The SEM Reliability Paradox in a Bayesian Framework

Within the frequentist structural equation modeling (SEM) framework, adjudicating model quality through measures of fit has been an active area of methodological research. Complicating this conversation is research revealing that a higher quality measurement portion of a SEM can result in poorer estimates of overall model fit than lower quality measurement models, given the same structural misspecifications. Through population analysis and Monte Carlo simulation, we extend the earlier research to recently developed Bayesian SEM measures of fit to evaluate whether these indices are susceptible to the same reliability paradox, in the context of using both uninformative and informative priors. Our results show that the reliability paradox occurs for RMSEA, and to some extent, gamma-hat and PPP (measures of absolute fit); but not CFI or TLI (measures of relative fit), across Bayesian (MCMC) and frequentist (maximum likelihood) SEM frameworks alike. Taken together, these findings indicate that the behavior of these newly adapted Bayesian fit indices map closely to their frequentist analogs. Implications for their utility in identifying incorrectly specified models are discussed.