A generalized skew probit class link for binary regression

We introduce a generalized skew probit (gsp) class of links for the modeling of binary regression giving some properties and conditions for the existence of the maximum likelihood estimator and of the posterior distributions of the parameters of the model when improper uniform priors are established. As shown, asymmetric links already proposed in the literature are special cases of the general family of links proposed. A Bayesian inference approach using MCMC is developed and implementations of the approach are facilitated by considering the augmented likelihood proposed. Several models comparison criteria are introduced and confirm that the gsp class are more adequate for the biological data sets analyzed than other asymmetrical and symmetrical links in the literature. Moreover, extensions of the methods developed in this paper for dichotomous responses to ordinal response data and mixed models for binary response data are indicated.