Adaptive Regression for Modeling Nonlinear Relationships
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 i
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George J. Knafl Kai Ding
Adaptive Regression for Modeling Nonlinear Relationships
Statistics for Biology and Health
Series Editors Mitchell Gail Jonathan M. Samet B. Singer Anastasios Tsiatis
More information about this series at http://www.springer.com/series/2848
George J. Knafl • Kai Ding
Adaptive Regression for Modeling Nonlinear Relationships
George J. Knafl University of North Carolina at Chapel Hill Chapel Hill, NC, USA
Kai Ding University of Oklahoma Health Sciences Center Oklahoma City, OK, USA
Additional material to this book can be downloaded from http://www.unc.edu/~gknafl/AdaptReg.html ISSN 1431-8776 ISSN 2197-5671 (electronic) Statistics for Biology and Health ISBN 978-3-319-33944-3 ISBN 978-3-319-33946-7 (eBook) DOI 10.1007/978-3-319-33946-7 Library of Congress Control Number: 2016940407 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Preface
This book addresses how to incorporate nonlinearity in one or more predictor (or explanatory or independent) variables in regression models for different types of outcome (or response or dependent) variables. Such nonlinear dependence is often not considered in applied research. While relationships can reasonably be treated as linear in some cases, it is not unusual for them to be distinctly nonlinear. A standard linear analysis in the latter cases can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data not otherwise possible. A variety of examples of the benefits to the modeling of nonlinear relationships are presented throughout the book. Methods are needed for deciding whether relationships are linear or nonlinear and for fitting appropriate models when they are nonlinear. Methods for these purposes are covered in this book using what are called fractional
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