Modern Multidimensional Scaling: Theory and Applications

✍ Scribed by Ingwer Borg, Patrick J. F. Groenen (auth.)

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 614
• Edition: 2
• Category: Library

✦ Synopsis

The book provides a comprehensive treatment of multidimensional scaling (MDS), a family of statistical techniques for analyzing the structure of (dis)similarity data. Such data are widespread, including, for example, intercorrelations of survey items, direct ratings on the similarity on choice objects, or trade indices for a set of countries. MDS represents the data as distances among points in a geometric space of low dimensionality. This map can help to see patterns in the data that are not obvious from the data matrices. MDS is also used as a psychological model for judgments of similarity and preference.

This book may be used as an introduction to MDS for students in psychology, sociology, and marketing. The prerequisite is an elementary background in statistics. The book is also well suited for a variety of advanced courses on MDS topics. All the mathematics required for more advanced topics is developed systematically.

This second edition is not only a complete overhaul of its predecessor, but also adds some 140 pages of new material. Many chapters are revised or have sections reflecting new insights and developments in MDS. There are two new chapters, one on asymmetric models and the other on unfolding. There are also numerous exercises that help the reader to practice what he or she has learned, and to delve deeper into the models and its intricacies. These exercises make it easier to use this edition in a course. All data sets used in the book can be downloaded from the web. The appendix on computer programs has also been updated and enlarged to reflect the state of the art.

Ingwer Borg is Scientific Director at the Center for Survey Methodology (ZUMA) in Mannheim, Germany, and Professor of Psychology at the University of Giessen, Germany. He has authored or edited 14 books and numerous articles on data analysis, survey research, theory construction, and various substantive topics of psychology. He also served as president of several professional organizations.

Patrick Groenen is Professor in Statistics at the Econometric Institute of the Erasmus University Rotterdam, the Netherlands. Before, he was assistant professor at the Department of Data Theory at Leiden University in the Netherlands. He is an associate editor for three international journals. He has published on MDS, unfolding, optimization, multivariate analysis, and data analysis in various top journals.

✦ Table of Contents

Front Matter....Pages 1-1
The Four Purposes of Multidimensional Scaling....Pages 3-18
Constructing MDS Representations....Pages 19-35
MDS Models and Measures of Fit....Pages 37-61
Three Applications of MDS....Pages 63-85
MDS and Facet Theory....Pages 87-109
How to Obtain Proximities....Pages 111-133
Front Matter....Pages 135-135
Matrix Algebra for MDS....Pages 137-168
A Majorization Algorithm for Solving MDS....Pages 169-197
Metric and Nonmetric MDS....Pages 199-225
Confirmatory MDS....Pages 227-246
MDS Fit Measures, Their Relations, and Some Algorithms....Pages 247-260
Classical Scaling....Pages 261-267
Special Solutions, Degeneracies, and Local Minima....Pages 269-289
Front Matter....Pages 291-291
Unfolding....Pages 293-316
Avoiding Trivial Solutions in Unfolding....Pages 317-334
Special Unfolding Models....Pages 335-355
Front Matter....Pages 357-357
MDS as a Psychological Model....Pages 359-388
Scalar Products and Euclidean Distances....Pages 389-409
Euclidean Embeddings....Pages 411-426
Front Matter....Pages 427-427
Procrustes Procedures....Pages 429-447
Front Matter....Pages 427-427
Three-Way Procrustean Models....Pages 449-472
Three-Way MDS Models....Pages 473-494
Modeling Asymmetric Data....Pages 495-518
Methods Related to MDS....Pages 519-540

✦ Subjects

Statistics and Computing/Statistics Programs