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.

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