Advancing Multigroup Mediation Using Bayesian Regularization

A common challenge in multigroup structural modeling is establishing the correct partial measurement invariance model. Recently, Bayesian regularization methods have been adapted for detecting measurement bias, though their performance in multigroup structural models remains unexplored. This study evaluated the performance of Bayesian regularization approaches for a multigroup mediation model. We compared small-variance priors (SV), Bayesian lasso (BLasso), Bayesian adaptive lasso (BaLasso), spike-and-slab priors (SSP), and horseshoe priors to a traditional approach common in multiple-group confirmatory factor analysis (MGCFA) and Bayesian alignment (BAlign). Results indicated that BAlign yielded lower bias and adequate coverage of indirect effects, even under conditions of pervasive noninvariance. The SSP outperformed the other methods in terms of the estimation of factor means. The BLasso and BaLasso yielded higher coverage under many conditions, while the SV and MGCFA performed poorly under many conditions. This study offers recommendations for researchers conducting multigroup mediation in the presence of measurement noninvariance.