Statistics and Its Interface

Volume 13 (2020)

Number 4

Bayesian meta-regression model using heavy-tailed random-effects with missing sample sizes for self-thinning meta-data

Pages: 437 – 447



Zhihua Ma (Department of Statistics, School of Economics, Shenzhen University, Shenzhen, China)

Ming-Hui Chen (Department of Statistics, University of Connecticut, Storrs, Ct., U.S.A.)

Yi Tang (School of Life Science, Liaoning University, Shenyang, China)


Motivated by the self-thinning meta-data, a randomeffects meta-analysis model with unknown precision parameters is proposed with a truncated Poisson regression model for missing sample sizes. The random effects are assumed to follow a heavy-tailed 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 self-thinning law is more supported by the meta-data, a measure called “Plausibility Index (PI)” is developed. 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 a self-thinning meta-data set in details.


outliers, plausibility index, self-thinning law, truncated Poisson model

Dr. Chen’s research was partially supported by NIH grants #GM70335 and #P01CA142538, and Dr. Tang’s research was supported by National Nature Science Foundation of China #41870709.

Received 25 January 2019

Accepted 7 January 2020

Published 31 July 2020