Comparing exemplar and prototype models of categorization

Canadian Journal of Experimental Psychology, Sep 1997 by Stephen Dopkins, Theresea Gleason

A number of other choices must be made to fully delineate a prototype model. First, one must specify: (1) whether the psychological space has a Euclidean or a cityblock metric; (2) whether dimensional weighting occurs; and (3) what system is used for obtaining similarity from distance in psychological space. Our model generalized across these distinctions. This was possible because the model was tested in terms of qualitative patterns rather than quantitative measures of goodness-of-fit. In past work, similarity judgment data have typically been used to create a "map" of the way a set of stimuli are represented in psychological space. Distances in the resulting spatial representation have been used to estimate theoretical values of similarity for the various pairs of stimuli in the set. These values have been used to predict categorization responses for the stimuli. To the degree that a given model's predictions have matched observed results better than a rival model, the former model has been supported (Nosofsky, 1987; Reed, 1972; Shin & Nosofsky, 1992). To construct a spatial representation in this way, and to derive similarity values from distances in the representation, it has been necessary to make choices with respect to the above distinctions. In the present study, we made qualitative predictions concerning responses to small numbers of key stimuli directly on the basis of similarity judgments with respect to these stimuli (this will be explained more fully as we proceed). Thus, we did not need to make such choices.

To fully delineate a prototype model, one must also specify whether the categorization judgment is based on a probabilistic or a deterministic decision rule. Our model generalized across this distinction as well. This was again possible because the model was tested in terms of qualitative rather than quantitative results. In past comparisons of probabilistic and deterministic models, data have typically been analyzed for entire sets of stimuli. The key question has been whether a sharp transition emerges when the frequencies of response to contending categories are plotted as a function of stimulus parameters (Ashby & Gott, 1988). In the present study, the important results were patterns of responding to small numbers of test stimuli. As a result this question did not arise.

EXEMPLAR MODELS

In exemplar models, categories are mentally represented simply as collections of exemplars; categories themselves have no independent representation (Brooks, 1978; Estes, 1986; Hintzman, 1986; Medin & Florian, 1992; Nosofsky, 1986; Reed, 1972). In most exemplar models, exemplars are mentally represented as points in a psychological space. Again, the space can have either a Euclidean or a city-block metric, and its dimensions can be weighted or not (Nosofsky, 1986; Reed, 1972).

In exemplar models, categorization judgments are based on information about the exemplars of the contending categories. Different models use different kinds of information. In proximity algorithm models, the crucial information comes from the exemplars that are represented in the vicinity of the test stimulus in psychological space. The test stimulus is assigned to the category that is most prevalent among these exemplars (Reed, 1972; see also Hintzman, 1986). In matching models, the crucial information comes from sets of exemplars that characterize each of the categories to which the test stimulus might be assigned. The test stimulus is assigned to the category to whose exemplars it is most closely related (Medin & Schaffer, 1978; Nosofsky, 1986). Both probabilistic and deterministic decision rules have been used in exemplar models (Maddox & Ashby, 1993; Nosofsky, 1986,1991).