Modeling Non-Gaussian Longitudinal Data Using Bayesian Copula Methods

• Activity Number: 608
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Zhiguang Xu*+ and Steven N. MacEachern and Xinyi Xu
• Companies: and Ohio State University and Ohio State University
• Keywords: longitudinal ; non-Gaussian ; copula ; prediction

Abstract

We propose a Bayesian copula method to model the non-normal longitudinal data. In our method, we model the observed response series from each subject as a transformation from a latent series; the transformation function specifies the dependence structure of the observed series and the marginal distribution of response variable through the Probability Integral Transformation (PIT). Under the transformation, the marginal distribution of the response variable follows the mixture of Dirichlet Process prior and therefore has a flexible shape. We conduct both simulation and the 100km-race real dataset study where the response variable is remarkably non-normal. Our method estimates the coefficients of the predictors accurately, captures the stationary or non-stationary within-subject correlation structure effectively and outperforms the normal-based longitudinal model in forecasting.