Mixed Beta Regression: A Bayesian Perspective

TL;DR

This paper introduces a Bayesian mixed beta regression model for continuous bounded data, detailing parameterization, prior specification, and Gibbs sampling, with illustrative examples demonstrating its application.

Contribution

It presents a novel Bayesian approach to mixed beta regression, incorporating both fixed and random effects with detailed computational methods.

Findings

Effective modeling of bounded continuous data

Implementation of Gibbs sampling for Bayesian inference

Illustrative examples demonstrating model performance

Abstract

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian approach. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter, and allow both parameters to be modeled through regression structures that may involve fixed and random effects. Specification of prior distributions is discussed, computational implementation via Gibbs sampling is provided, and illustrative examples are presented.