Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 3, pp. 322-343

BAYESIAN MODELING OF CORRELATED BINARY RESPONSES VIA SCALE MIXTURE OF MULTIVARIATE NORMAL LINK FUNCTIONS

By

MING-HUI CHEN, *Worcester Polytechnic Institute, Worcester*

and

DIPAK K. DEY, * University of Connecticut, Storrs*

*SUMMARY. *In this article, we consider using scale mixture of multivariate
normal links (SMMVN) to model binary responses when binary observations
are taken from the same individuals or are taken over time
in a longitudinal fashion. SMMVN-links are quite rich, which include
multivariate probit, Student's $t$ links, logit, symmetric stable link,
and exponential power link. Fully parametric classical approaches to these
are intractable and thus Bayesian methods are pursued using a
Markov chain Monte Carlo (MCMC) sampling based
approach. Necessary theory involved in Bayesian modeling and
computation is provided.
In particular, we produce a new look at the multivariate logit model,
the most popular model in this context. Further, we develop
various efficient computational algorithms for this complex simulation problem.
Finally, a real data example from
the Indonesian Children's Health Study is used to illustrate
the proposed methodology.

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

*Key words and phrases. * Bayesian computation;
Bayesian hierarchical model; exponential power link;
Gibbs sampler; Markov chain Monte Carlo;
multivariate generalized linear models;
multivariate logit; multivariate probit;
multivariate Student's $t$ link; positive stable link.