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.