A Causal-Model Theory of Categorization

In this article I propose that categorization decisions are often made relative to causal models of categories that people possess. According to this causal-model theory o f categorization, evidence of an exemplar's membership in a category consists of the likelihood that such an exemplar can be generated by the category's causal model. Bayesian networks are proposed as a representation of these causal models. Causal-model theory was fit to categorization data from a recent study, and yielded better fits than either the prototype model or the exemplar-based context model, by accounting, for example, for the confirmation and violation of causal relationships and the asymmetries inherent in such relationships. Several investigators have argued that category learning and categorization are strongly influenced by the theoretical, explanatory, and causal knowledge that people bring to bear (Murphy & Medin, 1985; Murphy, 1993; Heit, 1998). For example, manipulations of stimulus materials affect category learning by eliciting different aspects of people's background knowledge (e.g., Pazzani, 1989; Murphy & Allopenna, 1994). Performance on a variety of tasks has been correlated with the amount of relevant domain knowledge individuals possess (Keil, 1989; Medin, Lynch, Coley, & Atran, 1997). However, there has been relatively little development of this "theory-based" view of categories in terms of detailed theory and computational models (c.f. Heit, 1994). This state of affairs arises in part because of the uncertainty surrounding exactly what knowledge participants deploy in an experimental task. A few recent studies have addressed this problem by employing novel domains and teaching participants "background" knowledge as part of the experimental session (e.g., Ahn & Lassaline, 1996; Rehder & Hastie, 1999; Sloman, et al. 1998). For example, Rehder and Hastie taught participants about fictitious categories described as possessing causal relationships between binaryvalued category attributes, and manipulated experimentally whether those causal relationships formed a common-cause or a common-effect causal schema (Figure 1). In the common-cause schema, one attribute (A1) is described as causing the three other attributes, whereas in the commoneffect schema one attribute (A4) is caused by three other attributes. For example, one of the fictitious categories was Kehoe Ants, a species of ants described as living on an island in the Pacific Ocean, and one of that category's causal relationships was "Blood high in iron sulfate causes a hyperactive immune system. The iron sulfate molecules are detected as foreign by the immune system, and the immune system is highly active as a result. " After learning about such categories and their causal relationships participants performed a transfer categorization task. Rehder and Hastie found that the presence of both a cause and its effect in an instance (e.g., an ant with iron sulfate blood and a hyperactive immune system) led to the instance receiving a higher category membership rating compared to control categories with no causal relationships. Because ratings were also higher when both the cause and effect were absent (normal blood and normal immune system), and lower when either the cause or the effect was present and the other absent (iron sulfate blood and normal immune system, or normal blood and hyperactive immune system), Rehder and Hastie concluded that participants were attending not merely to the presence of the cause/effect configuration, but rather to whether instances confirmed or violated causal relationships. Category membership ratings also reflected the asymmetries inherent in causal relationships. For example, a distinct characteristic of common-cause causal networks is that the effect attributes (e.g., A2, A3, and A4 in Figure 1) will be correlated, and indeed the categorization ratings of substantial numbers of common-cause participants were sensitive to whether those correlations were preserved or violated. Although these results are suggestive of explicit causal reasoning in participants, it is important to consider whether they can be accounted for by the well-known similaritybased categorization models, such as the prototype model and the context model (Medin & Shaffer, 1978; Nosofsky, 1986). Similarity-based models are able to accommodate seemingly disparate categorization strategies by adjusting similarity parameters to differentially shrink or expand the dimensions of the stimulus space. In fact, Rehder and Hastie fitted these models to their transfer categorization data, and found that the models yielded only moderate-quality fits. The fits of instances that possessed many confirmations or many violations of causal relationships were particularly poor. The failure of the similarity-based models to account for these data leads to a search for alternative categorization models that can account for people's apparent ability to reason causally while categorizing. In this article I propose that categorization decisions are often made relative to causal models of categories that people possess, and test Bayesian networks as a candidate representation of such models. A1 A2