A Model Comparison Approach to Posterior Predictive Model Checks in Bayesian Confirmatory Factor Analysis

Posterior Predictive Model Checking (PPMC) is frequently used for model fit evaluation in Bayesian Confirmatory Factor Analysis (BCFA). In standard PPMC procedures, misfit quantified by comparing the location of an ML-based point estimate to predictive distribution a statistic. When far from center posterior distribution, poor. Not included this approach, however, variability Maximum Likelihood (ML)-based estimates. We propose new method based on distributions hypothesized and saturated BCFA model. The uses as reference Kolmogorov-Smirnov (KS) statistic quantify local models. results simulation study suggest that approach was accurate determining could be comparison. A real data example also provided study.