Bayesian Adaptive Lasso for Variable Selection in Beta Regression Models

Ayat Salim  Al-jajawi; Taha  Alshaybawee

Ayat Salim Al-jajawi Department of Statistics, College of Administration and Economics, University of Al-Qadisiyah, Iraq
Taha Alshaybawee Department of Statistics, College of Administration and Economics, University of Al-Qadisiyah, Iraq

Keywords: Beta Regression, Bayesian Inference, Adaptive Lasso, Variable Selection, Shrinkage

Abstract

This paper presents a Bayesian Adaptive Lasso approach for variable selection in Beta regression models. The method improves classical Beta regression by incorporating coefficient-specific shrinkage through adaptive penalty weights. A hierarchical prior structure is adopted to allow flexible shrinkage, enabling the model to effectively eliminate irrelevant predictors while retaining important ones. A simulation study under various sparsity and precision conditions is conducted to assess the model’s performance in terms of estimation accuracy, bias, and selection ability. The proposed Bayesian Adaptive Lasso Beta Regression (BALBR) model is evaluated against standard BR, Bayesian BR, and Bayesian Lasso BR models. Results demonstrate that BALBR provides superior variable selection and estimation efficiency. An application to a real-world dataset further confirms the practical effectiveness of the proposed methodology.

References

S. Al-jajawi and T. Alshaybawee, “Bayesian Variable Selection for Beta Regression

D. F. Andrews and C. L. Mallows, “Scale Mixtures of Normal Distributions,” J. R. Stat. Soc. Ser. B (Methodological), vol. 36, no. 1, pp. 99–102, 1974.

J. Fan and J. Lv, “A Selective Overview of Variable Selection in High Dimensional Feature Space,” Statistica Sinica, vol. 20, no. 1, pp. 101–148, 2010.

S. Ferrari and F. Cribari‑Neto, “Beta Regression for Modelling Rates and Proportions,” J. Appl. Stat., vol. 31, no. 7, pp. 799–815, 2004.

I. Guyon and A. Elisseeff, “An Introduction to Variable and Feature Selection,” J. Mach. Learn. Res., vol. 3, pp. 1157–1182, Mar. 2003.

T. Park and G. Casella, “The Bayesian Lasso,” J. Am. Stat. Assoc., vol. 103, no. 482, pp. 681–686, 2008.

R. Tibshirani, “Regression Shrinkage and Selection via the Lasso,” J. R. Stat. Soc. Ser. B (Statistical Methodology), vol. 58, no. 1, pp. 267–288, 1996.

H. Zou, “The Adaptive Lasso and Its Oracle Properties,” J. Am. Stat. Assoc., vol. 101, no. 476, pp. 1418–1429, 2006.

Ray Bai, V. Rockova, and E. I. George, “Spike-and-Slab Meets LASSO: A Review of the Spike-and-Slab LASSO,” arXiv, Oct. 2020.

C. Leng, M. N. Tran, and D. Nott, “Bayesian Adaptive Lasso,” arXiv, Sep. 2010.

Y. Yang, M. J. Wainwright, and M. I. Jordan, “On the Computational Complexity of High‑Dimensional Bayesian Variable Selection,” arXiv, May 2015.

“Variance Prior Forms for High‑Dimensional Bayesian Variable Selection,” Bayesian Anal., vol. 14, no. 4, 2019.

“Spike-and‑Slab Lasso: Stochastic Search vs. Penalization,” in Psychol. Methods, 2023.

“Review of Bayesian Selection Methods for Categorical Predictors,” PMCID, 2022.

Y. Wasserman and K. Roeder, “High‑Dimensional Variable Selection,” arXiv, Apr. 2007.