I. Borg - Böcker

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.

Multidimensionalscaling(MDS)isatechniquefortheanalysisofsimilarity or dissimilarity data on a set of objects. Such data may be intercorrelations of test items, ratings of similarity on political candidates, or trade indices forasetofcountries.MDSattemptstomodelsuchdataasdistancesamong pointsinageometricspace.Themainreasonfordoingthisisthatonewants a graphical display of the structure of the data, one that is much easier to understand than an array of numbers and, moreover, one that displays the essential information in the data, smoothing out noise. There are numerous varieties of MDS. Some facets for distinguishing among them are the particular type of geometry into which one wants to mapthedata,themappingfunction,thealgorithmsusedto?ndanoptimal data representation, the treatment of statistical error in the models, or the possibility to represent not just one but several similarity matrices at the same time. Other facets relate to the di?erent purposes for which MDS has been used, to various ways of looking at or “interpreting” an MDS representation, or to di?erences in the data required for the particular models. Inthisbook,wegiveafairlycomprehensivepresentationofMDS.Forthe reader with applied interests only, the ?rst six chapters of Part I should be su?cient. They explain the basic notions of ordinary MDS, with an emphasis on how MDS can be helpful in answering substantive questions.

Multidimensional Similarity Structure Analysis comprises a class of models that represent similarity among entities (for example, variables, items, objects, persons, etc.) in multidimensional space to permit one to grasp more easily the interrelations and patterns present in the data. The book is oriented to both researchers who have little or no previous exposure to data scaling and have no more than a high school background in mathematics and to investigators who would like to extend their analyses in the direction of hypothesis and theory testing or to more intimately understand these analytic procedures. The book is repleted with examples and illustrations of the various techniques drawn largely, but not restrictively, from the social sciences, with a heavy emphasis on the concrete, geometric or spatial aspect of the data representations.