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Bayesian meta-analysis with dependent effect sizes in R: A tutorial on the bayesRVE package

Year: 2026
Type: preprint
Abstract: Meta-analytic data in psychology typically contain several effect sizes per study, arising from multiple measures, informants, time points or treatment contrasts, and effect sizes from the same study are statistically dependent. Two approaches to this problem have developed largely separately. Robust variance estimation with small-sample corrections provides standard errors that remain valid when the assumed dependence structure is wrong, but offers no Bayesian machinery; Bayesian multilevel modeling provides shrinkage estimation and full posterior distributions, but its interval estimates are only as trustworthy as the assumed within-study covariance structure. We describe the bayesRVE package for R, which combines the two approaches: the point estimate is the Bayesian posterior mean, the interval width is governed by a bias-reduced (CR2) cluster-robust sandwich estimate, and the interval tails use per-coefficient Satterthwaite degrees of freedom. The workflow consists of four functions, bm_fit(), sandwich(), ccc() and summary(), and is illustrated in a complete analysis of a publicly available psychology dataset comprising 113 correlations between school-motivation risk and later delinquency from 17 samples, including meta-regression with moderators, Markov chain Monte Carlo diagnostics, and the package's small-sample guardrails. We show that the calibrated interval does not depend on an assumed within-study correlation, describe cross-checks against the metafor and clubSandwich packages, and suggest what to report. All data and code are publicly available, and the analyses reproduce in about a minute on a standard laptop.
DOI: 10.5281/zenodo.22118900
Language: English
Open Access status: green
OpenAlex ID: W7204457901
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