IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v207y2025ics0167947325000180.html
   My bibliography  Save this article

Confidence intervals for tree-structured varying coefficients

Author

Listed:
  • Spuck, Nikolai
  • Schmid, Matthias
  • Monin, Malte
  • Berger, Moritz

Abstract

The tree-structured varying coefficient (TSVC) model is a flexible regression approach that allows the effects of covariates to vary with the values of the effect modifiers. Relevant effect modifiers are identified inherently using recursive partitioning techniques. To quantify uncertainty in TSVC models, a procedure to construct confidence intervals of the estimated partition-specific coefficients is proposed. This task constitutes a selective inference problem as the coefficients of a TSVC model result from data-driven model building. To account for this issue, a parametric bootstrap approach, which is tailored to the complex structure of TSVC, is introduced. Finite sample properties, particularly coverage proportions, of the proposed confidence intervals are evaluated in a simulation study. For illustration, applications to data from COVID-19 patients and from patients suffering from acute odontogenic infection are considered. The proposed approach may also be adapted for constructing confidence intervals for other tree-based methods.

Suggested Citation

  • Spuck, Nikolai & Schmid, Matthias & Monin, Malte & Berger, Moritz, 2025. "Confidence intervals for tree-structured varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 207(C).
    • Handle: RePEc:eee:csdana:v:207:y:2025:i:c:s0167947325000180
    DOI: 10.1016/j.csda.2025.108142
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947325000180
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2025.108142?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Rügamer, David & Greven, Sonja, 2018. "Selective inference after likelihood- or test-based model selection in linear models," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 7-12.
    2. Bürgin, Reto & Ritschard, Gilbert, 2017. "Coefficient-Wise Tree-Based Varying Coefficient Regression with vcrpart," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 80(i06).
    3. Lee, Jihui & Li, Gen & Wilson, James D., 2020. "Varying-coefficient models for dynamic networks," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    4. Marie-Therese Puth & Gerhard Tutz & Nils Heim & Eva Münster & Matthias Schmid & Moritz Berger, 2020. "Tree-based modeling of time-varying coefficients in discrete time-to-event models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 545-572, July.
    5. Rügamer, David & Baumann, Philipp F.M. & Greven, Sonja, 2022. "Selective inference for additive and linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    6. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    7. Bürgin, Reto & Ritschard, Gilbert, 2015. "Tree-based varying coefficient regression for longitudinal ordinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 65-80.
    8. 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.
    9. Qingyuan Zhao & Dylan S. Small & Ashkan Ertefaie, 2022. "Selective inference for effect modification via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 382-413, April.
    10. Ryan J. Tibshirani & Jonathan Taylor & Richard Lockhart & Robert Tibshirani, 2016. "Exact Post-Selection Inference for Sequential Regression Procedures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 600-620, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jelle J Goeman & Aldo Solari, 2024. "On selection and conditioning in multiple testing and selective inference," Biometrika, Biometrika Trust, vol. 111(2), pages 393-416.
    2. Pirenne, Sarah & Claeskens, Gerda, 2024. "Exact post-selection inference for adjusted R squared selection," Statistics & Probability Letters, Elsevier, vol. 211(C).
    3. Rügamer, David & Baumann, Philipp F.M. & Greven, Sonja, 2022. "Selective inference for additive and linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    4. 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.
    5. Gregory Vaughan & Robert Aseltine & Kun Chen & Jun Yan, 2017. "Stagewise generalized estimating equations with grouped variables," Biometrics, The International Biometric Society, vol. 73(4), pages 1332-1342, December.
    6. Yongsheng Jiang & Dong Zhao & Andrew Sanderford & Jing Du, 2018. "Effects of Bank Lending on Urban Housing Prices for Sustainable Development: A Panel Analysis of Chinese Cities," Sustainability, MDPI, vol. 10(3), pages 1-16, February.
    7. Dzemski, Andreas & Okui, Ryo & Wang, Wenjie, 2025. "Location Characteristics of Conditional Selective Confidence Intervals via Polyhedral Methods," Working Papers in Economics 851, University of Gothenburg, Department of Economics.
    8. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    9. Michael J. Weir & Thomas W. Sproul, 2019. "Identifying Drivers of Genetically Modified Seafood Demand: Evidence from a Choice Experiment," Sustainability, MDPI, vol. 11(14), pages 1-21, July.
    10. Olarreaga, Marcelo & Sperlich, Stefan & Trachsel, Virginie, 2016. "Export Promotion: what works?," CEPR Discussion Papers 11270, C.E.P.R. Discussion Papers.
    11. Gerhard Tutz, 2020. "Modelling heterogeneity: on the problem of group comparisons with logistic regression and the potential of the heterogeneous choice model," 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. 14(3), pages 517-542, September.
    12. The Tien Mai, 2023. "Reliable Genetic Correlation Estimation via Multiple Sample Splitting and Smoothing," Mathematics, MDPI, vol. 11(9), pages 1-13, May.
    13. Breunig, Christoph, 2021. "Varying random coefficient models," Journal of Econometrics, Elsevier, vol. 221(2), pages 381-408.
    14. Nazemi, Abdolreza & Fabozzi, Frank J., 2018. "Macroeconomic variable selection for creditor recovery rates," Journal of Banking & Finance, Elsevier, vol. 89(C), pages 14-25.
    15. Rand R. Wilcox, 2018. "Robust regression: an inferential method for determining which independent variables are most important," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 100-111, January.
    16. Christian Gross & Pierre L. Siklos, 2020. "Analyzing credit risk transmission to the nonfinancial sector in Europe: A network approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 61-81, January.
    17. Johannes Rude Jensen & Mohsen Pourpouneh & Kurt Nielsen & Omri Ross, 2021. "The Homogenous Properties of Automated Market Makers," Papers 2105.02782, arXiv.org.
    18. Weijie J Su, 2018. "When is the first spurious variable selected by sequential regression procedures?," Biometrika, Biometrika Trust, vol. 105(3), pages 517-527.
    19. Zhou, Niwen & Guo, Xu & Zhu, Lixing, 2024. "Significance test for semiparametric conditional average treatment effects and other structural functions," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    20. Monica Billio & Roberto Casarin & Fausto Corradin & Antonio Peruzzi, 2025. "Bayesian Outlier Detection for Matrix-variate Models," Papers 2503.19515, arXiv.org.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:207:y:2025:i:c:s0167947325000180. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.