Multicollinearity and misleading statistical results
Multicollinearity and misleading statistical results
复制标题
DOI：
10.4097/kja.19087
复制
发表时间：
2019-12-01
影响因子：
2.9
通讯作者：
Kim, Jong Hae
中科院分区：
文献类型：
--
作者：
Kim, Jong Hae
多重共线性是指多元回归模型中解释变量之间的高度线性相关，导致回归分析结果不正确。多重共线性的诊断工具包括方差膨胀因子（VIF）、条件指数和条件数以及方差分解比例（VDP）。多重共线性可以用多元回归模型的决定系数（R-h（2））来表示，其中一个解释变量（X-h）作为模型响应变量，其他解释变量（X-i [i不等于h]）作为其解释变量。构成最终回归模型的回归系数的方差（sigma（2）（h））与VIP（1/1-R-h（2））成比例。因此，R-h（2）的增加（强多重共线性）增加sigma（2）（h）。较大的sigma（2）（h）产生不可靠的概率值和回归系数的置信区间。最大特征值与标准化解释变量相关矩阵中每个特征值之比的平方根称为条件指数。条件数是最大条件索引。当VIP高于5至10或条件指数高于10至30时，存在多重共线性。但是，它们不能表示多重共线性解释变量。从特征向量获得的VDPs可以通过根据每个条件指标显示sigma（2）（h）的膨胀程度来识别多重共线性变量。当对应于高于10至30的共同条件指数的两个或更多个VDP高于0.8至0.9时，它们的相关解释变量是多重共线的。排除多重共线性解释变量导致统计稳定的多元回归模型。
Multicollinearity represents a high degree of linear intercorrelation between explanatory variables in a multiple regression model and leads to incorrect results of regression analyses. Diagnostic tools of multicollinearity include the variance inflation factor (VIF), condition index and condition number, and variance decomposition proportion (VDP). The multicollinearity can be expressed by the coefficient of determination (R-h(2)) of a multiple regression model with one explanatory variable (X-h) as the moders response variable and the others (X-i [i not equal h]) as its explanatory variables. The variance (sigma(2)(h)) of the regression coefficients constituting the final regression model are proportional to the VIP (1/1-R-h(2)). Hence, an in- crease in R-h(2) (strong multicollinearity) increases sigma(2)(h). The larger sigma(2)(h) produces unreliable probability values and confidence intervals of the regression coefficients. The square root of the ratio of the maximum eigenvalue to each eigenvalue from the correlation matrix of standardized explanatory variables is referred to as the condition index. The condition number is the maximum condition index. Multicollinearity is present when the VIP is higher than 5 to 10 or the condition indices are higher than 10 to 30. However, they cannot indicate multicollinear explanatory variables. VDPs obtained from the eigenvectors can identify the multicollinear variables by showing the extent of the inflation of sigma(2)(h) according to each condition index. When two or more VDPs, which correspond to a common condition index higher than 10 to 30, are higher than 0.8 to 0.9, their associated explanatory variables are multicollinear. Excluding multicollinear explanatory variables leads to statistically stable multiple regression models.