Bayesian Inference for Gaussian Copula Regression Models

• Activity Number: 658
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Lisa Henn*+ and John Hughes
• Companies: University of Minnesota and University of Minnesota
• Keywords: composite likelihood ; continuous extension ; curvature correction ; discrete data ; distributional transform ; Gaussian copula

Abstract

The Gaussian copula regression model provides a flexible framework in which to model associations among responses of a variety of types. The feasibility of evaluating the true likelihood directly is limited by the size of the problem. We evaluate Gaussian copula regression of discrete outcomes using three distinct approaches that circumvent this issue. Those approaches, evaluated in a Bayesian framework, are the continuous extension, the distributional transform, and the composite likelihood, the latter two with curvature correction. A Bayesian procedure with strong frequentist performance should be more attractive to a wider range of practitioners, so we evaluate the frequentist properties, along with computational performance, of these three approaches for several types of discrete data. In most cases, the distributional transform with curvature correction has acceptable performance with considerably shorter run times, making it an attractive option for evaluating models for multi-dimensional, mutually dependent discrete responses.