A Tutorial on Fitting Flexible Meta-Analytic Models with Structural Equation Modeling in R

There are various statistical models with different features and assumptions in meta-analysis. Popular models are, for example, the fixed-effect (or common effect), random-effects, and mixed-effects models. Apart from these models, several alternative models, such as the multiplicative error model (unrestricted weighted least squares model), the hybrid of additive and multiplicative error models, and the location-scale model, have been proposed in the literature. Understanding these models can be challenging for researchers without a solid mathematical background. Implementing or modifying these models is even more challenging for researchers unless they have advanced statistical and programming knowledge. This tutorial elucidates a structural equation modeling (SEM) framework to understand these models. Several R packages are introduced to facilitate thespecifications and generation of graphical models for these meta-analytic models. More importantly, researchers may use the full information maximum likelihood (FIML) estimation method to fit these models. This holds significant potential across two domains. First, it can be used as an educational tool in teaching and learning meta-analytic models. Second, the framework supports developing and evaluating novel meta-analytical models,which have not yet been implemented in current meta-analysis software, fostering advancements in meta-analytic methods. This tutorial also demonstrates with three real datasets how to extend it to address research questions involving complicated meta-analytic models, including nonlinear models, multivariate meta-analysis, and meta-analytic structural equation modeling (MASEM). Limitations and future directions to extend the SEM-based meta-analysis are discussed.