Bayesian Variable Selection for Beta Regression Model

Abstract

Beta regression has emerged as a widely used technique for modeling the relationship between a response variable and a set of covariates. It assumes that the dependent variable follows a beta distribution, making it especially well-suited for continuous outcomes restricted to the interval (0, 1). This paper presents a Bayesian Lasso framework for variable selection and parameter estimation within the Beta Regression Model (BRM), which is particularly suited for modeling continuous response variables constrained to the (0, 1) interval such as proportions and rates. By incorporating Laplace priors through a hierarchical Bayesian structure, the proposed Bayesian Lasso Beta Regression model enables simultaneous coefficient shrinkage and variable selection, thereby improving both model interpretability and predictive performance. Monte Carlo simulations and a real data analysis are conducted to evaluate and compare the performance of the proposed Bayesian Lasso Beta Regression with the non-Bayesian Beta Regression  and Bayesian Beta regression.