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Association models for a multivariate binary response

Ekholm, Anders, McDonald, John W. and Smith, Peter W.F. (2000) Association models for a multivariate binary response Biometrics, 56, (3), pp. 712-718. (doi:10.1111/j.0006-341X.2000.00712.x).

Record type: Article


Models for a multivariate binary response are parameterized by univariate marginal probabilities 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.

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Published date: 2000
Keywords: binary time series, correlated binary data, dependence ratio, familial data, longitudinal data, marginal regression, moment parameter


Local EPrints ID: 34318
PURE UUID: 051bf3da-ec20-4ad0-902f-347c7ce1816e
ORCID for Peter W.F. Smith: ORCID iD

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Date deposited: 26 Jul 2006
Last modified: 17 Jul 2017 15:50

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Author: Anders Ekholm
Author: John W. McDonald

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