A Flexible Skewed Link Function for Binary Response Data

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Summary The objective of this paper is to introduce a flexible skewed link function for modeling binary data with covariates. The commonly used complementary log-log link is prone to link misspecification because of its positive and fixed skewness parameter. We propose a new link function based on the generalized extreme value (GEV) distribution. The generalized extreme value link is flexible in fitting the skewness in the data with the unknown shape parameter. Using Bayesian methodology, it automatically detects the skewness in the data along with the model fitting. The propriety of posterior distributions under proper and improper priors is explored in details.