When parameters collide: A warning about categorization models

Abstract

Similarity-choice (S-C) models of categorization contain two principal mathematical transformations: an exponential-decay similarity function and a choice rule. However, there is a tension between the psychological processes that models emulate and the mathematics they use to do so. To illustrate this, I show that in these models an unappreciated interaction occurs between the mathematical transformations so that the stages of the model essentially cancel each other out The result is that the model's output reflects its input linearly. This cancellation phenomenon has potentially serious implications regarding the interpretation and use of S-C models. The phenomenon also raises questions about the simplification and psychological grounding of categorization models. Modelers broadly might benefit from an internal analysis of their models, such as that described here. Copyright 2006 Psychonomic Society, Inc.