A Practical Tutorial in R for Meta-Analytic Structural Equation Modeling With Hierarchical Effect-Size Dependency and Study-Level Moderators

In this tutorial, I provide a comprehensive, step-by-step guide to conducting two-stage meta-analytic structural equation modeling with hierarchical effect-size dependency and moderation analyses. I illustrate the procedure using a data set of correlations between Big Five personality traits and psychological flow across multiple studies. The proposed workflow uses multilevel-multivariate random-effects pooling in Stage 1 and structural equation modeling in Stage 2. A key feature is a working-model approach to Stage 1 heterogeneity: I fit and compare interpretable heterogeneity structures (e.g., compound-symmetry and heterogeneous compound-symmetry variants) and select the best-fitting pooling model before constructing the Stage 2 inputs. I then demonstrate how to evaluate a categorical moderator (i.e., flow questionnaire) via multigroup comparison. I also illustrate how to test heterogeneity in individual path coefficients and conduct post hoc pairwise comparisons. By walking through the full two-stage meta-analytic structural-equation-modeling workflow using real data and reproducible R code, I intend this tutorial for researchers in psychology, education, and the social sciences who seek to synthesize findings across studies regardless of prior experience with meta-analytic structural equation modeling.