Mixture multigroup Bayesian SEM with approximate measurement invariance for comparing structural relations across many groups

In social sciences, researchers often compare relations between constructs, referred to as “structural relations”, across a large number of groups. This paper proposes Mixture Multigroup Bayesian SEM (MixMG-BSEM), a novel method for comparing structural relations across many groups while accounting for approximate measurement invariance in factor loadings. Traditional methods often assume exact measurement invariance, which may not reflect real-world data where small differences in measurement parameters commonly occur across many groups. MixMG-BSEM addresses this by using Multigroup Bayesian CFA with small-variance priors to allow for these small differences, and groups are then clustered based on their structural relations using Mixture Modeling. This is done in a stepwise estimation procedure built on the structural-after-measurement approach. By combining cluster-specific structural relations with small between-group differences in measurement parameters, MixMG-BSEM obtains a clustering that is driven only by the structural relations. The robustness and effectiveness of MixMG-BSEM are demonstrated through a simulation study.