Resurgence of derived stimulus relations.

Resurgence has been shown in human and nonhuman operant behavior, but not in derived relational responses. The present study examined this issue. Twenty-three undergraduates were trained to make conditional discriminations in a three-choice matching-to-sample paradigm. The training resulted in three equivalence classes, each consisting of four arbitrarily configured visual stimuli. The same 12 stimuli were then reorganized, and the conditional discrimination training was repeated such that three new classes were possible. In a subsequent test of derived relations, most subjects showed response patterns that were consistent with the altered conditional discriminations. Subjects were then exposed to conditional discrimination trials under extinction. Most subjects continued to respond consistently with the most recently reinforced conditional discrimination trials. During the next phase, subjects were exposed to symmetry and equivalence trials. Responses consistent with the most recent training produced feedback saying that the responses were incorrect, whereas other responses produced no feedback. Most subjects showed a resurgence of responding that was consistent with their earlier training. Finally, subjects were exposed to conditional discrimination trials carried out in extinction. Most subjects continued to show a resurgence of responding that was consistent with their early training.     

Speed analyses of stimulus equivalence.

The functional substitutability of stimuli in equivalence classes was examined through analyses of the speed of college students'' accurate responding. After training subjects to respond to 18 conditional relations, subjects'' accuracy and speed of accurate responding were compared across trial types (baseline, symmetry, transitivity, and combined transitivity and symmetry) and nodal distance (one- through five-node transitive and combined transitive and symmetric relations). Differences in accuracy across nodal distance and trial type were significant only on the first tests of equivalence, whereas differences in speed were significant even after extended testing. Response speed was inversely related to the number of nodes on which the tested relations were based. Significant differences in response speed were also found across trial types, except between transitivity and combined trials. To determine the generality of these comparisons, three groups of subjects were included: An instructed group was given an instruction that specified the interchangeability of stimuli related through training; a queried group was queried about the basis for test-trial responding: and a standard group was neither instructed nor queried. There were no significant differences among groups. These results suggest the use of response speed and response accuracy to measure the strength of matching relations.     

The relationship between Fisher's exact test and Pearson's chi-square test: A bayesian perspective

It is demonstrated in this paper that two major tests for 2 × 2 talbes are highly related from a Bayesian perspective. Although it is well-known that Fisher's exact and Pearson's chi-square tests are asymptotically equivalent, the present analysis shows that a formal similarity also exists in small samples. The key assumption that leads to the resemblance is the presence of a continuous parameter measuring association. In particular, it is shown that Pearson's probability can be obtained by integrating a two-moment approximation to the posterior distribution of the log-odds ratio. Furthermore, Pearson's chi-square test gave an excellent approximation to the actual Bayes probability in all 2×2 tables examined, except for those with extremely disproportionate marginal frequencies.     

Relations between baseline contingencies and equivalence probe performances

Following the emergence of two three-member equivalence classes (A1B1C1 and A2B2C2), 5 college students were exposed to one or more changes in the reinforcement contingencies controlling baseline conditional discriminations. AC relations were either reversed (i.e., C2 was reinforced and C1 punished when A1 was the sample; C1 was reinforced and C2 punished when A2 was the sample) or arranged randomly (i.e., C2 and C1 were reinforced and punished equally often in the presence of A1 and A2). In a third condition, the original AB and AC relations were reversed. Results showed that although baseline conditional discrimination performances were under the control of reinforcement contingencies, and performances on symmetry trials varied with baseline responding for 3 of 4 subjects when contingencies were reversed, performances on transitivity probes remained consistent with the initial equivalence class. These inconsistencies between probe and baseline performances were striking because conditional discriminations are thought to be the determinants of equivalence class performance. Similarly, the contrast between performances on symmetry and transitivity probes was of theoretical interest because equivalence classes are defined by congruent patterns of responding on probe trials.     

The effects of nodality on the formation of equivalence classes

A four-member equivalence class (A → B → C → D) can be formed by training AB, BC, and CD. The nodal stimuli, B and C, mediate all of the derivative (transitive and equivalence) relations in the class. The derivative relations AC, CA, BD, and DB are separated by one node, whereas AD and DA are separated by two nodes. How do the number of nodes that separate the stimuli in a derivative relation influence the induction of stimulus control exerted by that relation? Seven college students learned two four-member classes made up of nonsense syllables. After training, all derivative relations were presented repeatedly without informative feedback. Stimulus control exerted by each derivative relation was assessed concurrently. For the 7 subjects, control exerted by the derivative relations increased gradually with repeated presentations. With 6 of the 7 subjects, the one-node relations exerted more control than the two-node relations during the process. However, the disparity between the one- and two-node relations decreased with repeated presentations. Eventually, all derivative relations exerted complete control. The control exerted by derivative relations during induction was inversely related to the number of nodes separating the terms in the derivative relations. These results demonstrate that nodal distance is a determinant of the relatedness of stimuli in equivalence classes. The findings are discussed in terms of remote association, semantic memory networks, and the study of transitive inference.     

The Problem of local optimality with OSMOD

The possibility of obtaining locally optimal solutions with categorical data is pointed out for the original version of OSMOD development by Saito and Otsu. A revision of the initialization strategy in OSMOD is suggested, and its effectiveness in diminishing this possibility is demonstrated.     

A test of symmetry and transitivity in the conditional discrimination performances of pigeons

In a matching-to-sample context, pigeons were taught two conditional discriminations according to one of three equivalence paradigms: train if A, then select B and if B, then select C; train if B, then A and if B, then C; or train if A, then B and if C, then B. Test trials without reinforcement revealed that the conditional relations did not satisfy the symmetrical and transitive properties of an equivalence relation. Apparently, only specific if... then relations were learned. Contrary to Kendall's (1983) findings, and probably as a consequence of procedural differences, none of the pigeons in the present experiment were observed to emit mediating behavior during the transitivity probe trials. The absence of symmetry and transitivity may be related to the individual stimuli not being reflexive. Behavioral techniques other than the commonly used matching-to-sample technique might better succeed in avoiding unintended stimulus control in the study of the formation of stimulus classes.     

Nonhumans have not yet shown stimulus equivalence

Recently, two published articles have reported finding stimulus equivalence in nonhumans. One suggested that equivalence was due to the mediation of names. The procedure used trained all components of all tested relations. Because nothing was derived, the defining characteristics of equivalence were not achieved. In the second study a definition of equivalence was proposed that fails to distinguish functional stimulus classes from equivalence classes. The resulting data are not clearly relevant to stimulus equivalence in Sidman's sense of the term. Stimulus equivalence has not yet been shown in nonhumans.