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Bayesian Meta-Analysis with Weakly Informative Prior Distributions
Open accessAbstract
Developing meta-analytic methods is an important goal for psychological science. When there are few studies in particular, commonly used methods have several limitations, most notably of which is underestimating between-study variability. Although Bayesian methods are often recommended for small sample situations, their performance has not been thoroughly examined in the context of meta-analysis. Here, we characterize and apply weakly informativepriors for estimating meta-analytic models and demonstrate with extensive simulations that fully Bayesian methods overcome boundary estimates of exactly zero between-study variance, better maintain error rates, and have lower frequentist risk according toKullback-Leibler divergence. While our results show that combining evidence with few studiesis non-trivial, we argue that this is an important goal that deserves further considerationin psychology. Further, we suggest that frequentist properties can provide importantinformation for Bayesian modeling. We conclude with meta-analytic guidelines for appliedresearchers that can be implemented with the provided computer code.
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“12 Results from a complementary Bayesian multilevel meta-analysis model (Harrer etal., 2019; Williams etal., 2018) with weakly informative priors for true pooled effect size (µ ~ N (0, 1)) and between-study heterogeneity ( τ ~ HC (0, 0.5)) aligned with these pooled effect size estimates: Hedge's g = 0.36, 95% CI [0.19, 0.52].”
From When Problem Solving Followed by Instruction Works: Evidence for Productive Failure (2021) · cites this paper as Williams et al., 2018
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Self-citationStatistical Decision Theory and Bayesian Analysis
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A global meta-analysis of soil organic carbon in the Anthropocene
Beillouin, D., Corbeels, M., Demenois, J., Berre, D., Boyer, A., Fallot, A., Feder, F., & Cardinael, R. (2023) · Nature Communications · doi:10.1038/s41467-023-39338-z · Cited by 524
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When Problem Solving Followed by Instruction Works: Evidence for Productive Failure
Sinha, T., & Kapur, M. (2021) · Review of Educational Research · doi:10.3102/00346543211019105 · Cited by 212
“12 Results from a complementary Bayesian multilevel meta-analysis model (Harrer et al., 2019; Williams et al., 2018) with weakly informative priors for true pooled effect size (µ ~N(0, 1)) and between-study heterogeneity (τ ~ HC(0, 0.5)) aligned with these pooled effect size estimates: Hedge’s g =…”
InfluentialRöver, C., Bender, R., Dias, S., Schmid, C. H., Schmidli, H., Sturtz, S., Weber, S., & Friede, T. (2021) · Research Synthesis Methods · doi:10.1002/jrsm.1475 · Cited by 209
Reptile responses to anthropogenic habitat modification: A global meta‐analysis
Doherty, T. S., Balouch, S., Bell, K., Burns, T. J., Feldman, A., Fist, C. N., Garvey, T. F., Jessop, T. S., Meiri, S., & Driscoll, D. A. (2020) · Global Ecology and Biogeography · doi:10.1111/geb.13091 · Cited by 182
Metadata
- Authors
- Williams, D. R., Rast, P., & Bürkner, P. C.
- Affiliations
- University of California, Davis (US)
- University of Münster (DE)
- Publisher
- Center for Open Science
- Published
- 2018-01-10
- OpenAlex
- W2785297454
- Cited by
- 124
- References
- 81
- Citations by year
- 2026: 18 · 2025: 18 · 2024: 27 · 2023: 18 · 2022: 14 · 2021: 15 · 2020: 10 · 2019: 4
- Type
- posted content
- Language
- en
- Open access
- green
- doi.org
- Locations
- PsyArXiv (OSF Preprints) (submittedVersion, cc-by)
- PsyArXiv (OSF Preprints) (submittedVersion)
- OSF Preprints (OSF Preprints) (submittedVersion)
- OSF Preprints (OSF Preprints) (submittedVersion, cc-by)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Psychology Research and Bibliometrics
- Keywords
- Bayesian meta-analysis, weakly informative priors, study heterogeneity, Kullback-Leibler divergence
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