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A Note on Collinearity Diagnostics and Centering

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  • Santiago Velilla

Abstract

The usual approach for diagnosing collinearity proceeds by centering and standardizing the regressors. The sample correlation matrix of the predictors is then the basic tool for describing approximate linear combinations that may distort the conclusions of a standard least-square analysis. However, as indicated by several authors, centering may eventually fail to detect the sources of ill-conditioning. In spite of this earlier claim, there does not seem to be in the literature a fully clear explanation of the reasons for this bad potential behavior of the traditional strategy for analyzing collinearity. This note studies this issue in some detail. Results derived are motivated by the analysis of a well-known real dataset. Practical conclusions are illustrated with several examples.

Suggested Citation

  • Santiago Velilla, 2018. "A Note on Collinearity Diagnostics and Centering," The American Statistician, Taylor & Francis Journals, vol. 72(2), pages 140-146, April.
    • Handle: RePEc:taf:amstat:v:72:y:2018:i:2:p:140-146
    DOI: 10.1080/00031305.2016.1264312
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    References listed on IDEAS

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    1. David A. Belsley, 1987. "Well-Conditioned Collinearity Indices?," Boston College Working Papers in Economics 132, Boston College Department of Economics.
    2. Raj Echambadi & James D. Hess, 2007. "Mean-Centering Does Not Alleviate Collinearity Problems in Moderated Multiple Regression Models," Marketing Science, INFORMS, vol. 26(3), pages 438-445, 05-06.
    3. Donald R. Jensen & Donald E. Ramirez, 2008. "Anomalies in the Foundations of Ridge Regression," International Statistical Review, International Statistical Institute, vol. 76(1), pages 89-105, April.
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    Cited by:

    1. Román Salmerón-Gómez & Ainara Rodríguez-Sánchez & Catalina García-García, 2020. "Diagnosis and quantification of the non-essential collinearity," Computational Statistics, Springer, vol. 35(2), pages 647-666, June.
    2. Román Salmerón Gómez & Catalina García García & José García Pérez, 2020. "Detection of Near-Nulticollinearity through Centered and Noncentered Regression," Mathematics, MDPI, vol. 8(6), pages 1-17, June.

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