Trading-off Local versus Global Effects of Regression Nodes in Model Trees

Model trees are an extension of regression trees that associate leaves with multiple regression models. In this paper a method for the top-down induction of model trees is presented, namely the Stepwise Model Tree Induction (SMOTI) method. Its main characteristic is the induction of trees with two types of nodes: regression nodes, which perform only straight-line regression, and split nodes, which partition the sample space. The multiple linear model associated to each leaf is then obtained by combining straight-line regressions reported along the path from the root to the leaf. In this way, internal regression nodes contribute to the definition of multiple models and have a “global” effect, while straight-line regressions at leaves have only “local” effects. This peculiarity of SMOTI has been evaluated in an empirical study involving both real and artificial data.