Rotation Techniques in Asymmetric Multidimensional Scaling

Multidimensional scaling (MDS) is a set of techniques, used especially in behavioral and social sciences, that enable a researcher to visualize proximity data in a multidimensional space. This article focuses on a particular class of MDS models proposed to deal with proximities which describe asymmetric relationships (i.e., trade indices for a set of countries,brand switching data, occupationalmobility tables, and so on). They are based on the decomposition of the relationships into a symmetric and a skew-symmetric part. In this way the objects are represented as points in a multidimensional space and the intensity of their relationships as scalar products (symmetry) or triangle areas (skew-symmetry).These models are seen as special cases of a general model and their rotational indeterminacy is investigated.The aimis to proposea rotationmethod thatmakes easier the visual inspection of the graphical representation,highlightingthe simple structureof the data. In particularan orthomax-likefamily of rotationmethods and a general algorithmare proposed.Advantages of the proposal are illustrated by analysis of import-exportdata.