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.     

Discrimination learning in a foraging situation

Rats were allowed to forage in a simulated natural environment made up of eight food sources (patches) each containing a fixed number of pellets. Two of the eight contained an extra supply of peanuts. The peanut patches were signaled by an olfactory/visual cue located at the bottom of the ladder leading to the patch. In successive phases the number of sessions per day, height of the patches, and availability of peanuts were manipulated. Subjects showed evidence of discrimination learning under these conditions, although the degree of discriminatory behavior varied as a function of environmental manipulations. Assessment of behavior within foraging sessions showed that subjects systematically changed their patterns of utilization of patches across time. Sampling or exploration, as well as food reinforcement, seem implicated in these results.     

Pigeons can discriminate locations presented in pictures

The present experiments were designed to teach pigeons to discriminate two locations represented by color photographs. Two sets of photographs were taken at two distinctive locations on a university campus. These sets represented several standpoints at each location. For the true-discrimination group, pictures from the two locations were differentially associated with reward; for the pseudodiscrimination group, half of the views from each location were arbitrarily but consistently associated with reward. The former group acquired the discrimination much more rapidly. These birds also showed good transfer to new views from the standpoints used in training and to a new standpoint at each location not used in training. In a second experiment, another group of pigeons could terminate any training trial by pecking an “advance” key. Three of 4 subjects used this option to reduce the duration of trials in which pictures from the negative location were presented. These data suggest that pigeons can integrate views shown in pictures into a “concept” of a location. The method used here may be the experimental analogue of a common, natural process by which animals learn to identify locations.     

Stimulus effects on concurrent performance in transition

Six experimentally naive pigeons were exposed to concurrent variable-interval variable-interval schedules in a three-key procedure in which food reinforcement followed pecks on the side keys and pecks on the center key served as changeover responses. In Phase 1, 3 birds were exposed to 20 combinations of five variable-interval values, with each variable-interval value consistently associated with a different color on the side keys. Another 3 pigeons were exposed to the same 20 conditions, but with a more standard procedure that used a nondifferential discriminative stimulus on the two side keys throughout all conditions. In Phase 2, the differential and nondifferential stimulus conditions were reversed for each pigeon. Each condition lasted for one 5-hr session and one subsequent 1-hr session. In the last 14 conditions of each phase, the presence of differential discriminative stimuli decreased the time necessary for differential responding to develop and increased the sensitivity of behavior to reinforcement distribution in the 1st hr of training; during the last hours of training in each condition, however, the effects of the differential discriminative stimuli could not be distinguished from the effects of reinforcement distribution per se. These results show the importance of studying transitions in behavior as well as final performance. They may also be relevant to discrepancies in the results of previous experiments that have used nonhuman and human subjects.     

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.     

Subjects' inferential performance and the interaction of data and hypotheses in probabilistic inference tasks

In a recent paper, Knez (1991) showed an interaction of data and hypotheses in probabilistic inference tasks. The results illustrated two, earlier not obtained, significant main effects on subjects' hypothesis sampling , viz. the effect of different forms of data presentation and subjects' execution of cognitive control over their hypothesis pool throughout the series of trials. The present paper followed up these results in that the subjects' hypothesis testing , in Knez (1991) was subjected to an analysis. Hence, to see if the effects mentioned above significantly influenced the subjects' hypothesis testing, as they did for subjects' hypothesis sampling. The results showed a consistency with Knez (1991), i.e. the results emphasize the interaction of data and hypothesis in probabilistic inference tasks, as well as the subjects' execution of cognitive control over their hypothesis pool concerning both the subjects' hypothesis sampling and testing.     

Functional classes and equivalence relations

Three adult subjects were taught a set of two-choice simultaneous discriminations, with three positive and three negative stimuli; all possible combinations of positive and negative stimuli yielded nine different pairs. The discriminations were repeatedly reversed and rereversed, the former positive stimuli becoming negative and the former negative stimuli becoming positive. With all subjects, a reversal of the contingencies for one pair of stimuli became sufficient to change their responses to all of the other pairs. The reversals had produced functional stimulus classes. Then, all subjects showed conditional discriminations emerging between members of a functional class; given a sample from one class and comparisons from both classes, they selected the comparison that was in the same class as the sample. Next, 2 of the subjects showed that the within-class conditional relations possessed the symmetric and transitive properties of equivalence relations; after having been taught to relate new stimuli to existing class members, the subjects then matched other class members to the new stimuli. Subsequent tests of two-choice discriminations showed that the conditional discriminations had transferred functional class membership to the new stimuli. The 3rd subject, who did not show equivalence relations among functional class members, was also found to have lost the within-class conditional relations after the equivalence tests.     

The role of observing and attention in establishing stimulus control.

Early theorists (Skinner, Spence) interpreted discrimination learning in terms of the strengthening of the response to one stimulus and its weakening to the other. But this analysis does not account for the increasing independence of the two performances as training continues or for increases in control by dimensions of a stimulus other than the one used in training. Correlation of stimuli with different densities of reinforcement produces an increase in the behavior necessary to observe them, and greater observing of and attending to the relevant stimuli may account for the increase in control by these stimuli. The observing analysis also encompasses errorless training, and the selective nature of observing explains the feature-positive effect and the relatively shallow gradients of generalization generated by negative discriminative stimuli. The effectiveness of the observing analysis in handling these special cases adds to the converging lines of evidence supporting its integrative power and thus its validity.     

Statistical consistency and hypothesis testing for nonmetric multidimensional scaling

The properties of nonmetric multidimensional scaling (NMDS) are explored by specifying statistical models, proving statistical consistency, and developing hypothesis testing procedures. Statistical models with errors in the dependent and independent variables are described for quantitative and qualitative data. For these models, statistical consistency often depends crucially upon how error enters the model and how data are collected and summarized (e.g., by means, medians, or rank statistics). A maximum likelihood estimator for NMDS is developed, and its relationship to the standard Shepard-Kruskal estimation method is described. This maximum likelihood framework is used to develop a method for testing the overall fit of the model.