A Pólya–Gamma sampler for a generalized logistic regression

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.

Keywords:

• Bayesian inference
• generalized logistic regression
• Pólya–Gamma sampler
• recidivism data

Acknowledgements

The authors gratefully acknowledge Alex Diana for advising on the PGdraw sampler and Michael Wögerer for useful feedback on a previous version of the paper. Also the authors are grateful to the referee, the associate editor for the useful comments that help us improving the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 We performed other convergence tests for the ten-dimensional case. These results are omitted for lack of space but are available on request.

2 Results for the ten-dimensional case are omitted for lack of space but are available on request.

3 See the following website for details: https://data.iowa.gov/Correctional-System/3-Year-Recidivism-for-Offenders-Released-from-Pris/mw8r-vqy4.

Additional information

Funding

W. Zhu is supported by the National Natural Science Foundation of China [grant number 11901488] and the Chinese Fundamental Research Funds for the Central Universities [grant number 20720181062]. This work was supported by European Community's Seventh Framework Programme [grant number 630677] and European Union Horizon 2020 research and innovation programme [grant number 796902].