Some Discussion On Multi-collinearity Detection Indices

In the multivariate regression problem,the variance of the regression coefficient may become very large due to the influence of multi-collinearity between the explanatory variables.Similarly,as the unbiased estimator of the coefficient variance,the estimated variance will also be affected.Estimating the variance change and combined with the traditional definition of the variance expansion factor(VIF)find that the sample variance of the interpreted variable is used to correct VIF to obtain a new indicator that can be used to detect the severity of multiple collinearity when the explanatory variable does not contain any redundant information of the interpreted variableIn addition,from the perspective of eigenvalues,this paper proposes the A indicator for multi-collinearity detection,theoretically verifies the rationality of the A indicator.and gives the control range of the upper and lower bounds of the indicator combined with the ? indicator and the VIF indicator.At the same time,the relationship between the ? indicator,the Red indicator and the A indicator is given in the two-dimensional case.Compared with ? indicator and VIF indicator,A indicator has obvious upper and lower bounds,and is more controllable;and compared to Red indicator,A indicator is easy to calculate and more easy to operate.Through the elimination and introduction of variables,each explanatory variable can be quantified using the A indicator,so that the explanatory variables that cause multi-collinearity can be found.Finally,through the data experiment,six different detection indicators are compared,and it is found that there are obvious consistency among the six indicators for detecting the multi-collinearity Meanwhile,the Red indicator and the A indicator have strong correlation.