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), 712-718. (doi:10.1111/j.0006-341X.2000.00712.x).
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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.
|Keywords:||binary time series, correlated binary data, dependence ratio, familial data, longitudinal data, marginal regression, moment parameter|
|Subjects:||H Social Sciences > HA Statistics|
|Divisions:||University Structure - Pre August 2011 > School of Social Sciences > Social Statistics
|Date Deposited:||26 Jul 2006|
|Last Modified:||27 Mar 2014 18:21|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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