Bayesian Analysis of the Beta Regression Model Subject to Linear Inequality Restrictions with Application

TL;DR

This paper develops a Bayesian estimation method for beta regression models with linear inequality restrictions, demonstrating improved accuracy over traditional estimators through simulations and real data analysis.

Contribution

It introduces a novel Bayesian restricted estimator for beta regression models with inequality constraints, outperforming standard and ridge estimators in various scenarios.

Findings

Proposed estimator outperforms ordinary estimators in simulations.

Estimator reduces standard deviation and mean squared error, even with multicollinearity.

Real data analysis confirms effectiveness of the Bayesian restricted estimator.

Abstract

ReRecent studies in machine learning are based on models in which parameters or state variables are bounded restricted. These restrictions are from prior information to ensure the validity of scientific theories or structural consistency based on physical phenomena. The valuable information contained in the restrictions must be considered during the estimation process to improve estimation accuracy. Many researchers have focused on linear regression models subject to linear inequality restrictions, but generalized linear models have received little attention. In this paper, the parameters of beta Bayesian regression models subjected to linear inequality restrictions are estimated. The proposed Bayesian restricted estimator, which is demonstrated by simulated studies, outperforms ordinary estimators. Even in the presence of multicollinearity, it outperforms the ridge estimator in terms of the standard deviation and the mean squared error. The results confirm that the proposed Bayesian restricted estimator makes sparsity in parameter estimating without using the regularization penalty. Finally, a real data set is analyzed by the new proposed Bayesian estimation method.