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.

广义估计方程（GEE）方法已广泛用于纵向数据分析。王 [GEE 分析具有不同数量协变量的聚类二进制数据。安统计。2011;39:389–417] 开发了一种渐近理论，用于 GEE 分析具有不同数量协变量的聚类二进制数据。她建议了工作相关矩阵中有害参数的几个矩估计量。然而，当工作相关结构被错误指定时，这些估计量可能不存在。当协变量的数量有限时，Xu 等人。[在广义估计方程中工作相关矩阵的有限混合模型。统计辛。2012;22:755–776] 提出了一种基于有限混合模型的混合 GEE 方法，以捕获重复测量之间的相关性。在本文中，我们为具有不同数量的协变量的混合 GEE 估计器开发了一种渐近理论。模拟研究用于证明混合 GEE 的性能协变量的发散数量，这表明该方法在数值上更稳定，并且比在发散协变量框架中具有指定工作相关矩阵的 GEE 具有更高的效率。最后，使用真实的数据集进行说明。