Unbiased Recursive Partitioning: A Conditional Inference Framework
Open accessAbstract
Recursive binary partitioning is a popular tool for regression analysis. Two fundamental problems of exhaustive search procedures usually applied to fit such models have been known for a long time: overfitting and a selection bias towards covariates with many possible splits or missing values. While pruning procedures are able to solve the overfitting problem, the variable selection bias still seriously affects the interpretability of tree-structured regression models. For some special cases unbiased procedures have been suggested, however lacking a common theoretical foundation. We propose a unified framework for recursive partitioning which embeds tree-structured regression models into a well defined theory of conditional inference procedures. Stopping criteria based on multiple test procedures are implemented and it is shown that the predictive performance of the resulting trees is as good as the performance of established exhaustive search procedures. It turns out that the partitions and therefore the models induced by both approaches are structurally different, confirming the need for an unbiased variable selection. Moreover, it is shown that the prediction accuracy of trees with early stopping is equivalent to the prediction accuracy of pruned trees with unbiased variable selection. The methodology presented here is applicable to all kinds of regression problems, including nominal, ordinal, numeric, censored as well as multivariate response variables and arbitrary measurement scales of the covariates. Data from studies on glaucoma classification, node positive breast cancer survival and mammography experience are re-analyzed.
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- Authors
- Hothorn, T., Hornik, K., & Zeileis, A.
- Affiliations
- Vienna University of Economics and Business (AT)
- Venue
- Journal of Computational and Graphical Statistics
- Publisher
- Informa UK Limited
- Published
- 2006-09
- Volume
- 15
- Issue
- 3
- Pages
- 651-674
- ISSN
- 1061-8600 (ISSN-L)
- 1537-2715
- OpenAlex
- W2123998733
- Cited by
- 4,021
- References
- 57
- Citations by year
- 2026: 171 · 2025: 247 · 2024: 272 · 2023: 310 · 2022: 348 · 2021: 381 · 2020: 332 · 2019: 340 · 2018: 292 · 2017: 258 · 2016: 198 · 2015: 228 · 2014: 171 · 2013: 139 · 2012: 117
- FWCI
- 27.53
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Locations
- Journal of Computational and Graphical Statistics (publishedVersion)
- ePubWU Institutional Repository (Vienna University of Economics and Business) (submittedVersion)
- WU Research (submittedVersion)
- Zenodo (CERN European Organization for Nuclear Research)
- Funders
- Deutsche Forschungsgemeinschaft
- Linköpings Universitet
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Computer Science › Information Systems › Data Mining Algorithms and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- conditional inference, variable selection bias, overfitting, stopping rules, multiple comparisons, early stopping, tree pruning, missing data, prediction accuracy, censored responses, multivariate response
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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