Efficient estimation for covariance parameters in analysis of longitudinal data

Abstract

In longitudinal data analysis, the Generalized estimation equation(GEE) approach is a milestone for estimation of regression parameters. Much theoretic work has been done in the literature and the GEE is also found to be a convenient tool for real data analysis. However, the choice of ``working'' covariance structures in the GEE approach affects the estimation efficiency greatly. In most cases, we only focus on the specification in correlation structures and neglect the importance of specification in variance functions. In this thesis, the variance function will be estimated instead of being assumed to be known, and the effects of the variance parameters estimates on estimation of regression parameters are considered. The Gaussian method is proposed to estimate the variance parameters because it can provide consistent estimation even without any information of correlation structures. Quasi-likelihood and weighted least square estimation methods are also introduced. Simulation studies are carried out to verify the analytical results. We also illustrate our findings by analyzing the well known epileptic dataset.