Optimal Bias in Ridge Regression Approaches To Multicollinearity

John D. Kasarda and Wen-Fu P. Shih
Additional contact information
John D. Kasarda: University of North Carolina, Chapel Hill
Wen-Fu P. Shih: Florida Atlantic Universitv

Sociological Methods & Research, 1977, vol. 5, issue 4, 461-470

Abstract: Ridge regression, based on adding a smally quantity, k, to the diagonal of a correlation matrix of highly collinear independent variables, can reduce the error variance of estimators, but at the expense of introducing bias. Because bias is a monotonic increasing function of k, the problem of the appropriate amount of k to introduce as the ridge analysis increment has yet to be resolved This paper proposes a method for selecting the optimal value of k in terms of minimizing the mean square error of estimation. First, we demonstrate mathematically the existence of a minimum mean square error point of the ridge estimator along the scale k. Second, we present an iterative procedure for locating the k value which will minimize the mean square error of estimates for any correlated data set.

Date: 1977
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://journals.sagepub.com/doi/10.1177/004912417700500405 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sae:somere:v:5:y:1977:i:4:p:461-470

DOI: 10.1177/004912417700500405

Access Statistics for this article

More articles in Sociological Methods & Research
Bibliographic data for series maintained by SAGE Publications ().