Nodality effects during equivalence class formation: An extension to sight-word reading and concept development

Three students with moderate disabilities were taught to read and match-to-sample sight words comprising stimulus sets based upon the four food groups. We taught students conditional discriminations within four four-member sets using a single-sample/four-comparison procedure. Students were taught A-B, B-C, and C-D conditional discriminations for each of the four potential stimulus classes. Subsequent probes tested for relations based upon symmetry and one-node and two-node transitivity. The performances for all students indicated that symmetric relations emerged before one-node transitive relations, and that one-node transitive relations emerged before two-node transitive relations. These results are consistent with a pattern of responding, referred to as a "nodality effect," in which relations with fewer nodes are demonstrated prior to the demonstration of relations with a greater number of nodes. These results extend this area of research to sight-word reading for students with moderate disabilities.     

The Basic Constructive Logic for a Weak Sense of Consistency defined with a Propositional Falsity Constant

The logic B_Kc1 is the basic constructive logic in the ternaryrelational semantics (without a set of designated points) adequateto consistency understood as the absence of the negation ofany theorem. Negation is introduced in B_Kc1 with a negationconnective. The aim of this paper is to define the logic B_Kc1F.In this logic negation is introduced via a propositional falsityconstant. We prove that B_Kc1 and B_Kc1F are definitionally equivalent.     

Comparative Evaluations

My response to Engelmann (2008) will be based on several questions that will allow both its author and the general reader to determine whether the assumptions I make as an interpreter of this complex paper are congruent or incongruent with their own interpretations of the text. The interpretations by the writer, by any commentator, and the diverse interpretations of a general audience together with my own interpretations will, I hope, facilitate some fruitful ‘comparative evaluations.’ I articulate my inferences of the most dense part of the paper, namely the ‘concrete immediate Consciousness and the developing absent outside.’ My hope is to address Engelmann’s question: “Am I in a better disposition to judge modern theories of consciousness?” The last section of my response spells out more personal comments to my all too brief and single encounter with Arno Engelmann. It is there that Arno Engelmann’s fascinating statement “I am a citizen of the world” is addressed through its counterparts in my life.     

Limited information estimation and testing of discretized multivariate normal structural models

Discretized multivariate normal structural models are often estimated using multistage estimation procedures. The asymptotic properties of parameter estimates, standard errors, and tests of structural restrictions on thresholds and polychoric correlations are well known. It was not clear how to assess the overall discrepancy between the contingency table and the model for these estimators. It is shown that the overall discrepancy can be decomposed into a distributional discrepancy and a structural discrepancy. A test of the overall model specification is proposed, as well as a test of the distributional specification (i.e., discretized multivariate normality). Also, the small sample performance of overall, distributional, and structural tests, as well as of parameter estimates and standard errors is investigated under conditions of correct model specification and also under mild structural and/or distributional misspecification. It is found that relatively small samples are needed for parameter estimates, standard errors, and structural tests. Larger samples are needed for the distributional and overall tests. Furthermore, parameter estimates, standard errors, and structural tests are surprisingly robust to distributional misspecification. This research was supported by the Department of Universities, Research and Information Society (DURSI) of the Catalan Government, and by grants BSO2000-0661 and BSO2003-08507 of the Spanish Ministry of Science and Technology.     

Mediated conditioning versus retrospective revaluation in humans: The influence of physical and functional similarity of cues

Two experiments assessed whether similarity between the two elements of a compound would influence the degree of mediated extinction versus recovery from overshadowing in human causal judgements. In both Experiments 1 and 2, we assessed the influence of extinguishing one element of a two-element compound on judgements about the other element. In Experiment 1 we manipulated the physical similarity of the two elements of the compound; in Experiment 2, we used equivalence and distinctiveness pretraining in order to vary their functional similarity. We found that these procedures influenced mediated extinction and recovery from overshadowing as a function of both physical and acquired similarity and distinctiveness, respectively. The implications of these results for previously reported differences between humans and nonprimate animals are discussed.     

Measurement invariance in mentoring research: A cross-cultural examination across Taiwan and the U.S.

Workplace mentoring in the international context is an emerging research area with significant potential for global integration. However, although measurement equivalence is a prerequisite for examining cross-cultural differences, this assumption has yet to be examined in mentoring research. This study contributes to the mentoring literature by assessing the measurement equivalence of the Mentoring Functions Questionnaire (MFQ-9) across two diverse cultural settings, the U.S. and Taiwan. Results of a series of multi-group confirmatory factor analyses supported full configural invariance, full metric invariance, and partial scalar invariance across the two groups. These findings suggest MFQ-9 may provide acceptable comparisons and meaningful interpretations across cultures. Implications for future international mentoring research and managerial practice are discussed.     

Equivalence relations and the reinforcement contingency

Where do equivalence relations come from? One possible answer is that they arise directly from the reinforcement contingency. That is to say, a reinforcement contingency produces two types of outcome: (a) 2‐, 3‐, 4‐, 5‐, or n‐term units of analysis that are known, respectively, as operant reinforcement, simple discrimination, conditional discrimination, second‐order conditional discrimination, and so on; and (b) equivalence relations that consist of ordered pairs of all positive elements that participate in the contingency. This conception of the origin of equivalence relations leads to a number of new and verifiable ways of conceptualizing equivalence relations and, more generally, the stimulus control of operant behavior. The theory is also capable of experimental disproof.     

Do Coping Styles Differ Across Sociocultural Groups? The Role of Measurement Equivalence in Making This Judgment

Cross-sociocultural group measurement equivalency is an important issue that generally has not been studied in the coping literature. Measurement equivalency of the COPE (Carver, Scheier, & Weintraub, 1989) was assessed across two sociocultural groups, a sample of 100 Anglo middle-class divorced mothers and a sample of 122 low-income Mexican American/Mexican immigrant mothers. A series of restrictive confirmatory factor analyses revealed that seven of the COPE's subscales may be measuring the same underlying construct across populations. However, scores derived from the subscales may not represent the same magnitude of the construct in these two groups. This study makes an important first step in furthering the understanding of coping strategies in low-income Mexican American/Mexican immigrant mothers. This study also illustrates the importance of testing for measurement equivalency before conducting comparative research in disparate populations.     

Functional classes and equivalence relations

Three adult subjects were taught a set of two-choice simultaneous discriminations, with three positive and three negative stimuli; all possible combinations of positive and negative stimuli yielded nine different pairs. The discriminations were repeatedly reversed and rereversed, the former positive stimuli becoming negative and the former negative stimuli becoming positive. With all subjects, a reversal of the contingencies for one pair of stimuli became sufficient to change their responses to all of the other pairs. The reversals had produced functional stimulus classes. Then, all subjects showed conditional discriminations emerging between members of a functional class; given a sample from one class and comparisons from both classes, they selected the comparison that was in the same class as the sample. Next, 2 of the subjects showed that the within-class conditional relations possessed the symmetric and transitive properties of equivalence relations; after having been taught to relate new stimuli to existing class members, the subjects then matched other class members to the new stimuli. Subsequent tests of two-choice discriminations showed that the conditional discriminations had transferred functional class membership to the new stimuli. The 3rd subject, who did not show equivalence relations among functional class members, was also found to have lost the within-class conditional relations after the equivalence tests.     

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.