Frequentist and Bayesian Factorial Invariance Using R

The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian factorial invariance, as well as the frequentist approach, using the recent add-on R packages to show the procedures systematically for testing measurement equivalence via multigroup confirmatory factor analysis. The practical procedure and guidelines for carrying out factorial invariance under MCFA using a classic empirical example are demonstrated. Comparison between the frequentist and the Bayesian procedures and demonstration using priors are another two nuclei of the paper.