# Modern Multidimensional Scaling

## Theory and Applications

• Ingwer Borg
• Patrick J. F. Groenen
Book

Part of the Springer Series in Statistics book series (SSS)

1. Front Matter
Pages i-xxi
2. ### Fundamentals of MDS

1. Front Matter
Pages 1-1
2. Pages 19-35
3. Pages 37-61
4. Pages 63-85
5. Pages 87-109
6. Pages 111-133
3. ### MDS Models and Solving MDS Problems

1. Front Matter
Pages 135-135
2. Pages 137-168
3. Pages 169-197
4. Pages 199-225
5. Pages 227-246
6. Pages 261-267
7. Pages 269-289
4. ### Unfolding

1. Front Matter
Pages 291-291
2. Pages 293-316
3. Pages 317-334
4. Pages 335-355
5. ### MDS Geometry as a Substantive Model

1. Front Matter
Pages 357-357
2. Pages 359-388
3. Pages 389-409
4. Pages 411-426
6. ### MDS and Related Methods

1. Front Matter
Pages 427-427
2. Pages 429-447
3. Pages 449-472
4. Pages 473-494
5. Pages 495-518
6. Pages 519-540
7. Back Matter
Pages 541-614

### Introduction

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.

### Keywords

algorithms best fit correlation marketing modeling multidimensional scaling statistics

#### Authors and affiliations

• Ingwer Borg
• 1
• Patrick J. F. Groenen
• 2
1. 1.ZUMAMannheimGermany
2. 2.Econometric InstituteErasmus UniversityRotterdamThe Netherlands

### Bibliographic information

• DOI https://doi.org/10.1007/0-387-28981-X