Extension of CART using multiple splits under order restrictions

CART was introduced by Breiman et al. (1984) as a classification tool. It divides the whole sample recursively in two subpopulations by finding the best possible split with respect to a optimisation criterion. This method, restricted up to date to binary splits, is extended in this paper for allowing also multiple splits. The main problem with this extension is related to the optimal number of splits and the location of the corresponding cutpoints. In order to reduce the computational effort and enhance parsimony, the reduced isotonic regression was used in order to solve this problem. The extended CART method was tested in a simulation study and was compared with the classical approach in an epidemiological study. In both studies the extended CART turned out to be a useful and reliable alternative.