Tree-structured modelling of varying coefficients

Statistics and Computing volume 29, pages217–229(2019)Cite this article

Abstract

The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a set of explanatory variables, and it is unknown which covariates are modified by which variables. A recursive partitioning strategy is proposed that is able to deal with this complex selection problem. The tree-structured modelling yields for each covariate, which is modified by other variables, a tree that visualizes the modified effects. The performance of the method is investigated in simulations, and two applications illustrate its usefulness.

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Acknowledgements

The authors thank the reviewers for their thorough reading and helpful suggestions for improving the article.

Author information

Affiliations

  1. Institut für Medizinische Biometrie, Informatik und Epidemiologie, Universitätsklinikum Bonn, Sigmund-Freud-Straße 25, 53105, Bonn, Germany

    Moritz Berger & Matthias Schmid

  2. Institut für Statistik, Ludwig-Maximilians-Universität München, Akademiestraße 1, 80799, Munich, Germany

    Gerhard Tutz

Authors
  1. Moritz Berger
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  2. Gerhard Tutz
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  3. Matthias Schmid
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Correspondence to Moritz Berger.

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Berger, M., Tutz, G. & Schmid, M. Tree-structured modelling of varying coefficients. Stat Comput 29, 217–229 (2019). https://doi.org/10.1007/s11222-018-9804-8

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Keywords

  • Varying-coefficient models
  • Interactions
  • Recursive partitioning
  • Tree-based models