Robust Bayesian Model-Averaged Meta-Regression (original) (raw)

2025-09-10

Robust Bayesian model-averaged meta-regression (RoBMA-reg) extends the robust Bayesian model-averaged meta-analysis (RoBMA) by including covariates in the meta-analytic model. RoBMA-reg allows for estimating and testing the moderating effects of study-level covariates on the meta-analytic effect in a unified framework (e.g., accounting for uncertainty in the presence vs. absence of the effect, heterogeneity, and publication bias). This vignette illustrates how to fit a robust Bayesian model-averaged meta-regression using the RoBMA R package. We reproduce the example from Bartoš et al. (2025), who re-analyzed a meta-analysis of the effect of household chaos on child executive functions with the mean age and assessment type covariates based on Andrews et al. (2021)’s meta-analysis.

First, we fit a frequentist meta-regression using themetafor R package. Second, we explain the Bayesian meta-regression model specification, the default prior distributions for continuous and categorical moderators, and standardized effect sizes input specification. Third, we estimate Bayesian model-averaged meta-regression (without publication bias adjustment). Finally, we estimate the complete robust Bayesian model-averaged meta-regression.

Data

We start by loading the Andrews2021 dataset included in the RoBMA R package, which contains 36 estimates of the effect of household chaos on child executive functions with the mean age and assessment type covariates. The dataset includes correlation coefficients (r), standard errors of the correlation coefficients (se), the type of executive function assessment (measure), and the mean age of the children (age) in each study.

library(RoBMA)
data("Andrews2021", package = "RoBMA")
head(Andrews2021)
#>       r         se measure      age
#> 1 0.070 0.04743416  direct 4.606660
#> 2 0.033 0.04371499  direct 2.480833
#> 3 0.170 0.10583005  direct 7.750000
#> 4 0.208 0.08661986  direct 4.000000
#> 5 0.270 0.02641969  direct 4.000000
#> 6 0.170 0.05147815  direct 4.487500

References

Andrews, K., Atkinson, L., Harris, M., & Gonzalez, A. (2021). Examining the effects of household chaos on child executive functions:A meta-analysis. Psychological Bulletin,147(1), 16–32. https://doi.org/10.1037/bul0000311

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., Doucouliagos, H., & Stanley, T. D. (2023). Robust Bayesian meta-analysis:Model-averaging across complementary publication bias adjustment methods. Research Synthesis Methods, 14(1), 99–116. https://doi.org/10.1002/jrsm.1594

Lenth, R. V., Bolker, B., Buerkner, P., Giné-Vázquez, I., Herve, M., Jung, M., Love, J., Miguez, F., Riebl, H., & Singmann, H. (2017).emmeans: Estimated marginal means, aka least-squares means. https://cran.r-project.org/package=emmeans

Stanley, T., Doucouliagos, H., Maier, M., & Bartoš, F. (2024). Correcting bias in the meta-analysis of correlations. Psychological Methods. https://doi.org/10.1037/met0000662

Wolfgang, V. (2010). Conducting meta-analyses in R with themetafor package. Journal of Statistical Software, 36(3), 1–48. https://www.jstatsoft.org/v36/i03/