PA条件不成立时GEE方法中的检验问题

边际回归模型和与此有关的广义估计方程(GEE)在纵向数据分析中得到了广泛的应用. Pepe和Anderson在1994指出在边际模型和GEE方法的应用中必须满足一个重要条件, 即PA条件. 如果该假定不能满足, 可能得不到相合估计, 由此进行的统计推断的效率可能不高. 本文通过简单的AR(1)模型, 在理论上和数值模拟上讨论了PA条件对基于广义估计方程方法所作的关于回归系数的检验的影响. 由于PA条件不成立, 回归系数的GLS估计不再是渐近无偏的, 构造的Wald和Score统计量的分布不再是中心卡方分布, 从而对于检验的效率也产生了严重影响.

The Testing in GEE Method without PA Condition

Marginal regression model and its associated generalized estimating equation (GEE) are becoming increasingly being used in longitudinal studies. Pepe and Anderson (1994) pointed out that there is an important assumption called PA condition behind GEE method. If the assumption is violated and nondiagonal working correlation matrix is used in GEE, the statistical inference may bedeficient. This paper focused on PA condition's influence on the testing of regression coefficients in GEE method by theoretic and numeric analysis. Due to the violation of the PA condition, the distributions of Wald statistics and Score statistics based on GLS estimators are noncentral $\chi^{2}$ distributions. The efficiency of testing based on the GEE method is largely influenced.