Cognitive lunch -- Cynthia Tong. Zoom.

Bayesian methods have been widely used to estimate models with complex structures. To assess model fit and compare different models, researchers typically use model selection criteria such as Deviance Information Criteria (DIC) and Watanabe-Akaike Information Criteria (WAIC), the calculation of which is based on the likelihoods of the models. When models contain latent variables, the likelihood is specified as conditional on the latent variables in popular Bayesian software (e.g., BUGS, JAGS, Stan). Although it reduces computation work and does not affect model estimation, our previous findings have shown that model comparisons based on the conditional likelihood could be misleading. In contrast, marginal likelihoods can be obtained by integrating out the latent variables and be used to calculate model selection criteria. In this study, we evaluate the effect of using conditional likelihoods and marginal likelihoods in model selection for a series of models (e.g., growth curve models, growth mixture models, etc.). Simulation results suggest that marginal likelihoods are much more reliable and should be generally used for models with latent variables.