Multidimensional Item Response Theory
Multidimensional Item Response Theory is the first book to give thorough coverage to this emerging area of psychometrics. The book describes the commonly used multidimensional item response theory (MIRT) models and the important methods needed for their p
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Mark D. Reckase
Multidimensional Item Response Theory
Statistics for Social and Behavioral Sciences Advisors: S.E. Fienberg W.J. van der Linden
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Mark D. Reckase
Multidimensional Item Response Theory
123
Mark D. Reckase Michigan State University Counseling, Educational, Psychology, and Special Education Department 461 Erickson Hall East Lansing MI 48824-1034 USA
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ISBN 978-0-387-89975-6 e-ISBN 978-0-387-89976-3 DOI 10.1007/978-0-387-89976-3 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009927904 c Springer Science+Business Media, LLC 2009 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)
Preface
Item response theory (IRT) is a general framework for specifying mathematical functions that describe the interactions of persons and test items. It has a long history, but its popularity is generally attributed to the work of Fredrick Lord and Georg Rasch starting in the 1950s and 1960s. Multidimensional item response theory (MIRT) is a special case of IRT that is built on the premise that the mathematical function includes as parameters a vector of multiple person characteristics that describe the skills and knowledge that the person brings to a test and a vector of item characteristics that describes the difficulty of the test item and the sensitivity of the test item to differences in the characteristics of the persons. MIRT also has a long history, going back to the work of Darrel Bock, Paul Horst, Roderick McDonald, Bengt Muthen, Fumiko Samajima, and others starting in the 1970s. The goal of this book is to draw together in one place the developments in the area of MIRT that have occurred up until 2008. Of course, it is not possible to be totally comprehensive, but it is believed that most of the major developments have been included. The book is organized into three major parts. The first three chapters give background information that is useful for the understanding of MIRT. Chapter 1 is a general conceptual overview. Chapter 2 provides a summary of unidimensional IRT. Chapter 3 provides a summary of the historical underpinnings of MIRT. Chapter 2 can be skipped if the
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