Molecular contingencies in schedules of intermittent punishment

In two experiments, key pecking of pigeons was maintained by a variable-interval 180-s schedule of food presentation. Conjointly, a second schedule delivered response-dependent electric shock. In the first experiment, shocks were presented according to either a variable-interval or a nondifferential interval-percentile schedule. The variable-interval shock schedule differentially delivered shocks following long interresponse times. Although the nondifferential shock schedules delivered shocks less differentially with respect to interresponse times, the two shock schedules equally reduced the relative frequency of long interresponse times. The second experiment differentially shocked long or short interresponse times in different conditions, with resulting decreases in the relative frequency of the targeted interresponse times. These experiments highlight the importance of selecting the appropriate level of analysis for the interaction of behavior and environment. Orderly relations present at one level of analysis (e.g., interresponse times) may not be revealed at other levels of analysis (e.g., overall response rate).     

Inelastic supply: An economic approach to simple interval schedules

Economic theory predicts an inverse relationship between the quantity of a commodity supplied to the marketplace and the equilibrium market price of that commodity. This prediction was tested in three experiments. Pigeons responded on simple variable-interval schedules, and quantity of reinforcement supplied was varied in a different way in each experiment. In Experiment 1, quantity supplied was varied by manipulating reinforcement rate while keeping session length constant. In Experiment 2, quantity supplied was varied by manipulating reinforcement rate while keeping reinforcers per session constant. In Experiment 3, quantity supplied was varied by manipulating reinforcer magnitude while keeping number of reinforcers constant. As predicted by economic theory, the obtained behavioral cost (responses per reinforcer) increased as supply decreased. The results could not be explained by simple artifacts such as satiation and time available to respond. In addition, the function relating response rate to reinforcement rate was bitonic in 7 of 9 animals in Experiments 1 and 2, which supports economic and regulatory theories over more traditional reinforcement theories.     

Choice between repleting/depleting patches: A concurrent-schedule procedure

Six pigeons responded on two concurrently available keys that defined patches with the following characteristics. Reinforcer stores repleted on a patch as a linear function of time when the bird had last responded to the other patch, or else did not replete. Repletion schedules thus timed only when the bird was absent from the patch. Reinforcer stores on a patch could be depleted and reinforcers obtained, again as a linear function of time, when the bird responded on a key. Depletion schedules thus timed only when the birds were present at a patch. Experiment 1 investigated changing relative depletion rates when repletion rates were constant and equal (Part 1) and changing relative repletion rates when the depletion rates were constant and equal (Part 2). Response- and time-allocation ratios conformed to a generalized matching relation with obtained reinforcer ratios, and there appeared to be no control by the size of the reinforcer stores. In Experiment 2, absolute depletion rates were varied with a pair of unequal repletion rates (Part 3), and absolute repletion rates were varied with a pair of unequal depletion rates (Part 4). Dwell times in the patches were not affected by either variation. Melioration theory predicted the results of Experiment 1 quite closely but erroneously predicted changing dwell times in Experiment 2. Molar maximization theory did not accurately predict the results of either experiment.     

Fixed-ratio pausing: Joint effects of past reinforcer magnitude and stimuli correlated with upcoming magnitude

Pigeons responded on fixed-ratio schedules ending in small or large reinforcers (grain presentations of different duration) interspersed within each session. In mixed-schedule conditions, the response key was lit with a single color throughout the session, and pausing was directly related to the past reinforcer (longer pauses after large reinforcers than after small ones). In multiple-schedule conditions, different colors accompanied the ratios ending in small and large reinforcers, and pausing was affected by the upcoming reinforcer as well as the past one. Pauses were shorter before large reinforcers than before small ones, but they continued to be longer after large reinforcers than after small ones. The influence of the past reinforcer was modulated by the magnitude of the upcoming reinforcer; in the presence of the stimulus before the small reinforcer, the effect of the past reinforcer was enhanced relative to its effect in the stimulus before the large reinforcer. These results show that pausing between ratios is jointly determined by two competing factors: past conditions of reinforcement and stimuli correlated with upcoming conditions.     

Discriminability between alternatives in a switching-key concurrent schedule

Six pigeons were trained to discriminate between two intensities of white light in a symbolic matching-to-sample procedure. These stimuli were then used to signal which schedule was available on the main key in a switching-key concurrent schedule. The concurrent schedules led to a symbolic matching-to-sample phase in which the subject identified the concurrent schedule to which it last responded before a reinforcer could be obtained. The concurrent schedules were varied across conditions. Discriminability, measured during the symbolic matching-to-sample performance, was high throughout and did not differ across the two procedures. Performance in the concurrent schedules was like that typically obtained using these schedules. Delays were then arranged between completion of the concurrent schedules and presentations of the symbolic matching-to-sample phase. A series of conditions with an intervening delay of 10 s showed that both concurrent-schedule performance and symbolic matching-to-sample performance were affected by the delay in a similar way; that is, choice responding was closer to indifference.     

Alternating least squares algorithms for simultaneous components analysis with equal component weight matrices in two or more populations

Millsap and Meredith (1988) have developed a generalization of principal components analysis for the simultaneous analysis of a number of variables observed in several populations or on several occasions. The algorithm they provide has some disadvantages. The present paper offers two alternating least squares algorithms for their method, suitable for small and large data sets, respectively. Lower and upper bounds are given for the loss function to be minimized in the Millsap and Meredith method. These can serve to indicate whether or not a global optimum for the simultaneous components analysis problem has been attained.Financial support by the Netherlands organization for scientific research (NWO) is gratefully acknowledged.     

Children's choice: Sensitivity to changes in reinforcer density

Two experiments were carried out in which children's sensitivity to changes in reinforcer density (number of reinforcers per session) was measured in a choice paradigm. In Experiment 1, 24 girls (ages 6, 9, and 12 years) performed on concurrent-chain schedules of reinforcement. The initial links were variable-interval 10-s schedules. One terminal link always gave three tokens after 30 s, but the parameters associated with the other were varied. Independent manipulations of reinforcer size (two tokens or four tokens) and prereinforcement delay (25 s or 65 s) led to equal changes in the relative density of tokens that could be earned on the schedules. Subjects at all ages were sensitive to changes in reinforcer density brought about by changes in reinforcer size, whereas only 3 12-year-olds showed sensitivity to the changes brought about by manipulation of prereinforcer delay. In Experiment 2, titration procedures were used to test the extent of this insensitivity to delay in 32 6- and 12-year-old children. In these procedures, a repeated choice of the large reinforcer increased the delay to its delivery, and a repeated choice of the small reinforcer reduced the delay to the delivery of the large reinforcer. Whereas 6-year-old boys and girls tended to maintain a strong preference for the large reinforcer, so increasing the delay to its delivery, 12-year-olds tended to distribute their responses to both alternatives, thus producing a stable level of delay to the large reinforcer. The results from the two experiments support the idea of two stages in the development of adaptive intertemporal choice.     

A quantitative analysis of chain-schedule performance

Six pigeons were trained with a chain variable-interval variable-interval schedule on the left key and with reinforcers available on the right key on a single variable-interval schedule arranged concurrently with both links of the chain. All three schedules were separately and systematically varied over a wide range of mean intervals. During these manipulations, the obtained reinforcer rates on constant arranged schedules also frequently changed systematically. Increasing reinforcer rates in Link 2 of the chain increased response rates in both links and decreased response rates in the variable-interval schedule concurrently available with Link 2. Increasing Link-1 reinforcer rates increased Link-1 response rates and decreased Link-2 response rates. Increasing reinforcer rates on the right-key schedule decreased response rates in Link 1 of the chain but did not affect the rate in Link 2. The results extend and amplify previous analyses of chain-schedule performance and help define the effects that a quantitative model must describe. However, the complexity of the results, and the fact that constant arranged reinforcer schedules did not necessarily lead to constant obtained reinforcer rates, precluded a quantitative analysis.     

Connectionist models of conditioning: A tutorial

Models containing networks of neuron-like units have become increasingly prominent in the study of both cognitive psychology and artificial intelligence. This article describes the basic features of connectionist models and provides an illustrative application to compound-stimulus effects in respondent conditioning. Connectionist models designed specifically for operant conditioning are not yet widely available, but some current learning algorithms for machine learning indicate that such models are feasible. Conversely, designers for machine learning appear to have recognized the value of behavioral principles in producing adaptive behavior in their creations.     

EFFECTS OF WAIT-TIME AND INTERTRIAL INTERVAL DURATIONS ON LEARNING BY CHILDREN WITH MULTIPLE HANDICAPS

We investigated the influence of teacher wait-time and intertrial interval durations on the performance of 4 multiply handicapped students during instruction in 10 skills. Four experimental conditions were evaluated: long wait-time and long intertrial interval, long wait-time and short intertrial interval, short wait-time and long intertrial interval, and short wait-time and short intertrial interval. Instructors attempted to keep short intervals as close as possible to 1 s and long intervals as close as possible to 10 s for both variables. Results showed that student performance was superior under the long wait-time conditions irrespective of the length of the intertrial interval.