Flexible generalized t-link models for binary response data

Abstract

A critical issue in modelling binary response data is the choice of the links. We introduce a new link based on the generalized t-distribution. There are two parameters in the generalized t-link: one parameter purely controls the heaviness of the tails of the link and the second parameter controls the scale of the link. Two major advantages are offered by the generalized t-links. First, a symmetric generalized t-link with an unknown shape parameter is much more identifiable than a Student t-link with unknown degrees of freedom and a known scale parameter. Secondly, skewed generalized t-links with both unknown shape and scale parameters provide much more flexible and improved skewed link regression models than the existing skewed links. Various theoretical properties and attractive features of the proposed links are examined and explored in detail. An efficient Markov chain Monte Carlo algorithm is developed for sampling from the posterior distribution. The deviance information criterion measure is used for guiding the choice of links. The proposed methodology is motivated and illustrated by prostate cancer data.