Table Of ContentL a te n t
V a ria b le
and L a te n t
m i
S tructure
M odels
George A. Marcoulides
Irini Moustaki
Latent Variable
and Latent Structure
Models
QUANTITATIVE METHODOLOGY SERIES
Methodology for Business and Management
___________George A. Marcoulides, Series Editor___________
The purpose of this series is to present methodological techniques to
investigators and students from all functional areas of business,
although individuals from other disciplines will also find the series
useful. Each volume in the series will focus on a specific method (e.g.,
Data Envelopment Analysis, Factor Analysis, Multilevel Analysis,
Structural Equation Modeling). The goal is to provide an
understanding and working knowledge of each method with a
minimum of mathematical derivations.
Proposals are invited from all interested authors. Each proposal should
consist of the following: (i) a brief description of the volume’s focus and
intended market, (ii) a table of contents with an outline of each chapter,
and (iii) a curriculum vita. Materials may be sent to Dr. George A.
Marcoulides, Department of Management Science, California State
University, Fullerton, CA 92634.
Marcoulides • Modem Methods for Business Research
Duncan/Duncan/Strycker/Li/Alpert • An Introduction to
Latent Variable Growth Curve Modeling: Concepts, Issues,
and Applications
Heck/Thomas • An Introduction to Multilevel Modeling
Techniques
Marcoulides/Moustaki • Latent Variable and Latent Structure
Models
Hox • Multilevel Analysis: Techniques and Applications
Latent Variable
and Latent Structure Models
Edited, by
George A. Marcoulides
California State University, Fullerton
Irini Moustaki
London School of Economics and Political Science
Routledge
Taylor & Francis Group
New York London
Copyright © 2002 by Lawrence Erlbaum Associates, Inc.
All rights reserved. No part of this book may be reproduced in
any form, by photostat, microform, retrieval system, or any other
means, without prior written permission of the publisher.
First published by
Lawrence Erlbaum Associates, Inc., Publishers
10 Industrial Avenue
Mahwah, NJ 07430
This edition published 2012 by Routledge
Routledge Routledge
Taylor & Francis Group Taylor & Francis Group
711 Third Avenue 2 Park Square, Milton Park
New York, NY 10017 Abingdon, Oxon 0X14 4RN
Cover design by Kathryn Houghtaling Lacey
Library of Congress Cataloging-in-Publication Data
Latent variable and latent structure models / edited by George A.
Marcoulides, Irini Moustaki.
p. cm. — (Quantitative methodology series)
Includes bibliographical references and indexes.
ISBN 0-8058-4046-X (alk. paper)
1. Latent structure analysis. 2. Latent variables. I. Marcoulides,
George A. II. Moustaki, Irini. III. Series.
QA278.6 .L336 2002
519.5’35—dc21 2001057759
CIP
Contents
Preface................................................................................................................. Ill
About the Authors........................................................................................ V
1 Old and New Approaches to Latent Variable Modelling ... 1
David J. Bartholomew
2 Locating ‘Don’t Know’, ‘No Answer’ and Middle Alterna
tives on an Attitude Scale: A Latent Variable Approach........... 15
Irini Moustaki, Colm 0 ’Muircheartaigh
3 Hierarchically Related Nonparametric IRT Models, and
Practical Data Analysis Methods........................................................... 41
L. Andries van der Ark, Bas T. Hemker, Klaas Sijtsma
4 Fully Semipararaetric Estimation of the Two-Parameter
Latent Trait Model for Binary Data.................................................... 63
Panagiota Tzamourani, Martin Knott
5 Analysing Group Differences: A Comparison of SEM Ap
proaches ............................................................................................................... 85
Pilar Rivera, Albert Satorra
6 Strategies for Handling Missing Data in SEM: A User’s
Perspective........................................................................................................105
Richard D. Wiggins, Amanda Sacker
7 Exploring Structural Equation Model Misspecifications via
Latent Individual Residuals.......................................................................121
Tenko Raykov, Spirinov Penev
8 On Confidence Regions of SEM Models .....................................135
Jian-Qing Shi, Sik-Yum Lee, Bo-Cheng Wei
9 Robust Factor Analysis: Methods and Applications ...............153
Peter Filzmoser
10 Using Predicted Latent Scores in General Latent Struc
ture M odels......................................................................................................195
Marcel Croon
II
11 Multilevel Factor Analysis Modelling Using Markov Chain
Monte Carlo Estimation...........................................................................225
Harvey Goldstein, William Browne
12 Modelling Measurement Error in Structural Multilevel
Models..............................................................................................................245
Jean-Paul Fox, Cees A. W. Glas
Author Index.................................................................................................271
Subject Index 277
Ill
Preface
This volume is based on material presented at the 22nd biennial conference
of the Society for Multivariate Analysis in the Behavioural Sciences (SMABS)
held by the Department of Statistics at the London School of Economics and
Political Science in July 2000. SMABS is an international research society
for advancing research in the area of measurement and psychometrics with
emphasis in comparative studies. The SMABS biennial meetings bring to
gether researchers interested in many research disciplines within the social
measurement area (e.g., item response theory, test theory, measurement the
ory, covariance structure analysis, multidimensional scaling, correspondence
analysis, multilevel modeling, survey analysis and measurement error, classi
fication, clustering and neural networks).
The theme of the 22nd SMABS conference - theoretical developments and
applications in latent variable modeling and structural equation modeling -
was realized in the many papers presented during the three days of the meet
ing. Each paper described original research and developments concerned with
the theory and practice of multivariate analysis in the behavioural sciences.
At the conclusion of the conference, we asked the authors of specific papers
to put together their contributions for publication in a single volume. Chap
ters presented here represent a particular focused coverage of topics related
to latent variable and latent structure models. Although the words in the
name of the Society, “Analysis in the Behavioural Sciences”, indicate that
the contributions are all generally related to methods that provide answers
to questions about human behaviour, the methods apply equally well to an
swers to questions about non-human behaviour.
We have tried to compile a volume that will be of interest to researchers
from a wide variety of disciplines including biology, business, economics, edu
cation, medicine, psychology, sociology, and other social and health sciences.
As such, the chapters are aimed at a broad audience concerned with keeping
up on the latest developments and techniques related to latent variable and
latent structure models. Each chapter assumes that the reader has already
mastered the equivalent of basic multivariate statistics and measurement the
ory courses that included coverage of issues related to latent variable models.
This volume could not have been completed without the assistance and
support provided by many individuals. First, we would like to thank all the
contributors and reviewers for their time and effort in getting the various
chapters ready for publication. They all worked diligently through the various
publication stages. We are particularly indebted to the contributing authors,
who gave so generously of their time and expertise to this volume. Their
chapters were a genuine pleasure to read and they greatly enhanced our own
knowledge of the techniques covered in this volume. Their responsiveness
to our editorial suggestions greatly eased our work as editors. We are also
grateful to Larry Erlbaum for his continued encouragement and support of
our work. Thanks are also due to all the wonderful people on the editorial staff
IV
of Lawrence Erlbaum Associates for their assistance and support in putting
together this volume. Finally, a special thank you to our colleague and friend
Zvi Drezner for his skillful help with handling the various technical issues
related to preparing the volume for publication.
George A. Marcoulides
Irini Moustaki
V
About the Authors
David J. Bartholomew is Emeritus Professor of Statistics at the Lon
don School of Economics and Political Science, which he first joined in 1973
having previously been Professor of Statistics at the University of Kent. He
is a former ProDirector of the LSE and President of the Royal Statistical
Society. His main interest is in the application of statistical ideas in the so
cial sciences especially the development of latent variable methods. Recent
publications include The Statistical Approach to Social Measurement (Aca
demic Press, 1996) and (with M. Knott) Latent Variable Models and Factor
Analysis (Arnold, 1999).
William Browne has been a research officer on the Multilevel Models
Project at the Institute of Education since 1998. Prior to that he completed
a PhD entitled ‘Applying MCMC Methods to Multilevel Models’ at the Uni
versity of Bath under the supervision of Professor David Draper. His main
research interests are Monte Carlo Markov Chain (MCMC) methodology and
the application of these methods to the modelling of complex data structures.
He is currently involved in developing new methodology to fit such complex
models and programming them in the widely used multilevel modelling soft
ware package MLwiN. He is also interested in the dissemination of complex
models to applied researchers.
Marcel Croon is an associate professor in the Department of Methodol
ogy and Statistics at the Faculty of Social Sciences of Tilburg University (The
Netherlands). He teaches courses in research methodology, applied statistics
and latent structure models. His research interests are measurement theory
in applied statistics for the social and behavioral sciences, and, more specifi
cally, in the general theory of latent structure for continuous and categorical
data.
Peter Filzmoser is an assistant professor at the Vienna University of
Technology. He received an award for his thesis on ‘Principal Planes’ from the
Vienna University of Technology. He has collaborated extensively with Pro
fessor Rousseeuw from the University of Antwerp and with Professor Croux
from the Universite Libre de Bruxelles. His research interests are on robust
multivariate methods.
Jean-Paul Fox is a post-doctoral researcher in the department of Ed
ucational Measurement and Data Analysis at the University of Twente. He
received his PhD in 1996 from the University of Twente. Previously, he was
employed as a statistician at I\&0 Research in Enschede. His research inter
ests include multilevel modeling and item response theory.
Cees A.W. Glas studied psychology with a specialization in mathemat
ical and statistical psychology. From 1981 to 1995 he worked at the National
Institute of Educational Measurement (Cito) in the Netherlands. In 1995 he
joined the department of Educational Measurement and Data Analysis, at
the University of Twente, where he specializes in item response theory and
multilevel modeling.
