A Pólya–Gamma sampler for a generalized logistic regression. Issue 14 (22nd September 2021)

• Record Type: Journal Article
• Authors: Dalla Valle, Luciana; Leisen, Fabrizio; Rossini, Luca; Zhu, Weixuan
• Is Part Of: Journal of statistical computation and simulation. Volume 91:Issue 14(2021)
• Page Start: 2899
• Page End: 2916
• Publication Date: 2021-09-22
• Subjects: Bayesian inference -- generalized logistic regression -- Pólya–Gamma sampler -- recidivism data; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2021.1910947
• Languages: English
• ISSNs: 0094-9655

Abstract

Abstract : In this paper, we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalized logistic regression model. We propose a Pólya–Gamma sampler algorithm that allows us to sample from the exact posterior distribution, rather than relying on approximations. A simulation study illustrates the flexibility and accuracy of the proposed approach to capture heavy and light tails in binary response data of different dimensions. The algorithm performance is tested on simulated data. Furthermore, the methodology is applied to two different real datasets, where we demonstrate that the Pólya–Gamma sampler provides more precise estimates than the empirical likelihood method, outperforming approximate approaches.