Bayesian Item Response Modeling Theory and Applications
This book presents a thorough treatment and unified coverage of Bayesian item response modeling with applications in a variety of disciplines, including education, medicine, psychology, and sociology. Breakthroughs in computing technology have made the Ba
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Jean-Paul Fox
Bayesian Item Response Modeling Theory and Applications
Jean-Paul Fox Department of Research Methodology, Measurement, and Data Analysis Faculty of Behavioral Sciences University of Twente 7500 AE Enschede The Netherlands Series Editors Stephen E. Fienberg Department of Statistics Carnegie Mellon University Pittsburgh, PA 15213-3890 USA
Wim J. van der Linden CTB/McGraw-Hill 20 Ryan Ranch Road Monterey, CA 93940 USA
ISBN 978-1-4419-0741-7 e-ISBN 978-1-4419-0742-4 DOI 10.1007/978-1-4419-0742-4 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010927930 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Jasmijn and Kae
Preface
The modeling of item response data is governed by item response theory, also referred to as modern test theory. The field of inquiry of item response theory has become very large and shows the enormous progress that has been made. The mainstream literature is focused on frequentist statistical methods for estimating model parameters and evaluating model fit. However, the Bayesian methodology has shown great potential, particularly for making further improvements in the statistical modeling process. The Bayesian approach has two important features that make it attractive for modeling item response data. First, it enables the possibility of incorporating nondata information beyond the observed responses into the analysis. The Bayesian methodology is also very clear about how additional information can be used. Second, the Bayesian approach comes with powerful simulation-based estimation methods. These methods make it possible to handle all kinds of priors and data-generating models. One of my motives for writing this book is to give an introduction to the Bayesian methodology for modeling and analyzing item response data. A Bayesian counterpart is presented to the many popular item response theory books (e.g., Baker and Kim 2004; De Boeck and Wilson, 2004; Hambleton and Swaminathan, 1985; van der Linden and Hambleton, 1997) that are mainly or completely focused on frequentist methods. The usefulness of the Bayesian methodology is illustrated by disc
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