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A comparison of methods for multivariate familial binary responses Latif, Abu Hena M. Mahbub-ul

Abstract

Among the existing methods for analysing the multivariate familial binary response, we discuss latent variable models and the estimating equations based methods. A brief description of the multivariate Plackett distribution is given and the role of this distribution in developing the estimating equations based methods is pointed out. The maximum likelihood and estimating equations based methods for estimating the parameters of the multivariate logistic model are compared. For this comparison, a simulation study examines the effects of the sample sizes, dependence structures, the within-family dependence, etc. in estimating the parameters. The data are generated from the multivariate probit models. The multivariate logistic and probit models are compared for estimating conditional probabilities of interest in a genetics context and the respective standard errors. Numerical methods are used to estimate the parameters of the models considered. Because the original GEE2 code cannot handle multivariate binary data for arbitrary family structures, we have a new implementation of the GEE2 method for familial data; this routine used automatic differentiation for computing the Hessian matrix.

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