Cognitive Geometry: An Analysis of Structure Underlying Representations of Similarity

This paper discusses the formal analysis of the structure underlying distance-based representations of consumer similarity judgments. Four models common in the marketing and psychological literature are examined-Euclidean and city-block spaces and ultrametric and additive trees. The analysis uses the distinction between "algebraic" and "geometric" structures as the basis for a unifying framework within which the four representations are compared and contrasted. The framework is then used to understand (1) the conditions under which model structure is theoretically revealing of the cognitive structure behind consumer behavior and (2) the degree to which similarity judgments and the resultant distance patterns are diagnostic of the appropriateness of a particular model. An important implication of the analysis is that there is a basic measurement indeterminacy associated with distance patterns, so that similarity data may not always reveal which is the "true" model in a given application. The consequences arising from this indeterminacy for the problem of model selection in marketing are illustrated with an empirical experiment designed to test the implications of the formal analysis in practical settings.