Abstract:
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The past couple of decades have seen several developments of models for clustered binary outcomes. However, likelihood models for clustered bivariate binary outcomes are limited. In this paper, we will adopt the approach by Bonney (2003) and extend it to model bivariate binary outcomes taking into consideration both clustering and overdispersion. The motivation of this proposal is to develop a joint statistical modeling approach allowing for (i) characterization of the dependency of each binary response separately on covariates and (ii) the characterization of the degree of association between the pairs of responses and the dependence of this association on covariates. We will compare the approach to traditional methods including, Dales Model, the Alternating Logistic model and to a recent model developed by Del Fava et al (2014). Inferential procedures based on Maximum Likelihood and Bayesian methods will be developed. An application to real dataset will be presented.
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