The asymptotic posterior normality of the latent trait in an IRT model

It has long been part of the item response theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general and nonrestrictive nonparametric assumptions, we make this claim rigorous for a broad class of latent models.This research was partially supported by Office of Naval Research Cognitive and Neural Sciences Grant N0014-J-90-1940, 442-1548, National Science Foundation Mathematics Grant NSF-DMS-91-01436, and the National Center for Supercomputing Applications. We wish to thank Kumar Joag-dev and Zhiliang Ying for enlightening suggestions concerning the proof of the basic result.The authors wish to thank Kumar Joag-Dev, Brian Junker, Bert Green, Paul Holland, Robert Mislevy, and especially Zhiliang Ying for their useful comments and discussions.     

Category discrimination by pigeons using five polymorphous features

Eight pigeons were trained to discriminate between sets of color photographs of natural scenes. The scenes differed along five two-valued dimensions (site, weather, camera distance, camera orientation, and camera height), and all combinations of the feature values were used. One value of each dimension was designated as positive, and slides containing three or more positive feature values were members of the positive stimulus set. Thus, each feature had an equal, low, correlation with reinforcement, and all features had zero correlations with each other. Seven of the 8 pigeons learned this discrimination, and their responding came under the control of all five features. Within the positive and negative stimulus sets, response rates were higher to stimuli that contained more positive feature values. Once discrimination had been achieved, reversal training was given using a subset of the slides. In this subset, only a single feature was correlated with reinforcement. All pigeons learned this reversal successfully and generalized it to additional photographs with the same feature content. After reversal, the original reinforcement contingencies were reinstated, and training was continued using all the slides except those that had been used in reversal. Reversal generalized to these slides to some extent. Analysis of the response rates to individual slides showed that, compared with prereversal training, only the feature that had been subjected to reversal contingencies showed a reversed correlation with response rate. The remaining features showed the same correlation with response rate as they had before reversal training. Thus, reversal on some members of a category following category discrimination training led to generalization to stimuli within the category that were not involved in the reversal, but not to features that were not reversed. It is therefore inappropriate to refer to the pigeons as learning a concept.     

Toward a theory of verbal behavior

This paper is a reply to an accompanying set of six commentaries by Sidman; Hayes and Barnes; Schusterman, Kastak, and Reichmuth; Tonneau and Sokolowski; Lowenkron; and Moerk. Those commentaries were prompted by our article “On the Origins of Naming and Other Symbolic Behavior” (1996), which was, in turn, followed by 26 commentaries and a reply. In the course of the present reply, we further develop the naming account to embrace more complex verbal relations such as same, different, more, and less. We also examine what we see as the lack of conceptual coherence in equivalence theories, including relational frame theory, and the disparities between these accounts and the findings from empirical research.     

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.     

Treatment of escape-maintained aberrant behavior with escape extinction and predictable routines

We evaluated the effects of two daily activity schedules on 2 participants' rates of aberrant behavior and their compliance. Functional analysis identified the operant function of the participants' aberrant behaviors to be escape from tasks. Participants were taught to use stimuli contained in daily schedules, and were tested based on a modified stimulus-equivalence model that consisted of flash cards and activity schedules comprised of words or photographs that corresponded to the participants' daily activities. On pretests, the participants demonstrated simple and conditional discriminations with the photographs but not with the printed stimuli. A time-delay procedure was used to teach the participants to name the flash cards. Following training, the printed activity schedules corresponded to lower rates of problem behavior and higher rates of compliance than the photographic activity schedules. Performance on posttests indicated the establishment of functional classes of stimuli involving the flash cards and activity schedules even though this type of correspondence was not directly trained.     

Formation of transitivity in conditional matching to sample by pigeons

Four homing pigeons were trained over 5 months in a zero-delay, “arbitrary” matching-to-sample procedure with sample and comparison stimuli presented on any of three response keys. Birds were also required to complete a fixed-ratio 10 requirement on both sample and comparison stimuli to terminate their presentation. The procedure resulted in the establishment of relations that were not specifically trained and that can be characterized by the property of transitivity in a stimulus equivalence context. This result was in contrast with the findings obtained from most previous research with nonhuman subjects.     

The transfer of respondent eliciting and extinction functions through stimulus equivalence classes

Two studies investigated the transfer of respondent elicitation through equivalence classes. In Experiment 1, match-to-sample procedures were used to teach 8 subjects two four-member equivalence classes. One member of one class was then paired with electric shock, and one member of the other class was presented without shock. All remaining stimuli were then presented. Using skin conductance as the measure of conditioning, transfer of conditioning was demonstrated in 6 of the 8 subjects. In Experiment 2, similar procedures were used to replicate the results of Experiment 1 and investigate the transfer of extinction. Following equivalence training and conditioning to all members of one class, one member was then presented in extinction. When the remaining stimuli from this class were then presented, they failed to elicit skin conductance. In the final phase of the experiment, the stimulus that was previously presented in extinction was reconditioned. Test trials with other members of the class revealed that they regained elicitation function. These results demonstrate that both respondent elicitation and extinction can transfer through stimulus classes. The clinical and applied significance of the results is discussed.     

Interactive effects of dispositional mindfulness and PETTLEP imagery training on basketball shooting performance: A randomized controlled trial

The purpose of this study was to examine the interactive effects of dispositional mindfulness and visualized PETTLEP imagery training on basketball mid-range shooting performance and retention. Seventy-three participants (M age = 20.32 ± 1.09) with high/low dispositional mindfulness (high n = 35; low n = 38) selected out of 302 college students were randomly assigned into the following six groups: (a) high mindfulness internal imagery (H-II, n = 13); (b) high mindfulness external imagery (H-EI, n = 11); (c) high mindfulness control (H–CO, n = 11); (d) low mindfulness internal imagery (L-II, n = 13); (e) low mindfulness external imagery (L-EI, n = 12); and (f) low mindfulness control (L-CO, n = 13). Participants engaged in a pretest to measure their basketball shooting performance, then participated in a 6-week (3 times/per-week) intervention, plus a posttest and retention test. A three-way 2 (high/low mindfulness) X 3 (treatments: internal-, external imagery, and control) X 3 (measurement time: pretest, posttest, and retention) mixed ANOVA statistical analysis found dispositional mindfulness interacted with treatments and measurement time. The main effects showed high dispositional mindfulness performed better than low dispositional mindfulness, and internal imagery training performed better than external imagery training on mid-range basketball performance at retention. The 3–way interaction indicated that when using either internal or external imagery, high dispositional mindfulness performed better than low mindfulness on retention but not posttest. For 2-way interaction, high dispositional mindfulness performed better than low dispositional mindfulness on retention but not posttest. Our results extended current knowledge on sport imagery and dispositional mindfulness and gained several theoretical implications for researchers. The limitations, future research directions, and practical implications were also discussed.     

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.     

Parameter estimation in latent trait models

Latent trait models for binary responses to a set of test items are considered from the point of view of estimating latent trait parameters=( ₁, , _n ) and item parameters=( ₁, , _k ), where _j may be vector valued. With considered a random sample from a prior distribution with parameter, the estimation of (, ) is studied under the theory of the EM algorithm. An example and computational details are presented for the Rasch model.This work was supported by Contract No. N00014-81-K-0265, Modification No. P00002, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank an anonymous reviewer for several valuable suggestions.