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Tree-structured modelling of categorical predictors in generalized additive regression

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  • Gerhard Tutz

    (Ludwig-Maximilians-Universität München)

  • Moritz Berger

    (Universitätsklinikum Bonn)

Abstract

Generalized linear and additive models are very efficient regression tools but many parameters have to be estimated if categorical predictors with many categories are included. The method proposed here focusses on the main effects of categorical predictors by using tree type methods to obtain clusters of categories. When the predictor has many categories one wants to know in particular which of the categories have to be distinguished with respect to their effect on the response. The tree-structured approach allows to detect clusters of categories that share the same effect while letting other predictors, in particular metric predictors, have a linear or additive effect on the response. An algorithm for the fitting is proposed and various stopping criteria are evaluated. The preferred stopping criterion is based on p values representing a conditional inference procedure. In addition, stability of clusters is investigated and the relevance of predictors is investigated by bootstrap methods. Several applications show the usefulness of the tree-structured approach and small simulation studies demonstrate that the fitting procedure works well.

Suggested Citation

  • Gerhard Tutz & Moritz Berger, 2018. "Tree-structured modelling of categorical predictors in generalized additive regression," 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. 12(3), pages 737-758, September.
    • Handle: RePEc:spr:advdac:v:12:y:2018:i:3:d:10.1007_s11634-017-0298-6
    DOI: 10.1007/s11634-017-0298-6
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    References listed on IDEAS

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