Adaptive Regression for Modeling Nonlinear Relationships / by George J. Knafl, Kai Ding.

Format:

Book

Author/Creator:

Knafl, George J., Author.

Ding, Kai, Author.

Series:

Statistics for Biology and Health, 2197-5671

Language:

English

Subjects (All):

Biometry.

Statistics.

Biostatistics.

Statistical Theory and Methods.

Local Subjects:

Biostatistics.

Statistical Theory and Methods.

Physical Description:

1 online resource (XXV, 372 p. 57 illus., 13 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

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.

Contents:

Introduction

Adaptive Regression Modeling of Univariate Continuous Outcomes

Adaptive Regression Modeling of Univariate Continuous Outcomes in SAS

Adaptive Regression Modeling of Multivariate Continuous Outcomes

Adaptive Regression Modeling of Multivariate Continuous Outcomes in SAS

Adaptive Transformation of Positive Valued Continuous Outcomes

Adaptive Logistic Regression Modeling of Univariate Dichotomous and Polytomous Outcomes

Adaptive Logistic Regression Modeling of Univariate Dichotomous and Polytomous Outcomes in SAS

Adaptive Logistic Regression Modeling of Multivariate Dichotomous and Polytomous Outcomes

Adaptive Logistic Regression Modeling of Multivariate Dichotomous and Polytomous Outcomes in SAS

Adaptive Poisson Regression Modeling of Univariate Count Outcomes

Adaptive Poisson Regression Modeling of Univariate Count Outcomes in SAS

Adaptive Poisson Regression Modeling of Multivariate Count Outcomes

Adaptive Poisson Regression Modeling of Multivariate Count Outcomes in SAS

Generalized Additive Modeling

Generalized Additive Modeling in SAS

Multivariate Adaptive Regression Spline Modeling

Multivariate Adaptive Regression Spline Modeling in SAS

Adaptive Regression Modeling Formulation. .

Notes:

Includes bibliographical references and index.

ISBN:

3-319-33946-X