A Nonparametric Hyperprior for Between-studies Heterogeneity in Bayesian Meta-analysis

• In Event: Advancing Meta-Analytic Methods

Abstract

In Bayesian meta-analysis, the meta-analyst typically places a parametric hyperprior on the between-studies heterogeneity parameter, τ – often half-normal, uniform, or inverse-gamma distributions. Such priors may unrealistically concentrate prior mass near zero or impose restrictive shape assumptions of the between-studies heterogeneity parameter. This paper proposes a novel approach for modeling the τ hyperprior: Placing a Polya tree prior on τ to create a fully nonparametric hyperprior. The approach centers a prior on a reasonable parametric choice, but allows flexible shape behavior, skewness, and multimodality when implemented. This paper presents the construction, theoretical advantages, and implications for research synthesis in educational research. A small simulation and worked example will illustrate the Polya tree prior’s performance relative to conventional priors.

Author

• Christopher G. Thompson, Texas A&M University