Relative reinforcer rates and magnitudes do not control concurrent choice independently

One assumption of the matching approach to choice is that different independent variables control choice independently of each other. We tested this assumption for reinforcer rate and magnitude in an extensive parametric experiment. Five pigeons responded for food reinforcement on switching-key concurrent variable-interval variable-interval schedules. Across conditions, the ratios of reinforcer rates and of reinforcer magnitudes on the two alternatives were both manipulated. Control by each independent variable, as measured by generalized-matching sensitivity, changed significantly with the ratio of the other independent variable. Analyses taking the model-comparison approach, which weighs improvement in goodness-of-fit against increasing number of free parameters, were inconclusive. These analyses compared a model assuming constant sensitivity to magnitude across all reinforcer-rate ratios with two alternative models. One of those alternatives allowed sensitivity to magnitude to vary freely across reinforcer-rate ratios, and was less efficient than the common-sensitivity model for all pigeons, according to the Schwarz-Bayes information criterion. The second alternative model constrained sensitivity to magnitude to be equal for pairs of reinforcer-rate ratios that deviated from unity by proportionately equal amounts but in opposite directions. This model was more efficient than the common-magnitude-sensitivity model for 2 of the pigeons, but not for the other 3. An analysis of variance, carried out independently of the generalized-matching analysis, also showed a significant interaction between the effects of reinforcer rate and reinforcer magnitude on choice. On balance, these results suggest that the assumption of independence inherent in the matching approach cannot be maintained. Relative reinforcer rates and magnitudes do not control choice independently.     

Conditional Reinforcers and Informative Stimuli in A Constant Environment

Five pigeons responded on steady-state concurrent variable-interval variable-interval schedules of food presentation in which half of the foods were removed and replaced with nonfood stimuli. Across conditions, the stimuli were either paired or unpaired with food, and the correlation between the ratio of food deliveries on the two alternatives and the ratio of nonfood stimuli was either −1, 0, or +1. Neither the pairing of stimuli with food, nor the correlation between stimuli and food, affected generalized-matching performance, but paired stimuli had a demonstrable effect at a local level of analysis. This effect was independent of the food–stimulus correlation. These results differ from results previously obtained in a frequently changing environment. We attribute this difference in results to differences in the information value of response-contingent stimuli in frequently changing versus relatively constant environments, as well as to differences between forward pairing and simultaneous pairing of the stimuli with food.     

Leaving patches: Effects of travel requirements

Five pigeons were trained in an analogue foraging procedure in which, by completing a travel requirement, they entered a “patch” in which a reinforcer might be available after an unpredictable time. They also had the opportunity, by emitting a defined response, to exit the patch and travel to another patch. Prey availability in a patch was not signaled. Data were collected on the length of time that subjects stayed in patches before exiting (residence times) as a function of various travel requirements: travel for a fixed time in blackout, fixed-interval schedule traveling, fixed-time traveling with an added response required to terminate traveling, and fixed-ratio traveling. For each of these conditions, the required amount of travel (time or responses) was varied over a wide range. As previously reported, residence times increased with increases in fixed-time traveling, as they did with increasing fixed-interval or fixed-ratio traveling. There was no evidence that adding response or work requirements systematically affected residence time except via increased travel time, although 3 of the 5 birds stayed longer in a patch under higher fixed-ratio values. A “threshold-maximization” model described the data well with a single parameter that was consistent across subjects, procedures, and experiments.     

The control of choice by its consequences

Five pigeons were trained on concurrent variable-interval schedules in which equal rates of reinforcement were always arranged for left- and right-key responses, but different overall rates were signaled by key colors. Sessions began with both keys lit yellow for the instrumental phase. If, after 20 s of this phase, the relative number of responses that had been made to the left key equaled or exceeded .75, both keys changed red for the contingent phase. The contingent phase arranged another concurrent variable-interval schedule for a further 20 s before the instrumental phase was reinstated. However, if preference in the instrumental phase did not exceed .75, the instrumental phase continued for a further 20 s before preference was again compared with the criterion. In Part 1, the reinforcer rate arranged in the instrumental phase was held constant at 4.8 reinforcers per minute, while the reinforcer rate arranged in the contingent phase was varied across conditions from 0 to 19.2 over five steps. In Part 2, reinforcer rates in the contingent phase were kept constant at 36 per minute, while reinforcer rates in the instrumental phase were varied from 0 to 36 over seven steps. Part 3 replicated Part 2 but used reinforcer rates in both phases that were one third of those arranged in Part 2. Measures of choice obtained by summing responses across presentations of the instrumental phase became more extreme toward the left key as the reinforcer rate obtained in the contingent phase was increased (Part 1) and as the reinforcer rate obtained in the instrumental phase was decreased (Parts 2 and 3). Changes in these measures of choice were accompanied by systematic changes in the relative frequency with which the criterion was exceeded. Changes in both these measures were correlated with changes in the relative frequency with which subjects responded exclusively to the left key. These results are discussed with respect to the two choices that were concurrently available in this procedure and the response alternatives that might constitute the concurrent operants in each choice.     

Delayed signal detection, differential reinforcement, and short-term memory in the pigeon.

In two discrete-trial delayed-detection experiments, six pigeons were trained on dependent concurrent variable-interval schedules. Pecking a red side key was reinforced when the brighter of two white lights (S1) had been presented on the center key, and pecking a green side key was reinforced when the duller of two white lights (S2) had been presented on the center key. Incorrect responses were red side-key pecks following S2 presentations and green side-key pecks following S1 presentations; these resulted in three-second blackouts. In Experiment 1, the time between presentation of S1 or S2 on the center key and the onset of the red and green side keys was varied nonsystematically from 0.06 seconds to 19.69 seconds across experimental conditions. Stimulus discriminability decreased as the stimulus-choice delay increased. A rectangular-hyperbolic function better described this decrease in discriminability over time than did a negative-exponential function. In Experiment 2, at each of three stimulus-choice delays (0.06, 3.85, and 10.36 seconds), relative reinforcer frequency for correct responses to the red and green side keys was varied by changing the values of the dependent concurrent variable-interval schedules. The sensitivity of choice to relative reinforcer frequency was independent of the decrease in stimulus discriminability with increasing stimulus-choice delay.     

Mothers' attributions and expectancies regarding their conduct-disordered children

As an extension of Patterson's family coercion model, we hypothesized that parental attributions about the causes of child misbehavior and parental expectancies concerning the effectiveness of parenting techniques are involved in the establishment and maintenance of coercive exchanges. Mothers of 40 conduct-disordered children and 40 matched control children completed questionnaires measuring their attributions regarding the causes of their children's misbehavior and their expectations concerning the general and personal effectiveness of parenting techniques. Results supported the hypotheses: parents of conduct-disordered children were more likely to regard their children's misbehavior as intentional and to attribute it to stable, global causes beyond the parents' control. They also were less likely to see their own parenting as effective. We speculate that these parents hold cognitive stances of blame and helplessness that contribute to aversive parent behavior as well as to parent withdrawal in the face of escalating child aggressiveness.This article is based on a doctoral dissertation conducted by Anne Davison Baden while at Peabody College of Vanderbilt University, and was presented in part at the annual meeting of the American Psychological Association, New Orleans, August 1989.     

Independence of response force and reinforcement rate on concurrent variable-interval schedule performance

Five pigeons were trained over 43 experimental conditions on a variety of concurrent variable-interval schedules on which the forces required on the response keys were varied. The results were well described by the generalized matching law with log reinforcement ratios and log force ratios exerting independent (noninteractive) effects on preference. A further analysis using the Akaike criterion, an information-theoretic measure of the efficiency of a model, showed that overall reinforcement rate and overall force requirement did not affect preference. Unlike reinforcement rate changes, force requirement increases did not change the response rate on the alternate key, and an extension of Herrnstein's absolute response rate function for force variation on a single variable-interval schedule is suggested.     

Sensitivity to reinforcement in concurrent arithmetic and exponential schedules

The generalized matching law states that the logarithm of the ratio of responses emitted or time spent responding in concurrent variable-interval schedules is a linear function of the logarithm of the ratio of reinforcements obtained. The slope of this relation, sensitivity to reinforcement, varies about 1.0 but has been shown to be different when obtained in different laboratories. The present paper analyzed the results from 18 experiments on concurrent variable-interval schedule performance and showed that response-allocation sensitivity to reinforcement was significantly smaller when arithmetic, rather than exponential, progressions were used to produce variable-interval schedules. There were no differences in time-allocation sensitivity between the two methods of constructing variable-interval schedules. Since the two laboratories have consistently used different methods for constructing variable-interval schedules, the differences in obtained sensitivities to reinforcement are explained. The reanalysis suggests that animals may be sensitive to differences in the distribution of reinforcements in time.