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Assessing global influential observations in modified ridge regression

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  • Jahufer, Aboobacker
  • Jianbao, Chen

Abstract

We occasionally find that a small subset of the data exerts a disproportionate influence on the fitted regression model. That is, parameter estimates or predictions may depend more on the influential subset than on the majority of the data. We would like to locate these influential points and assess their impact on the model. If these influential points are bad values then they should be eliminated. On the other hand, there may be nothing wrong with these points, but if they control key model properties, as we would like for them to, they could affect the use of the model. When modified ridge regression (MRR) is used to mitigate the effects of multicollinearity, the influence of observations can be drastically modified. In this paper, we propose a case deletion formula to detect influential points in MRR. The [Longley, J.W., 1967. An appraisal of least squares programs for electronic computers from the point of view of the user. Journal of American Statistical Association 62, 819-841] data is used to illustrate our methodology.

Suggested Citation

  • Jahufer, Aboobacker & Jianbao, Chen, 2009. "Assessing global influential observations in modified ridge regression," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 513-518, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:4:p:513-518
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    References listed on IDEAS

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    1. Groß, Jürgen, 2003. "Restricted ridge estimation," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 57-64, October.
    2. Shi, Lei & Wang, Xueren, 1999. "Local influence in ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 341-353, September.
    3. Hernán Rubio & Luis Firinguetti, 2002. "The Distribution of Stochastic Shrinkage Parameters in Ridge Regression," Working Papers Central Bank of Chile 137, Central Bank of Chile.
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    Cited by:

    1. Hadi Emami, 2018. "Local influence for Liu estimators in semiparametric linear models," Statistical Papers, Springer, vol. 59(2), pages 529-544, June.
    2. Hadi Emami & Mostafa Emami, 2016. "New influence diagnostics in ridge regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 476-489, March.
    3. M. Revan Özkale & Stanley Lemeshow & Rodney Sturdivant, 2018. "Logistic regression diagnostics in ridge regression," Computational Statistics, Springer, vol. 33(2), pages 563-593, June.
    4. T. Söküt Açar & M.R. Özkale, 2016. "Influence measures based on confidence ellipsoids in general linear regression model with correlated regressors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2791-2812, November.
    5. Aboobacker Jahufer & Jianbao Chen, 2012. "Identifying local influential observations in Liu estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 425-438, April.

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