Multivariate and mixture distribution Rasch models: extensions and applications PDF
Preview Multivariate and mixture distribution Rasch models: extensions and applications
Statistics for Social and Behavioral Sciences Advisors: S.E.Fienberg W.J.van der Linden Statistics for Social and Behavioral Sciences Brennan:Generalizability Theory. DeBoeck/Wilson:Explanatory Item Response Models:A Generalized Linear and Nonlinear Approach Devlin/Fienberg/Resnick/Roeder (Eds.):Intelligence,Genes,and Success:Scientists Respond to The Bell Curve. Finkelstein/Levin:Statistics for Lawyers,Second Edition. Gastwirth (Ed.):Statistical Science in the Courtroom. Handcock/Morris:Relative Distribution Methods in the Social Sciences. Johnson/Albert:Ordinal Data Modeling. Kolen/Brennan:Test Equating,Scaling,and Linking:Methods and Practices,Second Edition. Longford:Missing Data and Small-Area Estimation:Modern Analytical Equipment for the Survey Statistician. Morton/Rolph:Public Policy and Statistics:Case Studies from RAND. van der Linden:Linear Models for Optimal Test Design. von Davier (A.A.)/Holland/Thayer:The Kernel Method of Test Equating. von Davier (M.)/Carstensen:Multivariate and Mixture Distribution Rasch Models. Zeisel/Kaye:Prove It with Figures:Empirical Methods in Law and Litigation. Matthias von Davier Claus H. Carstensen Multivariate and Mixture Distribution Rasch Models Extensions and Applications Matthias von Davier Claus H.Carstensen (Editors) Rosedale Road Leibniz-Institut für die Pädagogik Educational Testing Service der Naturwissenschaften (IPN) Princeton,NJ 08541 University of Kiel,Institute for Science USA Education [email protected] Kiel 24098 Germany [email protected] Advisors: Stephen E.Fienberg Wim J.van der Linden Department of Statistics Department of Measurement and Data Carnegie Mellon University Analysis Pittsburgh,PA 15213-3890 Faculty of Behavioral Sciences USA University of Twente 7500 AE Enschede The Netherlands Library ofCongress Control Number:2006926461 ISBN-10:0-387-32916-1 ISBN-13:978-0387-32916-1 Printed on acid-free paper. © 2007 Springer Science+Business Media,LLC All rights reserved.This work may not be translated or copied in whole or in part without the written permission ofthe 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 oftrade 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. 9 8 7 6 5 4 3 2 1 springer.com Preface This volume gathers together a set of extensions of the Rasch model, one of the most prominent models for measurement in educational research and so- cial science developed by Danish mathematician Georg Rasch. The idea for this volume emerged during a meeting of the Psychometric Society in Mon- terey, CA. At that meeting, friends and colleagues discussed news about the impending retirement of Dr. Ju¨rgen Rost, an important innovator and men- tor in this field. To recognize Ju¨rgen’s contributions, we decided to produce a collection of research on extending the Rasch model as well as embedding theRaschmodelinmorecomplexstatisticalmodels,anareathatisreceiving broad interest in many fields of social sciences at the current time. Thiscollectioncontains22chaptersbyrecognizedinternationalexpertsin thefield.Thecontributionscovertopicsrangingfromgeneralmodelextensions toapplicationinfieldsasdiverseascognition,personality,organizationaland sports psychology, and health sciences and education. TheRaschmodelisdesignedforcategoricaldata,oftencollectedasexam- inees’ responses to multiple tasks such as cognitive items from psychological testsorfromeducationalassessments.TheRaschmodel’selegantmathemati- calformissuitableforextensionsthatallowforgreaterflexibilityinhandling complexsamplesofexamineesandcollectionsoftasksfromdifferentdomains. In these extensions, the Rasch model is enhanced by additional structural el- ements that account either for differences between diverse populations or for differences among observed variables. Researchonextendingwell-knownstatisticaltoolssuchasregression,mix- ture distribution, and hierarchical linear models has led to the adoption of Rasch model features to handle categorical observed variables. We maintain both perspectives in the volume and show how these merged models—Rasch modelswithamorecomplexitemorpopulationstructure—arederivedeither from the Rasch model or from a structural model, how they are estimated, and where they are applied. This volume is centered on extensions of the Rasch model to multiple di- mensionsandcomplexsamplesofexamineesand/oritemresponses.Therefore, VI applications of the unidimensional Rasch model for simple random samples are not specifically mentioned. Such cases can be found in volumes geared toward applying the Rasch model. More importantly, simple data collection designscanbetreatedasspecialcasesoftheextensionspresentedhere,sothat data suitable for the ordinary Rasch model can be analyzed with virtually all the extensions presented in this volume. Thanks goes to our respective families, who helped us a lot with their encouragement and support: thank you Alina, Barbara, Thomas, and Luis! We are also deeply grateful to our academic teacher, Ju¨rgen Rost, who in- troduced us to the fascinating field of extended Rasch models. We would also like to thank our professional affiliations and colleagues for making this project possible by providing resources and support. We thank Daniel Eignor for the excellent help on clarifying and better organizing a lot of our writing, and thanks go to Kim Fryer for the superb editorial support and to Henning Voigtla¨nder for helping to convert and typeset many contributed chapters. Most of all, the diversity and coverage of topics presented in this volume would not have been possible without the excellent contributors in their roles as authors and reviewers for this volume. Matthias von Davier Princeton, NJ, USA Claus H. Carstensen Kiel, Germany March 2006 List of Contributors Raymond J. Adams Karl Bang Christensen Assessment Research Centre (ARC) Arbejdsmiljøinstituttet Faculty of Education Lersø Parkall´e 105 University of Melbourne 2100 Copenhagen, Denmark Victoria 3010 Australia [email protected] [email protected] Keith A. Boughton CTB/McGraw-Hill Matthias von Davier 20 Ryan Ranch Road Educational Testing Service Monterey, CA 93940, USA Rosedale Road keith [email protected] Princeton, NJ 08541, USA [email protected] Dirk Bu¨sch Universita¨t Bremen Fachbereich9-Kulturwissenschaften Studiengang Sport Karen Draney [email protected] Graduate School of Education University of California at Berkeley Claus H. Carstensen 4415 Tolman Hall Leibniz Institute for Berkeley, CA 94720 Science Education Olshausenstrasse 62 [email protected] 24098 Kiel, Germany [email protected] Clemens Draxler Yuk Fai Cheong Leibniz Institute for Division of Educational Studies Science Education Emory University 1784 North Decatur Road, Suite 240 Olshausenstrasse 62 Atlanta, GA 30322 24098 Kiel, Germany [email protected] [email protected] VIII List of Contributors Michael Eid Chun-Wei Huang Institut fu¨r Psychologie WestEd Freie Universit¨at Berlin 730 Harrison Street Habelschwerdter Allee 45 San Francisco, CA 94107 D-14195 Berlin [email protected] Germany [email protected] Akihito Kamata Department of Educational Susan E. Embretson Psychology & Learning Systems School of Psychology Florida State University Georgia Institute of Psychology Tallahassee, FL 32306, U.S.A. 654 Cherry Street [email protected] Atlanta, Georgia USA 30332 [email protected] Henk Kelderman Vrije Universiteit Department of Psychology and Anton K. Formann Pedagogics Fakulta¨t fu¨r Psychologie Van der Boechorststraat 1 Universita¨t Wien 1081 BT Amsterdam Liebiggasse 5 The Netherlands A-1010 Wien, AUSTRIA [email protected] [email protected] Svend Kreiner Cees A. W. Glas Biostatistisk afdeling Institut for Faculty of Educational Science and Folkesundhedsvidenskab Technology Øster Farimagsgade 5 opg. B University of Twente Postboks 2099 PO Box 217 1014 Copenhagen, Denmark 7500 AE Enschede, The Netherlands [email protected] [email protected] Klaus D. Kubinger Judith Glu¨ck Fakulta¨t fu¨r Psychologie Fakulta¨t fu¨r Psychologie Universita¨t Wien Universita¨t Wien Liebiggasse 5 Liebiggasse 5 A-1010 Wien, AUSTRIA A-1010 Wien, AUSTRIA [email protected] [email protected] Thorsten Meiser Shelby J. Haberman Institut fu¨r Psychologie Educational Testing Service Universita¨t Jena Rosedale Road Humboldtstr. 11 Princeton, NJ 08541, USA D-07743 Jena, Germany [email protected] [email protected] List of Contributors IX Robert J. Mislevy Gershon Tenenbaum University of Maryland at Department of Educational College Park Psychology & Learning Systems Department of Measurement, Florida State University Statistics and Evaluation Tallahassee, FL 32306, U.S.A. Benjamin 1230-C [email protected] College Park, MD 20742 [email protected] Mark Wilson Carl P.M. Rijkes Graduate School of Education Bogortuin 145 University of California at Berkeley 1019PE Amsterdam 4415 Tolman Hall The Netherlands Berkeley, CA 94720 [email protected] [email protected] Ju¨rgen Rost Leibniz Institute for Margaret L. Wu Science Education Assessment Research Centre (ARC) Olshausenstrasse 62 Faculty of Education 24098 Kiel, Germany University of Melbourne [email protected] Victoria 3010 Australia [email protected] Bernd Strauss Westf¨alische Wilhelms-Universit¨at Mu¨nster Kentaro Yamamoto Institut fu¨r Sportwissenschaft Educational Testing Service Horstmarer Landweg 62b Rosedale Road D-48149 Mu¨nster Princeton, NJ 08541, USA [email protected] [email protected] Christiane Spiel Michael Zickar Fakulta¨t fu¨r Psychologie Bowling Green State University Universita¨t Wien Liebiggasse 5 Department of Psychology A-1010 Wien, AUSTRIA Bowling Green, OH 43403, USA [email protected] [email protected]
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