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Generalized additive models with unknown link function including variable selection

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  • Gerhard Tutz
  • Sebastian Petry

Abstract

The generalized additive model is a well established and strong tool that allows modelling smooth effects of predictors on the response. However, if the link function, which is typically chosen as the canonical link, is misspecified, estimates can be biased. A procedure is proposed that simultaneously estimates the form of the link function and the unknown form of the predictor functions including selection of predictors. The procedure is based on boosting methodology, which obtains estimates by using a sequence of weak learners. It strongly dominates fitting procedures that are unable to modify a given link function if the true link function deviates from the fixed function. The performance of the procedure is shown in simulation studies and illustrated by real world examples.

Suggested Citation

  • Gerhard Tutz & Sebastian Petry, 2016. "Generalized additive models with unknown link function including variable selection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2866-2885, November.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:15:p:2866-2885
    DOI: 10.1080/02664763.2016.1155109
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    1. Cui, Xia & Härdle, Wolfgang Karl & Zhu, Lixing, 2009. "Generalized single-index models: The EFM approach," SFB 649 Discussion Papers 2009-050, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
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