Adaptive Regression for Modeling Nonlinear Relationships

  • George J. Knafl
  • Kai Ding

Part of the Statistics for Biology and Health book series (SBH)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. George J. Knafl, Kai Ding
    Pages 1-8
  3. Adaptive Regression Modeling

  4. Adaptive Logistic Regression Modeling

  5. Adaptive Poisson Regression Modeling

    1. Front Matter
      Pages 253-253
  6. Alternative Nonparametric Regression Modeling

    1. Front Matter
      Pages 297-297
    2. George J. Knafl, Kai Ding
      Pages 299-314
    3. George J. Knafl, Kai Ding
      Pages 315-327
    4. George J. Knafl, Kai Ding
      Pages 329-338
    5. George J. Knafl, Kai Ding
      Pages 339-349
  7. The Adaptive Regression Modeling Process

    1. Front Matter
      Pages 351-351
    2. George J. Knafl, Kai Ding
      Pages 353-370
  8. Back Matter
    Pages 371-372

About this book


This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible.

A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the standard, logistic, and Poisson regression contexts with continuous, discrete, and counts outcomes, respectively, either univariate or multivariate. The book also provides a comparison of adaptive modeling to generalized additive modeling (GAM) and multiple adaptive regression splines (MARS) for univariate outcomes.

The authors have created customized SAS macros for use in conducting adaptive regression modeling. These macros and code for conducting the analyses discussed in the book are available through the first author's website and online via the book’s Springer website. Detailed descriptions of how to use these macros and interpret their output appear throughout the book. These methods can be implemented using other programs.

  • Provides insight into modeling of nonlinear relationships and also justifications for when to use them, thereby providing novel insights about relationships
  • Addresses not only adaptive generation of additive models but also of models based on nonlinear interactions
  • Discusses adaptive modeling of variances/dispersions as well as of means
  • Highlights both univariate and multivariate outcomes, rather than solely univariate outcomes


Adaptive Modeling Cross-validation Fractional polynomials Generalized additive modeling Heuristic search Nonlinear regression

Authors and affiliations

  • George J. Knafl
    • 1
  • Kai Ding
    • 2
  1. 1.University of North Carolina at Chapel HillChapel HillUSA
  2. 2.University of Oklahoma Health Sciences CenterOklahoma CityUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-33944-3
  • Online ISBN 978-3-319-33946-7
  • Series Print ISSN 1431-8776
  • Series Online ISSN 2197-5671
  • Buy this book on publisher's site