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Extending AIC to best subset regression

Author

Listed:
  • J. G. Liao

    (Penn State University)

  • Joseph E. Cavanaugh

    (University of Iowa)

  • Timothy L. McMurry

    (University of Virginia)

Abstract

The Akaike information criterion (AIC) is routinely used for model selection in best subset regression. The standard AIC, however, generally under-penalizes model complexity in the best subset regression setting, potentially leading to grossly overfit models. Recently, Zhang and Cavanaugh (Comput Stat 31(2):643–669, 2015) made significant progress towards addressing this problem by introducing an effective multistage model selection procedure. In this paper, we present a rigorous and coherent conceptual framework for extending AIC to best subset regression. A new model selection algorithm derived from our framework possesses well understood and desirable asymptotic properties and consistently outperforms the procedure of Zhang and Cavanaugh in simulation studies. It provides an effective tool for combating the pervasive overfitting that detrimentally impacts best subset regression analysis so that the selected models contain fewer irrelevant predictors and predict future observations more accurately.

Suggested Citation

  • J. G. Liao & Joseph E. Cavanaugh & Timothy L. McMurry, 2018. "Extending AIC to best subset regression," Computational Statistics, Springer, vol. 33(2), pages 787-806, June.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-018-0797-8
    DOI: 10.1007/s00180-018-0797-8
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    References listed on IDEAS

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    1. Liao J.G. & McGee D., 2003. "Adjusted Coefficients of Determination for Logistic Regression," The American Statistician, American Statistical Association, vol. 57, pages 161-165, August.
    2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    3. Bengtsson, Thomas & Cavanaugh, Joseph E., 2006. "An improved Akaike information criterion for state-space model selection," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2635-2654, June.
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    Cited by:

    1. Pereira Teodoro da Silva, Kairo & Kalbusch, Andreza & Henning, Elisa, 2023. "Detection of unauthorized consumption in water supply systems: A case study using logistic regression," Utilities Policy, Elsevier, vol. 84(C).

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