Title: Flexible joint models for correlated jittered discrete data via Gaussian copulas
Authors: Alexander de Leon - University of Calgary (Canada) [presenting]
Abstract: Although a latent variable description of discrete variables is practically appealing in many applications, such an approach does not work in all cases. Count data, for example, present a situation for which a latent variable framework may not be appropriate; this is also the case for nominally scaled categorical outcomes, such as gender and hair colour, for example. We adopt the jittering method (or ``continuous-ation'') in order to circumvent the complications engendered by the direct application of copulas to discrete variables (e.g., non-identifiability, non-margin-free dependence). The method entails transforming discrete data into continuous, hence the name, by the addition of independently generated continuous random variables, called ``jitters'', for which a joint model is constructed using the Gaussian copula. Such an approach to joint modelling of correlated discrete data is appealing in practice because it preserves the dependence structure of the data, in that the associations among discrete variables are the same as those between their corresponding jittered versions. We discuss likelihood estimation for such models and report simulation results on the finite-sample relative bias and efficiency of resulting estimates. We adopt the approach to develop spatial joint models for areal count data on the numbers of deaths due to cancers of lung and esophagus during the period 1991-1998 in the 87 counties of Minnesota, USA.