Three-structured smooth transition regression models based on CART algorithm

In the present work, a tree-based model that combines aspects of CART (Classification and Regression Trees) and STR (Smooth Transition Regression) is proposed. The main idea relies on specifying a parametric nonlinear model through a tree-growing procedure. The resulting model can be analysed either as a fuzzy regression or as a smooth transition regression with multiple regimes. Decisions about splits are entirely based on statistical tests of hypotheses and confidence intervals are constructed for the parameters within the terminal nodes as well as the final predictions. A Monte Carlo Experiment shows the estimators’ properties and the ability of the proposed algorithm to identify correctly several tree architectures. An application to the famous Boston Housing dataset shows that the proposed model provides better explanation with the same number of leaves as the one obtained with the CART algorithm.