Bayesian confirmatory factor analysis (CFA) offers an alternative to frequentist CFA based on, for example, Maximum Likelihood estimation for the assessment of reliability and validity of educational and psychological measures. For increasing sample sizes, however, the applicability of current fit statistics evaluating model fit within Bayesian CFA is limited. We propose, therefore, a Bayesian variant of the root mean square error of approximation (RMSEA), the BRMSEA. A simulation study was performed with variations in model misspecification, factor loading magnitude, number of indicators, number of factors, and sample size. This showed that the 90% posterior probability interval of the BRMSEA is valid for evaluating model fit in large samples (N ≥ 1,000), using cut-off values for the lower (<.05) and upper limit (< .08) as guideline. An empirical illustration further shows the advantage of the BRMSEA in large sample Bayesian CFA models. In conclusion it can be stated that the BRMSEA is well suited to evaluate model fit in large sample Bayesian CFA models by taking sample size and model complexity into account.

Hoofs, H., van de Schoot, R., Jansen, N. W. H., & Kant, IJ. (2018). Evaluating model fit in Bayesian confirmatory factor analysis with large samples: Simulation study introducing the BRMSEA. Educational and Psychological Measurement, 78 (4), 537-568.