Abstract

Abstract We describe a procedure for the classification and description of binary response data. The model is a special case of the multivariate adaptive regression splines (MARS) model; the emphasis is on piecewise constant basis functions, as in the classification and regression trees (CART) approach of Breiman, Friedman, Olshen, and Stone. The procedure is based on the logistic model for binary data. A binary logistic model is built up as the sum of products of indicator functions, as in MARS. The model is then pruned in a backward stepwise manner, using cross-validation as a guide. The pruning is strictly hierarchical (as in CART) to preserve interpretability of the final model. Through simulated and real examples, the procedure is shown to be more effective than CART in uncovering “main effects” and it can lead to a simpler description of the data. On the other hand, it is not as effective as CART in terms of classification error.

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