Some Statistical Approaches to Multidimensional Scaling Data

Statistical problems associated with multidimensional scaling are reviewed. Indices of similarity or dissimilarity have been fitted by two classes of models: point representation using a distance measure and vector representation using an inner product. In addition to these parameters representing stimulus-attribute relations, it is usual to require some subject-specific parameters to model idiosyncracies in response patterns and variance components. Techniques for coping with nuisance parameters and deriving interval estimates are discussed in the context of maximum likelihood estimation. Some generalizations to multivariate situations are also developed.