MULTIDIMENSIONAL SCALING

This technique comprises a family of geometric models for representation of data in one or, more frequently, two or more dimensions and a corresponding set of methods for fitting such models to actual data. A much narrower definition would limit the term to spatial distance models for similarities, dissimilarities, or other proximity data. The usage we espouse includes nonspatial (e.g., such discrete geometric models as tree structures) and nondistance (e.g., scalar product or projection) models that apply to nonproximity (e.g., preference or other dominance) data as well as to proximities. As this chapter demonstrates, a large class of these nonspatial models can still be characterized as dimensional modelsmbut with discrete rather than continuously valued dimensions. The successful development of any multivariate technique and its incorporation in widely available statistical software inevitably lead to substantive applications over an increasingly wide range both within and among disciplines. Multidimensional scaling (MDS) is no exception, and within psychology and closely related areas we could catalog an immense variety of different applications (not all of them cause for celebration, however); several thousand are given in the annual bibliographic survey SER VICE (Murtagh, 1997) published by the Classification Society of North America.

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