Typical delay determines waiting time on periodic-food schedules: Static and dynamic tests

Pigeons and other animals soon learn to wait (pause) after food delivery on periodic-food schedules before resuming the food-rewarded response. Under most conditions the steady-state duration of the average waiting time, t, is a linear function of the typical interfood interval. We describe three experiments designed to explore the limits of this process. In all experiments, t was associated with one key color and the subsequent food delay, T, with another. In the first experiment, we compared the relation between t (waiting time) and T (food delay) under two conditions: when T was held constant, and when T was an inverse function of t. The pigeons could maximize the rate of food delivery under the first condition by setting t to a consistently short value; optimal behavior under the second condition required a linear relation with unit slope between t and T. Despite this difference in optimal policy, the pigeons in both cases showed the same linear relation, with slope less than one, between t and T. This result was confirmed in a second parametric experiment that added a third condition, in which T + t was held constant. Linear waiting appears to be an obligatory rule for pigeons. In a third experiment we arranged for a multiplicative relation between t and T (positive feedback), and produced either very short or very long waiting times as predicted by a quasi-dynamic model in which waiting time is strongly determined by the just-preceding food delay.     

Examining differential item functioning due to item difficulty and alternative attractiveness

A method for analyzing test item responses is proposed to examine differential item functioning (DIF) in multiple-choice items through a combination of the usual notion of DIF, for correct/incorrect responses and information about DIF contained in each of the alternatives. The proposed method uses incomplete latent class models to examine whether DIF is caused by the attractiveness of the alternatives, difficulty of the item, or both. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as a chi-square random variable.     

Provision of step-level public goods with continuous contribution

Twelve groups of five subjects each participated in a nonco-operative game in which each member of a group receives the same endowment and must then decide independently and anonymously how much of it to contribute to the group benefit. Regardless of the size of his or her contribution, each member receives the same reward if, and only if, the sum of contributions is equal to or larger than a prespecified provision threshold. The results show that the level of contribution depends on the provision threshold, and that it increases when contributions are not restricted to be all-or-none. We present, discuss, and competitively test two models for this class of social dilemmas, one postulating maximization of expected utility and the other yielding an equitable solution.     

A note on the computation of the second-order derivatives of the elementary symmetric functions in the rasch model

Jansen (1984) gave explicit formulas for the computation of the second-order derivatives of the elementary symmetric functions. But they are only applicable to those pairs of items which have unequal parameters. It is shown here that for equal parameters similar explicit formulas do exist, too, facilitating the application of the Newton-Raphson procedure to estimate the parameters in the Rasch model and related models according to the conditional maximum likelihood principle.The author wishes to thank the reviewers for their helpful comments on an earlier draft of this paper.     

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.     

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.     

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。     

Rasch's multiplicative poisson model with covariates

As a multivariate model of the number of events, Rasch's multiplicative Poisson model is extended such that the parameters for individuals in the prior gamma distribution have continuous covariates. The parameters for individuals are integrated out and the hyperparameters in the prior distribution are estimated by a numerical method separately from difficulty parameters that are treated as fixed parameters or random variables. In addition, a method is presented for estimating parameters in Rasch's model with missing values. The author is now affiliated with the Otara University of Commerce. The author is grateful to Yoshio Takane, Haruo Yanai, Eiji Muraki, the editor and referees for their careful readings and helpful suggestions on earlier versions of this paper. Part of this work was presented at the third European Congress of Psychology at Tampere, Finland in 1993.