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