Violations of the Local Independence Assumption in Categorization

Violations of the Local Independence Assumption in Categorization Jesse Zee (jesse.zee@student.kuleuven.be) Gert Storms (gert.storms@ppw.kuleuven.be) Steven Verheyen (steven.verheyen@ppw.kuleuven.be) Faculty of Psychology and Educational Sciences, University of Leuven Tiensestraat 102, B-3000 Leuven, Belgium Abstract The Threshold Theory of categorization posits that prior to making a categorization decision a respondent assesses the similarity between item and category and compares it against a personal threshold. Only if the item-category similarity exceeds this threshold should the respondent endorse the item as a category member. The Threshold Theory thus assumes that a single latent variable, item-category similarity, suffices to explain all categorization patterns. We put this assumption, known as local independence, to test by providing respondents with sets of four items to categorize. These items are equated in terms of their similarity to the target category, but are by design comprised of two pairs of similar items, such as rollerskates-skateboard and horse-mule for the category of VEHICLES . Contrary to the local independence assumption, the items within the pairs are more likely to receive the same categorization decision than the items across pairs. We explain how these categorization patterns can be accommodated within the Threshold Theory framework, either by giving up the assumption that everyone assesses item-category similarity in the same way for differently weighted category information, or by explicitly incorporating item-item similarity in addition to item-category similarity. Keywords: categories; concepts; similarity; Threshold Theory; vagueness. typicality; Introduction Perceptions, thoughts, beliefs and other such mental phenomena are the product of the constant interaction of the embodied brain with the world. Indeed, the intentionality and meaning of these mental phenomena are most commonly about the outside world, as is the case with perception (Koendrink, 1999). Analogously, mental representations of categories and items are assumed to exist in our minds, to such an extent that we cannot trace the private meaning a person entails of any word. We can merely derive the mathematical models that best describe the patterns and behavior of such mental phenomena. Furthermore, the private nature of language and differences in brain and environment bring about the individually differential responses observed in many psychological studies and particularly in studies of vague concepts: concepts that specify categories without clearly defined boundaries. To elucidate the categorization decisions of people when confronted with categorization tasks involving such vague concepts, most accounts ground their theory on the notion of similarity. Categorization is assumed to occur when item and category are sufficiently similar. Hampton (1998), for instance, investigated the categorization of instances at the border of vague categories. He found that for the majority of borderline cases, the probability of being placed in the category was directly predictable from how typical or representative the items were of the category (a proxy of item-category similarity). The Threshold Theory of categorization (Hampton, 2007) offers a process account of how item-category similarity is used to arrive at categorization decisions. It posits that individuals verify whether the similarity meets a personal threshold in order to include the item in the category. Like most accounts of categorization, the Threshold Theory assumes local independence: the decisions pertaining to two items are considered conditionally independent of each other given their item-category similarity values. Any relationship that might exist between the categorization decisions should be explained by these similarity values. In other words, the theory invokes a latent variable, item- category similarity, that is believed to be sufficient to explain the entire range of categorization patterns one might observe. Verheyen and Storms (2011) used a formal procedure to demonstrate violations of the local independence assumption in semantic categorization. They applied a formalization of the Threshold Theory to categorization data from eight natural language categories and found unexplained structure in the residuals. This result shows that item-category similarity does not suffice to account for all categorization patterns. Verheyen and Storms continued to show that many of the dependencies between items that they observed could be accounted for by item-item similarity. In categorizing items as FURNITURE or not, participants might consistently provide the same response to dishwasher as to refrigerator because their similarity as electrical appliances is recognized, Verheyen and Storms suggested. Similarly, the answers towards the items psychology and sociology with respect to SCIENCES might be dependent because both are social sciences. Several other researchers have argued that consecutive categorization decisions are not made independently of one another. In a series of studies by Brooks and colleagues participants were provided with a cognitive rule, which they had to use explicitly when categorizing. Rule-irrelevant item-item similarities were found to contribute significantly to consecutive categorization judgments (Brooks & Allen, 1991; Brooks & Regehr, 1993). Similarly, Brooks, Norman, and Allen (1991) found that judgments of expert dermatologists, who are assumed to have many complex rules at their disposal for making a diagnosis, were also