Robust Bayesian Meta-Analyses

A framework for Bayesian meta-analysis, including model estimation, prior specification, model comparison, prediction, summaries, visualizations, and diagnostics. The package fits single and model-averaged meta-analytic, meta-regression, multilevel and multivariate, publication bias adjusted, and generalized linear mixed models. The model-averaged meta-analytic models combine competing models based on their predictive performance, weight inference by posterior model probabilities, and test model components using Bayes factors (e.g., effect vs. no effect; Bartoš et al., 2022, ; Maier, Bartoš & Wagenmakers, 2022, ; Bartoš et al., 2025, ). Users can specify flexible prior distributions for effect sizes, heterogeneity, publication bias (including selection models and PET-PEESE), and moderators.

README

Robust Bayesian Meta-Analysis (RoBMA)

The RoBMA R package fits a comprehensive collection of Bayesian meta-analytic models (Bartoš & Maier, 2020). It provides single-model fits, meta-regression, location-scale models, multilevel and multivariate models, fully Bayesian model-averaged ensembles, and built-in publication-bias adjustment using selection models, PET-PEESE, and Robust Bayesian Meta-Analysis (RoBMA). Posterior sampling is performed by JAGS through a custom C++ module that implements the weighted distributions used in selection models. Prior handling, plotting, and Bayesian diagnostics are delegated to the companion BayesTools package.

This introduction maps the package at a high level and points to the more detailed vignettes that follow.

System Requirements

The RoBMA R package requires JAGS 4.x (4.3.1 or newer; JAGS 5 is not supported) (Plummer, 2003). Install JAGS from https://mcmc-jags.sourceforge.io/ before installing the R package.

install.packages("RoBMA")

Note on backwards compatibility. The 4.0 release is not backwards compatible with earlier versions of the package. The Manuscript Companions section accompanies the methodological papers in which the RoBMA R package was originally developed and illustrated; the vignettes there have been updated to the 4.0 version of the package, and the numerical results differ from the published values because the underlying algorithms have changed. To reproduce the published analyses exactly, install RoBMA version 3.6.1 together with BayesTools version 0.2.23:

remotes::install_version("BayesTools", version = "0.2.23")
remotes::install_version("RoBMA",      version = "3.6.1")

Main Functions

The package exposes a small set of high-level fitting functions.

brma() and RoBMA() are the main workhorses. brma() fits a single model in the same spirit as metafor::rma(); RoBMA() averages across an ensemble that includes publication-bias adjustment. BMA() is RoBMA() without the bias-adjustment models. The .mv variants extend these models to multivariate and multilevel data with a known sampling covariance matrix (V) and random-effect formulas (random, e.g., ~ 1 | study / esid), in the same spirit as metafor::rma.mv().

All fitting functions

• share an effect-size interface (yi, sei / vi, measure arguments; the .mv variants also accept V, and the .glmm variants take outcome counts),
• can be extended into a meta-regression (mods argument),
• can be extended into a location-scale model (scale argument),
• can be extended into a multilevel model (cluster argument; random in the .mv variants),
• and produce objects that work with the same set of inference helpers (summary(), plot(), predict(), loo(), funnel(), regplot(), residuals and influence diagnostics, …); see Feature Coverage for the exceptions.

Vignette Map

The vignettes are organized into four sections.

Foundations

The foundations section gives the package overview, prior specification, a baseline brma() workflow, and current feature coverage. The Bayesian Meta-Analysis vignette walks through the BCG-vaccine example from the metafor package in brma(), covering summaries, meta-regression, marginal means, residuals, influence, LOO, and the standard meta-analytic plots.

Correspondence with metafor

Each vignette starts from a metafor package analysis and shows the matching RoBMA R package syntax, output, and diagnostics.

Bayesian Model Averaging

The first vignette introduces model averaging on an ensemble of models with and without effect and heterogeneity. The second extends the ensemble to publication-bias models used in RoBMA().

Manuscript Companions

These vignettes reproduce or update analyses from published papers and serve as references when citing the corresponding methodological work.

Where to Start

• For readers familiar with the metafor package: read Bayesian Meta-Analysis, then the Correspondence with metafor vignettes for the model family they use most.
• For readers new to Bayesian meta-analysis: read Prior Distributions and then Bayesian Meta-Analysis.
• For publication-bias adjustment: read Robust Bayesian Meta-Analysis, with Adjusting for Publication Bias Tutorial as a worked example.

References