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New model fit and evaluation tools have been introduced into the Bayesian structural equation modeling framework, including Bayesian versions of classic approximate fit measures (RMSEA, CFI, and TLI), as well as a new adjustment of the posterior predictive  p -value to properly account for missing data. We examine the performance of these indices for model fit and selection through a simulation study. This study was designed to assess the performance of several indices in the context of model misspecification and missing data across different sample sizes. Findings suggest that Bayesian approximate fit indices may be better suited for model  selection  than they are as direct measures of model  fit . Implications for applied researchers are discussed.

Performance of Model Fit and Selection Indices for Bayesian Structural Equation Modeling with Missing Data