Selecting an Optimal Measurement Model and Detecting Differential Item Functioning Using Bayesian Confirmatory Factor Analysis

Abstract

I investigated the sampling behavior of DIC and WAIC in the context of selecting an optimal measurement model in Bayesian SEM, as well as the utility of highly constrained parameter estimates in detecting differential item functioning (DIF). I assessed the relative efficiency of WAIC compared to DIC, evaluated analytical WAIC SEs by calculating relative bias, and reported how often WAIC and DIC indicated a preference for each invariance model. I compared the power and Type I error rates for DIF detection across conditions, and assessed the quality of estimates by calculating bias and 95% CI coverage rates for key parameters. Results indicate that although WAIC has less sampling variability than DIC, their model preferences are similar. Both WAIC and DIC have greater power to detect that invariance constraints are untenable than AIC in using maximum likelihood (ML) estimation. In tests of null hypotheses that DIF parameters are zero, Bayesian credible intervals and ML modification indices have similar power, but Bayesian credible intervals have much lower Type I error rates.