Introducing the New ADAPTIVEREG Procedure for Adaptive Regression
the future is one of the most basic human desires. In previous centuries, prediction methods included studying the stars, reading tea leaves, and even examining the entrails of animals. Statistical methodology brought more scientific techniques such as linear and generalized linear models, discriminant analysis, logistic regression, and so on. In this paper, you will learn about multivariate adaptive regression splines (Friedman 1991) a nonparametric technique that combines regression splines and model selection methods. It extends linear models to analyze nonlinear dependencies and to produce parsimonious models that do not overfit the data and thus have good predictive power. This paper shows you how to use PROC ADAPTIVEREG (a new SAS/STAT (r) procedure for multivariate adaptive regression spline models) by presenting a series of examples that show the relationship between adaptive regression models and other statistical modeling techniques. INTRODUCTION ADAPTIVEREG procedure fits multivariate adaptive regression splines, which were proposed by Friedman (1991) Multivariate adaptive regression splines extend linear models to analyze nonlinear dependencies and produce parsi monious models that do not overfit the data and thus have good predictive power. This method is a nonparametric regression technique that combines both regression splines and model selection. It constructs spline basis functions in an adaptive way by automatically selecting appropriate knot values for different variables, and it obtains reduced models by applying model selection techniques. The method does not assume parametric model forms and does not require specification of knot values. This paper explains the basics of PROC ADAPTIVEREG by using a series of examples that include linear, logistic, and Poisson models. The first three examples demonstrate some basic capabilities of PROC ADAPTIVEREG and show how it constructs the basis functions. These examples explain the algorithms that are used by PROC ADAPTIVEREG by showing you ways in which they correspond to more familiar multiple regression models. The logistic regression junk e mail example is the most comprehensive example and illustrates the most important capability of PROC ADAPTIVEREG, namely prediction. That example shows you how to build a model and use it to score observations that were not used in the initial model. When the correct classification is known, the scored observations are used to evaluate the goodness of the predictions. The final example illustrates a nonparametric Poisson regression model.