# Chapter 14 Structural Equation Modeling Meta-Analysis

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In the last chapters on Three-Level Meta-Analysis Models and Bayesian Meta-Analysis, we were able to generalize our conceptual knowledge of meta-analyses by showing that meta-analytic models have an **inherent multilevel structure**, which can be used, for example, to extend conventional meta-analysis models to three-level models. A peculiar thing about statistical methods is that they are often put into seperate “boxes”, and treated as unrelated in research and practice, when in fact they are not. For many social scientists, for example, it is often surprising to find out that Analysis of Variance (ANOVA) and dummy-coded Regression are doing essentially the same thing (Montgomery 2001). This often happens because two methods are traditionally used in different contexts, and taught as separate entities.

It might thus have been only fairly recently that researchers recognized that **multilevel models** are simply a special form of a **Structural Equation Model**, or **SEM** (Bauer 2003; Mehta and Neale 2005). As said before, every meta-analysis model is in itself a multilevel model, so this association also has exciting implications for meta-analysts: **we can treat our meta-analysis as a structural equation model**, in which the pooled effect size we want to estimate is the **latent** (or unobserved) variable (Cheung 2015b, 2015a). This does not *only* mean that we can model previous types of meta-analyses we presented before from a SEM perspective, but also allows us to use structural equation modeling to test more complex models meta-analytically. This is a great advantage; for example, using this approach, we can test **mediation** models, **factor analytic** models, or perform **multivariate meta-analyses** based on effect size data obtained from several independent studies. This is a great way to evaluate if certain models or theories in the literature are actually correct if we use all available evidence, if the theory’s assumptions are not backed by the evidence, or, even more interestingly, if the theory does only apply to a subgroup of individuals or entities.

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### References

Montgomery, Douglas C. 2001. “Design and Analysis of Experiments, 2001.” *New York: John Wiley & Sons*, 394–95.

Bauer, Daniel J. 2003. “Estimating Multilevel Linear Models as Structural Equation Models.” *Journal of Educational and Behavioral Statistics* 28 (2). Sage Publications Sage CA: Los Angeles, CA: 135–67.

Mehta, Paras D, and Michael C Neale. 2005. “People Are Variables Too: Multilevel Structural Equations Modeling.” *Psychological Methods* 10 (3). American Psychological Association: 259.

Cheung, Mike W-L. 2015b. “MetaSEM: An R Package for Meta-Analysis Using Structural Equation Modeling.” *Frontiers in Psychology* 5. Frontiers: 1521.

Cheung, Mike W-L. 2015a. *Meta-Analysis: A Structural Equation Modeling Approach*. John Wiley & Sons.