Gaussian Copula Mixed Models for Non-Gaussian Correlated Data

• Activity Number: 410
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Alex de Leon*+ and Beilei Wu and Niroshan Withanage
• Companies: Univ of Calgary and PAREXEL International and University of Calgary
• Keywords: Biserial correlation ; Joint models ; Latent variables ; Logit-normal mixed model ; Mixed binary-continuous data ; Tetrachoric correlation

Abstract

This talk identifies and develops the class of Gaussian copula mixed models for the analysis of non-Gaussian dependent observations. The class provides a natural extension of traditional generalized linear mixed models (GLMMs) with Gaussian correlated errors and random effects. The models are flexible in that they facilitate the joint modeling and analysis of continuous, discrete and categorical responses, or any mixtures of them. Dependence is conveniently modelled in terms normal correlations, which are analogous to measures of associations commonly used in conventional settings. Inference is performed through a likelihood approach, and residual analysis and model fit criteria are suggested for validating the adequacy of the assumed joint model. Methodology is implemented in standard statistical software and packages such as PROC NLMIXED in SAS. Illustrations include simulations and real data applications in developmental toxicology with clustered mixed binary and continuous outcomes and in a comet assay involving hierarchically clustered and overdispersed non-Gaussian endpoints.