A Primer on Bayesian Model-Averaged Meta-Analysis
Quentin F. Gronau, Daniel W. Heck, Sophie Wilhelmina Berkhout, Julia M. Haaf, Eric‐Jan Wagenmakers
Abstract
Meta-analysis is the predominant approach for quantitatively synthesizing a set of studies. If the studies themselves are of high quality, meta-analysis can provide valuable insights into the current scientific state of knowledge about a particular phenomenon. In psychological science, the most common approach is to conduct frequentist meta-analysis. In this primer, we discuss an alternative method, Bayesian model-averaged meta-analysis. This procedure combines the results of four Bayesian meta-analysis models: (1) fixed-effect null hypothesis, (2) fixed-effect alternative hypothesis, (3) random-effects null hypothesis, and (4) random-effects alternative hypothesis. These models are combined according to their plausibilities in light of the observed data to address the two key questions "Is the overall effect non-zero?" and "Is there between-study variability in effect size?". Bayesian model-averaged meta-analysis therefore avoids the need to select either a fixed-effect or random-effects model and instead takes into account model uncertainty in a principled manner.