Hierarchical classes: Model and data analysis

A discrete, categorical model and a corresponding data-analysis method are presented for two-way two-mode (objects × attributes) data arrays with 0, 1 entries. The model contains the following two basic components: a set-theoretical formulation of the relations among objects and attributes; a Boolean decomposition of the matrix. The set-theoretical formulation defines a subset of the possible decompositions as consistent with it. A general method for graphically representing the set-theoretical decomposition is described. The data-analysis algorithm, dubbed HICLAS, aims at recovering the underlying structure in a data matrix by minimizing the discrepancies between the data and the recovered structure. HICLAS is evaluated with a simulation study and two empirical applications.This research was supported in part by a grant from the Belgian NSF (NFWO) to Paul De Boeck and in part by NSF Grant BNS-83-01027 to Seymour Rosenberg. We thank Iven Van Mechelen for clarifying several aspects of the Boolean algebraic formulation of the model and Phipps Arabie for his comments on an earlier draft.     

Stimulus class membership established via stimulus-reinforcer relations

In an arbitrary matching-to-sample procedure, two mentally retarded subjects learned conditional discriminations with two sets of stimuli. Each set included a spoken name (N1 or N2), an object (O1 or O2), and a printed symbol (S1 or S2). One subject selected conditionally (a) O1 upon N1, and O2 upon N2, and (b) S1 upon O1, and S2 upon O2. The other subject selected conditionally (a) S1 upon N1, and S2 upon N2, and (b) O1 upon S1, and O2 upon S2. For both subjects, selections of O1 and S1 produced one type of food, F1; selections of O2 and S2 produced a different type of food, F2. Both subjects also learned identity-matching performances, selecting O1, O2, S1, S2, F1, and F2 conditionally upon those stimuli as samples; F1 followed selections of O1, S1, and F1; F2 followed selections of O2, S2, and F2. Matching performances consistent with stimulus class formation involving the names, objects, symbols, and foods were demonstrated on probe trials, even though these performances had not been taught explicitly. Next, new objects, X1 and X2, were presented on identity-matching trials, producing F1 and F2, respectively. Without further training, X1 was selected conditionally upon N1, S1, and O1, and X2 was selected upon N2, S2, and O2. When the contingencies were changed so that selections of X1 and X2 were now followed by F2 and F1, respectively, X2 was selected conditionally upon N1, S1, and O1, and X1 was selected upon N2, S2, and O2. Class membership of X1 and X2 had apparently changed. This study provides evidence that reinforcers may become members of stimulus classes, and that new stimuli may become class members through relations with reinforcers.     

FUNCTIONAL COMMUNICATION TRAINING WITH AND WITHOUT EXTINCTION AND PUNISHMENT

Functional communication training has been reported to be a promising treatment for severe behavior problems. In this study, functional communication training alone and combined with extinction and/or punishment was evaluated for 4 clients with severe retardation, behavior problems, and communication deficits. The participants were inpatients on a hospital unit for treatment of severe behavior disorders. They received individualized interventions based on functional assessment that included reinforcement of a communication response with the same function as their destructive behavior. Results showed that for some patients, functional communication training was not sufficient to produce clinically significant reductions in destructive behavior, and the combination of training plus punishment produced the largest and most consistent reductions.     

The development of derived stimulus relations through training in arbitrary-matching sequences

Five-year-old children were taught three-stage sequences of arbitrary matching: A-C, B-C, A-D; A-C, B-D, B-C; or A-C, A-D, B-C. Each stage refers to a sample-comparison relation between stimuli. Unreinforced test probes revealed untrained arbitrary matches (B-D, A-D, and B-D, respectively), derivable by substitution of stimuli with a common sample or comparison function. Additional probes revealed further untrained sample-comparison relations derivable by substitution and identity, including the commuted relations D-B, D-A, and D-B, respectively. These processes may have relevance to conceptual and verbal behavior.     

CONDITIONAL DISCRIMINATION VS. MATCHING TO SAMPLE: AN EXPANSION OF THE TESTING PARADIGM

A subject's performance under a conditional-discrimination procedure defines conditional relations between stimuli: “If A1, then B1; if A2, then B2.” The procedure may also generate matching to sample. If so, the stimuli will be related not only by conditionality, but by equivalence: A1 and B1 will become equivalent members of one stimulus class, A2 and B2 of another. One paradigm for testing whether a conditional-discrimination procedure has generated equivalence relations uses three sets of stimuli, A, B, and C, three stimuli per set. Subjects learn to select Set-B and Set-C comparisons conditionally upon Set-A samples. Having been explicitly taught six sample-comparison relations, A1B1, A1C1, A2B2, A2C2, A3B3, and A3C3, subjects prove immediately capable of matching the B- and C-stimuli; six new relations emerge (B1C1, B2C2, B3C3, C1B1, C2B2, C3B3). The 12 stimulus relations, six taught and six emergent, define the existence of three three-member stimulus classes, A1B1C1, A2B2C2, and A3B3C3. This paradigm was expanded by introducing three more stimuli (Set D), and teaching eight children not only the AB and AC relations but DC relations also—selecting Set-C comparisons conditionally upon Set-D samples. Six of the children proved immediately capable of matching the B- and D-stimuli to each other. By selecting appropriate Set-B comparisons conditionally upon Set-D samples, and Set-D comparisons conditionally upon Set-B samples, they demonstrated the existence of three four-member stimulus classes, A1B1C1D1, A2B2C2D2, and A3B3C3D3. These larger classes were confirmed by the subjects' success with the prerequisite lower-level conditional relations; they were also able to select Set-D comparisons conditionally upon samples from Sets A and C, and to do the BC and CB matching that defined the original three-member classes. Adding the three DC relations therefore generated 12 more, three each in BD, DB, AD, and CD. Enlarging each class by one member brought about a disproportionate increase in the number of emergent relations. Ancillary oral naming tests suggested that the subject's application of the same name to each stimulus was neither necessary nor sufficient to establish classes of equivalent stimuli.     

Being student leaders or ‘ordinary’ students: Children's emotional experiences of relationships with others in a Chinese school

The student leader system is commonly used in Chinese schools. Student leaders are children who are elected by classmates, then assigned by teachers, to be responsible for monitoring classmates' behaviour. Based on the data collected through an intensive ethnographic study in a rural primary boarding school in China in 2016, this article discusses emotional experiences in peer relationships reported by both student leaders and other ‘ordinary’ students, who were not student leaders. The article argues that China's student leader system is likely to create hierarchical relationships between student leaders and ‘ordinary’ students, and exposes ‘ordinary’ students to the potential risk of being exploited by student leaders. The article also argues that because of this student leader system and relevant student evaluation values, student leaders and ‘ordinary’ students all feel stressed when they are building up and maintaining peer relationships, such as friendships, with each other.     

Stress and subjective life expectancy: Cross-sectional and longitudinal associations in early adolescence

Using data from a longitudinal study, the present study employed a latent class mover-stayer analytical strategy to examine both the cross-sectional and longitudinal (+33 months) relationship between membership of stress classes, and subjective life expectancy. Participants were from 21 High schools in Scotland and Northern Ireland. Data were collected in the first year of High school (mean age = 12.5 years), and at +33 months (fourth year, or school year 11). Sample 1 consisted of 1171 adolescents (40.82% females, 2.56% unreported) in Northern Ireland. Sample 2 consisted of 1059 adolescents (52.79% females, 1.32% unreported) in Scotland. Adolescents with the lowest levels of stress projected the highest subjective life expectancy scores. Longitudinal analyses were jumbled and not in keeping with cross-sectional results. More research may be needed on the trajectory of subjective life expectancy over time before it can be depended upon as a reliable outcome variable in adolescent development.     

The formation of a generalized categorization repertoire: effect of training with multiple domains,samples, and comparisons

The present experiment explored the effects of three variables on the spontaneous categorization of stimuli in perceptually distinct and novel domains. Each of six stimulus domains was created by morphing two images that were the domain endpoints. The endpoints of the domains were male and female faces, two abstract drawings, a car and a truck, two banded-elevation satellite land images, a tree and a cat, and two false-color satellite images. The stimulus variants at each end of a domain defined two potential perceptual classes. Training was conducted in a matching-to-sample format and used stimuli from one or two domains, one or three variants per class as samples, and one or three variants per class as comparisons. The spontaneous categorization of stimuli in the untrained stimulus domains showed the emergence of a generalized categorization repertoire. The proportion of spontaneously categorized stimuli in the new domains was positively related to the number of domains and samples used in training, and was inversely related to the number of comparisons used in training. Differential reaction times demonstrated the discriminability of the stimuli in the emergent classes. This study is among the first to provide an empirical basis for a behavior-analytic model of the development of generalized categorization repertoires in natural settings.     

Naming and categorization in young children: vocal tact training

In three experiments, 2- to 4-year-old children, following pretraining with everyday objects, were presented with arbitrary stimuli of differing shapes. In Experiment 1A, 9 subjects were trained one common tact response, "zag," to three of these and a second tact, "vek," to another three. In category match-to-sample Test 1, 4 subjects sorted accurately when required only to look at the sample before selecting from five comparisons. The remaining 5 subjects succeeded in Test 2, in which they were required to tact the sample before selecting comparisons. Experiment 1B showed, for 2 of these subjects, that tact training with 12 arbitrary stimuli established two six-member classes that were still intact 6 weeks later. In Experiment 2, 3 new subjects participated in a common tact training procedure that ensured that none of the exemplars from the same class were presented together prior to the test for three-member classes. Two subjects passed category Test 1 and the third passed Test 2. Tests showed subjects' listener behavior in response to hearing /zog/ and /vek/ to be in place. These experiments indicate that common naming is effective in establishing arbitrary stimulus classes and that category match-to-sample testing provides a robust measure of categorization.     

The influence of hierarchy on probability judgment

Consider the task of predicting which soccer team will win the next World Cup. The bookmakers may judge Brazil to be the team most likely to win, but also judge it most likely that a European rather than a Latin American team will win. This is an example of a non-aligned hierarchy structure: the most probable event at the subordinate level (Brazil wins) appears to be inconsistent with the most probable event at the superordinate level (a European team wins). In this paper we exploit such structures to investigate how people make predictions based on uncertain hierarchical knowledge. We distinguish between aligned and non-aligned environments, and conjecture that people assume alignment. Participants were exposed to a non-aligned training set in which the most probable superordinate category predicted one outcome, whereas the most probable subordinate category predicted a different outcome. In the test phase participants allowed their initial probability judgments about category membership to shift their final ratings of the probability of the outcome, even though all judgments were made on the basis of the same statistical data. In effect people were primed to focus on the most likely path in an inference tree, and neglect alternative paths. These results highlight the importance of the level at which statistical data are represented, and suggest that when faced with hierarchical inference problems people adopt a simplifying heuristic that assumes alignment.