Package: RoBMA 4.0.0

RoBMA: 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, 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, <doi:10.1002/jrsm.1594>; Maier, Bartoš & Wagenmakers, 2022, <doi:10.1037/met0000405>; Bartoš et al., 2025, <doi:10.1037/met0000737>). Users can specify flexible prior distributions for effect sizes, heterogeneity, publication bias (including selection models and PET-PEESE), and moderators.

Authors:František Bartoš [aut, cre], Maximilian Maier [aut], Eric-Jan Wagenmakers [ths], Joris Goosen [ctb], Matthew Denwood [cph], Martyn Plummer [cph]

RoBMA_4.0.0.tar.gz
RoBMA_4.0.0.zip(r-4.7)RoBMA_4.0.0.zip(r-4.6)RoBMA_4.0.0.zip(r-4.5)
RoBMA_4.0.0.tgz(r-4.6-x86_64)RoBMA_4.0.0.tgz(r-4.6-arm64)RoBMA_4.0.0.tgz(r-4.5-x86_64)RoBMA_4.0.0.tgz(r-4.5-arm64)
RoBMA_4.0.0.tar.gz(r-4.7-arm64)RoBMA_4.0.0.tar.gz(r-4.7-x86_64)RoBMA_4.0.0.tar.gz(r-4.6-arm64)RoBMA_4.0.0.tar.gz(r-4.6-x86_64)
manual.pdf |manual.html
DESCRIPTION |NEWS
card.svg |card.png
RoBMA/json (API)

# Install 'RoBMA' in R:
install.packages('RoBMA', repos = c('https://fbartos.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/fbartos/robma/issues

Pkgdown/docs site:https://fbartos.github.io

Uses libs:
  • jags– Just Another Gibbs Sampler for Bayesian MCMC
  • c++– GNU Standard C++ Library v3
Datasets:
  • Anderson2010 - 23 experimental studies from Anderson et al. (2010) that meet the best practice criteria
  • Andrews2021 - 39 study rows on household chaos and child executive functions from a meta-analysis by Andrews et al.
  • Bem2011 - 9 experimental studies from Bem
  • Havrankova2025 - 1159 effect sizes from a meta-analysis of beauty and professional success by Havránková et al.
  • Hoppen2025 - 37 studies from a meta-analysis of social comparison as a behavior change technique by Hoppen et al.
  • Johnides2025 - 412 effect sizes from a meta-analysis of secondary benefits of family-based treatments by Johnides et al.
  • Kroupova2021 - 881 estimates from 69 studies of a relationship between employment and educational outcomes collected by Kroupova et al.
  • Lui2015 - 18 studies of a relationship between acculturation mismatch and intergenerational cultural conflict collected by Lui
  • ManyLabs16 - 55 effect sizes from Many Labs 2 replication studies of Tversky and Kahneman (1981) framing effects
  • Poulsen2006 - 5 studies with a tactile outcome assessment from Poulsen et al. (2006) of the effect of potassium-containing toothpaste on dentine hypersensitivity
  • Wang2025 - 70 effect sizes from a meta-analysis of ChatGPT's impact on student learning by Wang and Fan
  • Weingarten2018 - 582 effect sizes examining the ease-of-retrieval effect from a meta-analysis by Weingarten and Hutchinson

On CRAN:

Conda:

meta-analysismodel-averagingpublication-biasjagscpp

7.86 score 11 stars 55 scripts 858 downloads 1 mentions 73 exports 49 dependencies

Last updated from:09d07b90f9. Checks:12 OK, 1 FAIL. Indexed: yes.

TargetResultTimeFilesSyslog
linux-devel-arm64OK215
linux-devel-x86_64OK235
source / vignettesOK661
linux-release-arm64OK224
linux-release-x86_64OK265
macos-release-arm64OK130
macos-release-x86_64OK292
macos-oldrel-arm64OK151
macos-oldrel-x86_64OK453
windows-develOK212
windows-releaseOK188
windows-oldrelOK210
wasm-releaseFAIL185

Exports:add_looadd_marglikadd_waicas_drawsas_draws_arrayas_draws_dfas_draws_listas_draws_matrixas_draws_rvarsas_zplotbayes_factorbfblupBMABMA.glmmBMA.normbPEESEbPETbridge_samplerbrmabrma.glmmbrma.normbselmodelcheck_loocontr.independentcontr.meandifcontr.orthonormalcovratiodffitsestimate_unit_information_sdfunnelgalbraithinterpretlogmllooloo_compareloo_weightsmarginal_meansplot_diagnosticplot_diagnostic_autocorrelationplot_diagnostic_densityplot_diagnostic_traceplot_pet_peeseplot_priorplot_weightfunctionpooled_effectpooled_heterogeneitypost_probprint_priorpriorprior_factorprior_informedprior_noneprior_PEESEprior_PETprior_weightfunctionradialranefregplotRoBMARoBMA.get_optionRoBMA.optionsset_autofit_controlset_convergence_checkssummary_heterogeneitysummary_modelstrue_effectsvifwaicwf_cumulativewf_fixedwf_independentzplot

Dependencies:abindbackportsBayesToolsbridgesamplingBrobdingnagcheckmateclicodacpp11distributionalextraDistrfarvergenericsggplot2gluegtableisobandlabelinglatticelifecycleloomagrittrMASSMatrixmatrixStatsmvtnormnumDerivpillarpkgconfigposteriorR6rbibutilsRColorBrewerRcppRcppArmadilloRdpackrjagsrlangrunjagsS7scalesstringistringrtensorAtibbleutf8vctrsviridisLitewithr

Bayesian Meta-Analysis
Random-Effects Model | Heterogeneity | Funnel Plot | Meta-Regression with a Continuous Moderator | Comparing Models with Bayes Factors | Adding a Categorical Moderator | Model Diagnostics | References

Last update: 2026-05-07
Started: 2026-05-07

Bayesian Model Averaging
Dataset | Comparing Fixed and Random Effects | From Two Fits to Model Averaging | Adding Effect Averaging | Meta-Regression with Model Averaging | Customizing Prior Components | Other brma Features | References

Last update: 2026-05-07
Started: 2026-05-07

Feature Coverage
References

Last update: 2026-05-07
Started: 2026-05-07

Generalized Linear Mixed-Effects Meta-Analysis
Binomial Random-Effects Model | Default Prior Distributions and the Auxiliary Parameter | Other Inference Helpers | References

Last update: 2026-05-07
Started: 2026-05-07

Informed Bayesian Model-Averaged Meta-Analysis in Medicine
Reproducing Informed Bayesian Model-Averaged Meta-Analysis (BMA) | Visualizing the Results | Adjusting for Publication Bias with Robust Bayesian Meta-Analysis | Footnotes | References

Last update: 2026-05-07
Started: 2026-05-07

Informed Bayesian Model-Averaged Meta-Analysis with Binary Outcomes
Binomial-Normal Bayesian Model-Averaged Meta-Analysis | References

Last update: 2026-05-07
Started: 2026-05-07

Introduction to RoBMA

Last update: 2026-05-07
Started: 2026-05-07

Location-Scale Meta-Analysis
Random-Effects Model | Adding a Scale Predictor | Different Variables in Location and Scale | Scale Predictor Prior Distributions | Other Inference Helpers | References

Last update: 2026-05-07
Started: 2026-05-07

Multilevel Meta-Analysis
Multilevel Random-Effects Model | Heterogeneity: $\tau$ and $\rho$ | Other Inference Helpers | References

Last update: 2026-05-07
Started: 2026-05-07

Multilevel Robust Bayesian Meta-Analysis
When to Use Multilevel RoBMA | Loading the Data | Prior Distributions | Fitting the Multilevel Model | Interpreting the Results | Components Summary | Model-Averaged Estimates | Model Types Summary | Visualizing the Weight Function | Comparison with Single-Level RoBMA | References

Last update: 2026-05-07
Started: 2026-05-07

Multilevel Robust Bayesian Model-Averaged Meta-Regression
Rescaling Prior Distributions for Non-Standardized Effect Sizes | Interpreting the Results | Visual Fit Assessment | References

Last update: 2026-05-07
Started: 2026-05-07

Prior Distributions
Specifying Prior Distributions | Default Prior Distributions | Basic example | Effect-size measures and their scales | Standardized effect-size inputs | Non-standardized inputs | Meta-regression | Per-moderator overrides | Informed Empirical Prior Distributions | Custom Prior Distributions | Prior Distributions and Bayesian Model Averaging | Publication-Bias Prior Distributions | General Considerations and Reporting | References

Last update: 2026-05-07
Started: 2026-05-07

Publication-Bias Adjustment
Default Bias-Adjustment Prior Distributions | Default Fits | PET | PEESE | Weight Function Selection Model | Asymmetric Sampling Funnels | Flexible Bias Prior Distributions | PET without truncation | PEESE without truncation | Selection-model Weight Prior Distributions | Other Inference Helpers | References

Last update: 2026-05-07
Started: 2026-05-07

Robust Bayesian Meta-Analysis
Dataset | Default RoBMA Ensemble | Preset Ensembles | Custom Bias Ensembles | Other Inference Helpers | References

Last update: 2026-05-07
Started: 2026-05-07

Robust Bayesian Model-Averaged Meta-Regression
Data | Frequentist Meta-Regression | Bayesian Meta-Regression Specification | Continuous vs. Categorical Moderators and Prior Distributions | Prior Distributions | Bayesian Model-Averaged Meta-Regression | Publication-Bias-Adjusted Model-Averaged Meta-Regression | References

Last update: 2026-05-07
Started: 2026-05-07

Tutorial: Adjusting for Publication Bias in JASP and R - Selection Models, PET-PEESE, and Robust Bayesian Meta-Analysis
Set-up | Lui (2015) | Data manipulation | Effect size transformations | Re-analysis with random effect meta-analysis | PET-PEESE | Selection models | Robust Bayesian meta-analysis | Specifying Different Prior Distributions | References

Last update: 2026-05-07
Started: 2026-05-07

Zplot Publication-Bias Diagnostics
Getting Started | Applied Examples | Example 1: Ease-of-Retrieval Effect in the Few/Many Paradigm | Example 2: Social Comparison and Behavior Change | Example 3: ChatGPT and Learning Performance | Example 4: Framing Effects from Many Labs 2 | Conclusions | References

Last update: 2026-05-07
Started: 2026-05-07

Readme and manuals

Help Manual

Help pageTopics
RoBMA: Robust Bayesian Meta-AnalysisRoBMA-package RoBMA.package RoBMA_package
Add LOO-PSIS to brma Objectsadd_loo add_loo.brma
Add Marginal Likelihood to brma Objectsadd_marglik add_marglik.brma
Add WAIC to brma Objectsadd_waic add_waic.brma
23 experimental studies from Anderson et al. (2010) that meet the best practice criteriaAnderson2010
39 study rows on household chaos and child executive functions from a meta-analysis by Andrews et al. (2021)Andrews2021
Convert brma Objects to posterior Draws Formatsas_draws as_draws.brma as_draws.default as_draws_array as_draws_array.brma as_draws_array.default as_draws_df as_draws_df.brma as_draws_df.default as_draws_list as_draws_list.brma as_draws_list.default as_draws_matrix as_draws_matrix.brma as_draws_matrix.default as_draws_rvars as_draws_rvars.brma as_draws_rvars.default
Convert brma_samples to posterior Draws Formatsas_draws.brma_samples as_draws_array.brma_samples as_draws_df.brma_samples as_draws_list.brma_samples as_draws_matrix.brma_samples as_draws_rvars.brma_samples
Transform brma Object to Zplotas_zplot as_zplot.brma
Convert brma_samples to Matrixas.matrix.brma_samples
9 experimental studies from Bem (2011) as described in Bem et al. (2011)Bem2011
Bayes Factor for brma Objectsbayes_factor.brma bf.brma
Best Linear Unbiased Predictions (BLUPs)blup
Best Linear Unbiased Predictions for brma Objectsblup.brma
Bayesian Model-Averaged Meta-AnalysisBMA BMA.norm
Bayesian Model-Averaged Generalized Meta-AnalysisBMA.glmm
Bayesian Precision-Effect Estimate with Standard Errors (PEESE) ModelbPEESE
Bayesian Precision-Effect Test (PET) ModelbPET
Bridge Sampling for brma Objectsbridge_sampler.brma
Bayesian Meta-Analysisbrma brma.norm
Bayesian Generalized Meta-Analysisbrma.glmm
Bayesian Selection Modelbselmodel
Check LOO Diagnostics for brma Objectscheck_loo check_loo.brma
Extract Model Coefficients for brma Objectscoef.brma
BayesTools Contrast Matricescontr.BayesTools contr.independent contr.meandif contr.orthonormal
Cook's Distance for brma Objectscooks.distance.brma
COVRATIO for brma Objectscovratio covratio.brma
Input Data Specificationdata_input
DFBETAS for brma Objectsdfbetas.brma
DFFITS for brma Objectsdffits dffits.brma
Estimate Unit Information Standard Deviationestimate_unit_information_sd
Fitted Values for brma Objectsfitted.brma
Fitting specificationfitting_specification
Funnel Plot for brma Objectfunnel funnel.brma
Hat Values for brma Objectshatvalues.brma
1159 effect sizes from a meta-analysis of beauty and professional success by Havránková et al. (2025)Havrankova2025
Histogram of Z-Statisticshist.zplot_brma
37 studies from a meta-analysis of social comparison as a behavior change technique by Hoppen et al. (2025)Hoppen2025
Measure Influence for brma Objectsinfluence.brma
Interpret brma Resultsinterpret interpret.brma interpret.default print.interpret.brma
412 effect sizes from a meta-analysis of secondary benefits of family-based treatments by Johnides et al. (2025)Johnides2025
881 estimates from 69 studies of a relationship between employment and educational outcomes collected by Kroupova et al. (2021)Kroupova2021
Add Zplot Density Lineslines.zplot_brma
Extract Log-Likelihood Matrix from brma ObjectlogLik.brma
Log Marginal Likelihood for brma Objectslogml.brma
Compare brma Models Using LOOloo_compare loo_compare.brma
Compare loo Objects Using LOOloo_compare.loo
Extract Normalized PSIS Weights from brma Objectloo_weights loo_weights.brma
LOO-PSIS for brma Objectsloo loo.brma
18 studies of a relationship between acculturation mismatch and intergenerational cultural conflict collected by Lui (2015)Lui2015
55 effect sizes from Many Labs 2 replication studies of Tversky and Kahneman (1981) framing effectsManyLabs16
Estimated Marginal Meansmarginal_means
Estimated Marginal Means for brma Objectsmarginal_means.brma
Number of Observations for brma Objectsnobs.brma
Plot MCMC Diagnosticsplot_diagnostic plot_diagnostic.brma plot_diagnostic_autocorrelation plot_diagnostic_autocorrelation.brma plot_diagnostic_density plot_diagnostic_density.brma plot_diagnostic_trace plot_diagnostic_trace.brma
Plot PET-PEESE Fit of brma Objectplot_pet_peese plot_pet_peese.brma
Plot Prior Distributionsplot_prior plot_prior.brma plot_prior.prior
Plots Weight Function of brma Objectplot_weightfunction plot_weightfunction.brma
Plots brma Objectplot.brma
Plot Estimated Marginal Meansplot.marginal_means.brma
Plot Zplot Resultsplot.zplot_brma
Pooled Effect Sizepooled_effect
Pooled Effect Size for brma Objectspooled_effect.brma
Pooled Heterogeneitypooled_heterogeneity
Pooled Heterogeneity for brma Objectspooled_heterogeneity.brma
Posterior Model Probabilities for brma Objectspost_prob.brma
5 studies with a tactile outcome assessment from Poulsen et al. (2006) of the effect of potassium-containing toothpaste on dentine hypersensitivityPoulsen2006
Predict From brma Objectpredict.brma
Print Prior Distributionsprint_prior print_prior.brma print_prior.prior
Print brma_samples Objectprint.brma_samples
Print Estimated Marginal Meansprint.marginal_means.brma
Print method for RoBMA_data objectsprint.RoBMA_data
Print Summary of Heterogeneityprint.summary_heterogeneity.brma
Print summary.brma_samples Objectprint.summary.brma_samples
Print Summary of Estimated Marginal Meansprint.summary.marginal_means.brma
Print Zplot Summaryprint.summary.zplot_brma
Print VIF Resultsprint.vif.brma
Prior Distributionprior
Factor Priorprior_factor
Informed Priorprior_informed
Empty Priorprior_none
PEESE Priorprior_PEESE
PET Priorprior_PET
Prior specificationprior_specification
Weightfunction Priorprior_weightfunction wf_cumulative wf_fixed wf_independent
Publication-bias prior specificationbias_prior_specification publication_bias_prior_specification
Normal QQ Plot for brma Objectqqnorm.brma
Radial (Galbraith) Plot for brma Objectgalbraith galbraith.brma radial radial.brma
Random Effectsranef
Random Effects for brma Objectsranef.brma
Regression Plot (Bubble Plot) for brma Objectregplot regplot.brma
Residuals for brma Objectsresiduals.brma
Robust Bayesian Model-Averaged Meta-AnalysisRoBMA
Control MCMC fitting processRoBMA_control set_autofit_control set_convergence_checks
Options for the RoBMA packageRoBMA.get_option RoBMA.options RoBMA_options
Prior specification for model-averagingRoBMA_prior_specification
Internally Standardized Residuals for brma Objectsrstandard.brma
Externally Standardized (Studentized) Residuals for brma Objectsrstudent.brma
Summary of Heterogeneitysummary_heterogeneity
Summary of Heterogeneity for brma Objectssummary_heterogeneity.brma
Summarize Model-Averaged Component Weightsprint.summary_models.RoBMA summary_models summary_models.RoBMA
Summarize brma Objectprint.brma print.summary.brma summary.brma
Summarize brma_samples Objectsummary.brma_samples
Summarize Estimated Marginal Meanssummary.marginal_means.brma
Summarize Zplot Resultssummary.zplot_brma
True Effectstrue_effects
True Effects for brma Objectstrue_effects.brma
Update a brma Fitupdate.brma
Variance Inflation Factorsvif
Variance Inflation Factors for brma Objectsvif.brma
WAIC for brma Objectswaic waic.brma
70 effect sizes from a meta-analysis of ChatGPT's impact on student learning by Wang and Fan (2025)Wang2025
582 effect sizes examining the ease-of-retrieval effect from a meta-analysis by Weingarten and Hutchinson (2018)Weingarten2018
Plot Zplot Diagnostics Directlyzplot zplot.brma zplot.zplot_brma