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Count regression trees

Author

Listed:
  • Nan-Ting Liu

    (National Chung Cheng University)

  • Feng-Chang Lin

    (University of North Carolina at Chapel Hill)

  • Yu-Shan Shih

    (National Chung Cheng University)

Abstract

Count data frequently appear in many scientific studies. In this article, we propose a regression tree method called CORE for analyzing such data. At each node, besides a Poisson regression, a count regression such as hurdle, negative binomial, or zero-inflated regression which can accommodate over-dispersion and/or excess zeros is fitted. A likelihood-based procedure is suggested to select split variables and split sets. Node deviance is then used in the tree pruning process to avoid overfitting. CORE is able to eliminate variable selection bias. In the simulations and real data studies, we show that CORE has some advantages over the existing method, MOB.

Suggested Citation

  • Nan-Ting Liu & Feng-Chang Lin & Yu-Shan Shih, 2020. "Count regression 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. 14(1), pages 5-27, March.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:1:d:10.1007_s11634-019-00358-7
    DOI: 10.1007/s11634-019-00358-7
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    References listed on IDEAS

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    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, November.
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    3. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    4. Seong-Keon Lee & Seohoon Jin, 2006. "Decision tree approaches for zero-inflated count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(8), pages 853-865.
    5. Ciampi, Antonio, 1991. "Generalized regression trees," Computational Statistics & Data Analysis, Elsevier, vol. 12(1), pages 57-78, August.
    6. Wei-Yin Loh, 2014. "Fifty Years of Classification and Regression Trees," International Statistical Review, International Statistical Institute, vol. 82(3), pages 329-348, December.
    7. Choi, Yunhee & Ahn, Hongshik & Chen, James J., 2005. "Regression trees for analysis of count data with extra Poisson variation," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 893-915, June.
    8. 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.
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