Testing a stochastic foraging model in an operant simulation: Agreement with qualitative but not quantitative predictions

An operant simulation of foraging through baited and empty patches was studied with 4 pigeons. On a three-key panel, side keys were designated as patches, and successive opportunities to complete 16 fixed-ratio 10 schedules on side keys were defined as encounters with feeders. In a random half of the patches in any session, some of the fixed-ratio 10 schedules yielded reinforcement (baited feeders) and the other schedules yielded nonreinforcement (empty feeders). In the other half of the patches, all feeders were empty. Pigeons could travel between patches at any time by completing a fixed-ratio schedule on the center key. An optimal foraging model was tested in Experiments 1 and 2 by varying center-key travel time and number of baited feeders in baited patches. The ordinal predictions that number of feeders visited in empty patches would increase with travel time and decrease as number of baited feeders increased were supported, but pigeons visited far more feeders in empty patches than the optimal number predicted by the model to maximize energy/time. In Experiment 3, evidence was found to suggest that the number of empty feeders encountered before the first baited feeder in baited patches is an important factor controlling leaving empty patches.     

Effects of differences between stimuli, responses, and reinforcer rates on conditional discrimination performance

In a discrete-trial conditional discrimination procedure, 4 pigeons obtained food reinforcers by pecking a key with a short latency on trials signaled by one stimulus and by pecking the same key with a long latency on trials signaled by a second stimulus. The physical difference between the two stimuli and the temporal separation between the latency values required for reinforcement were varied factorially over four sets of conditions, and the ratio of reinforcer rates for short and long latencies was varied within each set of conditions. Stimulus discrimination varied directly with both stimulus and response differences and was unaffected by the reinforcer ratio. Sensitivity to reinforcement, estimated by generalized-matching-law fits to the data within each set of conditions, varied directly with the response difference but inversely with the stimulus difference arranged between sets of conditions. Because variations in stimulus differences, response differences, and reinforcer differences did not have equivalent effects, these findings question the functional equivalence of the three terms of the discriminated operant: antecedent stimuli, behavior, and consequences.     

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 many null distributions of person fit indices

This paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fittingitems may be removed, this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting ofk symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called ability parameter, although our results are equally valid for Rasch scales measuring other attributes.As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.The authors express their gratitude to the reviewers and to many colleagues for comments on an earlier version.     

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.     

分时距认知特点的研究

本研究探讨了分时距估计的认知特点,检验了SS模型、PT模型和CS模型的预测效度,结果表明：分时距估计主要是在信息提取阶段采用分段推算策略对时间信息进行重建的过程,变化／分割和注意分配对分时距估计有显著影响;SS模型的预测效度最低,PT、CS模型的预测效度较高。     

小学儿童对习俗时间的周期性特点的认知

本研究探讨了小学儿童对习俗时间周期性特点的认知发展．实验任务是让被试判断两个给定日期之间的时间距离是正向接近还是反向接近。结果表明:儿童对习俗时间的周期性特点的认知成绩随年龄增长而不断提高;随着两个日期之间距离的增大,反应时不断增加,正确率不断降低,在两个日期相互接近的方向发生改变的边界处,反应时最长,正确率最低,表现出显著的“距离效应”和“边界效应”;儿童可以利用数字系统进行判断,他们的认知加工策略包括计数、数字运算和凭借习俗时间的空间表象进行模拟加工等等。