Multidimensional Scaling

Abstract

Suppose dissimilarity data have been collected on a set of n objects or individuals, where there is a value of dissimilarity measured for each pair.The dissimilarity measure used might be a subjective judgement made by a judge, where for example a teacher subjectively scores the strength of friendship between pairs of pupils in her class, or, as an alternative, more objective, measure, she might count the number of contacts made in a day between each pair of pupils. In other situations the dissimilarity measure might be based on a data matrix. The general aim of multidimensional scaling is to find a configuration of points in a space, usually Euclidean, where each point represents one of the objects or individuals, and the distances between pairs of points in the configuration match as well as possible the original dissimilarities between the pairs of objects or individuals. Such configurations can be found using metric and non-metric scaling, which are covered in Sects. 2 and 3. A number of other techniques are covered by the umbrella title of multidimensional scaling (MDS), and here the techniques of Procrustes analysis, unidimensional scaling, individual differences scaling, correspondence analysis and reciprocal averaging are briefly introduced and illustrated with pertinent data sets.