Small-Variance Priors Can Prevent Detecting Important Misspecifications in Bayesian Confirmatory Factor Analysis

We simulated Bayesian CFA models to investigate the power of PPP to detect model misspecification by manipulating sample size, strongly and weakly informative priors for nontarget parameters, degree of misspecification, and whether data were generated and analyzed as normal or ordinal. Rejection rates indicate that PPP lacks power to reject an inappropriate model unless priors are unrealistically restrictive (essentially equivalent to fixing nontarget parameters to zero) and both sample size and misspecification are quite large. We suggest researchers evaluate global fit without priors for nontarget parameters, then search for neglected parameters if PPP indicates poor fit.