Identifiability and bias reduction in the skew-probit model for a binary response

The skew-probit link function is one of the popular choices for modelling the success probability of a binary variable with regard to covariates. This link deviates from the probit link function in terms of a flexible skewness parameter. For this flexible link, the identifiability of the parameters is investigated. Next, to reduce the bias of the maximum likelihood estimator of the skew-probit model we propose to use the penalized likelihood approach. We consider three different penalty functions, and compare them via extensive simulation studies. Based on the simulation results we make some practical recommendations. For the illustration purpose, we analyse a real dataset on heart-disease.