Regression trees for analysis of count data with extra Poisson variation

  • Authors:

  • Yunhee Choi;Hongshik Ahn;James J. Chen

  • Affiliations:

  • Department of Preventive Medicine, School of Medicine, Seoul National University, 28 Yongeon-Dong, Chongro-Gu, Korea;Department of Applied Mathematics and Statistics, Stony Brook University, Math Tower, Stony Brook, NY 11794-3600, USA;Division of Biometry and Risk Assessment, National Center for Toxicological Research, FDA, Jefferson, AR 72079, USA

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2005

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Abstract

This article proposes methods for fitting piecewise loglinear models to count data with an extra-Poisson variation. Both SUPPORT (Statistica Sinica, 4 (1994) 143) and GUIDE (Statistica Sinica, 12 (2002) 361) are used for splitting methods. We developed a new bootstrap resampling method performed at each node of the tree to determine the proper size of a tree. The quasi-likelihood approach is used for fitting an extra-Poisson model at each stratum to take into account the extra variability. An adjusted Anscombe residual for the extra-Poisson model is used in this procedure. Performance of the proposed method is evaluated by a Monte Carlo simulation study. The proposed method is used to investigate geographic variability in mortality rates on lung cancer as well as effects of various demographic variability.