多元线性回归方程中共线影响点的诊断

Diagnosing Collinearity-influential Observation in Multiple Regression

目的 介绍在多元线性回归方程中共线影响点的来源及其诊断方法。方法 通过利用三种不同的方法 :①删除行变量观测条件数的变化②利用迹对行列式的比值和③杠杆成分来确定共线影响点。结果 在有异常点存在时可以利用三种诊断方法来确定该点是否对共线性产生了影响。结论 在建立多元线性回归方程时可以利用诊断共线影响点的方法来建立更符合实际规律的方程。

Objective A state of collinearity is sometimes masked or created by one or two observations. In the paper, we introduced definition, origin of collinearity-influential points.Methods We provided three measures that diagnosed collinearity- influential. The first measures is the collinearity influence of each row of X would be measured by the relative change in the condition number when it was deleted. The second measures is the Trace-to-Det Ratio, The final measures is Leverage.Results When there are outlers in the data,three kinds of diagnostic methods are available for detecting whether the observation have effect on collinarity.Conclusion We can use three methods of diagnosing collinearity-influential observation to construct regression model which is more suitable for the facts than others.