The Tilted Beta Binomial Linear Regression Model: a Bayesian Approach

TL;DR

This paper introduces tilted beta binomial regression models, a Bayesian approach for analyzing overdispersed binomial data, providing flexible modeling of binomial parameters through new distributions.

Contribution

It develops novel tilted beta and beta rectangular binomial regression models, fitted via Bayesian methods, to better handle overdispersion in binomial datasets.

Findings

Models effectively fit overdispersed binomial data

Bayesian methods enable flexible parameter estimation

Application demonstrates improved modeling of seed germination data

Abstract

This paper proposes new linear regression models to deal with overdispersed binomial datasets. These new models, called tilted beta binomial regression models, are defined from the tilted beta binomial distribution, proposed assuming that the parameter of the binomial distribution follows a tilted beta distribution. As a particular case of this regression models, we propose the beta rectangular binomial regression models, defined from the binomial distribution assuming that their parameters follow a beta rectangular distribution. These new linear regression models, defined assuming that the parameters of these new distributions follow regression structures, are fitted applying Bayesian methods and using the OpenBUGS software. The proposed regression models are fitted to an overdispersed binomial dataset of the number of seeds that germinate depending on the type of chosen seed androot.