# Introduction to RoBMA

#### František Bartoš

#### 28th of April 2026

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 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 4.3.1 or newer (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()` | Bayesian random-effects meta-analysis
`brma.glmm()` | Bayesian GLMM meta-analysis (binomial / log OR or Poisson / log IRR)
`bselmodel()` | Bayesian weight-function selection model
`bPET()`, `bPEESE()` | Bayesian PET / PEESE publication-bias adjustment
`BMA()`, `BMA.norm()` | Bayesian model-averaging across presence / absence of effect and heterogeneity (no bias adjustment)
`BMA.glmm()` | Bayesian model-averaging for GLMM meta-analysis
`RoBMA()` | 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.

All fitting functions

- share an effect-size interface (`yi`, `sei` / `vi`, `measure` arguments; apart from glmm),
- 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),
- and all produce objects that work with the same set of inference helpers (`summary()`, `plot()`, `predict()`, `loo()`, `funnel()`, `regplot()`, residuals and influence diagnostics, …).

## 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

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

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.