  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.
