Nonmetric Multidimensional Scaling of Asymmetric Proximities

Nonmetric multidimensional scaling which could be applied to a square asymmetric inter-stimulus proximity matrix is presented. In the model each stimulus is represented as a point and a circle (sphere, hypersphere) whose center is at that point in a multidimensional Euclidean space. The radius of a circle (sphere, hypersphere) tells the skew-symmetry of the corresponding stimulus. In a sense the model is a nonmetric generalization of Weeks and Bentler (1982) ’s model. An algorithm to derive the coordinates of points and radii of circles (spheres, hypers-pheres) which minimize the discrepancy of the coordinates and radii from the monotone relationship with given interstimulus proximities is described. An application to car switching data among 16 car segments is represented.

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