Mixture Multigroup Bayesian SEM With Approximate Measurement Invariance for Comparing Structural Relations Across Many Groups

Authors

  • Hongwei Zhao Orcid
    Quantitative Psychology and Individual Differences, KU Leuven, Leuven, Belgium
  • Jeroen K. Vermunt Orcid
    Department of Methodology, Tilburg School of Social and Behavioral Sciences, Tilburg University, Tilburg, the Netherlands
  • Kim De Roover Orcid
    Quantitative Psychology and Individual Differences, KU Leuven, Leuven, Belgium; Department of Methodology, Tilburg School of Social and Behavioral Sciences, Tilburg University, Tilburg, the Netherlands

Abstract

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.