Multidimensional scaling (MDS) is a family of statistical techniques that represent the structure of proximity (similarity or dissimilarity) data as distances in a geometric space. In psychology, MDS reveals the latent dimensions along which people mentally represent stimuli — for example, showing that colors are organized in a two-dimensional hue-saturation space, or that consonant sounds are organized by manner and place of articulation.
Metric and Nonmetric MDS
Metric MDS (Torgerson, 1952) assumes that the input dissimilarities are on an interval or ratio scale and seeks a configuration whose inter-point distances approximate the data. Nonmetric MDS (Kruskal, 1964; Shepard, 1962) makes the weaker assumption that only the rank order of dissimilarities is meaningful, seeking a configuration that preserves rank order while minimizing stress (a measure of departure from monotonicity).
Applications
MDS has been applied extensively in psychology: mapping the psychological structure of faces, emotions, musical timbre, semantic concepts, and personality traits. The number of dimensions required for a good fit reveals the complexity of the underlying psychological representation, while the identity of the dimensions (determined by rotating the solution and examining the correlates of each dimension) reveals what features people attend to. Roger Shepard's work on MDS provided the empirical basis for his universal law of generalization.