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Simultaneous variable selection and outlier identification in linear regression using the mean-shift outlier model

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  • Sung-Soo Kim
  • Sung Park
  • W. J. Krzanowski

Abstract

We provide a method for simultaneous variable selection and outlier identification using the mean-shift outlier model. The procedure consists of two steps: the first step is to identify potential outliers, and the second step is to perform all possible subset regressions for the mean-shift outlier model containing the potential outliers identified in step 1. This procedure is helpful for model selection while simultaneously considering outlier identification, and can be used to identify multiple outliers. In addition, we can evaluate the impact on the regression model of simultaneous omission of variables and interesting observations. In an example, we provide detailed output from the R system, and compare the results with those using posterior model probabilities as proposed by Hoeting et al. [Comput. Stat. Data Anal. 22 (1996), pp. 252-270] for simultaneous variable selection and outlier identification.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:3:p:283-291
    DOI: 10.1080/02664760701833040
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    References listed on IDEAS

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    1. Anthony C. Atkinson, 2002. "Forward search added-variable t-tests and the effect of masked outliers on model selection," Biometrika, Biometrika Trust, vol. 89(4), pages 939-946, December.
    2. 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.
    3. Hoeting, Jennifer & Raftery, Adrian E. & Madigan, David, 1996. "A method for simultaneous variable selection and outlier identification in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 22(3), pages 251-270, July.
    4. 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.
    5. Kim, S. S. & Park, S. H., 1995. "Dynamic plots for displaying the roles of variables and observations in regression model," Computational Statistics & Data Analysis, Elsevier, vol. 19(4), pages 401-418, April.
    6. Chatterjee, Samprit & Hadi, Ali S., 1988. "Impact of simultaneous omission of a variable and an observation on a linear regression equation," Computational Statistics & Data Analysis, Elsevier, vol. 6(2), pages 129-144, March.
    7. Wisnowski, James W. & Montgomery, Douglas C. & Simpson, James R., 2001. "A Comparative analysis of multiple outlier detection procedures in the linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 36(3), pages 351-382, May.
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    Cited by:

    1. 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.
    2. 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.
    3. Nikolas Kuschnig & Gregor Zens & Jesús Crespo Cuaresma, 2021. "Hidden in Plain Sight: Influential Sets in Linear Models," CESifo Working Paper Series 8981, CESifo.
    4. Marc Aerts & Niel Hens & Jeffrey Simonoff, 2010. "Model selection in regression based on pre-smoothing," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1455-1472.

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