A recursive partitioning tool for interval prediction

Abstract

The traditional approach to regression trees involves partitioning the space of predictor variables into subsets that optimise a function of the response variable(s), and then predicting future response values by a single-valued summary statistic in each subset. Our belief is that a prediction interval is of greater practical use than a predictive value, and that the criterion for the partitioning should be based on such intervals rather than on single values. We define four potential criteria in the case of a single response variable, discuss computational aspects of producing the partition, evaluate the criteria on both real and simulated data, and draw some tentative conclusions about their relative efficacies. The methodology is extended to the case of multiple response variables, and its viability is demonstrated by application to some further real data. The possibility of fitting distributions to within-subsets data is discussed, and some potential extensions are briefly outlined.