A tutorial on fitting flexible meta-analytic models with structural equation modeling in R

Abstract

There are various statistical models with different features and assumptions in meta-analysis. Popular models include 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 (also known as the 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 the specification and generation of graphical models for these meta-analytic models. Researchers may fit these models with the full information maximum likelihood estimation method. 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 the development and evaluation of novel meta-analytical models, which have not yet been implemented in current meta-analysis software, thereby fostering advancements in meta-analytic methods. This tutorial also demonstrates, using two real datasets, how to extend it to address research questions involving complex meta-analytic data. Limitations and future directions to extend the SEM-based meta-analysis are discussed.