Correcting for publication bias in multivariate and multilevel meta-analysis: A multivariate step function selection model approach.

Univariate meta-analysis models assume that all effect sizes are independent. This assumption is violated if, for example, two outcomes are reported in a study of interest to the meta-analyst or a study reports multiple experiments administered by the same researchers. The multivariate and multilevel meta-analysis models allow modeling dependent effect sizes. These two models have recently gained in popularity among meta-analysts in psychology, where one of the largest threats to validity of meta-analysis is publication bias where a selective subset of studies remain unpublished. We extend the univariate step function selection model approach, for modeling publication bias, to multivariate and multilevel meta-analyses. We propose strict and relaxed selection models that assign a different publication probability to studies that have only statistically significant outcomes or at least one significant outcome. These two selection models are straightforward approaches for modeling publication bias. Our method can also accommodate more sophisticated alternative selection models, and we discuss possibilities for this. We primarily focus on the method's implementation as a sensitivity analysis where publication probabilities in the selection model are assumed as known but also show how these can be estimated. Simulation studies tailored to two applications show that the proposed method as a sensitivity analysis outperforms the multivariate and multilevel meta-analysis models that do not correct for publication bias. The simulations also show that the publication probability is imprecisely estimated. We offer guidance for applying the proposed method in practice and share R code to facilitate the application of our proposed methodology. (PsycInfo Database Record (c) 2026 APA, all rights reserved).