Yet Another Look at Thirty Categorization Results

We re-analyzed thirty data sets reported in the literature and summarized by Smith and Minda (2000), based on Medin and Schaffer’s (1978) 5-4 structure. In their meta-analysis, Smith and Minda (2000) focused on comparing the prototype and the exemplar model. In our meta-analysis, we applied the varying abstraction model, a multiple-prototype model proposed by Vanpaemel, Storms, and Ons (2005), that reduces to the prototype and the exemplar model in special cases. While we found a lot of heterogeneity in the best performing model across data sets, overall, the exemplar model turned out to account for the data best. However, a slight modification of the exemplar model improved performance in one condition, while in another condition, a modification of the prototype model recovered the data best. Although categorization is an essential and thoroughly studied cognitive task, the debate about which model describes human category learning best hasn’t settled yet. Two theories have been dominating this debate. According to the prototype theory (Nosofsky, 1987; Reed, 1972), people store an abstract summary of a category and categorize a new item by comparing the item to the summary. According to the exemplar theory (Medin & Schaffer, 1978; Nosofsky, 1986), people do not make any abstraction at all. Instead, a category is represented by stored memories of all previously encountered category exemplars. A new item is categorized by comparing it to all the category exemplars. Due to the influential studies of Medin and his colleagues, the focus has shifted from prototype theory to exemplar theory (Medin, Dewey, & Murphy, 1983; Medin & Schaffer, 1978). The traditional representational assumptions are perfectly viable with small categories and fairly similar stimuli. However, when categories are large, remembering all exemplars seen, as the exemplar model claims, might not be possible. And when stimuli are very dissimilar, taking the average, as the prototype model claims, might be a strange thing to do. Everyday natural language categories, such as fruits and furniture, can be large, containing very dissimilar exemplars, so in this context both traditional views are problematic. Vanpaemel et al. (2005) presented a model called the varying abstraction model that tries to find middle ground between both unrealistic representational assumptions. Therefore, the varying abstraction model introduces a set of new models which formalize the idea that people use multiple prototypes to represent a category. The model is particularly useful to uncover if and which multiple prototypes are used to represent a category. The present paper describes an elaborate application of the varying abstraction model. In a critical review, Smith and Minda (2000) summarized and re-analyzed 30 data sets that made use of (a certain instantiation) of the so called 5-4 category structure. This category structure was introduced by Medin and Schaffer (1978) and has been particularly influential in artificial category learning studies, yielding ample evidence in support of the exemplar model (Medin, Altom, & Murphy, 1984; Medin et al., 1983; Nosofsky, Palmeri, & McKinley, 1994) (but see, Smith and Minda (2000) who questioned the evidence). The varying abstraction model puts new challengers to the exemplar model in the modeling arena. Not only the prototype model, but also all multiple-prototype models of the varying abstraction model family give a possible account of human category learning. Both the experimental and theoretical importance of the 5-4 structure and the direct availability of the data sets motivated us to analyze the 30 data sets using the varying abstraction model. The purpose of this paper is twofold. First, we illustrate how the varying abstraction model can be applied to uncover the way people represent categories when making categorization decisions. Second, we re-analyze data from a category structure that has provided influential evidence for the exemplar model to investigate if this evidence still holds when the exemplar model is challenged by more than one model. This paper is organized as follows. First, we review the varying abstraction model. Second, we briefly discuss the 54 category structure and the 30 data sets. In the third section the results of the varying abstraction model analysis of the 30 data sets are presented. The varying abstraction model The basic idea of the varying abstraction model is (1) to make up a partition1 for each category and (2) to construct for every subset of the partition the prototype by averaging over all the exemplars in that subset. These prototypes are called the pseudo-exemplars and are used to represent the category. Specifying, for all categories, a partition is enough to define a model. Such a model is called a pseudo-exemplar model and can be fitted to empirically obtained data. In a pseudoexemplar model, a stimulus is categorized based on its simi1A partition of a set S is defined as a collection of disjoint, nonempty subsets of S whose union is S.