­­Fit for a Bayesian: An Evaluation of PPP and DIC

Despite its importance to structural equation modeling, model evaluation remains underdeveloped in the Bayesian SEM framework. Posterior predictive p-values (PPP) and deviance information criteria (DIC) are now available in Mplus and WinBUGS for Bayesian model evaluation, but they remain under-utilized. This is largely due to the lack of recommendations and guidelines on their use and interpretation. To address this problem, PPP and DIC were evaluated in a series of Monte Carlo simulation studies. The results from these studies show that both PPP and DIC are influenced by severity of model misspecification, sample size, model size, and choice of prior, and that PPP is additionally influenced by data distribution. It was also found that the cut-offs PPP 0.10 and DIC>7 work best in the conditions and models tested here. This and other recommendations provided in this study will help researchers evaluate their models in a Bayesian SEM analysis, and set the stage for future development and evaluation of PPP, DIC, and other Bayesian SEM fit indices.