线性模型中拟合优度的局部影响分析与诊断

DIAGNOSTICS AND ASSESSMENT OF LOCAL INFLUENCE ON GOODNESS OF FIT IN LINEAR REGRESSION MODEL

本文首先针对线性模型的拟合优度统计量Ｒ２提出了删除值诊断方法。同时，对拟合优度Ｒ２所构成的扰动曲面进行研究，通过计算该曲面上零扰动点处的斜率和二阶导数或者曲率来检验扰动面的局部影响程度。实际例子说明了本文提出的方法非常有效而且简洁，尤其在处理具有掩盖现象的局部影响分析问题时，本方法更为有效。

Contributing to diagnostic methods of measuring model deviation and the influence of a particular data set,this paper first presents a deletion diagnostic based on the goodness-of-fit statistic and then studies the properties of the perturbation-formed surface of the goodness-of-fit statistic to examine the local influence by evaluating both the slopes and second derivatives or curvatures related to the surface,which are referred to as the first and second order approaches to local influence. Examiples show that the methods are evidently powerful and simple,especially for locating cases of masked influence.and therefore these methods are superior to many current diagnostic schemes.