Dynamic Generalized Linear Model for Correlated Binary Responses with Skewed Link

• Activity Number: 192
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Amitabha Bhaumik*+ and Ming-Hui Chen and Dipak K. Dey
• Companies: Bristol-Myers Squibb Company and University of Connecticut and University of Connecticut
• Keywords: Bayesian computation ; generalized t distribution ; latent variables ; Markov chain Monte Carlo

Abstract

The logit, probit, and student t-link are used to model time series of correlated binary response data via dynamic generalized linear model. All of these link functions are symmetric. However in some applications the overall fit can be significantly improved by the use of asymmetric link function. A new skewed link model is introduced in this paper to model time series of binary responses through dynamic linear model. A new class of distributions which is more versatile than student's t distribution is used to model the data. Skewness is introduced by using a skewed distribution for the underlying latent variable. The new class of distribution is developed by using scale mixture of normal distribution with suitably chosen mixing density. This distribution overcome the limitation of student's t distribution arises due to its two boundary normal and Cauchy distributions. Analytic form of the distributions are obtained. Markov chain Monte Carlo method is used to simulate from posterior distributions. Bayesian inference, model diagnostics and model selections are considered. The proposed methodology is illustrated on a real dataset on house price from Dade county, Florida.