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.

Function	What it fits
brma(), brma.norm(), brma.mv()	Bayesian random-effects meta-analysis
brma.glmm()	Bayesian GLMM meta-analysis (binomial / log OR or Poisson / log IRR)
bselmodel(), bselmodel.mv()	Bayesian weight-function selection model
bPET(), bPEESE(), bPET.mv(), bPEESE.mv()	Bayesian PET / PEESE publication-bias adjustment
BMA(), BMA.norm(), BMA.mv()	Bayesian model-averaging across presence / absence of effect and heterogeneity (no bias adjustment)
BMA.glmm()	Bayesian model-averaging for GLMM meta-analysis
RoBMA(), RoBMA.mv()	Robust Bayesian model-averaging including publication-bias models

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

Vignette	Topic
Introduction to RoBMA	Package overview, fitting functions, and vignette map
Prior Distributions	Default, informed, and custom prior distributions; rescaling guidance
Bayesian Meta-Analysis	Random-effects meta-analysis with brma(), compared with metafor::rma()
Feature Coverage	Overview of available functionality across model families

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

Vignette	Topic
Multilevel Meta-Analysis	brma() with cluster and metafor::rma.mv() for 3-level data
Publication-Bias Adjustment	bselmodel() / bPET() / bPEESE() and metafor::selmodel()
Location-Scale Models	brma() with scale and metafor::rma.ls()
Generalized Linear Mixed-Effects Meta-Analysis	brma.glmm() and metafor::rma.glmm() for binomial and Poisson outcomes
Multivariate and Multilevel Meta-Analysis	brma.mv() with known sampling covariance matrices and structured random effects

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

Bayesian Model Averaging

Vignette	Topic
Bayesian Model Averaging	Accounting for model uncertainty across presence and absence of effect and heterogeneity, with posterior model probabilities and inclusion Bayes factors
Robust Bayesian Meta-Analysis	Extending the ensemble to publication-bias models used in RoBMA(), with PSMA, PP, and bespoke ensemble specifications
Posterior Densities and Parameter Tests	Likelihood-aware posterior densities and hypothesis tests with qCMDE and IWMDE

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

Vignette	Companion paper / dataset
Adjusting for Publication Bias Tutorial	Bartoš et al. (2022), JASP / R tutorial on Lui2015
Robust Bayesian Meta-Regression	Bartoš et al. (2025), RoBMA-reg on Andrews2021
Multilevel Robust Bayesian Meta-Analysis	Bartoš et al. (2026), Multilevel RoBMA on Johnides2025
Multilevel Robust Bayesian Meta-Regression	Multilevel RoBMA-reg on Kroupova2021
Informed Bayesian Meta-Analysis in Medicine	Bartoš et al. (2021), informed prior distributions for medical meta-analysis (continuous outcomes)
Informed Bayesian Meta-Analysis with Binary Outcomes	Bartoš et al. (2023), informed prior distributions for medical meta-analysis (binary and time-to-event outcomes)
Zplot Publication-Bias Diagnostics	Bartoš & Schimmack (2025), zplot diagnostics on Hoppen2025

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

Bartoš, F., Gronau, Q. F., Timmers, B., Otte, W. M., Ly, A., & Wagenmakers, E.-J. (2021). Bayesian model-averaged meta-analysis in medicine. Statistics in Medicine, 40(30), 6743–6761. https://doi.org/10.1002/sim.9170

Bartoš, F., & Maier, M. (2020). RoBMA: An R package for robust Bayesian meta-analyses. https://CRAN.R-project.org/package=RoBMA

Bartoš, F., Maier, M., Quintana, D. S., & Wagenmakers, E.-J. (2022). Adjusting for publication bias in JASP and R — Selection models, PET-PEESE, and robust Bayesian meta-analysis. Advances in Methods and Practices in Psychological Science, 5(3), 1–19. https://doi.org/10.1177/25152459221109259

Bartoš, F., Maier, M., Stanley, T., & Wagenmakers, E.-J. (2025). Robust Bayesian meta-regression: Model-averaged moderation analysis in the presence of publication bias. Psychological Methods. https://doi.org/10.1037/met0000737

Bartoš, F., Maier, M., & Wagenmakers, E.-J. (2026). Robust Bayesian multilevel meta-analysis: Adjusting for publication bias in the presence of dependent effect sizes. Behavior Research Methods. https://doi.org/10.31234/osf.io/9tgp2_v2

Bartoš, F., Otte, W. M., Gronau, Q. F., Timmers, B., Ly, A., & Wagenmakers, E.-J. (2023). Empirical prior distributions for Bayesian meta-analyses of binary and time-to-event outcomes. https://doi.org/10.48550/arXiv.2306.11468

Bartoš, F., & Schimmack, U. (2025). Zplot: A visual diagnostic for publication bias in meta-analysis. In arXiv. https://doi.org/10.48550/arXiv.2509.07171

Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), 1–10.