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Subsampling based variable selection for generalized linear models

Author

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  • Capanu, Marinela
  • Giurcanu, Mihai
  • Begg, Colin B.
  • Gönen, Mithat

Abstract

A novel variable selection method for low-dimensional generalized linear models is introduced. The new approach called AIC OPTimization via STABility Selection (OPT-STABS) repeatedly subsamples the data, minimizes Akaike's Information Criterion (AIC) over a sequence of nested models for each subsample, and includes in the final model those predictors selected in the minimum AIC model in a large fraction of the subsamples. New methods are also introduced to establish an optimal variable selection cutoff over repeated subsamples. An extensive simulation study examining a variety of proposed variable selection methods shows that, although no single method uniformly outperforms the others in all the scenarios considered, OPT-STABS is consistently among the best-performing methods in most settings while it performs competitively for the rest. This is in contrast to other candidate methods which either have poor performance across the board or exhibit good performance in some settings, but very poor in others. In addition, the asymptotic properties of the OPT-STABS estimator are derived, and its root-n consistency and asymptotic normality are proved. The methods are applied to two datasets involving logistic and Poisson regressions.

Suggested Citation

  • Capanu, Marinela & Giurcanu, Mihai & Begg, Colin B. & Gönen, Mithat, 2023. "Subsampling based variable selection for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:csdana:v:184:y:2023:i:c:s0167947323000518
    DOI: 10.1016/j.csda.2023.107740
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Nicolai Meinshausen & Peter Bühlmann, 2010. "Stability selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 417-473, September.
    3. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Rajen D. Shah & Richard J. Samworth, 2013. "Variable selection with error control: another look at stability selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(1), pages 55-80, January.
    6. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    7. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    8. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    Full references (including those not matched with items on IDEAS)

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