Selection of Working Correlation Structure in Generalized Estimating Equations via Empirical Likelihood

Generalized estimating equations (GEE) are a popular class of models for analyzing discrete longitudinal data, and do not require the specification of a full likelihood. The GEE estimator for the regression parameter will be the most efficient if the working correlation matrix is correctly specified. Hence it is desirable to choose a working correlation matrix that is the closest to the underlying structure among a set of working structures. In the absence of a parametric likelihood, traditional likelihood-based model selection methods cannot be used for comparing GEE models. Combining the reliability of nonparametric methods with the flexibility and effectiveness of likelihood approaches, empirical likelihood (EL) has the potential to become a model selection tool for GEE. We propose an EL approach to select the working correlation structure in GEE. Our approach is compared to existing methods based on quasi-likelihood or resampling procedures. The effectiveness of the proposed method is demonstrated by simulations. Supplemental materials for this article are available online.