A group-specific prior distribution for effect-size heterogeneity in meta-analysis
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A group-specific prior distribution for effect-size heterogeneity in meta-analysis Christopher G. Thompson 1 & Betsy Jane Becker 2
# The Psychonomic Society, Inc. 2020
Abstract While both methodological and applied work on Bayesian meta-analysis have flourished, Bayesian modeling of differences between groups of studies remains scarce in meta-analyses in psychology, education, and the social sciences. On rare occasions when Bayesian approaches have been used, non-informative prior distributions have been chosen. However, more informative prior distributions have recently garnered popularity. We propose a group-specific weakly informative prior distribution for the between-studies standard-deviation parameter in meta-analysis. The proposed prior distribution incorporates a frequentist estimate of the between-studies standard deviation as the noncentrality parameter in a folded noncentral t distribution. This prior distribution is then separately modeled for each subgroup of studies, as determined by a categorical factor. Use of the new prior distribution is shown in two extensive examples based on a published meta-analysis on psychological interventions aimed at increasing optimism. We compare the folded noncentral t prior distribution to several non-informative prior distributions. We conclude with discussion, limitations, and avenues for further development of Bayesian meta-analysis in psychology and the social sciences. Keywords Bayesian meta-analysis . Prior distribution . Between-studies heterogeneity
Meta-analysis is a statistical tool for combining results from sets of related studies (Glass, 1976). Beyond presenting overall features of the effect sizes (e.g., central tendency, variability), a critical component of meta-analysis is the exploration of effect-size heterogeneity. All collections of effects exhibit sampling error because effects are based on sample data. However, sampling error alone rarely accounts for all effectsize heterogeneity. Other sources of variation are often present, including random error (which is not directly explainable), systematic error due to moderator(s), or both. Several approaches are available for the exploration of systematic error in meta-analysis. The most popular are “metaregression” methods (see Thompson & Higgins, 2002). Metaregressions specify effect sizes as outcomes and can incorporate both continuous and categorical moderators (see Berkey,
* Christopher G. Thompson [email protected] 1
Department of Educational Psychology, Texas A&M University, College Station, TX, USA
2
Department of Educational Psychology & Learning Systems, Florida State University, Tallahassee, FL, USA
Hoaglin, Mosteller, & Colditz, 1995; Greenland, 1987). Another class of heterogeneity-investigation methods relies on weighted analogues to ANOVA (Hedges, 1982). Such ANOVA-like methods again use effect sizes as outcomes and attempt to explain possible systematic error using categorical moderators. ANOVA-like models can either incorporate group-specific between-studies heterogeneity comp
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