In empirical analyses, structural equation models are often misspecified and the distributional assumption underlying normal-theorybased
estimators is routinely violated. This study investigated two alternative methods to the maximum likelihood estimation method in the context of
confirmatory factor analysis: robust maximum likelihood and Bayesian estimation with noninformative priors. A simulation study was conducted to
compare the performance of these two estimation methods when the model is misspecified and data do not follow multivariate normal distributions.
The design factors included factor structures, distributions of item scores, and sample sizes. The performance of these two methods was evaluated
based on model rejection rates, parameter estimates, and standard errors associated with parameter estimates. Results indicated that up to 21.45% of
replications encountered inadmissible solutions when models were analyzed using robust maximum likelihood estimation methods, whereas all models
converged to proper solutions when Bayesian estimation with noninformative priors were applied. Bayesian estimation yielded high power for detecting
model misspecification when data present nonnormality. However, caution should be made when using Bayesian estimation with non-informative
priors for data with small sample sizes and following normal distributions.