Extensions of Rasch's multiplicative poisson model

Consideration will be given to a model developed by Rasch that assumes scores observed on some types of attainment tests can be regarded as realizations of a Poisson process. The parameter of the Poisson distribution is assumed to be a product of two other parameters, one pertaining to the ability of the subject and a second pertaining to the difficulty of the test. Rasch's model is expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. The test parameters are considered fixed. Secondly, it will be shown how additional between- and within-subjects factors can be incorporated. Methods for testing the fit and estimating the parameters of the model will be discussed, and illustrated by empirical examples.     

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.     

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.     

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.     

Choice behavior of rats in a concurrent-chains schedule: Amount and delay of reinforcement

Rats were exposed to concurrent-chains schedules in which the terminal links were equal fixed-interval schedules terminating in one or three food pellets. Choice proportions for large reward increased with increases in delay intervals programmed on fixed-interval schedules and supported the predictions derived from a general choice model originally formulated by Fantino and later developed by Navarick and Fantino. In addition, a functional equivalence of two alternatives was established by increasing delay intervals with large reward, whereas delay intervals for small reward were held constant. Functionally equivalent delay intervals with large reward, for each delay interval with small reward, can be described by a power function with exponent smaller than 1.0. A better prediction of choice proportions resulted when this function was used to derive predicted choice proportions.     

The relationship between differential stimulus relatedness and implicit measure effect sizes

Implicit measures have been hypothesized to allow researchers to ascertain the existence and strength of relations between stimuli, often in the context of research on attitudes. However, little controlled behavioral research has focused on whether stimulus relations, and the degree of relatedness within such relations, are indexed by implicit measures. The current study examined this issue using a behavior‐analytic implicit‐style stimulus relation indexing procedure known as the Function Acquisition Speed Test (FAST). Using a matching‐to‐sample (MTS) procedure to train stimulus equivalence relations between nonsense syllables, the number of iterations of the procedure was varied across groups of participants, hence controlling stimulus relatedness in the resulting equivalence relations. Following final exposure to the MTS procedure, participants completed a FAST. Another group of participants was exposed to a FAST procedure with word pairs of known relatedness. Results showed that increasing relatedness resulted in a linear increase in FAST effect size. These results provide the first direct empirical support for a key process‐level assumption of the implicit literature, and offer a behavior‐analytic paradigm within which to understand these effects. These results also suggest that the FAST may be a viable procedure for the quantification of emergent stimulus relations in stimulus equivalence training.