Regression trees for analysis of count data with extra Poisson variation

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.