The Impact of Prior Specifications on Model Comparison in Bayesian Structural Equation Modeling

In Bayesian structural equation modeling (BSEM), prior settings may affect model fit, parameter estimation, and model comparison. This simulation study was to investigate how the priors impact evaluation of relative fit across competing models. The design factors for data generation included sample sizes, factor structures, data distributions, and values of parameters. Data were analyzed by fitting both the correctly specified and two misspecified models. Different sets of priors were applied to cross-loadings and error covariances. Models were compared based on Bayes factors, differences in Bayesian information criterion (BIC), and differences in deviance information criterion (DIC). Preliminary results show that the difference in DIC resulted in the highest power of rejecting misspecified models among these three indexes.