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A diagnostic method for simultaneous feature selection and outlier identification in linear regression

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  • Menjoge, Rajiv S.
  • Welsch, Roy E.

Abstract

A diagnostic method along the lines of forward search is proposed to simultaneously study the effect of individual observations and features on the inferences made in linear regression. The method operates by appending dummy variables to the data matrix and performing backward selection on the augmented matrix. It outputs sequences of feature-outlier combinations which can be evaluated by plots similar to those of forward search and includes the capacity to incorporate prior knowledge, in order to mitigate issues such as collinearity. It also allows for alternative ways to understand the selection of the final model. The method is evaluated on five data sets and yields promising results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3181-3193
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    References listed on IDEAS

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    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.
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    5. 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.
    6. 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.
    7. McCann, Lauren & Welsch, Roy E., 2007. "Robust variable selection using least angle regression and elemental set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 249-257, September.
    8. Khan, Jafar A. & Van Aelst, Stefan & Zamar, Ruben H., 2007. "Robust Linear Model Selection Based on Least Angle Regression," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1289-1299, December.
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    Cited by:

    1. Luca Insolia & Ana Kenney & Martina Calovi & Francesca Chiaromonte, 2021. "Robust Variable Selection with Optimality Guarantees for High-Dimensional Logistic Regression," Stats, MDPI, vol. 4(3), pages 1-17, August.
    2. Sue-Fen Huang & Ching-Hsue Cheng, 2013. "GMADM-based attributes selection method in developing prediction model," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(6), pages 3335-3347, October.
    3. 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.
    4. Thompson, Ryan, 2022. "Robust subset selection," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    5. Luca Insolia & Ana Kenney & Francesca Chiaromonte & Giovanni Felici, 2022. "Simultaneous feature selection and outlier detection with optimality guarantees," Biometrics, The International Biometric Society, vol. 78(4), pages 1592-1603, December.
    6. 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.
    7. Tianxiang Liu & Ting Kei Pong & Akiko Takeda, 2019. "A refined convergence analysis of $$\hbox {pDCA}_{e}$$ pDCA e with applications to simultaneous sparse recovery and outlier detection," Computational Optimization and Applications, Springer, vol. 73(1), pages 69-100, May.

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