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Regression Trees and Ensemble for Multivariate Outcomes

Author

Listed:
  • Evan L. Reynolds

    (University of Michigan)

  • Brian C. Callaghan

    (University of Michigan)

  • Michael Gaies

    (University of Cincinnati)

  • Mousumi Banerjee

    (University of Michigan)

Abstract

Tree-based methods have become one of the most flexible, intuitive, and powerful analytic tools for exploring complex data structures. The best documented, and arguably most popular uses of tree-based methods are in biomedical research, where multivariate outcomes occur commonly (e.g. diastolic and systolic blood pressure and nerve conduction measures in studies of neuropathy). Existing tree-based methods for multivariate outcomes do not appropriately take into account the correlation that exists in such data. In this paper, we develop goodness-of-split measures for building multivariate regression trees for continuous multivariate outcomes. We propose two general approaches: minimizing within-node homogeneity and maximizing between-node separation. Within-node homogeneity is measured using the average Mahalanobis distance and the determinant of the variance-covariance matrix. Between-node separation is measured using the Mahalanobis distance, Euclidean distance and standardized Euclidean distance. To enhance prediction accuracy we extend the single multivariate regression tree to an ensemble of multivariate trees. Extensive simulations are presented to examine the properties of our goodness-of-split measures. Finally, the proposed methods are illustrated using two clinical datasets of neuropathy and pediatric cardiac surgery.

Suggested Citation

  • Evan L. Reynolds & Brian C. Callaghan & Michael Gaies & Mousumi Banerjee, 2023. "Regression Trees and Ensemble for Multivariate Outcomes," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 77-109, May.
    • Handle: RePEc:spr:sankhb:v:85:y:2023:i:1:d:10.1007_s13571-023-00301-z
    DOI: 10.1007/s13571-023-00301-z
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    References listed on IDEAS

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    1. David R. Larsen & Paul L. Speckman, 2004. "Multivariate Regression Trees for Analysis of Abundance Data," Biometrics, The International Biometric Society, vol. 60(2), pages 543-549, June.
    2. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    3. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
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