Robust Bayesian multilevel meta-analysis: Adjusting for publication bias in the presence of dependent effect sizes

Meta-analyses often include multiple dependent effect sizes, yet current methods typically neglect the resulting within-study dependencies or fail to address model uncertainty and publication bias adequately. We extend robust Bayesian meta-analysis (RoBMA) to a multilevel framework, simultaneously handling within-study dependencies, model uncertainty, heterogeneity, moderators, and publication bias. Specifically, the three-level RoBMA integrates approximate Bayesian selection models with PET-PEESE adjustments within a hierarchical Bayesian setting. We illustrate the methodology through empirical examples and demonstrate its performance via simulations. The approach is implemented in the RoBMA R package and JASP.