Concepts and Applications of Multidimensional Scaling

Multidimensional scaling (MDS) is a general term for a class of techniques that can be used to develop spatial representations of psychological stimuli or other objects. The typical input data for these procedures is a matrix of distance-like numbers which indicate how similar or different every stimulus is to each of the others. These similarity or dissimilarity values may be based on objective measurements or subjective judgments. MDS techniques involve iterative algorithms, usually requiring high-speed computers, for constructing the spatial configuration, or “map.” Although some mention is made of earlier MDS procedures, primary attention is given to describing and illustrating a new technique called “INDSCAL,” for INdividual Differences SCALing. The input to INDSCAL is several matrices of similarities or dissimilarities among the objects, usually one for each subject participating in a study. The output from INDSCAL includes information about the weight, or perceptual importance, of each dimension for every subject, as well as a multidimensional space for the stimulus objects. The applications illustrate the wide range of stimuli and experimental methods that can be used in studies involving MDS, and demonstrate some special advantages of INDSCAL.