Storms, G. (Gert)

Verheyen, S. (Steven)

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Qualitative and Quantitative Individual Differences in Semantic CategorizationSteven Verheyen (steven.verheyen@ppw.kuleuven.be)Laboratory of Experimental Psychology, University of LeuvenTiensestraat 102 - box 3711, B-3000 Leuven, BelgiumGert Storms (gert.storms@ppw.kuleuven.be)Laboratory of Experimental Psychology, University of LeuvenTiensestraat 102 - box 3711, B-3000 Leuven, BelgiumKeywords: mixture models; IRT models; threshold models.IntroductionWhen asked to indicate which items from a set of candi-dates belong to a particular category, inter-individual differ-ences appear: Individuals disagree on the items that shouldbe considered category members (e.g., Black, 1937; Hamp-ton, Dubois, & Yeh, 2006; McCloskey & Glucksberg, 1978).Individuals might disagree about whether hiking and/or dartsare sports, for instance. We will argue that inter-individualdifferences in semantic categorization come in two kinds. (i)Qualitative differences reflect a different organization of thecandidate items with respect to the target category. (ii) Quan-titative differences reflect a different propensity to endorseitems as category members.Qualitative differences represent different views on whatare considered representative category members. Individu-als who consider hiking a better example of sports than dartspresumably find that the former meets the requirements ofcategory membership better than the latter does. They, forinstance, recognize that hiking is physically more demandingthan darts is. Individuals who consider darts to be the betterexample must then employ different requirements for cate-gory membership. When judging category membership theyplace more emphasis on elements such as rules or competi-tion, for instance. These requirements are better met by dartsthan by hiking.Among individuals who agree on the organization of itemswith respect to the target category, categorization differencesof a quantitative nature can arise. These are differences thatpertain to the propensity to endorse items as category mem-bers. The item organization reflects the varying extents towhich the items fulfill the requirements for category mem-bership (e.g., hiking is physically more demanding than dartsis). Certain individuals might want to see more evidence ofthese requirements than others. They might only deem hikingphysical enough to be considered a sport, while others findboth darts and hiking demanding enough.ModelOur goal is to elucidate these two kinds of inter-individualcategorization differences by means of the mixture item re-sponse theory model (Mislevy & Verhelst, 1990; Rost, 1990)that is expanded in Equation (1). Models like these are tradi-tionally employed to assess individuals’ aptitudes and dispo-sitions in response to a number of test items. However, theyhave also been shown to be flexible tools to analyze semanticcategorization data (e.g., Verguts, De Boeck, & Storms, 1998;Verheyen, Hampton, & Storms, 2010).Here the model will be used to partition a large sample ofcategorizers in a number of groups that are maximally differ-ent in terms of their organization of the items with respect tothe target category. These item organizations take the shapeof scales along which all candidate items are positioned ac-cording to their likelihood of being endorsed. Different or-ganizations capture qualitative categorization differences be-tween participants from different groups: They reveal howa particular item might be a likely category member in onegroup, but an unlikely category member in another group.Participants that end up together in a group are understoodto adopt the same item organization. These categorizers donot differ qualitatively, but can display varying degrees ofpropensity to endorse items as category members. These areinter-individual categorization differences of a quantitativenature. In the formal framework they take the shape of crite-ria that are imposed on the scales that organize the candidateitems: They reveal how some individuals in a group mightuse very liberal criteria, while others employ very stringentcriteria.Binary categorization decisions Yci constitute the input forthe model. Here the categorization data are comprised ofmember/non-member decisions Y by 250 categorizers c to-wards 24 items i in each of 8 natural language categories (fish,fruits, furniture, insects, sciences, sports, tools, vegetables).Every one of these categorization decisions is consideredthe outcome of a Bernoulli trial with the probability of a mem-ber response:Pr(Yci = 1) =eαg(βg,i−θgc)1+ eαg(βg,i−θgc)(1)In Equation (1) the betas capture the organization of the itemswith respect to the target category. g groups of categorizersare extracted, with separate item organizations that are max-imally different. For each group the organization takes theshape of a scale along which all candidate items are posi-tioned. βg,i indicates the position of item i along the scalefor group g. Higher values for βg,i indicate likelier categorymembers.251The thetas in Equation (1) capture the degree of liberal-ness/conservatism categorizers display. A separate indicationof the propensity to endorse items as category members isextracted for each categorizer c. It takes the shape of a crite-rion that is positioned along the same scale that organizes theitems for the group the participant belongs to. θgc indicatesthe position of the criterion for categorizer c along the scalefor group g. Higher values for θgc indicate more conservativecategorizers.Unlike the betas and thetas, the alphas in Equation (1) canonly take on positive values. A separate αg for each groupdetermines the shape of the response function that relates theunbounded difference βg,i−θgc to the probability of a mem-ber response (bounded between 0 and 1). Indeed, the relativeposition of item and criterion along a scale determines theprobability of a member response. If βg,i equals θgc the nu-merator of Equation (1) takes on the value of 1, while thedenominator takes on the value of 2. The resulting probabil-ity is .50, indicating that the categorization decision can goeither way. The odds change when item and criterion havea different position along the scale. If the item surpasses thecriterion, the odds are that the categorizer will endorse it. Thegreater the distance between item and criterion, the greaterthe odds of a member decision. If the item does not surpassthe criterion, the odds are that c will not endorse i. Under thiscircumstance, the odds of a non-member decision increasewith the distance between item and criterion.The one-group variant of the model in Equation (1) hasbeen applied to semantic categorization by Verheyen et al.(2010). That particular model only allows for quantitativeinter-individual categorization differences. Participants candiffer in terms of the categorization criterion they employ, butnot in terms of the scale along which the criteria are placed.They all adopt the same category organization. The model inEquation (1) is more general. It allows for qualitative differ-ences in addition to quantitative ones. It relaxes the assump-tion that all participants adhere to the same category organiza-tion. Instead, it assumes that the participants divide in groupswith a different item organization each. (One set of beta esti-mates is extracted for each group.) Within each group, indi-viduals are still thought to differ in terms of the employed cat-egorization criterion. (A theta estimate is extracted for everycategorizer.) The model in Equation (1), then, is a mixture ofdifferently parameterized quantitative differences-only mod-els of the kind employed by Verheyen et al. (2010).FindingsThe analysis of the categorization data with the mixturemodel in Equation (1) yields evidence for both qualitativeand quantitative inter-individual differences. For the cate-gories of fish, insects, sciences, sports, and tools the sam-ple of categorizers divides in distinct groups, who regard dif-ferent items likely category members (i.e., qualitative differ-ences). Within each of these groups categorizers differ intheir propensity to provide membership responses (i.e., quan-titative differences). The existence of multiple item organiza-tions for a single category suggests that it might be improperto assume a default category representation that is the samefor all language users. Rather, it would appear that thereexist a number of these default representations, which em-phasize different sets of category features. Indeed, a clearpattern emerged when we (i) determined to what extent fea-tures that participants consider important for category mem-bership are true of the different candidate items, (ii) obtaineda small number of principal components that convey the in-formation that is contained in these feature applicability judg-ments, and (iii) regressed the item organizations of differentgroups upon these principal components. For each of the cat-egories with multiple item organizations, there was at leastone component that had a similar effect on every item orga-nization. Common components indicate agreement amonggroups on what it means to be a category member. This isrequired for members of different groups to succesfully com-municate with one another using the studied natural languageterms. The item organizations could also be distinguished onthe basis of other components that were of importance to sin-gle subgroups only. These distinct components indicate dis-agreement among groups on what it means to be a categorymember but do not appear to hamper communication betweenmembers of different groups.AcknowledgmentsSteven Verheyen is a postdoctoral fellow at the ResearchFoundation-Flanders.ReferencesBlack, M. (1937). Vagueness: An exercise in logical analysis.Philosophy of Science, 4, 427-455.Hampton, J. A., Dubois, D., & Yeh, W. (2006). Effectsof classification context on categorization in natural cate-gories. Memory & Cognition, 34, 1431-1443.McCloskey, M. E., & Glucksberg, S. (1978). Natural cate-gories: Well defined or fuzzy sets? Memory & Cognition,6, 462-472.Mislevy, R. J., & Verhelst, N. (1990). Modeling item re-sponses when different subjects employ different solutionstrategies. Psychometrika, 55, 195-215.Rost, J. (1990). Rasch models in latent classes: An integra-tion of two approaches to item analysis. Applied Psycho-logical Measurement, 14, 271-282.Verguts, T., De Boeck, P., & Storms, G. (1998). Analyzingexperimental data using the Rasch model. Behavior Re-search Methods, 30, 501-505.Verheyen, S., Hampton, J. A., & Storms, G. (2010). A prob-abilistic threshold model: Analyzing semantic categoriza-tion data with the Rasch model. Acta Psychologica, 135,216-225.252

Qualitative and quantitative individual differences in semantic categorization

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Qualitative and quantitative individual differences in semantic categorization

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