Bayesian Meta-Analysis with Weakly Informative Prior Distributions

Developing meta-analytic methods is an important goal for psychological science. When there are few studies in particular, commonly used methods have several limitations, most notably of which is underestimating between-study variability. Although Bayesian methods are often recommended for small sample situations, their performance has not been thoroughly examined in the context of meta-analysis. Here, we characterize and apply weakly informativepriors for estimating meta-analytic models and demonstrate with extensive simulations that fully Bayesian methods overcome boundary estimates of exactly zero between-study variance, better maintain error rates, and have lower frequentist risk according toKullback-Leibler divergence. While our results show that combining evidence with few studiesis non-trivial, we argue that this is an important goal that deserves further considerationin psychology. Further, we suggest that frequentist properties can provide importantinformation for Bayesian modeling. We conclude with meta-analytic guidelines for appliedresearchers that can be implemented with the provided computer code.