Comparing decision bound and exemplar models of categorization

The performance of a decision bound model of categorization (Ashby, J992a; Ashby & Maddox, in press) is compared with the performance of two exemplar models. The first is the generalized context model (e.g., Nosofsky, 1986, 1992) and the second is a recently proposed deterministic exemplar model (Ashby & Maddox, in press), which contains the generalized context model as a special case. When the exemplars from each category were normally distributed and the optimal decision bound was linear, the deterministic exemplar model and the decision bound model provided roughly equivalent accounts of the data. When the optimal decision bound was nonlinear, the decision bound model provided a more accurate account of the data than did either exemplar model. When applied to categorization data collected by Nosofsky (1986, 1989), in which the category exemplars are not normally distributed, the decision bound model provided excellent accounts of the data, in many cases significantly outperforming the exemplar models. The decision bound model was found to be especially successful when(1) single subject analyses were performed, (2) each subject was given relatively extensive training, and (3) the subject's performance was characterized by complex suboptimalities. These results support the hypothesis that the decision bound is of fundamental importance in predicting asymptotic categorization performance and that the decision bound models provide a viable alternative to the currently popular exemplar models of categorization.     

Avoiding the dangers of averaging across subjects when using multidimensional scaling

Ashby, Maddox and Lee (Psychological Science, 5 (3) 144) argue that it can be inappropriate to fit multidimensional scaling (MDS) models to similarity or dissimilarity data that have been averaged across subjects. They demonstrate that the averaging process tends to make dissimilarity data more amenable to metric representations, and conduct a simulation study showing that noisy data generated using one distance metric, when averaged, may be better fit using a different distance metric. This paper argues that a Bayesian measure of MDS models has the potential to address these difficulties, because it takes into account data-fit, the number of dimensions used by an MDS representation, and the precision of the data. A method of analysis based on the Bayesian measure is demonstrated through two simulation studies with accompanying theoretical analysis. In the first study, it is shown that the Bayesian analysis rejects those MDS models showing better fit to averaged data using the incorrect distance metric, while accepting those that use the correct metric. In the second study, different groups of simulated ‘subjects’ are assumed to use different underlying configurations. In this case, the Bayesian analysis rejects MDS representations where a significant proportion of subjects use different configurations, or when their dissimilarity judgments contain significant amounts of noise. It is concluded that the Bayesian analysis provides a simple and principled means for systematically accepting and rejecting MDS models derived from averaged data.     

A response-time approach to comparing generalized rational and take-the-best models of decision making

The authors develop and test generalized versions of take-the-best (TTB) and rational (RAT) models of multiattribute paired-comparison inference. The generalized models make allowances for subjective attribute weighting, probabilistic orders of attribute inspection, and noisy decision making. A key new test involves a response-time (RT) approach. TTB predicts that RT is determined solely by the expected time required to locate the 1st discriminating attribute, whereas RAT predicts that RT is determined by the difference in summed evidence between the 2 alternatives. Critical test pairs are used that partially decouple these 2 factors. Under conditions in which ideal observer TTB and RAT strategies yield equivalent decisions, both the RT results and the estimated attribute weights suggest that the vast majority of subjects adopted the generalized TTB strategy. The RT approach is also validated in an experimental condition in which use of a RAT strategy is essentially forced upon subjects.     

On domain differences in categorization and context variety

Membership in many natural categories is considered all-or-none, while membership in most artifact categories is found to be graded. We introduce an alternative for the prevailing view that this domain difference in categorization results from representational differences. The context variety account posits that an item’s gradedness reflects the variety of contexts it appears in. Items that feature in a variety of contexts are assumed to be more likely to elicit a graded categorization response, since the suggested target category only provides one of many solutions to the question of the item’s identity. We review earlier work that suggested a domain difference in context variety, with artifactual items appearing in a greater variety of contexts than natural ones. The context variety domain difference is established in two separate experiments but is shown not to explain the domain difference in categorization. A selection of artifactual and natural items, for which the domain difference in context variety is reversed, is presented for categorization in a third experiment. This selection, too, fails to provide evidence for the context variety account of categorization differences. The domain difference in categorization is shown to be robust against this manipulation. Context variety appears to have no bearing on categorization, so the context variety account is not a sustainable alternative to accounts that posit representational differences between natural and artifact categories.     

On being imitated: Effects on models and observers

Forty first- and second-grade children were imitated by an adult confederate and not imitated by a second adult confederate. For each child exposed to the above treatment, another child observed the imitation and nonimitation. It was found that children tended to be attracted to the confederate who imitated them. More importantly, although the observers were not imitated, they also were attracted to the imitating confederate. The two groups did not differ significantly in subsequent imitation of the two confederates. The results, which were conceptualized within the framework of vicarious reinforcement, have methodological implications for research on the effects of being imitated.     

Stimulus averaging and the context for judgment

Loudness judgments of stimulus sets composed of four bursts of noise were analyzed for two types of contextual effects: between-set and within-set. Experiment I demonstrated between-set effects for these four-component stimuli; they were shown to be similar to those found in previous work with single stimuli. Experiment 2 tested an averaging model for within-set contextual effects. The results were inconsistent with the model. One interpretation is that there are within-set effects and that these are caused by shifts in the effective range of stimuli. Alternative interpretations attribute the apparent contextual effects either to an averaging of physical values or to an inappropriate scale of judgment.     

Negative priming is not task bound: A consistent pattern across naming and categorization tasks

When a word that was a to-be-ignored flanker on an initial prime trial becomes the target on the subsequent probe trial, responding to that word on the probe trial is slowed, a phenomenon callednegative priming. Virtually all prior studies have required subjects to perform the same task on both the prime and the probe trials. Thus, the extent to which negative priming is task bound is uncertain. We manipulated task factorially on the prime and probe trials, resulting in four groups: name-name, name-categorize, categorize-name, and categorize-categorize. The results showed equivalent negative priming of about 22 msec both within and between tasks for identical words, but no negative priming for semantically related words from the same category. These findings suggest (1) that negative priming for identical words can readily cross task types; and (2) that semantic negative priming does not occur for words, at least when categorical relatedness alone determines the semantic relation.     

On the relation between decision rules and perceptual representation in multidimensional perceptual categorization

This article examines the relation between changing categorization decision rules and the nature of the underlying perceptual representation. Observers completed a matching task that required them to adjust the length and orientation of a single line stimulus until they perceived it to "match" a second line stimulus (Alfonso-Reese, 1996, 1997). The same observers then completed four categorization tasks with the same stimuli. Data from the matching task were used to estimate a perceptual representation for each stimulus and observer. Three hypotheses regarding potential interactions between categorization decision rules and perceptual representation were examined. One assumed that there was no interaction between decision rules and perceptual representation. The second assumed that linear categorization rules affect the perceptual representation differently from nonlinear categorization rules. The third assumed that dimensional integration rules affected the perceptual representation differently from decision rules that require the observer to set a criterion along one stimulus dimension while ignoring the other; this is referred to as decisional selective attention. The results suggested that (1) the matching task perceptual representation provided a good account of the categorization data, (2) decisional selective attention affected the perceptual representation differently from decisional integration, and (3) decisional selective attention generally decreased the perceptual variability along the attended dimension.     

On the adequacy of current empirical evaluations of formal models of categorization

Categorization is one of the fundamental building blocks of cognition, and the study of categorization is notable for the extent to which formal modeling has been a central and influential component of research. However, the field has seen a proliferation of noncomplementary models with little consensus on the relative adequacy of these accounts. Progress in assessing the relative adequacy of formal categorization models has, to date, been limited because (a) formal model comparisons are narrow in the number of models and phenomena considered and (b) models do not often clearly define their explanatory scope. Progress is further hampered by the practice of fitting models with arbitrarily variable parameters to each data set independently. Reviewing examples of good practice in the literature, we conclude that model comparisons are most fruitful when relative adequacy is assessed by comparing well-defined models on the basis of the number and proportion of irreversible, ordinal, penetrable successes (principles of minimal flexibility, breadth, good-enough precision, maximal simplicity, and psychological focus).     

Cognitive models of choice: comparing decision field theory to the proportional difference model

People often face preferential decisions under risk. To further our understanding of the cognitive processes underlying these preferential choices, two prominent cognitive models, decision field theory (DFT; Busemeyer & Townsend, 1993 ) and the proportional difference model (PD; González-Vallejo, 2002 ), were rigorously tested against each other. In two consecutive experiments, the participants repeatedly had to choose between monetary gambles. The first experiment provided the reference to estimate the models' free parameters. From these estimations, new gamble pairs were generated for the second experiment such that the two models made maximally divergent predictions. In the first experiment, both models explained the data equally well. However, in the second generalization experiment, the participants' choices were much closer to the predictions of DFT. The results indicate that the stochastic process assumed by DFT, in which evidence in favor of or against each option accumulates over time, described people's choice behavior better than the trade-offs between proportional differences assumed by PD.     

Synonym comprehension and the generality of categorization models

Memory & Cognition - When subjects classify a two-word display as representing the “same” category or two “different” categories, semantic similarity between the words...     

Validation of the five-factor model of personality across instruments and observers

Two data sources--self-reports and peer ratings--and two instruments--adjective factors and questionnaire scales--were used to assess the five-factor model of personality. As in a previous study of self-reports (McCrae & Costa, 1985b), adjective factors of neuroticism, extraversion, openness to experience, agreeableness-antagonism, and conscientiousness-undirectedness were identified in an analysis of 738 peer ratings of 275 adult subjects. Intraclass correlations among raters, ranging from .30 to .65, and correlations between mean peer ratings and self-reports, from .25 to .62, showed substantial cross-observer agreement on all five adjective factors. Similar results were seen in analyses of scales from the NEO Personality Inventory. Items from the adjective factors were used as guides in a discussion of the nature of the five factors. These data reinforce recent appeals for the adoption of the five-factor model in personality research and assessment.     

Dissimilarity is used as evidence of category membership in multidimensional perceptual categorization: a test of the similarity-dissimilarity generalized context model

In exemplar models of categorization, the similarity between an exemplar and category members constitutes evidence that the exemplar belongs to the category. We test the possibility that the dissimilarity to members of competing categories also contributes to this evidence. Data were collected from two 2-dimensional perceptual categorization experiments, one with lines varying in orientation and length and the other with coloured patches varying in saturation and brightness. Model fits of the similarity-dissimilarity generalized context model were used to compare a model where only similarity was used with a model where both similarity and dissimilarity were used. For the majority of participants the similarity-dissimilarity model provided both a significantly better fit and better generalization, suggesting that people do also use dissimilarity as evidence.     

Influences of culture and visual context on real-time social categorization

Social categorization is often thought to be based on facial features and immune to visual context. Moreover, East Asians have been argued to attend to context more than Westerners. American and Chinese participants were presented with faces varying along a White-Asian morph continuum either in American, neutral, or Chinese contexts. American contexts made White categorizations more likely, and Chinese contexts made Asian categorizations more likely. Further, the compatibility between facial and contextual cues influenced the directness of participants' hand trajectories en route to selecting a category response. Even when an ultimate response was not biased by context, the trajectory was nevertheless partially attracted to the category response associated with the context. Importantly, such partial attraction effects in hand trajectories revealed that the influence of context began earlier in time for Chinese relative to American participants. Together, the results show that context systematically influences social categorization, sometimes altering categorization responses and other times only temporarily altering the process. Further, the timing of contextual influences differs by culture. The findings highlight the role of contextual and cultural factors in social categorization.     

On the generality of optimal versus objective classifier feedback effects on decision criterion learning in perceptual categorization

Biased category payoff matrices engender separate reward- and accuracy-maximizing decision criteria Although instructed to maximize reward, observers use suboptimal decision criteria that place greater emphasis on accuracy than is optimal. In this study, objective classifier feedback (the objectively correct response) was compared with optimal classifier feedback (the optimal classifier's response) at two levels of category discriminability when zero or negative costs accompanied incorrect responses for two payoff matrix multiplication factors. Performance was superior for optimal classifier feedback relative to objective classifier feedback for both zero- and negative-cost conditions, especially when category discriminability was low, but the magnitude of the optimal classifier advantage was approximately equal for zero- and negative-cost conditions. The optimal classifier feedback performance advantage did not interact with the payoff matrix multiplication factor. Model-based analyses suggested that the weight placed on accuracy was reduced for optimal classifier feedback relative to objective classifier feedback and for high category discriminability relative to low category discriminability. In addition, the weight placed on accuracy declined with training when feedback was based on the optimal classifier and remained relatively stable when feedback was based on the objective classifier. These results suggest that feedback based on the optimal classifier leads to superior decision criterion learning across a wide range of experimental conditions.     

On the nature of implicit categorization

Current categorization models disagree about whether people make a priori assumptions about the structure of unfamiliar categories. Data from two experiments provided strong evidence that people do not make such assumptions. These results rule out prototype models and many decision bound models of categorization. We review previously published neuropsychological results that favor the assumption that category learning relies on a procedural-memory-based system, rather than on an instance- based system (as is assumed by exemplar models). On the basis of these results, a new categorylearning model is proposed that makes no a priori assumptions about category structure and that relies on procedural learning and memory.     

The influence of averaging and noisy decision strategies on the recognition memory ROC

Many single- and dual-process models of recognition memory predict that the ratings and remember-know receiver operating characteristics (ROCs) are the same, but Rotello, Macmillan, and Reeder (2004) reported that the slopes of the remember-know and ratingsz-transformed ROCs (zROCs) are different. The authors show that averaging introduces nonlinearities to the form of thezROC and that ratings and remember-knowzROCs are indistinguishable when constructed in a conventional manner. The authors show, further, that some nonoptimal decision strategies have a distinctive, nonlinear effect on the form of the single-process continuous-statezROC. The conclusion is that many factors having nothing to do with the nature of recognition memory can affect the shape ofzROCs, and that therefore, the shape of thezROC does not, alone, characterize different memory models.     

Linear transformations of the payoff matrix and decision criterion learning in perceptual categorization

The effects of payoff-matrix multiplication, payoff-matrix addition, the presence of long-run gains versus long-run losses, category discriminability, and base rate on decision criterion learning were examined in 2 perceptual categorization experiments. Observers were found to be sensitive to the effects of payoff-matrix multiplication (and category discriminability) on the steepness of the objective reward function in line with predictions from the flat-maxima hypothesis and contrary to the predictions from the payoff-variance hypothesis. Decision criterion learning was best in base-rate conditions, was worst when losses were associated with incorrect responding, and was intermediate when no losses were associated with incorrect responding. This performance profile was well captured by the competition between reward and accuracy (COBRA) hypothesis. A hybrid model framework that instantiates both the flat-maxima and COBRA hypotheses was necessary to account for the data from both experiments.