Copula-Based Likelihood Modeling and Estimation of Repeated-Measure Ordinal Data

• Activity Number: 627
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Raghavendra Rao Kurada*+ and N. Rao Chaganty
• Companies: Old Dominion University and Old Dominion University
• Keywords: Gaussian copula ; Ordinal data ; Estimating equations ; Relative efficiency ; Probit ; Logit

Abstract

In epidemiological and medical studies often involving repeated measurements on independent subjects, distribution-free estimating equation approaches are often used. However, theoretical and practical challenges arise for repeated-measure categorical data, especially when the outcomes are ordinal in nature. In this talk we will discuss latent variable likelihood modeling for repeated-measure ordinal data using Gaussian copula with probit and logit link functions. We derive the score functions and simplified expressions for Hessian matrices, which allow easy computation of the standard errors for the dependence and marginal regression parameter estimates. Through asymptotic relative efficiency calculations we demonstrate that likelihood estimators are superior as compared to estimators arising from other estimating equation approaches. We apply this likelihood-based methodology in an analysis of real life data using an R package developed specifically for the likelihood estimation.