Handling within-study variability in moderators and dependence in correlation coefficients: Meta-analytic structural equation modeling.

Meta-analytic structural equation modeling (MASEM) is a flexible modeling framework that combines the strengths of meta-analysis and structural equation modeling. Despite the increasing popularity of the MASEM technique, its usage and scope are limited to relatively simple meta-analytic data structures and moderator hypotheses. Within-study variability in moderator variables and dependence in primary studies' correlation estimates tend to be handled using ad hoc methods. In this study, we demonstrate use of multilevel multivariate modeling with robust variance estimation (RVE) for handling within-study dependence when pooling studies' correlation estimates and we propose how to incorporate categorical moderator values directly into the structural equation model for moderators with values varying within studies. We outline the proposed approach using three stages: (a) specification of the structural equation model using moderator variable categories, (b) pooling correlation matrix elements using the three-level multivariate model with RVE, and (c) testing the moderator hypotheses through either model comparison or direct estimation of structural equation model's path differences. We illustrate the approach using three examples to demonstrate its flexibility across different MASEM models. This framework broadens the scope of moderator hypotheses that can be tested using MASEM and enhances the methodological rigor for handling dependencies in studies' correlation estimates for MASEM.