Tree-structured modelling of varying coefficients

  • Moritz Berger
  • Gerhard Tutz
  • Matthias Schmid


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.


Varying-coefficient models Interactions Recursive partitioning Tree-based models 



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

Supplementary material

11222_2018_9804_MOESM1_ESM.gz (17 kb)
Supplementary material 1 (gz 16 KB)


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Authors and Affiliations

  1. 1.Institut für Medizinische Biometrie, Informatik und EpidemiologieUniversitätsklinikum BonnBonnGermany
  2. 2.Institut für StatistikLudwig-Maximilians-Universität MünchenMunichGermany

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