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.     

A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

Hierarchical classes: Model and data analysis

A discrete, categorical model and a corresponding data-analysis method are presented for two-way two-mode (objects × attributes) data arrays with 0, 1 entries. The model contains the following two basic components: a set-theoretical formulation of the relations among objects and attributes; a Boolean decomposition of the matrix. The set-theoretical formulation defines a subset of the possible decompositions as consistent with it. A general method for graphically representing the set-theoretical decomposition is described. The data-analysis algorithm, dubbed HICLAS, aims at recovering the underlying structure in a data matrix by minimizing the discrepancies between the data and the recovered structure. HICLAS is evaluated with a simulation study and two empirical applications.This research was supported in part by a grant from the Belgian NSF (NFWO) to Paul De Boeck and in part by NSF Grant BNS-83-01027 to Seymour Rosenberg. We thank Iven Van Mechelen for clarifying several aspects of the Boolean algebraic formulation of the model and Phipps Arabie for his comments on an earlier draft.     

Computational behavior dynamics: an alternative description of Nevin (1969).

A computational processing behavior-dynamic model was instantiated in the form of a computer program that "behaved" on the task developed by Nevin (1969). In this classic discrete-trials experiment, the relative frequency of choosing a response alternative matched the relative frequency of reinforcement for that alternative, the local structure of responding was opposite that predicted by momentary maximizing (i.e., the probability of a changeover decreased with run length), and absolute and relative response rates varied independently. The behavior-dynamic model developed here qualitatively reproduced these three results (but not in quantitative and specific detail) and also generated some interesting, as-yet-untested predictions about performance in Nevin's task. The model was discussed as an example of a stochastic behavior-dynamic alternative to algebraic behavior theory.     

Reciprocal peer management: Improving staff instruction in a vocational training program

To test the feasibility and utility of involving peers as sources of feedback, 6 subjects, instructors in a vocational program for adults with mental retardation, participated in a staff training and management program. Subjects' teaching interactions were assessed during baseline, in-service training (on effective teaching), return-to-baseline, peer management, and follow-up phases. Peer management was introduced in multiple baseline fashion across pairs of subjects. Members of each pair were trained to monitor peer teaching, to record and graph data, to provide feedback, and to set goals with the peer. Each pair then performed these procedures on the job for several weeks, during which time 4 of the 6 subjects increased their use of effective teaching methods (over baseline). However, inconsistencies in the magnitude and durability of these increases require that the study be viewed as inconclusive, although it has heuristic value as a promising model for involving co-workers in staff management programs.     

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.     

Comparison of simultaneous prompting and constant time delay procedures in teaching sight words to elementary students with moderate mental retardation

Simultaneous prompting (a type of antecedent prompt and test procedure) and constant time delay were compared with four students with moderate mental retardation learning expressive sight words. A parallel treatments design across word sets and replicated across students was used. For acquisition, the simultaneous prompting procedures required fewer trials, sessions, and training time to criterion and resulted in fewer student errors during daily probe and training sessions. However, maintenance data indicated mixed results across the two procedures. Reliability data (both dependent and independent variables) revealed no differences between the two procedures in terms of the teacher's accuracy in recording student responses and implementing each procedure. Future research issues are discussed.     

Delayed constructed-response identity matching improves the spelling performance of students with mental retardation

We assessed the effects of a computerized matching-to-sample procedure on the spelling performances of three students with mental retardation. Initially, the students could 1) match pictures and printed words to one another, and 2) match pictures and printed words to spoken words. However, they could not construct words to either pictures or spoken words (e.g., touch, in order, the letters s->h->o->e given the spoken-word sample Shoe). Word constructions then improved markedly after exposure to delayed constructed-response identity matching (e.g., touch the letters s->h->o->e given the printed-word sample shoe). One subject's oral and written spelling also improved. The results extend previous research by showing multiple positive effects of a computerized spelling intervention. These effects may have occurred in part because of the formation of stimulus classes among pictures, printed words, and spoken words.     

Incorporating prior theory in covariance structure analysis: A bayesian approach

A Bayesian approach to the testing of competing covariance structures is developed. The method provides approximate posterior probablities for each model under consideration without prior specification of individual parameter distributions. The method is based on ayesian updating using cross-validated pseudo-likelihoods. Given that the observed variables are the samefor all competing models, the approximate posterior probabilities may be obtained easily from the chi square values and other known constants, using only a hand calculator. The approach is illustrated using and example which illustrates how the prior probabilities can alter the results concerning which model specification is preferred.