Multivariate and mixture distribution Rasch models: extensions and applications

398 Pages·2007·1.65 MB·English

by  Matthias von Davier, Claus H. Carstensen

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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
[e-mail] Kiel 24098
Germany
[e-mail]
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
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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
[e-mail]
[e-mail]
Keith A. Boughton
CTB/McGraw-Hill Matthias von Davier
20 Ryan Ranch Road Educational Testing Service
Monterey, CA 93940, USA
Rosedale Road
keith [e-mail]
Princeton, NJ 08541, USA
[e-mail]
Dirk Bu¨sch
Universita¨t Bremen
Fachbereich9-Kulturwissenschaften
Studiengang Sport Karen Draney
[e-mail] 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 [e-mail]
24098 Kiel, Germany
[e-mail]
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
[e-mail] [e-mail]
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 [e-mail]
Germany
[e-mail] 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 [e-mail]
Atlanta, Georgia USA 30332
[e-mail] 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
[e-mail]
[e-mail]
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
[e-mail]
[e-mail]
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 [e-mail]
[e-mail]
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
[e-mail] [e-mail]
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 [e-mail]
College Park, MD 20742
[e-mail]
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
[e-mail] [e-mail]
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
[e-mail] Victoria 3010 Australia
[e-mail]
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
[e-mail] [e-mail]
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
[e-mail] [e-mail]