Chapter 11 “Multilevel” Meta-Analysis

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By the time you reach this chapter, you have already fitted a multilevel meta-analytic model several times. This is because the meta-analytic random-effects model is, by definition, a two-level multilevel model. When people talk about “multilevel meta-analysis”, however, they more commonly what they often think of are three-level meta-analytic models. We introduce these here, because they are an excellent and convenient solution to the problem of dependent data: The situation that arises when you extract several effect sizes from ONE sample. For example, if a study applies one manipulation, and measures three similar dependent variables, then you can calculate three effect sizes from that study, which will be dependent. The best way to account for this dependency is by taking the sampling covariance (similar to the sampling variance of each effect size) between the effect sizes into account. This information is almost never reported by the original authors, however, so a very attractive solution is the three-level multilevel approach (Van den Noortgate et al. 2015), which merely assumes that the sampling covariances are the same between all pairs of effect sizes in all studies.

References

Van den Noortgate, Wim, José Antonio López-López, Fulgencio Marín-Martínez, and Julio Sánchez-Meca. 2015. “Meta-Analysis of Multiple Outcomes: A Multilevel Approach.” Behavior Research Methods 47 (4): 1274–94. https://doi.org/10.3758/s13428-014-0527-2.