Understanding Deviance Information Criterion for Bayesian Fit of SEM: Cautiousness in Prior Specification

Deviance information criterion (DIC) is a widely used Bayesian fit index. In Bayesian SEM, there are multiple ways to specify priors for parameters (e.g., variance versus standard deviation), which naturally impacts both the effective number of parameters (pD) and DIC. We investigate how priors impact the DIC and provide recommendations.