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Diagnosis and quantification of the non-essential collinearity

Author

Listed:
  • Román Salmerón-Gómez

    (University of Granada)

  • Ainara Rodríguez-Sánchez

    (University of Granada)

  • Catalina García-García

    (University of Granada)

Abstract

Marquandt and Snee (Am Stat 29(1):3–20, 1975), Marquandt (J Am Stat Assoc 75(369):87–91, 1980) and Snee and Marquardt (Am Stat 38(2):83–87, 1984) refer to non-essential multicollinearity as that caused by the relation with the independent term. Although it is clear that the solution is to center the independent variables in the regression model, it is unclear when this kind of collinearity exists. The goal of this study is to diagnose the non-essential collinearity parting from a simple linear model. The collinearity indices $$k_{j}$$kj, traditionally misinterpreted as variance inflation factors, are reinterpreted in this paper where they will be used to distinguish and quantify the essential and non-essential collinearity. The results can be immediately extended to the multiple linear model. The study also has some recommendations for statistical software such as SPSS, Stata, GRETL or R for improving the diagnosis of non-essential collinearity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00922-x
    DOI: 10.1007/s00180-019-00922-x
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    References listed on IDEAS

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    1. Belsley, David A., 1982. "Assessing the presence of harmful collinearity and other forms of weak data through a test for signal-to-noise," Journal of Econometrics, Elsevier, vol. 20(2), pages 211-253, November.
    2. Santiago Velilla, 2018. "A Note on Collinearity Diagnostics and Centering," The American Statistician, Taylor & Francis Journals, vol. 72(2), pages 140-146, April.
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