Mixture multigroup structural equation modeling: A novel method for comparing structural relations across many groups

Behavioral scientists often examine the relations between two or more latent variables(e.g., how emotions relate to life satisfaction) and Structural Equation Modeling (SEM) isthe state-of-the-art for doing so. When comparing these ‘structural relations’ among manygroups, they likely differ across the groups. However, it is equally likely that some groupsshare the same relations so that clusters of groups emerge. Latent variables are measuredindirectly by questionnaires and, for validly comparing their relations among groups, themeasurement of the latent variables should be invariant across the groups (i.e.,measurement invariance). However, across many groups, often at least some measurementparameters differ. Restricting these measurement parameters to be invariant, when theyare not, causes the structural relations to be estimated incorrectly and invalidates theircomparison. We propose Mixture Multigroup SEM (MMG-SEM) to gather groups withequivalent structural relations in clusters while accounting for the reality of measurementnon-invariance. Specifically, MMG-SEM obtains a clustering of groups focused on thestructural relations by making them cluster-specific, while capturing measurementnon-invariances with group-specific measurement parameters. In this way, MMG-SEMensures that the clustering is valid and unaffected by differences in measurement. Thispaper proposes an estimation procedure built around the R package ‘lavaan’ and evaluatesMMG-SEM’s performance through two simulation studies. The results demonstrate thatMMG-SEM successfully recovers the group-clustering as well as the cluster-specificrelations and the partially group-specific measurement parameters. To illustrate itsempirical value, we apply MMG-SEM to cross-cultural data on the relations betweenexperienced emotions and life satisfaction.