UCLA

In meta-analyses with outliers, Empirical Bayes estimates of extreme study results based on conventional random-effects models are often shrunk to an average effect size by a substantial amount. This can be particularly problematic when one is attempting to answer substantive questions concerning how large the largest effect size in a given sample of studies might be. In order to address this issue, I employ a fully Bayesian approach specifying t-distributional assumptions for random effects, using a Gibbs sampling algorithm. Through the empirical data-analysis and a targeted simulation, this study highlights that the Bayes-t models with heavy tails provide robust shrinkage estimates of outliers, thus protecting against over-shrinkage that can arise under maximum likelihood estimation, or when Bayesian models assuming normally-distributed random effects are used.