Abstract:
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Recent work on copula modelling has yielded flexible models that accommodate disparate non-Gaussian continuous outcomes and latent variables for joint analysis of non-Gaussian mixed data. However, a latent variable description of discrete variables, while practically appealing, is not always appropriate in applications that involve count and nominally scaled categorical outcomes. In this talk, we develop a new methodology that entails transforming binary outcomes into continuous by “jittering”– thus reducing the problem to one that involves only continuous variables and jointly modelling them with the continuous outcomes. We prove that jittering preserves the binary-continuous outcome dependence (in terms of Kendall’s tau), thus allowing for an elegant approach that avoids the pitfalls associated with copula modelling of discrete data. Although jittering has previously been used in copula modelling of discrete data, it was ostensibly only for alleviating computational difficulties arising from likelihood analysis of discrete data. We explore the finite-sample properties of likelihood-based estimates in simulations and revisit the ethylene glycol mice data for illustration.
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