Modern Multidimensional Scaling

This book provides a comprehensive treatment of multidimensional scaling. There are many examples of this type of data in statistics, psychology, sociology, political science, and marketing.

Second edition of a successful book Provides an up-to-date comprehensive treatment of multidimensional scaling (MDS), a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space

Autorentext
Ingwer Borg ist wissenschaftlicher Leiter der Abteilung Survey Design & Methodology (SDM) der GESIS (Mannheim) und Professor am Fachbereich Psychologie der Uni Gießen. Seine Forschung liegt überwiegend im Bereich von Mitarbeiterbefragungen, Werten und Einstellungen sowie Skalierungsverfahren.

Klappentext

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 alsoserved 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.

Inhalt
Fundamentals of MDS.- The Four Purposes of Multidimensional Scaling.- Constructing MDS Representations.- MDS Models and Measures of Fit.- Three Applications of MDS.- MDS and Facet Theory.- How to Obtain Proximities.- MDS Models and Solving MDS Problems.- Matrix Algebra for MDS.- A Majorization Algorithm for Solving MDS.- Metric and Nonmetric MDS.- Confirmatory MDS.- MDS Fit Measures, Their Relations, and Some Algorithms.- Classical Scaling.- Special Solutions, Degeneracies, and Local Minima.- Unfolding.- Unfolding.- Avoiding Trivial Solutions in Unfolding.- Special Unfolding Models.- MDS Geometry as a Substantive Model.- MDS as a Psychological Model.- Scalar Products and Euclidean Distances.- Euclidean Embeddings.- MDS and Related Methods.- Procrustes Procedures.- Three-Way Procrustean Models.- Three-Way MDS Models.- Modeling Asymmetric Data.- Methods Related to MDS.