New mixed binomial regression models to unbalancing data and extensions

Abstract

We introduce generalized links function for the modelling of binomial and binary responses which can be appropriate when the probability of a given binary response approaches 0 at a different rate than it approaches 1. It is to unbalancing data set. The proposal is based on exponentiated versions of distributions of base and their corresponding reverse distributions. As special case, known links are obtained. Properties of the proposed links are presented. Maximum Likelihood and Bayesian MCMC inference approaches are developed. Extensions of this models to ordinal regression models, mixed regression model and item response theory are considered too. Applications and simulation studies are also presented, showing the advantages of the proposal over commonly used models. (AU)