Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 3, pp. 372--387

BAYESIAN ANALYSIS OF BINARY REGRESSION USING SYMMETRIC AND ASYMMETRIC LINKS

By

SANJIB BASU, *Northern Illinis University, Dekalb, USA*

and

SAURABH MUKHOPADHYAY, *Merck Research Laboratories, Rahway, USA*

*SUMMARY.* Binary response regression is a useful technique for analyzing
categorical data. Popular binary models use special
link functions such as the logit or the probit link.
In this article, the inverse link function *H* is modeled to be a
scale mixture of cumulative distribution functions.
Two different models for *H* are proposed:
(i) *H* is a finite normal scale mixture with a Dirichlet
distribution prior on the mixing distribution; and
(ii) *H* is a scale mixture of truncated normal
distributions with the mixing distribution having a
Dirichlet prior. The second model allows symmetric as
well as asymmetric links. Bayesian analyses of these models
using data augmentation and Gibbs sampling are described.
Model diagnostics by cross validation of the conditional
predictive distributions are proposed. These analyses are
illustrated in the Beetle mortality data and the Challenger o-ring distress data.

*AMS (1991) subject classification.* 62F15, 62J12.

*Key words and phrases.* Asymmetric link, binary data, cross-validation,
Dirichlet distribution,
Gibbs sampling, normal scale mixture, predictive distribution.