Violation of Assumed Normality in Traditional Multidimensional Scaling

Abstract

Traditional multidimensional scaling is a two-stage procedure. Thurstone's comparative judgment model is often used in the initial stage to determine the perceived distance between pairs of objects, under the assumption that the perceived distance between each pair is normally distributed across a population of subjects. These distances are used in the second stage to construct a geometric configuration of the objects in multidimensional space. A stimulation method was employed to study the effect of nonnormally distributed distances on the accuracy of the recovered configuration. Accurate configurations were generated from a variety of nonnormal distributions. Thus, the multidimensional scaling procedure appears to be robust with respect to violations of the normality assumption inherent in the comparative judgment model.