Regression trees for multivalued numerical response variables

In the framework of regression trees, this paper provides a recursive partitioning methodology to deal with a non-standard response variable. Specifically, either multivalued numerical or modal response of the type histogram will be considered. These data are known as symbolic data, which special cases are classical data, imprecise data, conjunctive data as well as fuzzy data. In spite of pre-processing data in order to deal with standard regression tree methodology, this paper provides, as main contribution, a definition of the impurity measure and of the splitting criterion allowing for building the regression tree for multivalued numerical response variable. We analyze and evaluate the performance of our proposal, using simulated data as well as a real-world case studies.