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Practical variable selection for generalized additive models

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  • Marra, Giampiero
  • Wood, Simon N.

Abstract

The problem of variable selection within the class of generalized additive models, when there are many covariates to choose from but the number of predictors is still somewhat smaller than the number of observations, is considered. Two very simple but effective shrinkage methods and an extension of the nonnegative garrote estimator are introduced. The proposals avoid having to use nonparametric testing methods for which there is no general reliable distributional theory. Moreover, component selection is carried out in one single step as opposed to many selection procedures which involve an exhaustive search of all possible models. The empirical performance of the proposed methods is compared to that of some available techniques via an extensive simulation study. The results show under which conditions one method can be preferred over another, hence providing applied researchers with some practical guidelines. The procedures are also illustrated analysing data on plasma beta-carotene levels from a cross-sectional study conducted in the United States.

Suggested Citation

  • Marra, Giampiero & Wood, Simon N., 2011. "Practical variable selection for generalized additive models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2372-2387, July.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2372-2387
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    References listed on IDEAS

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    Cited by:

    1. Fabian Scheipl & Thomas Kneib & Ludwig Fahrmeir, 2013. "Penalized likelihood and Bayesian function selection in regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 349-385, October.
    2. repec:eee:jmvana:v:159:y:2017:i:c:p:49-66 is not listed on IDEAS
    3. Thi Huong Trinh & Christine Thomas-Agnan & Michel Simioni, 2016. "Calorie intake and income in China: new evidence using semiparametric modelling with generalized additive models," Post-Print hal-01515007, HAL.
    4. Zak-Szatkowska, Malgorzata & Bogdan, Malgorzata, 2011. "Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2908-2924, November.
    5. Antonio Musolesi & Hervé Cardot, 2017. "Modeling temporal treatment effects with zero inflated semi-parametric regression models: the case of local development policies in France," Working Papers 2017036, University of Ferrara, Department of Economics.
    6. McKay Curtis, S. & Banerjee, Sayantan & Ghosal, Subhashis, 2014. "Fast Bayesian model assessment for nonparametric additive regression," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 347-358.
    7. Guo, Jie & Tang, Manlai & Tian, Maozai & Zhu, Kai, 2013. "Variable selection in high-dimensional partially linear additive models for composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 56-67.
    8. Umberto Amato & Anestis Antoniadis & Italia De Feis, 2016. "Additive model selection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 519-564, November.
    9. repec:spr:nathaz:v:87:y:2017:i:1:d:10.1007_s11069-017-2770-1 is not listed on IDEAS

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