Posterior Predictive Distributions In Meta-Analysis: An Updated Hunter-Schmidt Analysis Using Bayesian Hierarchical Models

• Activity Number: 512
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): David G. Whiting*+ and Michael D. Ulrich
• Companies: Brigham Young University and The RBL Group
• Keywords: posterior predictive distributions ; meta-analysis ; correlations

Abstract

The traditional Hunter-Schmidt approach to meta-analysis includes fixed effect, random effect, and empirical Bayesian models for combining correlations from multiple studies. When modeling correlations, each of these approaches takes into account corrections for reliability. However, they do not fully account for the uncertainty introduced by estimating the reliability coefficients themselves. We propose a Bayesian hierarchical model for correlation meta-analysis which fully accounts for these sources of model variability. We demonstrate how the posterior predictive distributions of the study correlations yields more information for drawing overall conclusions. We examine a highly-cited meta-analysis from the organizational behavior literature, showing how its conclusions would have been different had reliability uncertainty been accounted for.