Random‐effects models for meta‐analytic structural equation modeling: review, issues, and illustrations

Meta‐analytic structural equation modeling (MASEM) combines the techniques of meta‐analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed‐effects and random‐effects models can be defined in MASEM. Random‐effects models are well known in conventional meta‐analysis but are less studied in MASEM. The primary objective of this paper was to address issues related to random‐effects models in MASEM. Specifically, we compared two different random‐effects models in MASEM—correlation‐based MASEM and parameter‐based MASEM—and explored their strengths and limitations. Two examples were used to illustrate the similarities and differences between these models. We offered some practical guidelines for choosing between these two models. Future directions for research on random‐effects models in MASEM were also discussed. Copyright © 2016 John Wiley & Sons, Ltd.