization performs as well as, or better than, REML. When there are more covariates than individuals, REML cannot be applied, but Bayesian penalization remains effective. We also find that adding more potential covariates does not significantly reduce the performance of Bayesian penalization, although strong correlations among covariates make selection slightly less accurate. We highlight the risk of drawing conclusions from the same data used to select covariates, as this can produce misleading results. To demonstrate the practical value of Bayesian penalization, we apply it to data from the Longitudinal Study of American Youth and provide accessible code to facilitate its application.