A test for perceptual independence with dissimilarity data

Abstract

The dominance axiom states that the dissimilarity of a pair of stimuli differing on two dimensions must exceed the dissimilarities of the corresponding pairs of stimuli that differ on only one of the dimensions. This axiom is presented as a test of dissimilarity data to determine if the dimensions of the perceptual space are perceived independently, and as a diagnostic tool in assessing the INDSCAL model’s assumption of independent dimensions. The general recognition theory of similarity, which contains both the three-mode and INDSCAL multidimensional scaling models as special cases, is used to motivate the test. It is shown that general recognition theory predicts consistent violations of the dominance axiom with dependent dimensions, but not independent dimensions. A consistent pattern of violations of dominance suggests that the three-mode model is most appropriate. When the test of dominance is satisfied, the INDSCAL model is appropriate for the data. A simulation study was conducted to examine the pattern of violations of the dominance axiom when varying degrees of perceptual dependence exist. An examination of dissimilarity data from a study of the size-weight illusion revealed the expected pattern of violations of the dominance axiom. Index terms: dominance axiom, general recognition theory, INDSCAL, MDS, perceptual independence, tiaree-mode model.