SAS Global Forum 2013 Statistics and Data Analysis - Paper 457-2013 - Introducing the New ADAPTIVEREG Procedure for Adaptive Regression

Aug 27, 2026

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SAS Global Forum 2013 paper introduces PROC ADAPTIVEREG for multivariate adaptive regression splines, a nonparametric approach that extends linear models to capture nonlinear dependencies. The method builds adaptive spline basis functions by automatically selecting knot values and applies model selection to obtain parsimonious models that avoid overfitting while maintaining predictive power. Through examples covering linear, logistic, and Poisson settings, the paper demonstrates algorithm-to-regression correspondence and shows how to train, score new observations, and assess prediction quality, including cross validation, diagnostics, and output datasets for fitted components.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages18

Reading Time45 min

AccessFree to download

Abstract

Introduction

PROC ADAPTIVEREG Features

Nonlinear Fit Function Example

SAS Global Forum 2013 Statistics and Data Analysis Paper 457-2013 Introducing the New ADAPTIVEREG Procedure for Adaptive Regression Warren F. Kuhfeld and Weijie Cai, SAS Institute Inc. ABSTRACT Predicting 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® 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 The 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 parsimonious 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 inan 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 requirespeciﬁcation 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 email 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. PROC ADAPTIVEREG is available as an experimental procedure in SAS/STAT 12.1, which was released in 2012 . The examples in this paper were run in SAS/STAT 13.1, which will be available in 2013 . All example code also works in the SAS/STAT 12.1, but the results might differ in some cases. PROC ADAPTIVEREG FEATURES The ADAPTIVEREG procedure provides the following features: • ﬁts nonparametric regression models (linear, logistic, and Poisson) • supports quantitative and classiﬁcation variables • can run using multiple threads • enables you to force effects in the ﬁnal model or restrict variables in linear forms • supports options for fast forward-selection • supports data that have response variables that are distributed in the exponential family (Buja et al. 1991) • supports partitioning of data into training, validation, and testing roles • provides leave-one-out and k-fold cross validation • produces a graphical representation of the selection process, model ﬁt, functional components, and ﬁt diagnostics • produces an output data set that contains predicted values and residuals • produces an output data set that contains the design matrix of basis functions

FAQs

What is PROC ADAPTIVEREG used for?

PROC ADAPTIVEREG fits multivariate adaptive regression splines, extending linear models to model nonlinear relationships with parsimonious, non-overfitting predictive models.

How does ADAPTIVEREG build the spline basis functions?

It constructs spline basis functions adaptively by automatically selecting appropriate knot values for different variables, without requiring knot specification.

How does the paper evaluate prediction performance in the examples?

In the logistic regression junk email example, the model is built on initial data, scored on observations not used for training, and evaluated using known classifications; the procedure also supports leave-one-out and k-fold cross validation.

Aug 27, 2026

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