Large Cluster Asymptotics for GEE: Working Correlation Models

This paper presents large cluster asymptotic results for generalized estimating equations. The complexity of working correlation model is characterized in terms of the number of working correlation components to be estimated. When the cluster size is relatively large, we may encounter a situation where a high-dimensional working correlation matrix is modeled and estimated from the data. In the present asymptotic setting, the cluster size and the complexity of working correlation model grow with the number of independent clusters. We show the existence, weak consistency and asymptotic normality of marginal regression parameter estimators using the results of empirical process theory and the work of Xie and Yang (2003). We also show the weak consistency of the sandwich variance estimator. Lastly, we present sufficient conditions for the increasing complexity of working correlation models using maximal inequalities