Testing mediation effects in cross-classified multilevel data

In this article, we propose an approach to test mediation effects in cross-classified multilevel data in which the initial cause is associated with one crossed factor, the mediator is associated with the other crossed factor, and the outcome is associated with Level-1 units (i.e., the 2^(A)?2^(B)?1 design). Multiple-membership models and cross-classified random effects models are used to estimate the indirect effects. The method is illustrated using real data from the Early Childhood Longitudinal Study–Kindergarten Cohort (1998). The results from the simulation study show that the proposed method can produce a consistent estimate of the indirect effect and reliable statistical inferences, given an adequate sample size.     

Reasoning with uncertain categories

Five experiments investigated how people use categories to make inductions about objects whose categorisation is uncertain. Normatively, they should consider all the categories the object might be in and use a weighted combination of information from all the categories: bet-hedging. The experiments presented people with simple, artificial categories and asked them to make an induction about a new object that was most likely in one category but possibly in another. The results showed that the majority of people focused on the most likely category in making inductions, although there was a group of consistently normative responders who used information from both categories (about 25% of our college population). Across experiments the overall pattern of results suggests that performance in the task is improved not by understanding the underlying principles of bet-hedging but by increasing the likelihood that multiple categories are in working memory at the time of the induction. We discuss implications for improving everyday inductions.     

The influence of category coherence on inference about cross-classified entities

A critical function of categories is their use in property inference (Heit, 2000). However, one challenge to using categories in inference is that most entities in the world belong to multiple categories (e.g., Fido could be a dog, a pet, a mammal, or a security system). Building on Patalano, Chin-Parker, and Ross (2006), we tested the hypothesis that category coherence (the extent to which category features go together in light of prior knowledge) influences the selection of categories for use in property inference about cross-classified entities. In two experiments, we directly contrasted coherent and incoherent categories, both of which included cross-classified entities as members, and we found that the coherent categories were used more readily as the source of both property transfer and property extension. We conclude that category coherence, which has been found to be a potent influence on strength of inference for singly classified entities (Rehder & Hastie, 2004), is also central to category use in reasoning about novel cross-classified ones.     

Monoidal categories with natural numbers object

The notion of a natural numbers object in a monoidal category is defined and it is shown that the theory of primitive recursive functions can be developed. This is done by considering the category of cocommutative comonoids which is cartesian, and where the theory of natural numbers objects is well developed. A number of examples illustrate the usefulness of the concept.This work was partially carried out while both authors were guests of McGill University and while the second author was a guest of Dalhousie University. Both authors acknowledge support from the Natural Sciences and Engineering Research Council of Canada and the Québec Department of Education.     

Relational categories are more mutable than entity categories

Across three experiments, we explore differences between relational categories—whose members share common relational patterns—and entity categories, whose members share common intrinsic properties. Specifically, we test the claim that relational concepts are more semantically mutable in context, and therefore less stable in memory, than entity concepts. We compared memory for entity nouns and relational nouns, tested either in the same context as at encoding or in a different context. We found that (a) participants show better recognition accuracy for entity nouns than for relational nouns, and (b) recognition of relational nouns is more impaired by a change in context than is recognition of entity nouns. We replicated these findings even when controlling for factors highly correlated with relationality, such as abstractness–concreteness. This suggests that the contextual mutability of relational concepts is due to the core semantic property of conveying relational structure and not simply to accompanying characteristics such as abstractness. We note parallels with the distinction between nouns and verbs and suggest implications for lexical and conceptual structure. Finally, we relate these patterns to proposals that a deep distinction exists between words with an essentially referential function and those with a predicate function.     

Cody's categories

Of the two main interpretations of Spinoza's theory of the identity of the attributes, in particular those of Thought and Extension, the objective interpretation is now almost universally preferred to the subjective. Rejection of the subjective interpretation, according to which the attributes are merely our ways of cognizing a reality whose real essence remains unknown, is certainly justified, but the objective theory comes too near to replacing the identity by a mere correlation of différents to be quite satisfactory. Is it not better to say that Thought and Extension represent two complementary conceptions of reality which are both correct? Yes, but in saying so some commentators ascribe to mind, as Spinoza conceives it, an unplausibly abstract status. An alternative proposal is made as to a way in which Spinoza might be right in essentials, though it requires that a certain tension in Spinozism as to the nature of body be resolved in a particular direction.     

Clinical expertise and reasoning with uncertain categories

Expert clinical psychologists, clinical psychology graduates, and nonclinical graduate students were presented with clinical and nonclinical cases in which the diagnosis or category membership of a character was uncertain; they then made feature predictions about the character. For each case, there was a diagnosis or category that was highly probable and a less likely alternative that either did (relevant condition) or did not (neutral condition) alter predictions. For clinical cases, clinical experts and graduate clinicians gave different predictions for the relevant and neutral conditions, indicating that they had considered the uncertain nature of the diagnosis in their predictions. Although they acknowledged that the diagnosis was uncertain, nonclinical students ignored the less likely diagnostic alternatives when making predictions. For the nonclinical cases, all three groups made predictions based on only the most likely category alternative. The results showed that clinical training and/or experience promote multiple-category reasoning, but that this effect is domain specific.     

Feature-based versus category-based induction with uncertain categories

Previous research has suggested that when feature inferences have to be made about an instance whose category membership is uncertain, feature-based inductive reasoning is used to the exclusion of category-based induction. These results contrast with the observation that people can and do use category-based induction when category membership is known. The present experiments examined the conditions that drive feature-based and category-based strategies in induction under category uncertainty. Specifically, 2 experiments investigated whether reliance on feature-based inductive strategies is a product of the lack of coherence in the categories used in previous research or is due to the use of a decision-only induction procedure. Experiment 1 found that feature-based reasoning remained the preferred strategy even when categories with relatively high internal coherence were used. Experiment 2 found a shift toward category-based reasoning when participants were trained to classify category members prior to feature induction. Together, these results suggest that an appropriate conceptual representation must be formed through experience with a category before it is likely to be used as a basis for feature induction.     

Natural categories

The hypothesis of the study was that the domains of color and form are structured into nonarbitrary, semantic categories which develop around perceptually salient “natural prototypes.” Categories which reflected such an organization (where the presumed natural prototypes were central tendencies of the categories) and categories which violated the organization (natural prototypes peripheral) were taught to a total of 162 members of a Stone Age culture which did not initially have hue or geometric-form concepts. In both domains, the presumed “natural” categories were consistently easier to learn than the “distorted” categories. Even when not central, natural prototype stimuli tended to be more rapidly learned and more often chosen as the most typical example of the category than were other stimuli. Implications for general differences between natural categories and the artificial categories of concept formation research were discussed.     

Classification versus inference learning contrasted with real-world categories

Categories are learned and used in a variety of ways, but the research focus has been on classification learning. Recent work contrasting classification with inference learning of categories found important later differences in category performance. However, theoretical accounts differ on whether this is due to an inherent difference between the tasks or to the implementation decisions. The inherent-difference explanation argues that inference learners focus on the internal structure of the categories—what each category is like—while classification learners focus on diagnostic information to predict category membership. In two experiments, using real-world categories and controlling for earlier methodological differences, inference learners learned more about what each category was like than did classification learners, as evidenced by higher performance on a novel classification test. These results suggest that there is an inherent difference between learning new categories by classifying an item versus inferring a feature.     

Inference using categories

How do people use category membership and similarity for making inductive inferences? The authors addressed this question by examining the impact of category labels and category features on inference and classification tasks that were designed to be comparable. In the inference task, participants predicted the value of a missing feature of an item given its category label and other feature values. In the classification task, participants predicted the category label of an item given its feature values. The results from 4 experiments suggest that category membership influences inference even when similarity information contradicts the category label. This tendency was stronger when the category label conveyed class inclusion information than when the label reflected a feature of the category. These findings suggest that category membership affects inference beyond similarity and that category labels and category features are 2 different things.     

Abstract coherent categories

Many studies have demonstrated the importance of the knowledge that interrelates features in people's mental representation of categories and that makes our conception of categories coherent. This article focuses on abstract coherent categories, coherent categories that are also abstract because they are defined by relations independently of any features. Four experiments demonstrate that abstract coherent categories are learned more easily than control categories with identical features and statistical structure, and also that participants induced an abstract representation of the category by granting category membership to exemplars with completely novel features. The authors argue that the human conceptual system is heavily populated with abstract coherent concepts, including conceptions of social groups, societal institutions, legal, political, and military scenarios, and many superordinate categories, such as classes of natural kinds.     

Noncategorical approaches to feature prediction with uncertain categories

In four experiments, we investigated how people make feature predictions about objects whose category membership is uncertain. Artificial visual categories were presented and remained in view while a novel instance with a known feature, but uncertain category membership was presented. All four experiments showed that feature predictions about the test instance were most often based on feature correlations (referred to as feature conjunction reasoning). Experiment 1 showed that feature conjunction reasoning was generally preferred to category-based induction in a feature prediction task. Experiment 2 showed that people used all available exemplars to make feature conjunction predictions. Experiments 3 and 4 showed that the preference for predictions based on feature conjunction persisted even when category-level information was made more salient and inferences involving a larger number of categories were required. Little evidence of reasoning based on the consideration of multiple categories (e.g., Anderson, (Psychological Review, 98:409–429, 1991)) or the single, most probable category (e.g., Murphy & Ross, (Cognitive Psychology, 27:148–193, 1994)) was found.     

Achromatic color categories

Sternheim and Boynton’s (1966) continuous judgmental color-naming technique was used to assess the elemental nature of achromatic colors. Results from three subjects indicate that the names “black” and “white” are necessary and sufficient to describe achromatic test lights associated with the name “gray.” On the basis of the criteria that establishes a color as elemental, black and white were confirmed as elemental, whereas gray was not. These findings support the assumption of various opponent processing models that there are only two elemental achromatic sensations. In addition, the results support Hering’s (1920) view that black and white differ from the paired-chromatic opponent colors in that they are not mutually exclusive.     

Learning time-varying categories

Many kinds of objects and events in our world have a strongly time-dependent quality. However, most theories about concepts and categories either are insensitive to variation over time or treat it as a nuisance factor that produces irrational order effects during learning. In this article, we present two category learning experiments in which we explored peoples’ ability to learn categories whose structure is strongly time-dependent. We suggest that order effects in categorization may in part reflect a sensitivity to changing environments, and that understanding dynamically changing concepts is an important part of developing a full account of human categorization.     

Ad hoc categories

People construct ad hoc categories to achieve goals. For example, constructing the category of “things to sell at a garage sale” can be instrumental to achieving the goal of selling unwanted possessions. These categories differ from common categories (e.g., “fruit,” “furniture”) in that ad hoc categories violate the correlational structure of the environment and are not well established in memory. Regarding the latter property, the category concepts, concept-to-instance associations, and instance-to-concept associations structuring ad hoc categories are shown to be much less established in memory than those of common categories. Regardless of these differences, however, ad hoc categories possess graded structures (i.e., typicality gradients) as salient as those structuring common categories. This appears to be the result of a similarity comparison process that imposes graded structure on any category regardless of type.     

Variation within categories

Two aspects of variation within categories, relating to different models of categorization, were investigated — frequency of dimensional values and typicality differences within values. The influence of range of typicality experienced during learning and of informational value of feedback was also studied. Finally, differential forgetting of values was examined.In the experiment subjects learned to categorize faces, and then performed a classification test task and pairwise comparisons of faces. A variety of dependent variables was employed, including the galvanic skin response (GSR).Typicality and frequency of values appeared to influence categorization performance independent of each other. It was concluded that both prototype distance models and frequency models explain different aspects of variation within the same categories, and that models of classification should account for frequency of values in contrasting categories. Results showed furthermore (1) the influence of typicality range on the extension of a category; (2) no influence of specific feedback regarding representativeness of a face; (3) less decay with more important values; and (4) a positive relationship between uncertainty reduction and GSR.