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Mixed effects regression trees for clustered data

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  • Hajjem, Ahlem
  • Bellavance, François
  • Larocque, Denis

Abstract

This paper presents an extension of the standard regression tree method to clustered data. Previous works extending tree methods to accommodate correlated data are mainly based on the multivariate repeated-measures approach. We propose a "mixed effects regression tree" method where the correlated observations are viewed as nested within clusters rather than as vectors of multivariate repeated responses. The proposed method can handle unbalanced clusters, allows observations within clusters to be split, and can incorporate random effects and observation-level covariates. We implemented the proposed method using a standard tree algorithm within the framework of the expectation-maximization (EM) algorithm. The simulation results show that the proposed regression tree method provides substantial improvements over standard trees when the random effects are non negligible. A real data example is used to illustrate the method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:4:p:451-459
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    References listed on IDEAS

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    1. Kai Yu & William Wheeler & Qizhai Li & Andrew W. Bergen & Neil Caporaso & Nilanjan Chatterjee & Jinbo Chen, 2010. "A Partially Linear Tree-based Regression Model for Multivariate Outcomes," Biometrics, The International Biometric Society, vol. 66(1), pages 89-96, March.
    2. Keon Lee, Seong, 2005. "On generalized multivariate decision tree by using GEE," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1105-1119, June.
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    Cited by:

    1. Steffen Nestler & Sarah Humberg, 2022. "A Lasso and a Regression Tree Mixed-Effect Model with Random Effects for the Level, the Residual Variance, and the Autocorrelation," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 506-532, June.
    2. Kim, Seheon & Rasouli, Soora & Timmermans, Harry & Yang, Dujuan, 2018. "Estimating panel effects in probabilistic representations of dynamic decision trees using bayesian generalized linear mixture models," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 168-184.
    3. Patrick Krennmair & Timo Schmid, 2022. "Flexible domain prediction using mixed effects random forests," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1865-1894, November.
    4. Shuwen Hu & You-Gan Wang & Christopher Drovandi & Taoyun Cao, 2023. "Predictions of machine learning with mixed-effects in analyzing longitudinal data under model misspecification," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 681-711, June.
    5. Zelenkov, Yu. & Solntsev, I., 2022. "Predicting the value of professional sport clubs. A study of European soccer, 2005-2018," Journal of the New Economic Association, New Economic Association, vol. 56(4), pages 28-46.
    6. 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.
    7. Wagner Martin & Zeileis Achim, 2019. "Heterogeneity and Spatial Dependence of Regional Growth in the EU: A Recursive Partitioning Approach," German Economic Review, De Gruyter, vol. 20(1), pages 67-82, February.
    8. Jiang, Cuiqing & Wang, Zhao & Zhao, Huimin, 2019. "A prediction-driven mixture cure model and its application in credit scoring," European Journal of Operational Research, Elsevier, vol. 277(1), pages 20-31.
    9. Tsionas, Mike, 2022. "Efficiency estimation using probabilistic regression trees with an application to Chilean manufacturing industries," International Journal of Production Economics, Elsevier, vol. 249(C).
    10. Tsubasa Ito & Shonosuke Sugasawa, 2023. "Grouped generalized estimating equations for longitudinal data analysis," Biometrics, The International Biometric Society, vol. 79(3), pages 1868-1879, September.
    11. 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.
    12. Peter Calhoun & Richard A. Levine & Juanjuan Fan, 2021. "Repeated measures random forests (RMRF): Identifying factors associated with nocturnal hypoglycemia," Biometrics, The International Biometric Society, vol. 77(1), pages 343-351, March.
    13. Messner, Wolfgang, 2024. "Exploring multilevel data with deep learning and XAI: The effect of personal-care advertising spending on subjective happiness," International Business Review, Elsevier, vol. 33(1).
    14. Hajjem, Ahlem & Larocque, Denis & Bellavance, François, 2017. "Generalized mixed effects regression trees," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 114-118.
    15. Fu, Wei & Simonoff, Jeffrey S., 2015. "Unbiased regression trees for longitudinal and clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 53-74.

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