Modeling Covariance Parameters for Purely Autoregressive Correlated Longitudinal Data

Abstract

In longitudinal data analysis, we usually introduce models for the response as well as the correlation among the repeated measurements. In this article, we present a method of modeling the variance-covariance parameters using the Gaussian estimating equation proposed by Whittle (1961) in the time series literature. Estimators are obtained by the direct differentiation of the Gaussian estimation function with respect to the variance-covariance parameters of interest where no distributional assumptions are made except for the first two moments. The Gaussian estimation method is applied to a simulated data in order to study the behavior of parameter estimates.