An application of Bayesian structural equation modeling: The sensitivity of Bayesian analysis for item-level measurement invariance

Current applications of structural equation modeling (SEM) are usually guided by the frequentist approach that relies on asymptotic, large-sample theory. Such practice is often too strict, however, leading to non-convergence or unwarranted rejection of the model. Recently Bayesian structural equation modeling (BSEM) has enjoyed increasing attention as a viable alternative to frequentist SEM. This article explores a BSEM approach to assessing measurement invariance. By means of Monte Carlo simulation, multiple indicators multiple causes (MIMIC) confirmatory factor analysis (CFA) is evaluated in terms of sensitivity to prior variance, model fit, bias in parameter estimate, and Type I error and power of testing item-level invariance. The results support BSEM as a potential solution for the well-known problems of a biased anchor. This article offers methodological guidelines and suggestions for applied researchers who are potential BSEM users.