Tilted beta regression and beta-binomial regression models: Mean and variance modeling

This paper proposes new parameterizations of the tilted beta binomial distribution, obtained from the combination of the binomial distribution and the tilted beta distribution, where the beta component of the mixture is parameterized as a function of their mean and variance.These new parameterized distributions include as particular cases the beta rectangular binomial and the beta binomial distributions.After that, we propose new linear regression models to deal with overdispersed binomial datasets.These new models are defined from the proposed new parameterization of the tilted beta binomial distribution, and assume regression structures for the mean and variance parameters.These new linear regression models are fitted by applying Bayesian methods and using the OpenBUGS software.The proposed regression models are fitted to a school absenteeism dataset and to the seeds germination rate according to the type seed and root.