IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v35y2020i2d10.1007_s00180-019-00922-x.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-019-00922-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-019-00922-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrea Poli & Angelo Gemignani & Mario Miccoli, 2022. "Randomized Trial on the Effects of a Group EMDR Intervention on Narrative Complexity and Specificity of Autobiographical Memories: A Path Analytic and Supervised Machine-Learning Study," IJERPH, MDPI, vol. 19(13), pages 1-18, June.
    2. Lee C. Adkins & Melissa S. Waters & R. Carter Hill, 2015. "Collinearity Diagnostics in gretl," Economics Working Paper Series 1506, Oklahoma State University, Department of Economics and Legal Studies in Business.
    3. Joseph, Agnes S. & Kiviet, Jan F., 2005. "Viewing the relative efficiency of IV estimators in models with lagged and instantaneous feedbacks," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 417-444, April.
    4. 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.
    5. repec:grm:oikosp:202007 is not listed on IDEAS
    6. Román Salmerón & José García & Catalina García & María del Mar López, 2018. "Transformation of variables and the condition number in ridge estimation," Computational Statistics, Springer, vol. 33(3), pages 1497-1524, September.
    7. Salmerón Gómez, Román & Rodríguez Martínez, Eduardo, 2017. "Métodos cuantitativos para un modelo de regresión lineal con multicolinealidad. Aplicación a rendimientos de letras del tesoro || Quantitative Methods for a Linear Regression Model with Multicollinear," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 24(1), pages 169-189, Diciembre.
    8. Roman Salmerón Gómez & José García Pérez & María Del Mar López Martín & Catalina García García, 2016. "Collinearity diagnostic applied in ridge estimation through the variance inflation factor," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1831-1849, August.
    9. Ehalaiye, Dimu & Tippett, Mark & van Zijl, Tony, 2017. "The predictive value of bank fair values," Pacific-Basin Finance Journal, Elsevier, vol. 41(C), pages 111-127.
    10. Marc de Bourmont, 2012. "La résolution d'un problème de multicolinéarité au sein des études portant sur les déterminants d'une publication volontaire d'informations : proposition d'un algorithme de décision simplifié basé sur," Post-Print hal-00691156, HAL.
    11. José García & Román Salmerón & Catalina García & María del Mar López Martín, 2016. "Standardization of Variables and Collinearity Diagnostic in Ridge Regression," International Statistical Review, International Statistical Institute, vol. 84(2), pages 245-266, August.
    12. Michael Miller & Frank Farmer, 1988. "Substantive nonadditivity in social science research A note on induced collinearity and measurement and testing of effects," Quality & Quantity: International Journal of Methodology, Springer, vol. 22(3), pages 221-237, September.
    13. Braden, J. B. & Kolstad, C. D. & Woock, R. A. & Machado, J. A., 2001. "Is coal desulphurisation worthwhile? Evidence from the market," Energy Policy, Elsevier, vol. 29(3), pages 217-225, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00922-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.