Bayesian Meta-Analysis with Weakly Informative Prior Distributions
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Description: 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 informative priors 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 to Kullback-Leibler divergence. While our results show that combining evidence with few studies is non-trivial, we argue that this is an important goal that deserves further consideration in psychology. Further, we suggest that frequentist properties can provide important information for Bayesian modeling. We conclude with meta-analytic guidelines for applied researchers that can be implemented with the provided computer code.