A Comprehensive Evaluation of Model Selection Indices for Class Enumeration in Bayesian Latent Growth Mixture Models
Sarah A. Depaoli, Ihnwhi Heo, Madelin Jauregui, Haiyan Liu, Fan Jia · Structural Equation Modeling A Multidisciplinary Journal · 2025
Class enumeration remains one of the most critical and error-prone steps in latent growth mixture modeling (LGMM), particularly within the Bayesian framework. This study provides a comprehensive simulation-based evaluation of Bayesian model selection indices, focusing on the impact of likelihood formulation (marginal used in this case) and Dirichlet prior specification for class proportions. Although Bayesian methods offer flexibility and robustness in estimating complex models, missteps in class enumeration or inappropriate prior specification can bias results, mislead substantive conclusions, and impair model fit. We systematically varied true population structures and prior specifications to assess how these factors interact to affect model selection accuracy across various indices. We examined the performance of several Bayesian indices: the deviance information criterion (DIC), the Watanabe-Akaike information criterion (WAIC), the leave-one-out information criterion (LOOIC), the expected Akaike information criterion (EAIC), and the expected Bayesian information criterion (EBIC). Our study contributes practical recommendations for researchers conducting Bayesian LGMM, highlighting methodological best practices and key areas for further development with respect to model comparison and selection indices in the Bayesian framework. These results advance our understanding of model selection behavior in complex Bayesian mixture models and provide a foundation for improving estimation and inference in applied research.