A test of harmful multicollinearity: A generalized ridge regression approach

Abstract

This paper introduces a new test of harmful multicollinearity based on the ratio of the levels of significance of ordinary least squares and generalized ridge regression estimates of the coefficients. Harmful multicollinearity is the degree of multicollinearity that leads to an incorrect statistical inference. The proposed test is based on a rule that an insignificant regressor will not change to a significant regressor by adding ridge factors to the design matrix; however, insignificant coefficients that have become insignificant because of multicollinearity will change to significant coefficients by using ridge estimation. The simulation results show that the power of the proposed test is high—even for small sample sizes—and converges to one as the sample size increases. In addition, the empirical size of the test is less than the nominal value in most cases, with a tendency to zero in larger samples. Therefore, the proposed test is consistent. The comparison of the proposed test with the main diagnostic measures confirms the success of the test because the diagnostic measures have the wrong nominal sizes in all cases. The application of the test to real-world data shows that it can be helpful for detecting harmful multicollinearity.

KEYWORDS:

• Diagnosis of multicollinearity
• generalized ridge regression
• harmful multicollinearity
• statistical test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J07
• 62F03

Acknowledgments

The author thanks anonymous referees and the editor for their helpful comments and suggestions which helped to improve the quality of the paper.

Notes

1 https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=2ahUKEwjH3fWYz9TfAhWSsqQKHagKAYwQFjAAegQIAhAC&url=http%3A%2F%2Feric.univlyon2.fr%2F∼ricco%2Ftanagra%2Ffichiers%2Fcar_consumption_colinearity_regression.xls&usg=AOvVaw2Gak235hL5CR69EHPe42Hd.