广义估计方程(GEE)框架下的回归诊断：基于均值和协方差结构同时拟合的研究

非正态相关数据（比如纵向数据）的统计建模和诊断分析是现代统计学研究的前沿课题，本项目拟在广义估计方程（GEE）框架下研究纵向数据的统计建模和回归诊断问题，具体内容包括：（1）GEE框架下纵向数据的均值与协方差结构联合建模方法；（2）GEE框架下回归参数和协方差结构参数的统计诊断；（3）GEE框架下均值与协方差结构联合建模基础上，回归参数和协方差结构参数的统计诊断；（4）在理论分析的基础上进行应用研究。本项目方法的优势在于拟合协方差矩阵，而不是设定工作协方差矩阵，这样可以避免工作协方差矩阵设定偏误带来的不良后果，从而提高了回归诊断的准确性。

Statistcial modeling and diagnostics for non-normal data such as longitudinal data are on the frontier of modern statistical research. In this project, by using generalized estimating equation (GEE) method, we will investigate both the statisctical modeling and diagnostics for non-normal data. The research mainly contains: (1) the method of joint modeling mean and covariance structures for longitudinal data within the framework of GEE; (2) the statistical diagnostics for regression coefficients and covariance parameters within the framework of GEE; (3) the statistical diagnostics for regression coefficients and covariance parameters based on joint modeling mean and covariance structures within the framework of GEE; (4) applications on the basis of theoretical analysis. The method proposed is joint modeling mean and covariance structures rather than setting the work matrix for regression estimation in GEE, which can avoid misleading the regression diagnostics and ensure the efficiency of statistcial diagnostics.