Bayesian Multilevel Latent Class Profile Analysis: Inference and Estimation for Exploring the Diverse Pathways to Academic Proficiency

Multilevel latent class profile analysis (MLCPA) is a recently developed technique for understanding latent class dynamics in longitudinal studies; however, conventional maximum likelihood (ML) estimation may face challenges, particularly with small sample sizes or boundary solutions. As an alternative method, we propose a Bayesian estimation for MLCPA by employing non-informative prior distributions. In addition, we shed light on the underflow problem, which denotes a phenomenon such that the logarithm of the likelihood is negative infinity due to the multilevel structure. We perform extensive numerical studies to compare the behaviors of the MLE and the Bayesian estimates and investigate the accuracies of approximated model selection criteria. The simulation study revealed that Bayesian estimates are preferred to ML estimates when the underlying latent classes are well-separated, while the ML estimates are preferred when the underlying latent classes overlap. Utilizing the Progress Monitoring and Reporting Network data, which includes longitudinal academic performance metrics, our analysis uncovers distinct pathways of latent classes for students, further differentiated by latent groups of schools. These findings shed light on the considerable variations in academic proficiency trajectories and thus may offer new perspectives on academic proficiency patterns, with important implications for policy development and targeted educational interventions.