Similarity, distance, and categorization: a discussion of Smith's (2006) warning about "colliding parameters"

The idea that categorization decisions rely on subjective impressions of similarities between stimuli has been prevalent in much of the literature over the past 30 years and has led to the development of a large number of models that apply some kind of decision rule to similarity measures. A recent article by Smith (2006) has argued that these similarity-choice models of categorization have a substantial design flaw, in which the similarity and the choice components effectively cancel one another out. As a consequence of this cancellation, it is claimed, the relationship between distance and category membership probabilities is linear in these models. In this article, I discuss these claims and show mathematically that in those cases in which it is sensible to discuss the relationship between category distance and category membership at all, the function relating the two is approximately logistic. Empirical data are used to show that a logistic function can be observed in appropriate contexts.