Addressing Heterogeneity with Bayesian Meta-Analytic Mixture Modelling

Unexplained heterogeneity is a pervasive challenge that undermines the validity of meta-analytic inferences, often even after accounting for plausible moderators. To address this issue, this paper introduces a Bayesian meta-analytic mixture modelling approach that enables data-driven clustering of effect sizes. The resulting mixture components can subsequently be interpreted in light of study characteristics and domain knowledge, providing a principled, data-driven way to understand heterogeneity. To accommodate publication bias, I combine the mixture modelling framework with selection models. The number of mixture components and the presence and type of publication bias can be evaluated using Bayes factors. Two simulation studies validate the method and compare it to existing publication bias correction methods. Results show that wrongly assuming effect sizes follow a single normal distribution can substantially distort inferences from standard publication bias correction methods, which can be addressed by using meta-analytic mixture modelling. To facilitate application in practice, I implemented the methods in the R-package metamix.