A new skewed link model for dichotomous quantal response data

The logit, probit, and student t-links are widely used in modeling dichotom ous quantal response data. Most of the commonly used link functions are sym metric, except the complementary log-log link. However, in some application s the overall fit can be significantly improved by the use of an asymmetric link. In this article we propose a new skewed link model for analyzing bin ary response data with covariates. Introducing a skewed distribution for th e underlying latent variable, we develop a class of asymmetric link models for binary response data. Using a Bayesian approach, we first characterize the propriety of the posterior distributions using standard improper priors . We further propose informative priors using historical data from a simila r previous study. We examine the proposed method through a large-scale simu lation study and use data from a prostate cancer study to demonstrate the u se of historical data in Bayesian model fitting and comparison of skewed li nk models.