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.     

Choice between delayed reinforcers and fixed-ratio schedules requiring forceful responding.

This experiment measured pigeons' choices between delayed reinforcers and fixed-ratio schedules in which a force of approximately 0.48 N was needed to operate the response key. In ratio-delay conditions, subjects chose between a fixed-ratio schedule and an adjusting delay. The delay was increased or decreased several times a session in order to estimate an indifference point--a delay duration at which the two alternatives were chosen about equally often. Each ratio-delay condition was followed by a delay-delay condition in which subjects chose between the adjusting delay and a variable-time schedule, with the components of this schedule selected to match the ratio completion times of the preceding ratio-delay condition. The adjusting delays at the indifference point were longer when the alternative was a fixed-ratio schedule than when it was a matched variable-time schedule, which indicated a preference for the matched variable-time schedules over the fixed-ratio schedules. This preference increased in a nonlinear manner with increasing ratio size. This nonlinearity was inconsistent with a theory that states that indifference points for both time and ratio schedules can be predicted by multiplying the choice response-reinforcer intervals of the two types of schedules by different multiplicative constants. Two other theories, which predict nonlinear increases in preference for the matched variable-time schedules, are discussed.     

The expected likelihood of transitivity of preference

May's model of pairwise preference determination is used to assess the expected likelihood that a subject's pairwise preference comparisons on three alternatives will be transitive. A closed form representation for this expected likelihood is obtained for each situation considered. When the subject is assumed to act precisely according to rankings on attributes with May's model, the computed expected likelihoods the relatively large. When the subject becomes a probabilistic chooser, as defined in a specific manner, expected likelihoods of transitivity decrease significantly from corresponding values with May's model. For a probabilistic Chooser, there is a significant likelihood that the subject might yield transitive pairwise preferences substantially different than the results suggested by May's model.This research was supported by a grant from the General University Research Program and through a fellowship from the Center for Advanced Study, both of the University of Delaware. Very helpful input from John H. Antil, Meryl P. Gardner, and James M. Munch is also acknowledged.     

Modeling item responses when different subjects employ different solution strategies

A model is presented for item responses when different subjects employ different strategies, but only responses, not choice of strategy, can be observed. Using substantive theory to differentiate the likelihoods of response vectors under a fixed set of strategies, we model response probabilities in terms of item parameters for each strategy, proportions of subjects employing each strategy, and distributions of subject proficiency within strategies. The probabilities that an individual subject employed the various strategies can then be obtained, along with a conditional estimate of proficiency under each. A conceptual example discusses response strategies for spatial rotation tasks, and a numerican example resolves a population of subjects into subpopulations of valid responders and random guessers.The first author's work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. We are grateful to Murray Aitkin, Isaac Bejar, Neil Dorans, Frederiksen, and Marklyn Wingersky for their comments and suggestions, and to Alison Gooding, Maxine Kingston, Donna Lembeck, Joling Liang, and Kentaro Yamamoto for their assistance with Example 2.     

Schedule interactions involving punishment with pigeons and humans

The principal aim of the present experiments was to assess whether punishment increased or decreased the rate of unpunished behavior (contrast and induction, respectively) for which reinforcement rate was held constant, with physical and nonphysical punishers (electric shock and response cost), pigeon and human subjects, signaled and unsignaled components (multiple and mixed schedules), and the presence or absence of a blackout period between components. Across the three experiments there were 20 punishment conditions. Induction was found in nine of those, less consistent response-rate reduction was found in three, contrast was found in four, and in four there was no change in responding from conditions without punishment. Contrast occurred consistently only with multiple schedules during the first exposure to electric-shock punishment. Induction and no change, however, were found with every combination of the independent variables studied. Four conclusions regarding the interactions between punished and unpunished responding emerged from the present results: (a) Both contrast and induction occurred with the reinforcement rate held constant and a blackout between components, (b) induction was more common than contrast, (c) contrast occurred only in the presence of a stimulus different from that correlated with the punisher, and (d) contrast diminished with prolonged exposure to punishment. None of the current theoretical accounts of punishment contrast can explain the present results.     

A Comparison of Active Student Response and On-Task Instruction on the Acquisition and Maintenance of Health Facts by Fourth Grade Special Education Students

An alternating treatments design was used to compare the effects of active student response (ASR) and on-task (OT) instruction on the acquisition and maintenance of health facts during small-group lessons. Five students with learning difficulties (4 students identified as developmentally handicapped and 1 student identified as learning disabled) participated in daily instruction on weekly sets of 20 unknown health facts (10 facts assigned to the ASR condition and 10 to the OT condition). During ASR instruction, the teacher modeled the correct response to a health question that was presented visually on a health fact card, and the students immediately repeated the correct response in unison three times. During OT instruction, students attended visually to the health fact card as the teacher modeled the correct response. All 5 students made more correct responses on end-of-day tests on health facts taught with ASR instruction than they did on health facts taught with OT instruction. ASR instruction also produced consistently superior results on maintenance tests administered 2 weeks after instruction.     

EMERGENCE OF REINFORCER PREFERENCE AS A FUNCTION OF SCHEDULE REQUIREMENTS AND STIMULUS SIMILARITY

Tustin (1994) recently observed that an individual's preference for one of two concurrently available reinforcers under low schedule requirements (concurrent fixed-ratio [FR] 1) switched to the other reinforcer when the schedule requirements were high (concurrent FR 10). We extended this line of research by examining preference for similar and dissimilar reinforcers (i.e., those affecting the same sensory modality and those affecting different sensory modalities). Two individuals with developmental disabilities were exposed to an arrangement in which pressing two different panels produced two different reinforcers according to progressively increasing, concurrent-ratio schedules. When two dissimilar stimuli were concurrently available (food and a leisure item), no clear preference for one item over the other was observed, regardless of the FR schedules in effect (FR 1, 2, 5, 10, and 20). By contrast, when two similar stimuli were concurrently available (two food items), a clear preference for one item emerged as the schedule requirements were increased from FR 1 to FR 5 or FR 10. These results are discussed in terms of implications for conducting preference assessments and for selecting reinforcers to be used under training conditions in which response requirements are relatively high or effortful.     

Comparisons of rats' choice behavior among three different radial-maze tasks

The present study compared rats' behavioral changes on three tasks on the radial-arm maze. In the free-choice task (0Fo/8Fr; no forced choice/eight free choices), rats performed efficiently with the simple response pattern of sequential adjacent-arm choices. In the two forced-choice tasks (3Fo/5Fr and 5Fo/3Fr), rats performed as efficiently as 0Fo/8Fr but showed no particular response patterns. The frequency of arm investigation was the highest in 5Fo/3Fr, and was higher in 3Fo/5Fr than in 0Fo/8Fr. The probability of correct rejection, avoiding re-entry to visited arms after investigation, was also higher in 3Fo/5Fr and 5Fo/3Fr than in 0Fo/8Fr. These results suggest that the rats could adjust their behavior to the task demands.     

THE EFFECTS OF CHOICE AND TASK PREFERENCE ON THE WORK PERFORMANCE OF ADULTS WITH SEVERE DISABILITIES

We evaluated the effects of choice versus the assignment of tasks of varying preferences on the work engagement of adults with severe disabilities. The combined results of two experiments suggest that the relative preference for a task may be an important variable in the effectiveness of choice for some individuals.     

REDUCING ESCAPE BEHAVIOR AND INCREASING TASK COMPLETION WITH FUNCTIONAL COMMUNICATION TRAINING,EXTINCTION AND RESPONSE CHAINING

The effects of functional communication training, extinction, and response chaining on 3 subjects' escape-maintained aberrant behavior were evaluated using a multielement design. Functional communication training consisted of teaching subjects a verbal response that was functionally equivalent to their aberrant behavior. Subjects initially were allowed to escape from a task contingent on the trained verbal response. In subsequent treatment phases, escape was contingent on the trained verbal response plus the completion of the specified number of steps in the task (response chaining). The number of steps was increased until a subject completed the task to obtain a break. Results showed that the treatment reduced rates of aberrant behavior and that the chaining procedure was effective in decreasing the availability of escape.