metaBMA: Bayesian Model Averaging for Random and Fixed Effects Meta-Analysis

Source: R/metaBMA.R

Fixed-effects meta-analyses assume that the effect size \(d\) is identical in all studies. In contrast, random-effects meta-analyses assume that effects vary according to a normal distribution with mean \(d\) and standard deviation \(\tau\). Both models can be compared in a Bayesian framework by assuming specific prior distribution for \(d\) and \(\tau\) (see prior). Given the posterior model probabilities, the evidence for or against an effect (i.e., whether \(d = 0\)) and the evidence for or against random effects can be evaluated (i.e., whether \(\tau = 0\)). By using Bayesian model averaging, both tests can be performed by integrating over the other model. This allows to test whether an effect exists while accounting for uncertainty whether study heterogeneity exists (so-called inclusion Bayes factors). For a primer on Bayesian model-averaged meta-analysis, see Gronau, Heck, Berkhout, Haaf, and Wagenmakers (2020).

Details

The most general functions in metaBMA is meta_bma, which fits random- and fixed-effects models, compute the inclusion Bayes factor for the presence of an effect and the averaged posterior distribution of the mean effect \(d\) (which accounts for uncertainty regarding study heterogeneity). Prior distributions can be specified and plotted using the function prior.

Moreover, meta_fixed and meta_random fit a single meta-analysis models. The model-specific posteriors for \(d\) can be averaged by bma and inclusion Bayes factors be computed by inclusion.

Results can be visualized with the functions plot_posterior, which compares the prior and posterior density for a fitted meta-analysis, and plot_forest, which plots study and overall effect sizes.

For more details how to use the package, see the vignette: vignette("metaBMA").

Funding

Funding for this research was provided by the Berkeley Initiative for Transparency in the Social Sciences, a program of the Center for Effective Global Action (CEGA), Laura and John Arnold Foundation, and by the German Research Foundation (grant GRK-2277: Statistical Modeling in Psychology).

References

Gronau, Q. F., Erp, S. V., Heck, D. W., Cesario, J., Jonas, K. J., & Wagenmakers, E.-J. (2017). A Bayesian model-averaged meta-analysis of the power pose effect with informed and default priors: the case of felt power. Comprehensive Results in Social Psychology, 2(1), 123-138. doi:10.1080/23743603.2017.1326760

Gronau, Q. F., Heck, D. W., Berkhout, S. W., Haaf, J. M., & Wagenmakers, E.-J. (2021). A primer on Bayesian model-averaged meta-analysis. Advances in Methods and Practices in Psychological Science, 4(3), 1–19. doi:10.1177/25152459211031256

Heck, D. W., Gronau, Q. F., & Wagenmakers, E.-J. (2019). metaBMA: Bayesian model averaging for random and fixed effects meta-analysis. https://CRAN.R-project.org/package=metaBMA

Author

Heck, D. W. & Gronau, Q. F.