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.
Part I. 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.- Part II. MDS models and solving MDS problems. Matrix algebra for MDS. A majorization algorithm for solving MDS. Metric and non-metric MDS. Confirmatory MDS. MDS fit measures, their relations, and some algorithms. Classical scaling. Special solutions, degeneracies, and local minima; III. Unfolding. Unfolding. Avoiding trivial solutions in unfolding. Special unfolding models.- Part IV. MDS geometry as a substantive model. MDS as a psychological model. Scalar products and Euclidean distances. Euclidean embeddings.- Part V. MDS and related methods. Procrustes procedures. Three-way Procrustean models. Three-way MDS models. Modeling asymmetric data. Methods related to MDS.- Part VI. Appendices.
The first edition was released in 1996 and has sold close to 2200 copies.
Provides an up-to-date comprehensive treatment of MDS, a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space.
The authors have added three chapters and exercise sets. The text is being moved from SSS to SSPP.
The book is suitable for courses in statistics for the social or managerial sciences as well as for advanced courses on MDS.
All the mathematics required for more advanced topics is developed systematically in the text.
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.