Two-Dimensional Configurations of Unidimensional Stimulus Sets in Nonmetric Multidimensional Scaling

Abstract

When unidimensional stimulus sets are subjected to a nonmetric scaling in two dimensions, the stimuli fre quently form a C- or S-shaped configuration. In simu lated unidimensional data scaled in two dimensions, stimuli formed a C-shaped configuration when the monotone function relating distances to dissimilarity data was negatively accelerating. They formed an S- shaped configuration when the monotone function was positively accelerating. Results suggest that when uni dimensional stimulus sets are scaled in two dimensions using a rational starting configuration, the nature of the two-dimensional configuration can indicate the general form of the function mapping psychological dissimilarity, represented as distance in the scaling model, onto the observed response scale. Index terms: data transformations, multidimensional scaling, paired comparisons, proximity data, unidimensional scaling, unidimensionality.