Two-step Estimation for Longitudinal Data When the Working Correlation Matrix is a Linear Combination of Some Known Matrices

The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correlation structure misspecification, the corresponding efficiency can be severely affected. In this paper, we propose a new two-step estimation method in which the correlation matrix is assumed to be a linear combination of some known working matrices. Asymptotic properties of the new estimators are developed. Simulation studies are conducted to examine the performance of the proposed estimators. We illustrate the methodology with an epileptic data set.