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Package

RoBMA-package RoBMA_package RoBMA.package
RoBMA: Robust Bayesian Meta-Analysis
RoBMA.options() RoBMA.get_option()
Options for the RoBMA package
set_autofit_control() set_convergence_checks()
Control MCMC fitting process

Model fitting

brma()
Bayesian Meta-Analysis
brma.glmm()
Bayesian Generalized Meta-Analysis
brma.mv()
Bayesian Meta-Analysis With Known Sampling Covariance
RoBMA()
Robust Bayesian Model-Averaged Meta-Analysis
RoBMA.mv()
Robust Bayesian Model-Averaged Multivariate Meta-Analysis
BMA()
Bayesian Model-Averaged Meta-Analysis
BMA.glmm()
Bayesian Model-Averaged Generalized Meta-Analysis
BMA.mv()
Bayesian Model-Averaged Multivariate Meta-Analysis
bselmodel()
Bayesian Selection Model
bselmodel.mv()
Bayesian Multivariate and Multilevel Selection Model
bPET()
Bayesian Precision-Effect Test (PET) Model
bPET.mv()
Bayesian Multivariate and Multilevel PET Model
bPEESE()
Bayesian Precision-Effect Estimate with Standard Errors (PEESE) Model
bPEESE.mv()
Bayesian Multivariate and Multilevel PEESE Model
update(<brma>)
Update a brma Fit

Inputs, priors, and model specification

data_input
Input Data Specification
fitting_specification
Fitting specification
prior_specification
Prior specification
RoBMA_prior_specification
Prior specification for model-averaging
publication_bias_prior_specification bias_prior_specification
Publication-bias prior specification
random_effect_formula_tags
Random-Effect Formula Structure Tags
random_effect_prior_specification random_prior_specification
Random-effect prior specification
prior()
Prior Distribution
prior_none()
Empty Prior
prior_factor()
Factor Prior
prior_ordered()
Ordered Factor Prior
prior_informed()
Informed Prior
prior_PET()
PET Prior
prior_PEESE()
PEESE Prior
prior_weightfunction() wf_cumulative() wf_fixed() wf_independent()
Weightfunction Prior
prior_random() random_block() random_variance_allocation() allocation_ref() random_covariance() prior_lkj() random_monitor() random_new_levels() random_sd_source()
Random-effect prior constructors
selection_model()
Selection Model
known_v_factor()
Declare a diagonal-plus-factor sampling covariance
set_selection_likelihood_control()
Control numerical integration of selection likelihoods
estimate_unit_information_sd()
Estimate Unit Information Standard Deviation
contr.orthonormal() contr.meandif() contr.independent()
BayesTools Contrast Matrices

Summaries and estimates

summary(<brma>) print(<summary.brma>) print(<brma>)
Summarize brma Object
interpret() print(<interpret.brma>)
Interpret brma Results
summary_models() print(<summary_models.RoBMA>)
Summarize Model-Averaged Component Weights
summary_heterogeneity()
Summary of Heterogeneity
summary_heterogeneity(<brma>) print(<summary_heterogeneity.brma_list>)
Summary of Heterogeneity for brma Objects
pooled_effect()
Pooled Effect Size
pooled_effect(<brma>)
Pooled Effect Size for brma Objects
pooled_heterogeneity()
Pooled Heterogeneity
pooled_heterogeneity(<brma>)
Pooled Heterogeneity for brma Objects
marginal_means()
Estimated Marginal Means
marginal_means(<brma>)
Estimated Marginal Means for brma Objects
summary(<marginal_means.brma>)
Summarize Estimated Marginal Means
true_effects()
True Effects
true_effects(<brma>)
True Effects for brma Objects
ranef()
Random Effects
ranef(<brma>)
Random Effects for brma Objects
blup()
Best Linear Unbiased Predictions (BLUPs)
blup(<brma>)
Best Linear Unbiased Predictions for brma Objects
coef(<brma>)
Extract Model Coefficients for brma Objects
fitted(<brma>)
Fitted Values for brma Objects
nobs(<brma>)
Number of Observations for brma Objects
predict(<brma>)
Predict From brma Object
hypothesis() bf_hypothesis() BF_hypothesis()
Hypothesis Bayes Factors
reexports bridge_sampler logml post_prob bf bayes_factor hypothesis_quantities loo_model_weights
Objects exported from other packages

Model comparison

add_marglik(<brma>)
Add Marginal Likelihood to brma Objects
bridge_sampler(<brma>)
Bridge Sampling for brma Objects
logml(<brma>)
Log Marginal Likelihood for brma Objects
post_prob(<brma>)
Posterior Model Probabilities for brma Objects
bf(<brma>) bayes_factor(<brma>)
Bayes Factor for brma Objects
add_loo(<brma>)
Add LOO-PSIS to brma Objects
loo(<brma>)
LOO-PSIS for brma Objects
loo_compare(<brma>)
Compare brma Models Using LOO
loo_compare(<loo>)
Compare loo Objects Using LOO
loo_model_weights(<brma>)
Predictive Model Weights for brma Objects
loo_weights(<brma>)
Extract Normalized PSIS Weights from brma Object
check_loo(<brma>)
Check LOO Diagnostics for brma Objects
add_waic(<brma>)
Add WAIC to brma Objects
waic(<brma>)
WAIC for brma Objects
log_lik()
Extract Pointwise Log-Likelihood Draws
logLik(<brma>)
Extract Log-Likelihood Matrix from brma Object
AIC(<brma>) BIC(<brma>)
Unsupported Information Criteria for brma Objects
reexports bridge_sampler logml post_prob bf bayes_factor hypothesis_quantities loo_model_weights
Objects exported from other packages

Diagnostics and influence

influence(<brma>)
Measure Influence for brma Objects
cooks.distance(<brma>)
Cook's Distance for brma Objects
dfbetas(<brma>)
DFBETAS for brma Objects
dffits(<brma>)
DFFITS for brma Objects
covratio(<brma>)
COVRATIO for brma Objects
hatvalues(<brma>)
Hat Values for brma Objects
residuals(<brma>)
Residuals for brma Objects
rstandard(<brma>)
Internally Standardized Residuals for brma Objects
rstudent(<brma>)
Externally Standardized (Studentized) Residuals for brma Objects
vif()
Variance Inflation Factors
vif(<brma>)
Variance Inflation Factors for brma Objects
density_diagnostics()
Extract qCMDE/IWMDE Density Diagnostics
selection_sensitivity_diagnostics() add_selection_sensitivity_diagnostics()
Diagnose Selection Conditioning Sensitivity
selection_cache_info()
Inspect or clear the native selection cache
selection_sampler_info()
Inspect corrected selection-sampler counters
remove_selection_cache()
Remove a fitted model's selection cache

Plots

plot(<brma>) lines(<brma>)
Plots brma Object
forest(<brma>) forest(<metafor_forest.brma>)
Forest Plot for brma Objects Using metafor
as_metafor_forest()
Prepare brma Data for metafor Forest Plots
funnel(<brma>) bfunnel()
Frequentist-Style and Bayesian Funnel Plots for brma Objects
radial(<brma>) galbraith(<brma>)
Radial (Galbraith) Plot for brma Object
regplot(<brma>)
Regression Plot (Bubble Plot) for brma Object
qqnorm(<brma>)
Normal QQ Plot for brma Object
plot_prior()
Plot Prior Distributions
print_prior()
Print Prior Distributions
plot_weightfunction()
Plots Weight Function of brma Object
plot_pet_peese()
Plot PET-PEESE Fit of brma Object
plot_diagnostic() plot_diagnostic_autocorrelation() plot_diagnostic_trace() plot_diagnostic_density()
Plot MCMC Diagnostics
plot(<marginal_means.brma>) lines(<marginal_means.brma>)
Plot Estimated Marginal Means

Posterior samples and zplot diagnostics

as_draws() as_draws_array() as_draws_df() as_draws_list() as_draws_matrix() as_draws_rvars()
Convert brma Objects to posterior Draws Formats
as_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>)
Convert brma_samples to posterior Draws Formats
as.matrix(<brma_samples>)
Convert brma_samples to Matrix
print(<brma_samples>)
Print brma_samples Object
summary(<brma_samples>)
Summarize brma_samples Object
print(<summary.brma_samples>)
Print summary.brma_samples Object
as_zplot(<brma>)
Transform brma Object to Zplot
zplot(<brma>) zplot(<zplot_brma>)
Plot Zplot Diagnostics Directly
summary(<zplot_brma>)
Summarize Zplot Results
print(<summary.zplot_brma>)
Print Zplot Summary
plot(<zplot_brma>)
Plot Zplot Results
hist(<zplot_brma>)
Histogram of Z-Statistics
lines(<zplot_brma>)
Add Zplot Density Lines

Example 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. (2021)
Bem2011
9 experimental studies from Bem (2011) as described in Bem et al. (2011)
Havrankova2025
1159 effect sizes from a meta-analysis of beauty and professional success by Havránková et al. (2025)
Hoogeveen2023
106 analyst-team effect-size estimates of the relation between religiosity and well-being from Hoogeveen et al. (2023)
Hoppen2025
37 studies from a meta-analysis of social comparison as a behavior change technique by Hoppen et al. (2025)
Johnides2025
412 effect sizes from a meta-analysis of secondary benefits of family-based treatments by Johnides et al. (2025)
Kroupova2021
881 estimates from 69 studies of a relationship between employment and educational outcomes collected by Kroupova et al. (2024)
Lui2015
18 studies of a relationship between acculturation mismatch and intergenerational cultural conflict collected by Lui (2015)
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 (2025)
Weingarten2018
582 effect sizes examining the ease-of-retrieval effect from a meta-analysis by Weingarten and Hutchinson (2018)
print(<RoBMA_data>)
Print method for RoBMA_data objects
print(<marginal_means.brma>)
Print Estimated Marginal Means
print(<summary.marginal_means.brma>)
Print Summary of Estimated Marginal Means
print(<summary_heterogeneity.brma>)
Print Summary of Heterogeneity
print(<vif.brma>)
Print VIF Results

Data frame coercion

as.data.frame(<brma>) as.data.frame(<summary.brma>)
Convert brma Summaries to a Data Frame
as.data.frame(<brma_samples>) as.data.frame(<summary.brma_samples>) as.data.frame(<brma_samples_list>)
Convert brma_samples Results to Data Frames
as.data.frame(<summary_heterogeneity.brma>) as.data.frame(<summary_heterogeneity.brma_list>)
Convert Heterogeneity Summaries to Data Frames
as.data.frame(<summary_models.RoBMA>)
Convert Model-Weight Summaries to a Data Frame
as.data.frame(<marginal_means.brma>) as.data.frame(<summary.marginal_means.brma>)
Convert Marginal Means to a Data Frame
as.data.frame(<zplot_brma>) as.data.frame(<summary.zplot_brma>)
Convert Z-Plot Summaries to a Data Frame
as.data.frame(<vif.brma>)
Convert VIF Results to a Data Frame
as.data.frame(<infl.brma>)
Convert Influence Results to a Data Frame
as.data.frame(<dfbetas.brma>)
Convert DFBETAS Results to a Data Frame
as.data.frame(<covratio.brma>)
Convert COVRATIO Results to a Data Frame