IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i7p2372-2387.html
   My bibliography  Save this article

Practical variable selection for generalized additive models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(11)00049-1
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Simila, Timo & Tikka, Jarkko, 2007. "Input selection and shrinkage in multiresponse linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 406-422, September.
    3. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114, February.
    4. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    5. Buhlmann P. & Yu B., 2003. "Boosting With the L2 Loss: Regression and Classification," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 324-339, January.
    6. Nott, David J. & Leng, Chenlei, 2010. "Bayesian projection approaches to variable selection in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3227-3241, December.
    7. Belitz, Christiane & Lang, Stefan, 2008. "Simultaneous selection of variables and smoothing parameters in structured additive regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 61-81, September.
    8. Shafik, Nivien & Tutz, Gerhard, 2009. "Boosting nonlinear additive autoregressive time series," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2453-2464, May.
    9. Gerhard Tutz & Harald Binder, 2006. "Generalized Additive Modeling with Implicit Variable Selection by Likelihood-Based Boosting," Biometrics, The International Biometric Society, vol. 62(4), pages 961-971, December.
    10. Simon N. Wood, 2008. "Fast stable direct fitting and smoothness selection for generalized additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 495-518, July.
    11. Eva Cantoni, 2002. "Degrees-of-freedom tests for smoothing splines," Biometrika, Biometrika Trust, vol. 89(2), pages 251-263, June.
    12. Göran Kauermann & Gerhard Tutz, 2001. "Testing generalized linear and semiparametric models against smooth alternatives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 147-166.
    13. Tutz, Gerhard & Binder, Harald, 2007. "Boosting ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6044-6059, August.
    14. Avalos, Marta & Grandvalet, Yves & Ambroise, Christophe, 2007. "Parsimonious additive models," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2851-2870, March.
    15. Philip T. Reiss & R. Todd Ogden, 2009. "Smoothing parameter selection for a class of semiparametric linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 505-523, April.
    16. Daye, Z. John & Jeng, X. Jessie, 2009. "Shrinkage and model selection with correlated variables via weighted fusion," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1284-1298, February.
    17. 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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    3. Faisal Zahid & Gerhard Tutz, 2013. "Multinomial logit models with implicit variable selection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(4), pages 393-416, December.
    4. Simon N. Wood, 2020. "Inference and computation with generalized additive models and their extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 307-339, June.
    5. Sariyar Murat & Schumacher Martin & Binder Harald, 2014. "A boosting approach for adapting the sparsity of risk prediction signatures based on different molecular levels," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(3), pages 343-357, June.
    6. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    7. Longhi, Christian & Musolesi, Antonio & Baumont, Catherine, 2014. "Modeling structural change in the European metropolitan areas during the process of economic integration," Economic Modelling, Elsevier, vol. 37(C), pages 395-407.
    8. Strasak, Alexander M. & Umlauf, Nikolaus & Pfeiffer, Ruth M. & Lang, Stefan, 2011. "Comparing penalized splines and fractional polynomials for flexible modelling of the effects of continuous predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1540-1551, April.
    9. Stefanie Hieke & Axel Benner & Richard F Schlenk & Martin Schumacher & Lars Bullinger & Harald Binder, 2016. "Identifying Prognostic SNPs in Clinical Cohorts: Complementing Univariate Analyses by Resampling and Multivariable Modeling," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-18, May.
    10. Lee, Dae-Jin & Durbán, María & Eilers, Paul, 2013. "Efficient two-dimensional smoothing with P-spline ANOVA mixed models and nested bases," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 22-37.
    11. Longhi, C. & Musolesi, A. & Baumont, C., 2013. "Modeling the industrial dynamics of the European metropolitan areas during the process of economic integration: a semiparametric approach," Working Papers 2013-10, Grenoble Applied Economics Laboratory (GAEL).
    12. Leitenstorfer, Florian & Tutz, Gerhard, 2007. "Knot selection by boosting techniques," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4605-4621, May.
    13. Musolesi Antonio & Mazzanti Massimiliano, 2014. "Nonlinearity, heterogeneity and unobserved effects in the carbon dioxide emissions-economic development relation for advanced countries," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 521-541, December.
    14. Kaixu Yang & Tapabrata Maiti, 2022. "Ultrahigh‐dimensional generalized additive model: Unified theory and methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 917-942, September.
    15. Massimiliano Mazzanti & Antonio Musolesi, 2013. "Nonlinearity, Heterogeneity and Unobserved Effects in the CO2-income Relation for Advanced Countries," Working Papers 2013.91, Fondazione Eni Enrico Mattei.
    16. 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.
    17. Wang Zhu & Wang C.Y., 2010. "Buckley-James Boosting for Survival Analysis with High-Dimensional Biomarker Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-33, June.
    18. Roberto Basile & Luigi Benfratello & Davide Castellani, 2012. "Geoadditive models for regional count data: an application to industrial location," ERSA conference papers ersa12p83, European Regional Science Association.
    19. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    20. Sergei Kharin & Zuzana Kapustova & Ivan Lichner, 2023. "Price transmission between maize and poultry product markets in the Visegrád Group countries: What is more nonlinear, egg or chicken?," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 69(12), pages 510-522.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2372-2387. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.