Conditional Classification Trees Using Instrumental Variables

The framework of this paper is supervised learning using classification trees. Two types of variables play a role in the definition of the classification rule, namely a response variable and a set of predictors. The tree classifier is built up by a recursive partitioning of the prediction space such to provide internally homogeneous groups of objects with respect to the response classes. In the following, we consider the role played by an instrumental variable to stratify either the variables or the objects. This yields to introduce a tree-based methodology for conditional classification. Two special cases will be discussed to grow multiple discriminant trees and partial predictability trees. These approaches use discriminant analysis and predictability measures respectively. Empirical evidence of their usefulness will be shown in real case studies.