On psychological similarity and psychological distance (1975)
AuthorsRosenberg, William Johnshow all
A distinction is commonly drawn between “Content” and “Distance” models of similarity. The set theoretic interpretation of Content models is developed using Restle’s (1959, 1961) structures. It is found that for spaces in which all dimensions are prothetic, a normalised type of model, similar to many vector content models, is correct: for x, yεIRn, ß > 0, [complicated formula here] or [complicated formula here]For spaces in which all dimensions are metathetic with no quantitative variation ("equal-measure metathetic") a Minkowski Distance model is correct. Different models are necessary for less simple cases. The properties of the D lβ and D 2β distance functions are investigated. They have most of the invariance properties of the Content models and do not in general obey the triangle inequality or have additivity on straight lines. Their isosimilarity contours may be non-convex, and they disobey the additivity, subtractivity and decomposability properties set out by Beals, Krantz and Tversky. Two similarity models of category scaling are suggested. Both predict the correct shape of the category-scale function for both prothetic and metathetic continua. The similarity models are applied to some data of Ekman (1965); they give an excellent fit and correctly predict the nature of the respective continua. A Monte Carlo multidimensional scaling study using the D 1β and D 2β models showed that the normalised types of model are quite incompatible with the distance types of model: scaling of one type by the other gave low stress, highly interpretable solutions which were nonetheless quite invalid. An experiment of Eisler's is interpreted in the light of this result and of an auxilliary experiment. It is concluded that, while the models have several weaknesses, they provide a rational basis, with prima facie empirical validity, for future similarity modelling. Two distinct types of model are identified - the normalised and the distance types - which are mathematically and psychologically incompatible. This demands a review of the validity of analyses of previous similarity experiments.