IngentaConnect Association Models for a Multivariate Binary Response

Authors: Ekholm, Anders¹; McDonald, John W.²; Smith, Peter W. F.²

Source: Biometrics, Volume 56, Number 3, September 2000 , pp. 712-718(7)

Abstract:

Summary.

Models for a multivariate binary response are parameterized by univariate marginal proba-bilities and dependence ratios of all orders. The w-order dependence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence. This parameterization supports likelihood-based inference for both regression parameters, relating marginal probabilities to explanatory variables, and association model parameters, relating dependence ratios to simple and meaningful mechanisms. Five types of association models are proposed, where responses are (1) independent given a necessary factor for the possibility of a success, (2) independent given a latent binary factor, (3) independent given a latent beta distributed variable, (4) follow a Markov chain, and (5) follow one of two first-order Markov chains depending on the realization of a binary latent factor. These models are illustrated by reanalyzing three data sets, foremost a set of binary time series on auranofin therapy against arthritis. Likelihood-based approaches are contrasted with approaches based on generalized estimating equations. Association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients.

Keywords: Binary time series; Correlated binary data; Dependence ratio; Familial data; Longitudinal data; Marginal regression; Moment parameter

Document Type: Research article

DOI: 10.1111/j.0006-341X.2000.00712.x

Affiliations: 1: Rolf Nevanlinna Institute, P.O. Box 4, FIN-00014 University of Helsinki, Finland 2: Department of Social Statistics, University of Southampton, Southampton SO17 lBJ, United Kingdom

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