Improving the guidelines to conduct multigroup invariance test in Bayesian SEM



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The aim of the study was to evaluate goodness-of-fit measures in the context of Bayesian Structural Equation Modeling (BSEM) and invariance testing in multigroup models. Garnier-Villarreal and Jorgensen (2020) adapted several approximate fit measures usually applied in frequentist approach. They provided evidence of these adapted measures in single group models, however there was a lack of guidance on how to make decisions in invariance testing in Bayesian approach. I focused my simulation design to test the Bayesian adaptations of the indices: Comparative Fit Index (CFI), Tucker Lewis Index (TLI), Normed Fit Index (NFI), McDonals Centrality Index (Mc), and Gamma Hat index. The results showed that more conditions need to be added to find more evidence of the qualities of these measures. However, this study showed preliminary findings that support the implementation of the Bayesian CFI and Bayesian Gamma Hat in invariance testing. This work is part of a boarder effort to provide more evidence of appropriate fit measures in BSEM.



Bayesian, SEM, Approximate measures, Invariance test