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Multicollinearity: Diagnosing its Presence and Assessing the Potential Damage It Causes Least Squares Estimation

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  • David A. Belsley

Abstract

This paper suggests and examines a straightforward diagnostic test procedure that 1) provides numerical indexes whose magnitudes signify the presence of one or more near dependencies among columns of a data matrix X, and 2) provides a means for determining, within the linear regression model, the extent to which each such near dependency is degrading the least- squares estimation of each regression coefficient. In most instances this latter information also enables the investigator to determine specifically which columns of the data matrix are involved in each near dependency. The diagnostic test is based on an interrelation between two analytic devices, the singular-value decomposition (closely related to eigensystems) and a matching regression-variance decomposition. Both these devices are developed in full. The test is successfully given empirical content through a set of experiments that examine its behavior when applied to several different series of data matrices having one or more known near dependencies that are weak to begin with and are made to became systematically more nearly perfectly collinear. The general diagnostic properties of the test that result from these experiments and the steps required to carry out the test are summarized, and then exemplified by application to real economic data.

Suggested Citation

  • David A. Belsley, 1976. "Multicollinearity: Diagnosing its Presence and Assessing the Potential Damage It Causes Least Squares Estimation," NBER Working Papers 0154, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:0154
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    References listed on IDEAS

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    1. David A. Belsley, 1974. "Estimation of Systems of Simultaneous Equations, and Computational Specifications of GREMLIN," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 551-614, National Bureau of Economic Research, Inc.
    2. Kumar, T Krishna, 1975. "Multicollinearity in Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 365-366, August.
    3. David A. Belsley & Virginia Klema, 1974. "Detecting and Assessing the Problems Caused by Multi-Collinearity: A Useof the Singular-Value Decomposition," NBER Working Papers 0066, National Bureau of Economic Research, Inc.
    4. Douglas M. Hawkins, 1973. "On the Investigation of Alternative Regressions by Principal Component Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 275-286, November.
    5. Haitovsky, Yoel, 1969. "Multicollinearity in Regression Analysis: Comment," The Review of Economics and Statistics, MIT Press, vol. 51(4), pages 486-489, November.
    6. O'Hagan, John W & McCabe, Brendan, 1975. "Tests for the Severity of Multicollinearity in Regression Analysis: A Comment," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 368-370, August.
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    Cited by:

    1. Roy E. Welsch & Edwin Kuh, 1977. "Linear Regression Diagnostics," NBER Working Papers 0173, National Bureau of Economic Research, Inc.
    2. H J P Timmermans, 1981. "Multiattribute Shopping Models and Ridge Regression Analysis," Environment and Planning A, , vol. 13(1), pages 43-56, January.
    3. G. Acosta & M. Graña & J. P. Pinasco, 2006. "Condition numbers and scale free graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 381-385, October.

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