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The generalized estimating equations (GEE) method has been widely used for longitudinal data analysis. Wang [GEE analysis of clustered binary data with diverging number of covariates. Ann Stat. 2011;39:389–417] developed an asymptotic theory for GEE analysis of clustered binary data with diverging number of covariates. She suggested several moment estimators of the nuisance parameter in the working correlation matrix. However, these estimators might not exist when the working correlation structure is misspecified. When the number of covariates is finite, Xu et al. [A finite mixture model for working correlation matrices in generalized estimating equations. Stat Sin. 2012;22:755–776] proposed a mix-GEE method based on a finite mixture model to capture correlations among repeated measurements. In this paper, we develop an asymptotic theory for the mix-GEE estimator with diverging number of covariates. Simulation studies are used to demonstrate the performance of the mix-GEE with  diverging  number of covariates, which indicate this method is more numerically stable and has a higher efficiency than the GEE with a specified working correlation matrix in diverging number of covariates framework. Finally, a real dataset is used for illustration.

Analysis of GEE with a mixture working correlation matrix for diverging number of covariates