Obtained versus programmed reinforcement practical considerations in the treatment of escape-reinforced aggression

This investigation provides a preliminary examination of the difference between programmed and obtained reinforcement rates and its potential influence during treatment of aggression in a natural setting. Following a functional analysis that suggested that the aggression of a boy with autism was negatively reinforced, intervention was implemented by the boy's mother. Concurrent fixed-ratio (FR) 1 FR 1 schedules of escape were arranged for manding and aggression. When mands failed to compete effectively with aggression, obtained reinforcement ratios were calculated; these indicated that obtained reinforcement varied from the programmed schedule for aggression but not for mands. Increasing the rate of prompts for mands resulted in an increase in mands and a decrease in aggression to near-zero levels.     

The effect of conditioned reinforcement rate on choice: a review

We review the nature of conditioned reinforcement, including evidence that conditioned reinforcers maintain choice behavior in concurrent schedules and that they elevate responding in the terminal links of concurrent‐chains schedules. A question has resurfaced recently: Do theories of choice in concurrent‐chains schedules need to include a term reflecting greater preference for higher rates of conditioned reinforcement? The review of several studies addressing this point suggests that such a term is inappropriate. Elevated rates of conditioned reinforcement (and responding) in the terminal links of concurrent‐chains schedules do not lead to greater preference in the initial link leading to the higher rate of conditioned reinforcement. If anything, the opposite preference is likely to occur. This result is not surprising, since the additional putative conditioned reinforcers in the terminal link are not correlated with a reduction in time to primary reinforcement nor with an increase in value.     

Choosing among multiple alternatives: Relative and overall reinforcer rates

Choice behavior among two alternatives has been widely researched, but fewer studies have examined the effect of multiple (more than two) alternatives on choice. Two experiments investigated whether changing the overall reinforcer rate affected preference among three and four concurrently scheduled alternatives. Experiment 1 trained six pigeons on concurrent schedules with three alternatives available simultaneously. These alternatives arranged reinforcers in a ratio of 9:3:1 with the configuration counterbalanced across pigeons. The overall rate of reinforcement was varied across conditions. Preference between the pair of keys arranging the 9:3 reinforcer ratio was less extreme than the pair arranging the 3:1 reinforcer ratio regardless of overall reinforcer rate. This difference was attributable to the richer alternative receiving fewer responses per reinforcer than the other alternatives. Experiment 2 trained pigeons on concurrent schedules with four alternatives available simultaneously. These alternatives arranged reinforcers in a ratio of 8:4:2:1, and the overall reinforcer rate was varied. Next, two of the alternatives were put into extinction and the random interval duration was changed from 60 s to 5 s. The ratio of absolute response rates was independent of interval length across all conditions. In both experiments, an analysis of sequences of visits following each reinforcer showed that the pigeons typically made their first response to the richer alternative irrespective of which alternative was just reinforced. Performance on these three‐ and four‐alternative concurrent schedules is not easily extrapolated from corresponding research using two‐alternative concurrent schedules.     

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.     

Earning and obtaining reinforcers under concurrent interval scheduling

Contingencies of reinforcement specify how reinforcers are earned and how they are obtained. Ratio contingencies specify the number of responses that earn a reinforcer, and the response satisfying the ratio requirement obtains the earned reinforcer. Simple interval schedules specify that a certain time earns a reinforcer, which is obtained by the first response after the interval. The earning of reinforcers has been overlooked, perhaps because simple schedules confound the rates of earning reinforcers with the rates of obtaining reinforcers. In concurrent variable-interval schedules, however, spending time at one alternative earns reinforcers not only at that alternative, but at the other alternative as well. Reinforcers earned for delivery at the other alternative are obtained after changing over. Thus the rates of earning reinforcers are not confounded with the rate of obtaining reinforcers, but the rates of earning reinforcers are the same at both alternatives, which masks their possibly differing effects on preference. Two experiments examined the separate effects of earning reinforcers and of obtaining reinforcers on preference by using concurrent interval schedules composed of two pairs of stay and switch schedules (MacDonall, 2000). In both experiments, the generalized matching law, which is based on rates of obtaining reinforcers, described responding only when rates of earning reinforcers were the same at each alternative. An equation that included both the ratio of the rates of obtaining reinforcers and the ratio of the rates of earning reinforcers described the results from all conditions from each experiment.     

Response to name in children with autism: Treatment,generalization, and maintenance

Deficits in response to name (RTN) are an early indicator of autism spectrum disorder (ASD), and RTN is a treatment goal in many early intervention curricula for children with ASD. However, little research has empirically evaluated methods for increasing RTN in children with ASD. We evaluated a series of conditions designed to increase RTN for 4 children with ASD using a multielement experimental design. The schedules of tangible reinforcement were thinned after mastery and generalization was tested across people and contexts. Tangible reinforcers were necessary to increase RTN for all 4 participants, and the schedule of reinforcement was successfully thinned with all participants after intervention. Generalization was also observed across people and experimental contexts.     

A local model of concurrent performance

Concurrent procedures may be conceptualized as consisting of two pairs of schedules with only one pair operating at a time. One schedule of each pair arranges reinforcers for staying in the current alternative, and the other schedule arranges reinforcers for switching to the other alternative. These pairs alternate operation as the animal switches between choices. This analysis of the contingencies suggests that variables operating within an alternative produce behavior that conforms to the generalized matching law. Rats were exposed to one pair of stay and switch schedules in each condition, and the probabilities of reinforcement varied across conditions. Both run length and visit duration were power functions of the ratio of the probabilities of reinforcement for staying and switching. The local model, a model of performance on concurrent procedures, was derived from this power function. Performance on concurrent schedules was synthesized from the performances on the separate pairs. Both the generalized matching law and the local model fitted the synthesized concurrent performances. These results are consistent with the view that the contingencies in the alternative, the probability of stay and switch reinforcement, are responsible for performance consistent with the generalized matching law. These results are compatible with momentary maximizing and molar maximizing accounts of concurrent performance. Models of concurrent performance that posit comparisons among the alternatives are not easily applied to these results.     

Preference for reinforcers under progressive- and fixed-ratio schedules: a comparison of single and concurrent arrangements

Progressive-ratio (PR) schedules were used to identify the break point (i.e., the last schedule value completed) for 2 reinforcers under single and concurrent schedules. After the respective break points were established, the same reinforcers were presented under concurrent fixed-ratio (FR) schedules that were yoked to the break points obtained with the PR schedules. Results suggested that the participants responded more for the high-preference item than for the low-preference item, regardless of the presentation arrangement (single or concurrent presentations). This pattern of responding was maintained when the reinforcers were presented under dissimilar FR schedules. The results suggest that responding for differentially preferred stimuli may vary as a function of differences in schedule requirements.     

Within-session Changes In Responding During Concurrent Variable-interval Schedules

Five rats and 4 pigeons responded for food delivered by several concurrent variable-interval schedules. The sum of the rates of reinforcement programmed for the two components varied from 15 to 480 reinforcers per hour in different conditions. Rates of responding usually changed within the experimental session in a similar manner for the two components of each concurrent schedule. The within-session changes were similar to previously reported changes during simple schedules that provided rates of reinforcement equal to the sum of all reinforcers obtained from the concurrent schedules. The number of changeovers also changed within sessions in a manner similar to the changes in instrumental responding. These results suggest that changeovers are governed by the same variables that govern instrumental responding. They also suggest that the within-session change in responding during each component of a concurrent schedule is determined by approximately the sum of the reinforcers obtained from both components when both components provide the same type of reinforcer.     

Nonstable concurrent choice in pigeons

Six pigeons were trained on concurrent variable-interval schedules in which the arranged reinforcer ratios changed from session to session according to a 31-step pseudorandom binary sequence. This procedure allows a quantitative analysis of the degree to which performance in an experimental session is affected by conditions in previous sessions. Two experiments were carried out. In each, the size of the reinforcer ratios arranged between the two concurrent schedules was varied between 31-step conditions. In Experiment 1, the concurrent schedules were arranged independently, and in Experiment 2 they were arranged nonindependently. An extended form of the generalized matching law described the relative contribution of past and present events to present-session behavior. Total performance in sessions was mostly determined by the reinforcer ratio in that session and partially by reinforcers that had been obtained in previous sessions. However, the initial exposure to the random sequence produced a lower sensitivity to current-session reinforcers but no difference in overall sensitivity to reinforcement. There was no evidence that the size of the reinforcer ratios available on the concurrent schedules affected either overall sensitivity to reinforcement or the sensitivity to reinforcement in the current session. There was also no evidence of any different performance between independent and nonindependent scheduling. Because of these invariances, this experiment validates the use of the pseudorandom sequence for the fast determination of sensitivity to reinforcement.     

ALTERNATIVE REINFORCEMENT INCREASES RESISTANCE TO CHANGE: PAVLOVIAN OR OPERANT CONTINGENCIES?

Two multiple-schedule experiments with pigeons examined the effect of adding food reinforcement from an alternative source on the resistance of the reinforced response (target response) to the decremental effects of satiation and extinction. In Experiment 1, key pecks were reinforced by food in two components according to variable-interval schedules and, in some conditions, food was delivered according to variable-time schedules in one of the components. The rate of key pecking in a component was negatively related to the proportion of reinforcers from the alternative (variable-time) source. Resistance to satiation and extinction, in contrast, was positively related to the overall rate of reinforcement in the component. Experiment 2 was conceptually similar except that the alternative reinforcers were contingent on a specific concurrent response. Again, the rate of the target response varied as a function of its relative reinforcement, but its resistance to satiation and extinction varied directly with the overall rate of reinforcement in the component stimulus regardless of its relative reinforcement. Together the results of the two experiments suggest that the relative reinforcement of a response (the operant contingency) determines its rate, whereas the stimulus-reinforcement contingency (a Pavlovian contingency) determines its resistance to change.     

An invariant relation between changing over and reinforcement

Although concurrent schedules may arrange reinforcers irregularly, relatively large numbers of reinforcers are obtained when an animal changes from one schedule to the other. This paper proposes a quantitative relation that predicts the proportion of reinforcers obtained when an animal is working on a schedule and the proportion when the animal changes over to a schedule. Basically the relation states that the number of reinforcers obtained while an animal works on a schedule varies directly with the relative amount of time spent working on that schedule; and the number of reinforcers obtained when an animal changes to a schedule varies directly with the relative amount of time spent on the alternate schedule. An important aspect of this relation is that when relative reinforcement rates are less than .50, more reinforcers are obtained just after an animal changes to a schedule than at all other times when this schedule is engaged. Data obtained both from a stat-bird and a live pigeon were in close agreement with the quantitative predictions. The relation between changing over and reinforcement held across several procedural changes that included changes in relative reinforcement rate, changes from independent to interdependent scheduling procedures, and changes in the variable-interval reinforcement distributions. The results are discussed in terms of the effects of the local distribution of reinforcement on responding. The local reinforcement distribution can affect local response rates and affects the resulting matching relation. This arrangement has implications for explanations of choice.     

Contrast and induction in multiple schedules of discrete-trial concurrent reinforcement

Three pigeons were exposed to two-key discrete-trial concurrent schedules of reinforcement. Red and white key colors alternated irregularly and the assignment of reinforcers depended on key color. The red-key schedules were held constant, with the scheduled relative frequency of reinforcement for left-key pecks set at 0.75, while the white-key schedules varied. When the location of white-key reinforcement was changed from one side to the other, while its overall frequency was constant, red-key choices shifted in the same direction as white-key choices, an induction effect. When the overall frequency of white-key reinforcement was changed while its location remained constant, red key choices shifted in a direction opposite to white-key choices, a contrast effect. Both induction and contrast effects were clearer when the overall frequency of red-key reinforcement was reduced. These data demonstrate that the allocation of responding may exhibit schedule interaction effects similar to those commonly reported for response rate.     

Choice, changeover, and travel: A quantitative model

Six pigeons were trained on concurrent variable-interval schedules in which responding on fixed-interval schedules was required to give access to the alternate schedule. Responding on the concurrent schedules was not allowed, after changing over had commenced, until the changeover schedule had been completed. In Parts 1 to 3 of the experiment, the changeover fixed-interval schedules were equal and were 0 s, 10 s, and 20 s, respectively. In each part, the relative frequency of reinforcement obtained on the concurrent schedules was varied over at least five conditions. In Part 4, the concurrent schedules were equal, and one changeover fixed-interval schedule was twice the other. Under these conditions, the absolute sizes of the changeover schedules were varied. Increasing the changeover requirement from 0 s to 10 s (Parts 1 and 2) resulted in increases in the sensitivity of behavior allocation to reinforcers obtained, but no further increase was obtained when the changeover schedules were increased to 20 s (Part 3). In Part 4, performance was biased towards the concurrent schedule that took less time to enter. These results are consistent with a subtractive punishment model of travel in which the degree of punishment is measured by the number of reinforcers apparently lost from a schedule when the subject changes to that schedule. Absolute times spent on the main keys could be accurately described by a previous model of changeover performance.     

Sensitivity to relative reinforcer rate in concurrent schedules: independence from relative and absolute reinforcer duration

Twelve pigeons responded on two keys under concurrent variable-interval (VI) schedules. Over several series of conditions, relative and absolute magnitudes of reinforcement were varied. Within each series, relative rate of reinforcement was varied and sensitivity of behavior ratios to reinforcer-rate ratios was assessed. When responding at both alternatives was maintained by equal-sized small reinforcers, sensitivity to variation in reinforcer-rate ratios was the same as when large reinforcers were used. This result was observed when the overall rate of reinforcement was constant over conditions, and also in another series of concurrent schedules in which one schedule was kept constant at VI ached 120 s. Similarly, reinforcer magnitude did not affect the rate at which response allocation approached asymptote within a condition. When reinforcer magnitudes differred between the two responses and reinforcer-rate ratios were varied, sensitivity of behavior allocation was unaffected although response bias favored the schedule that arranged the larger reinforcers. Analysis of absolute response rates ratio sensitivity to reinforcement occurrred on the two keys showed that this invariance of response despite changes in reinforcement interaction that were observed in absolute response rates on the constant VI 120-s schedule. Response rate on the constant VI 120-s schedule was inversely related to reinforcer rate on the varied key and the strength of this relation depended on the relative magnitude of reinforcers arranged on varied key. Independence of sensitivity to reinforcer-rate ratios from relative and absolute reinforcer magnitude is consistent with the relativity and independence assumtions of the matching law.     

Economic substitutability of electrical brain stimulation, food, and water.

Concurrent variable-ratio schedules of electrical brain stimulation, food, and water were paired in various combinations as reinforcement of rats' lever presses. Relative prices of the concurrent reinforcers were varied by changing the ratio of the response requirements on the two levers. Economic substitutability, measured by the sensitivity of response ratio to changes in relative price, was highest with brain stimulation reinforcement of presses on both levers and lowest with food reinforcement of presses on one lever and water reinforcement of presses on the other. Substitutability with brain stimulation reinforcement of presses on one lever and either food or water reinforcement for presses on the other was about as high as with brain stimulation for presses on both levers. Electrical brain stimulation for rats may thus serve as an economic substitute for two reinforcers, neither of which is substitutable for the other.     

ON THE RELATIVE REINFORCING EFFECTS OF CHOICE AND DIFFERENTIAL CONSEQUENCES

Research on the reinforcing effects of providing choice-making opportunities to individuals with developmental disabilities (i.e., allowing them to choose reinforcers or tasks) has produced inconsistent results, perhaps because the mechanisms underlying such effects remain unclear. Choice may produce a reinforcement effect because it is correlated with differential consequences (i.e., choice may increase one's access to higher preference stimuli), or it may have reinforcement value independent of (or in addition to) the chosen stimulus. In Experiment 1, we used a concurrent-operants arrangement to assess preference for a choice condition (in which participants selected one of two available reinforcers) relative to a no-choice condition (in which the therapist selected the same reinforcers on a yoked schedule). All 3 participants preferred the choice option. In Experiment 2, we altered the schedules so that the participant selected one of two lower preference reinforcers in the choice condition, whereas the therapist selected a higher preference stimulus for the participant either half or all of the time in the no-choice condition. Participants typically allowed the therapist to select reinforcers for them (i.e., they allocated responding to the no-choice condition) when it resulted in greater access to higher preference stimuli.     

Temporal constraint on choice: Sensitivity and bias in multiple schedules

In multiple schedules of reinforcement, ratios of responses in successive components are relatively insensitive to ratios of obtained reinforcers. An analysis is proposed that attributes changes in absolute response rates to concurrent interactions between programmed reinforcement and extraneous reinforcement in other components. The analysis predicts that ratios of responses in successive components vary with reinforcer ratios, qualified by a term describing the reinforcement context, that is, programmed and extraneous reinforcers. Two main predictions from the analysis were confirmed in an experiment in which pigeons' responses were reinforced in the components of a multiple schedule and analog extraneous reinforcement was scheduled for an alternative response in each component. Sensitivity of response and time ratios to reinforcer ratios in the multiple schedules varied as a function of the rate of extraneous reinforcers. Bias towards responding in one component of the multiple schedule varied as an inverse function of the ratios of extraneous reinforcer rate in the two components. The data from this and previous studies of multiple-concurrent performance were accurately predicted by our analysis and supported our contention that the allocation of behavior in multiple-schedule components depends on the relative values of concurrently-available reinforcers within each component.     

Melloration and maximization of reinforcement minus costs of behavior

Eight pigeons were exposed to independent concurrent schedules. Concurrent variable-interval 60-second variable-interval 60-second schedules were presented to one group of four subjects. Following baseline training, a limited hold was added to one of the schedules and the duration of the hold was decreased in successive conditions. Concurrent variable-interval 120-second variable-interval 40-second schedules were presented to another group of four subjects. These subjects were first exposed to decreasing durations of a limited hold in the variable-interval 40-second component. After replication of the baseline, a limited hold in the variable-interval 120-second component was decreased in duration. The initial durations of the holds were determined from the subjects' responding in the baseline conditions. A duration was chosen such that approximately 25% of the scheduled reinforcers would be canceled if responding remained unchanged.

Approximate matching of time proportions and reinforcement proportions was observed when the limited hold was added to the variable-interval 60-second schedule and when the limited hold was added to the variable-interval 40-second schedule. Time proportions were less extreme than reinforcement proportions when the limited hold operated in a variable-interval 120-second schedule. Overall reinforcement rates tended to decrease with continued training in concurrent schedules with a limited hold. Absolute deviations from time matching also decreased. The results provide evidence against the principle of reinforcement maximization, and support Herrnstein and Vaughan's (1980) melioration hypothesis.