Collinearity: revisiting the variance inflation factor in ridge regression

Ridge regression has been widely applied to estimate under collinearity by defining a class of estimators that are dependent on the parameter k. The variance inflation factor (VIF) is applied to detect the presence of collinearity and also as an objective method to obtain the value of k in ridge reg...

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Bibliographic Details
Published in:Journal of applied statistics 2015-03, Vol.42 (3), p.648-661
Main Authors: Garcia, C B, Garcia, J, Lopez Martin, MM, Salmeron, R
Format: Article
Language:English
Subjects:
Applied statistics
Collinearity
covariance matrix
Estimators
Inflation
linear regression
Mathematical analysis
Parameter estimation
Regression
Regression analysis
ridge regression
Ridges
Studies
Variance
variance inflation factor
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Summary:Ridge regression has been widely applied to estimate under collinearity by defining a class of estimators that are dependent on the parameter k. The variance inflation factor (VIF) is applied to detect the presence of collinearity and also as an objective method to obtain the value of k in ridge regression. Contrarily to the definition of the VIF, the expressions traditionally applied in ridge regression do not necessarily lead to values of VIFs equal to or greater than 1. This work presents an alternative expression to calculate the VIF in ridge regression that satisfies the aforementioned condition and also presents other interesting properties.
ISSN:0266-4763
1360-0532
DOI:10.1080/02664763.2014.980789