Gaussian copula distributions for mixed data, with application indiscrimination

Abstract

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The construction of a joint model for mixed discrete and continuous random variables that accounts for their associations is an important statistical problem in many practical applications. In this paper, we use copulas to construct a class of joint distributions of mixed discrete mid continuous random variables. In particular, w e employ die Gaussian copula to generate joint distributions for mixed variables. Examples include the tobh-nonnal and probit-normal-exponential distributions, die first for modelling die distribution of m ixed binary-continuous data and the second for a m ixture of continuous, binary and trichotomous variables. The new class of joint distributions is general enough to include many mixed-data models currently available. We study properties of the distributions and outline likelihood estim ation; a sm all sim ulation study is used to investigate the finite-sample properties of estim ates obtained by full and pairw ise lilmlihiwd TngrtireU Finally, w penent an application to discriminant analysis o f m nltiplc correlated binary and continuous data from a study involving advanced breast cancer patients.