IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v36y2009i5p507-520.html
   My bibliography  Save this article

The performance of diagnostic-robust generalized potentials for the identification of multiple high leverage points in linear regression

Author

Listed:
  • M. Habshah
  • M. R. Norazan
  • A.H.M. Rahmatullah Imon

Abstract

Leverage values are being used in regression diagnostics as measures of influential observations in the $X$-space. Detection of high leverage values is crucial because of their responsibility for misleading conclusion about the fitting of a regression model, causing multicollinearity problems, masking and/or swamping of outliers, etc. Much work has been done on the identification of single high leverage points and it is generally believed that the problem of detection of a single high leverage point has been largely resolved. But there is no general agreement among the statisticians about the detection of multiple high leverage points. When a group of high leverage points is present in a data set, mainly because of the masking and/or swamping effects the commonly used diagnostic methods fail to identify them correctly. On the other hand, the robust alternative methods can identify the high leverage points correctly but they have a tendency to identify too many low leverage points to be points of high leverages which is not also desired. An attempt has been made to make a compromise between these two approaches. We propose an adaptive method where the suspected high leverage points are identified by robust methods and then the low leverage points (if any) are put back into the estimation data set after diagnostic checking. The usefulness of our newly proposed method for the detection of multiple high leverage points is studied by some well-known data sets and Monte Carlo simulations.

Suggested Citation

  • M. Habshah & M. R. Norazan & A.H.M. Rahmatullah Imon, 2009. "The performance of diagnostic-robust generalized potentials for the identification of multiple high leverage points in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(5), pages 507-520.
    • Handle: RePEc:taf:japsta:v:36:y:2009:i:5:p:507-520
    DOI: 10.1080/02664760802553463
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760802553463
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760802553463?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. Sung-Soo Kim & Sung Park & W. J. Krzanowski, 2008. "Simultaneous variable selection and outlier identification in linear regression using the mean-shift outlier model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(3), pages 283-291.
    2. Sebert, David M. & Montgomery, Douglas C. & Rollier, Dwayne A., 1998. "A clustering algorithm for identifying multiple outliers in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 27(4), pages 461-484, June.
    3. Sung-Soo Kim & W. Krzanowski, 2007. "Detecting multiple outliers in linear regression using a cluster method combined with graphical visualization," Computational Statistics, Springer, vol. 22(1), pages 109-119, April.
    4. Billor, Nedret & Hadi, Ali S. & Velleman, Paul F., 2000. "BACON: blocked adaptive computationally efficient outlier nominators," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 279-298, September.
    5. Hadi, Ali S., 1992. "A new measure of overall potential influence in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 14(1), pages 1-27, June.
    6. A. H. M. Rahmatullah Imon, 2005. "Identifying multiple influential observations in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(9), pages 929-946.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. A.A.M. Nurunnabi & M. Nasser & A.H.M.R. Imon, 2016. "Identification and classification of multiple outliers, high leverage points and influential observations in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 509-525, March.
    2. Hock Ann Lim & Habshah Midi, 2016. "Diagnostic Robust Generalized Potential Based on Index Set Equality (DRGP (ISE)) for the identification of high leverage points in linear model," Computational Statistics, Springer, vol. 31(3), pages 859-877, September.

    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. A.A.M. Nurunnabi & M. Nasser & A.H.M.R. Imon, 2016. "Identification and classification of multiple outliers, high leverage points and influential observations in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 509-525, March.
    2. Vilijandas Bagdonavičius & Linas Petkevičius, 2020. "A new multiple outliers identification method in linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 275-296, April.
    3. Menjoge, Rajiv S. & Welsch, Roy E., 2010. "A diagnostic method for simultaneous feature selection and outlier identification in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3181-3193, December.
    4. Junlong Zhao & Chao Liu & Lu Niu & Chenlei Leng, 2019. "Multiple influential point detection in high dimensional regression spaces," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 385-408, April.
    5. Kondylis, Athanassios & Hadi, Ali S., 2006. "Derived components regression using the BACON algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 556-569, November.
    6. Nikolas Kuschnig & Gregor Zens & Jesús Crespo Cuaresma, 2021. "Hidden in Plain Sight: Influential Sets in Linear Models," CESifo Working Paper Series 8981, CESifo.
    7. L. Pitsoulis & G. Zioutas, 2010. "A fast algorithm for robust regression with penalised trimmed squares," Computational Statistics, Springer, vol. 25(4), pages 663-689, December.
    8. Sung-Soo Kim & Sung Park & W. J. Krzanowski, 2008. "Simultaneous variable selection and outlier identification in linear regression using the mean-shift outlier model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(3), pages 283-291.
    9. A.A.M. Nurunnabi & Ali S. Hadi & A.H.M.R. Imon, 2014. "Procedures for the identification of multiple influential observations in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1315-1331, June.
    10. Catherine Fuss & Angelos Theodorakopoulos, 2018. "Compositional Changes in Aggregate Productivity in an Era of Globalisation and Financial Crisis," Working Papers of VIVES - Research Centre for Regional Economics 627696, KU Leuven, Faculty of Economics and Business (FEB), VIVES - Research Centre for Regional Economics.
    11. Hong Choon Ong & Ekele Alih, 2015. "A Control Chart Based on Cluster-Regression Adjustment for Retrospective Monitoring of Individual Characteristics," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-30, April.
    12. Stefani, Gianluca & Gadanakis, Yiorgos & Lombardi, Ginevra Virginia & Tiberti, Marco, 2017. "The impact of financial leverage on farms capacity to react in market shocks," 2017 International Congress, August 28-September 1, 2017, Parma, Italy 261156, European Association of Agricultural Economists.
    13. Batalla-Bejerano, Joan & Costa-Campi, Maria Teresa & Trujillo-Baute, Elisa, 2016. "Collateral effects of liberalisation: Metering, losses, load profiles and cost settlement in Spain’s electricity system," Energy Policy, Elsevier, vol. 94(C), pages 421-431.
    14. Jiří Schwarz & Martin Pospíšil, 2018. "Bankruptcy, Investment, and Financial Constraints: Evidence from the Czech Republic," Eastern European Economics, Taylor & Francis Journals, vol. 56(2), pages 99-121, March.
    15. A. H. M. Rahmatullah Imon, 2005. "Identifying multiple influential observations in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(9), pages 929-946.
    16. José Ignacio Giménez-Nadal & José Alberto Molina & Jorge Velilla, 2024. "Intermediate activities while commuting," Review of Economics of the Household, Springer, vol. 22(3), pages 1185-1220, September.
    17. Sevvandi Kandanaarachchi & Mario A Munoz & Rob J Hyndman & Kate Smith-Miles, 2018. "On normalization and algorithm selection for unsupervised outlier detection," Monash Econometrics and Business Statistics Working Papers 16/18, Monash University, Department of Econometrics and Business Statistics.
    18. Balcazar Salazar,Carlos Felipe, 2015. "Long-run effects of democracy on income inequality : evidence from repeated cross-sections," Policy Research Working Paper Series 7153, The World Bank.
    19. Li-Chu Chien, 2013. "Multiple deletion diagnostics in beta regression models," Computational Statistics, Springer, vol. 28(4), pages 1639-1661, August.
    20. Claude Diebolt & Audrey-Rose Menard & Faustine Perrin, 2017. "Behind the fertility–education nexus: what triggered the French development process?," European Review of Economic History, European Historical Economics Society, vol. 21(4), pages 357-392.

    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:taf:japsta:v:36:y:2009:i:5:p:507-520. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.