Modern Multidimensional Scaling Theory and Applications

This book provides a comprehensive treatment of multidimensional scaling (MDS), a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space. There are many examples of such data, including intercorrelations of attitude items, direct ratings of similarity on choice objects, and trade indices for a set of countries. MDS models such data as distances between points in a geometric space of low dimensionality. This makes complex data sets accessible to visual exploration and thus makes it easier to see structure not obvious from the numbers. Other uses of MDS interpret the geometry and, in particular, the distance function as a psychological composition rule. The book may be used as an introduction to MDS for students in many areas, including statistics, psychology, sociology, political science, and marketing. The prerequisite is a two-semester course in statistics for the social or managerial sciences. The volume is also suited for various advanced courses on MDS, either with an emphasis on data analysis or a focus on the psychology of similarity. All the mathematics required for more advanced topics is developed systematically.