Response strength in multiple periodic and aperiodic schedules

Responding in multiple periodic and aperiodic schedules of equal mean reinforcement rate was examined during extinction, satiation, and in the presence of various free-food schedules. In Experiments I and II, pigeons were trained on multiple variable-interval–fixed-interval schedules. Decreases in the rate of responding due to extinction, satiation, or food schedules were approximately equal regardless of the temporal pattern of reinforcer presentation. In Experiment III, pigeons responded on a two-component multiple schedule in which each component was a two-member homogeneous response chain terminating in a fixed-interval schedule during one component and in a variable-interval schedule during the other. The length of both terminal links was varied over a series of conditions. Initial-link responding in the fixed-interval component was reduced more by increasing terminal-link length than was initial-link responding in the variable-interval component. However, no differences in resistance to satiation and extinction were obtained across the fixed and variable components. If the relative decrease in responding produced by satiation and extinction is used as an index of the “value” of the conditions maintaining responding, then these data suggest that fixed and variable schedules of equal mean length are equally valued. This conclusion, however, is not consistent with findings of preference for variable over fixed schedules obtained in studies using concurrent-chain procedures.     

Alternative fixed-ratio fixed-interval schedules of reinforcement

Five rats were trained under alternative fixed-ratio fixed-interval schedules, in which food reinforcement was provided for the completion of either a fixed-ratio or a fixed-interval requirement, whichever was met first. Overall response rate and running rate (the rate of responding after the postreinforcement pause) decreased for all subjects as the fixed-ratio value increased. As the proportion of reinforcements obtained from the fixed-ratio component increased and the alternative schedule approached a simple fixed ratio, overall response rate and running rate both increased; conversely, as the proportion of reinforcements obtained from the fixed-interval component increased and the alternative schedule approached a simple fixed interval, response rates decreased. Postreinforcement pause length increased linearly as the average time between reinforcements increased, regardless of the schedule parameters. A break-run pattern of responding was predominant at low- and medium-valued fixed ratios. All subjects displayed at least occasional positively accelerated responding within interreinforcement intervals at higher fixed-ratio values.     

A stochastic model for test-retest correlations

A simple stochastic model is formulated in order to determine the optimal time between the first test and the second test when the test-retest method of assessing reliability is used. A forgetting process and a change in true score process are postulated. The optimal time between tests is derived by maximizing the probability that the respondent has not remembered the response on the first test and has not had a change in true score. The resulting test-retest correlation is then found to be a linear function of the true reliability of the test, where the slope of this function is the key probability of not remembering and having no change in true score. Some numerical examples and suggestions for using the results in empirical studies are given. Specific recommendations are presented for improved design and analysis of intentions data.This research was made possible by a grant from the Center for Food Policy Research, Graduate School of Business, Columbia University, New York, New York, 10027.     

Timing the second response in two-response avoidance.

Rats were trained on a free-operant avoidance task requiring two lever presses within R seconds, with the opportunity for each response distinguished by differing stimuli. Response latencies at a variety of response-shock intervals were found to be proportional to the time available for the response. These results are shown to be consonant with a scalar expectancy model of timing behavior.     

Choice as a function of local versus molar reinforcement contingencies.

Rats were trained on a discrete-trial probability learning task. In Experiment 1, the molar reinforcement probabilities for the two response alternatives were equal, and the local contingencies of reinforcement differentially reinforced a win-stay, lose-shift response pattern. The win-stay portion was learned substantially more easily and appeared from the outset of training, suggesting that its occurrence did not depend upon discrimination of the local contingencies but rather only upon simple strengthening effects of individual reinforcements. Control by both types of local contingencies decreased with increases in the intertrial interval, although some control remained with intertrial intervals as long as 30 s. In Experiment 2, the local contingencies always favored win-shift and lose-shift response patterns but were asymmetrical for the two responses, causing the molar reinforcement rates for the two responses to differ. Some learning of the alternation pattern occurred with short intertrial intervals, although win-stay behavior occurred for some subjects. The local reinforcement contingencies were discriminated poorly with longer intertrial intervals. In the absence of control by the local contingencies, choice proportion was determined by the molar contingencies, as indicated by high exponent values for the generalized matching law with long intertrial intervals, and lower values with short intertrial intervals. The results show that when molar contingencies of reinforcement and local contingencies are in opposition, both may have independent roles. Control by molar contingencies cannot generally be explained by local contingencies.     

Sensory superstition on multiple interval schedules.

Pigeons were exposed to multiple schedules in which an irregular repeating sequence of five stimulus components was correlated with the same reinforcement schedule throughout. Stable, idiosyncratic, response-rate differences developed across components. Components were rank-ordered by response rate; an approximately linear relation was found between rank order and the deviation of mean response rate from the overall mean rate. Nonzero slopes of this line were found for multiple fixed-interval and variable-time schedules and for multiple variable-interval schedules both when number of reinforcements was the same in all components and when it varied. The steepest function slopes were found in the variable schedules with relatively long interfood intervals and relatively short component durations. When just one stimulus was correlated with all components of a multiple variable-interval schedule, the slope of the line was close to zero. The results suggest that food-rate differences may be induced initially by different reactions to the stimuli and subsequently maintained by food.     

Concurrent schedules: a quantitative relation between changeover behavior and its consequences

Data from several published experiments on concurrent variable-interval schedules were analyzed with respect to the effects of changeover delay on the time spent responding on a schedule before changing to an alternate schedule: i.e., the interchangeover time. Interchangeover time increases as the duration of the changeover delay increases, and the present analysis shows that a power function describes the relation. The power relation applied in spite of numerous differences in the experiments: different variable-interval schedules for the concurrent pairs; equal or unequal reinforcement rates for the schedules of the concurrent pairs; different durations of the changeover delay; response-dependent or response-independent reinforcers; pigeons or rats as subjects; different reinforcers. A power function also described the data in experiments where the changeover incurred a timeout, where a fixed ratio was required to changeover, and also when asymmetrical changeover delays were used.     

Fixed-interval responding under second-order schedules of food presentation or cocaine injection.

Squirrel monkeys operated a key under second-order schedules in which every tenth completion of a 5-minute fixed interval resulted in either presentation of food or intravenous injection of cocaine. When a 2-second light was presented at the completion of the component fixed-interval schedules, positively accelerated responding developed and was maintained in each component. Over a tenfold range of doses of cocaine(30 to 300 microgram/kg/injection) and amounts of food (0.75 to 7.5 g/presentation); the second-order schedule of cocaine injection maintained higher average rates of responding than the second-order schedule of food presentation. Substituting saline for cocaine or eliminating food presentation decreased average rates of responding. When no stimulus change occurred at the completion of the first nine component fixed-interval schedules, but the 2-second light and food presentation or cocaine injection still occurred after the tenth component, only low and relatively constant rates of responding were maintained in each component. Patterns of responding characteristic of 5-minute fixed-interval schedules were maintained by the 2-second light paired with either cocaine injection or food presentation, though the maximum frequency of cocaine injection or food presentation was less than once per 50 minutes.     

On Herrnstein's equation and related forms

In 1970, Herrnstein proposed a simple equation to describe the relation between response and reinforcement rates on interval schedules. Its empirical basis is firm, but its theoretical foundation is still uncertain. Two approaches to the derivation of Herrnstein's equation are discussed. It can be derived as the equilibrium solution to a process model equivalent to familiar linear-operator learning models. Modifications of this approach yield competing power-function formulations. The equation can also be derived from the assumption that response strength is proportional to reinforcement rate, given that there is a ceiling on response rate. The proportional relation can, in turn, be derived from a threshold assumption equivalent to Shimp's “momentary maximizing”. This derivation implies that the two parameters of Herrnstein's equation should be correlated, and may explain its special utility in application to internal schedules.     

A comparison of frequency, interval, and time-sampling methods of data collection

Data representing high, medium, and low response rates in constant and nonconstant patterns were generated by electromechanical equipment to determine whether the same data collected by time-sampling, interval recording, and frequency recording would be represented similarly by each method. Results indicated: (1) that time-sampling provided an extremely inaccurate estimate of responding, and (2) that interval recording accurately represented responding of low and medium rates, but grossly underestimated high-rate responding.