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Generalised linear model trees with global additive effects

Author

Listed:
  • Heidi Seibold

    (University of Zurich
    Institute for Medical Information Processing, Biometry, and Epidemiology Ludwig-Maximilans-Universität München)

  • Torsten Hothorn

    (University of Zurich)

  • Achim Zeileis

    (Universität Innsbruck)

Abstract

Model-based trees are used to find subgroups in data which differ with respect to model parameters. In some applications it is natural to keep some parameters fixed globally for all observations while asking if and how other parameters vary across subgroups. Existing implementations of model-based trees can only deal with the scenario where all parameters depend on the subgroups. We propose partially additive linear model trees (PALM trees) as an extension of (generalised) linear model trees (LM and GLM trees, respectively), in which the model parameters are specified a priori to be estimated either globally from all observations or locally from the observations within the subgroups determined by the tree. Simulations show that the method has high power for detecting subgroups in the presence of global effects and reliably recovers the true parameters. Furthermore, treatment–subgroup differences are detected in an empirical application of the method to data from a mathematics exam: the PALM tree is able to detect a small subgroup of students that had a disadvantage in an exam with two versions while adjusting for overall ability effects.

Suggested Citation

  • Heidi Seibold & Torsten Hothorn & Achim Zeileis, 2019. "Generalised linear model trees with global additive effects," 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. 13(3), pages 703-725, September.
    • Handle: RePEc:spr:advdac:v:13:y:2019:i:3:d:10.1007_s11634-018-0342-1
    DOI: 10.1007/s11634-018-0342-1
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    References listed on IDEAS

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    1. Achim Zeileis & Kurt Hornik, 2007. "Generalized M‐fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508, November.
    2. L. Doove & E. Dusseldorp & K. Deun & I. Mechelen, 2014. "A comparison of five recursive partitioning methods to find person subgroups involved in meaningful treatment–subgroup interactions," 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. 8(4), pages 403-425, December.
    3. Hajjem, Ahlem & Bellavance, François & Larocque, Denis, 2011. "Mixed effects regression trees for clustered data," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 451-459, April.
    4. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    5. Seibold Heidi & Hothorn Torsten & Zeileis Achim, 2016. "Model-Based Recursive Partitioning for Subgroup Analyses," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 45-63, May.
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    Cited by:

    1. Manlio Migliorati & Marica Manisera & Paola Zuccolotto, 2023. "Integration of model-based recursive partitioning with bias reduction estimation: a case study assessing the impact of Oliver’s four factors on the probability of winning a basketball game," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 271-293, March.
    2. Anna Gottard & Giulia Vannucci & Leonardo Grilli & Carla Rampichini, 2023. "Mixed-effect models with trees," 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. 17(2), pages 431-461, June.

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