Bayesian Modeling of the Dependence in Longitudinal Data via Partial Autocorrelations and Marginal Variances

• Activity Number: 518
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Yanpin Wang*+ and Michael Daniels
• Companies: University of Florida and University of Florida
• Keywords: Bayesian Modeling ; Lingitudinal Data ; Partial Autocorrelation ; Markov Chain Monte Carlo ; Generalized Linear Model

Abstract

Two major obstacles are high dimensionality and positive-definiteness as we estimate and model a correlation matrix for longitudinal data. In addition, incorrectly modeling the correlation matrix often results in bias in estimating mean regression parameters as missing data exists. In this work, we introduce regression models for partial autocorrelations using Fisher's z-transform as the link function. The partial autocorrelations proposed can freely vary in the interval (-1, 1) while preserving positive definiteness of the correlation matrix is a key factor of our work. We propose a class of priors for the regression coefficients of the transformed partial autocorrelations and examine their behavior via simulations. The approach is illustrated on data from a pharmacological treatment of schizophrenia clinical trial.