Bayesian Meta-Regression Model Using Heavy-Tailed Random-Effects with Missing Sample Sizes for Self-Thinning Meta-Data

• Activity Number: 542 - New Research Synthesis Methods in Data Science
• Type: Invited
• Date/Time: Wednesday, July 31, 2019 : 2:00 PM to 3:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Zhihau Ma and Ming-Hui Chen* and Yi Tang
• Companies: Jinan University and University of Connecticut and University of Connecticut and Liaoning University
• Keywords: logarithm of the pseudo-marginal likelihood; MCMC; Outliers; Plausibility index; Truncated Poisson model

Abstract

Motivated by the self-thinning meta-data, a random-effects meta-analysis model with unknown precision parameters is proposed with a truncated Poisson model for missing sample sizes. The random effects are assumed to follow a t distribution to accommodate outlying aggregate values in the response variable. The logarithm of the pseudo-marginal likelihood (LPML) is used for model comparison. In addition, in order to determine which thinning law is more supported by the meta-data, a measure called ``Plausibility Index (PI)" is proposed. A simulation study is conducted to examine empirical performance of the proposed methodology. Finally, the proposed model and the PI measure are applied to analyze the motivating self-thinning meta-data in details.