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.     

New lower and upper bounds for communality in factor analysis

We derive several relationships between communalities and the eigenvalues for ap ×p correlation matrix under the usual factor analysis model. For suitable choices ofj, _j (), where _j () is thej-th largest eigenvalue of , provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - _p () improves on the use of squared mulitiple correlation coefficient as a lower bound.This research was done while the second author was at Tokyo Institute of Technology.     

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.     

多点触觉定位

在左手食指第一节腹侧分别进行1个点、2个点和3个点的定位实验,探讨了多点定位的特点。实验发现,按单个点的定位误差来计算．1个点和3个点的定位误差无显著差异,且二者均显著地低于2个点的定位误差;在2个点的定位中,一个点的定位误差是此2个点的空间距离的函数．定位误差有随距离加大而增加的趋势;在3个点的定位中．同一个点在不同的3点组台中的定位误差无显著差异。结果指示,多点触觉定位除以受刺激的躯体部位框架为参照（基本参照）外,还受到诸刺激点构成的刺激模式（次级参照）的影响。     

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.     

MEMORY PROCESSES IN DELAYED SPATIAL DISCRIMINATIONS: RESPONSE INTENTIONS OR RESPONSE MEDIATION?

Pigeons were trained on a pair-comparison task in which left versus right choices were reinforced following different sequences of two center-key stimuli. Choice accuracy was higher when retention intervals occurred after the entire sequence than when they separated the two stimuli comprising it, and this effect occurred independently of whether the initial and terminal stimuli came from the same or different dimensions. The initial stimulus from the prior trial was a source of proactive interference only in groups for which the retention interval separated the two sequence stimuli. By contrast, differential delay-interval behavior was observed only in groups for which the retention interval followed presentation of the entire sequence. These results indicate that coding processes in delayed discriminations are influenced by the location of the retention interval, and that response mediation affects retention performances if the reinforced choice can be determined prior to the interval.     

Separability of item and person parameters in response time models

This paper discusses two forms of separability of item and person parameters in the context of response time (RT) models. The first is separate sufficiency: the existence of sufficient statistics for the item (person) parameters that do not depend on the person (item) parameters. The second is ranking independence: the likelihood of the item (person) ranking with respect to RTs does not depend on the person (item) parameters. For each form a theorem stating sufficient conditions, is proved. The two forms of separability are shown to include several (special cases of) models from psychometric and biometric literature. Ranking independence imposes no restrictions on the general distribution form, but on its parametrization. An estimation procedure based upon ranks and pseudolikelihood theory is discussed, as well as the relation of ranking independence to the concept of double monotonicity.I am indebted to Wim van der Linden for bringing Thissen's (1983) paper to my notice, and to Martijn Berger, Frans Tan, and the anonymous reviewers for their constructive comments on earlier drafts of this paper.     

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.