Efficient Estimation of Link Function Parameters in a Robust Bayesian Binary Regression Model

• Activity Number: 301
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Vivekananda Roy*+
• Companies: Iowa State University
• Keywords: robust regression ; importance sampling ; Markov chain Monte Carlo ; Bayes factors ; robit model ; data augmentation

Abstract

The logistic and probit regression models are most commonly used to analyze binary response data, but it is well known that the estimators of regression coefficients for these models are not robust to outliers. The robit model (Liu(2004)), which replaces the normal (logistic) distribution in the probit (logit) regression model with the Student's $t -$distribution, is a robust alternative to probit and logit models. We construct fast mixing MCMC algorithms that can be used for analyzing Bayesian robit models. Unlike probit and logistic model, the robit link has an extra degrees of freedom parameter. We propose an empirical Bayes approach for estimating the degrees of freedom parameter along with estimation of the regression coefficients. We show that a combination of importance sampling based on mixture of densities and an application of control variates can be used to efficiently estimate a large class of Bayes factors for selecting the degrees of freedom parameter of the robit model.