Influence of the cost of responding

In three experiments, the effect of costs associated with responding on judgments of the causal effectiveness of the response was examined. In Experiment 1, the temporal interval between outcomes was matched on a variable interval (VI) and a variable ratio (VR) schedule. When each response was made at some “cost,” and outcomes represented some “gain” for the subject, the rating of causal effectiveness for responses was higher on the VR than on the VI schedule. This relationship was absent when the outcome was a triangle Hash. In Experiment 2, the number of responses required per outcome on a VI and a VR schedule were matched, and responses on the VR schedule were rated as more causally effective. In Experiment 3, a VI-to-VR yoking procedure was used. With minimal response costs, judgments were similar on the VI and VR schedules, but with greater response costs, responses performed on the VR schedule were rated as more causally effective than those emitted on the VI schedule.     

Schedules of reinforcement as determinants of human causality judgments and response rates

Experiments examined the effect of relationships between a response and an outcome on human judgments of causal effectiveness. In Experiment 1, the time between outcomes obtained on a variable ratio (VR) schedule became the intervals for a yoked variable interval (VI) schedule. Response rates were higher on the VR than on the VI schedule. In Experiment 2, the number of responses required per outcome on a VR schedule were matched to that on a master VI 20-s schedule. Both ratings of causal effectiveness and response rates were higher in the VR schedule. In Experiment 3, tandem VI fixed-ratio (FR) schedules produced higher rates and judgments than equivalent conjunctive VI FR schedule. In Experiment 4, a VI schedule with a reinforcement requirement for a short interresponse time (IRT) produced higher rates and judgments than a simple VI schedule. These results corroborate the view that schedules are a determinant of both response rates and causal judgments. Few current theories of causal judgment predict this pattern of results.     

The schedule dependency of the signaled reinforcement effect

In Experiment 1, rats leverpressed for food reinforcement on either a variable ratio (VR) 30 schedule or a variable interval (VI) 15-s schedule. One group in each condition received a signal filling a 500-ms delay of reinforcement. This treatment enhanced rates on the VR schedule, and attenuated rates on the VI schedule, relative to the rate seen in an unsignaled control condition. In Experiment 2 there was no delay of reinforcement and the signal and food were presented simultaneously. Attenuated rates of responding were observed on VI schedules with a range of mean interval values (15 to 300 s). Experiment 3 used a range of VR schedules (10 to 150) with simultaneous presentations of signal and food. A signal-induced enhancement of response rate was found at all VR values. In Experiment 4, a signal elevated response rates on a tandem VI VR schedule, but depressed rates on a tandem VR VI schedule, compared to control conditions receiving unsignaled delayed reinforcement. These results are taken to show that the effect of a signal accompanying reinforcement depends upon the nature of the behavior that is reinforced during exposure to a given schedule.     

Effect of local context of responding on human judgment of causality

Two experiments examined the effect of various relationships between a response (pressing the space bar of a computer) and an outcome (a triangle flashing on a screen) on judgments of the causal effectiveness of the response. In Experiment 1, when responses were required to be temporarily isolated from each other prior to an outcome, ratings of the causal effectiveness of the responses were higher than in a condition in which the probability of an outcome following a response was the same but in which no temporal isolation was required. In Experiment 2, when a number of responses were required to be emitted temporally close to the outcome, ratings of the causal effectiveness of the responses were lower than in a condition in which the probability of an outcome following a response was the same but in which no temporal proximity was required. These results suggest that, in addition to the overall probability that an outcome will follow a response, the local context of responding at the time an outcome is presented is critical in influencing ratings of causal effectiveness.     

Free-operant performance on variable interval schedules with a linear feedback loop: no evidence for molar sensitivities in rats

Four experiments examined rats' sensitivity to molar and molecular factors on instrumental schedules of reinforcement. Rats were exposed to a variable interval schedule with a positive feedback loop (VI+), such that faster responding led to a shorter interreinforcement interval. In Experiments 1 and 2, rats responded faster on a variable response (VR) schedule than on either a VI schedule matched for reinforcement rate or a VI+ schedule matched for the feedback function. In Experiment 3, rats responded no differently on a VI schedule than they did on a VI+ schedule with equated rates of reinforcement. In Experiment 4, rats responded faster on a VI+ schedule with an interresponse time requirement yoked to that experienced on a VR schedule, than on a VI+ schedule with the same feedback function as the VR schedule. Taken together these results suggest that rats are more sensitive to the molecular than the molar properties of the schedules.     

On the primacy of molecular processes in determining response rates under variable-ratio and variable-interval schedules

This study focused on variables that may account for response-rate differences under variable-ratio (VR) and variable-interval (VI) schedules of reinforcement. Four rats were exposed to VR, VI, tandem VI differential-reinforcement-of-high-rate, regulated-probability-interval, and negative-feedback schedules of reinforcement that provided the same rate of reinforcement. Response rates were higher under the VR schedule than the VI schedule, and the rates on all other schedules approximated those under the VR schedule. The median reinforced interresponse time (IRT) under the VI schedule was longer than for the other schedules. Thus, differences in reinforced IRTs correlated with differences in response rate, an outcome suggestive of the molecular control of response rate. This conclusion was complemented by the additional finding that the differences in molar reinforcement-feedback functions had little discernible impact on responding.     

Rats' performance on variable-interval schedules with a linear feedback loop between response rate and reinforcement rate

Three experiments investigated whether rats are sensitive to the molar properties of a variable-interval (VI) schedule with a positive relation between response rate and reinforcement rate (i.e., a VI+ schedule). In Experiment 1, rats responded faster on a variable ratio (VR) schedule than on a VI+ schedule with an equivalent feedback function. Reinforced interresponse times (IRTs) were shorter on the VR as compared to the VI+ schedule. In Experiments 2 and 3, there was no systematic difference in response rates maintained by a VI+ schedule and a VI schedule yoked in terms of reinforcement rate. This was found both when the yoking procedure was between-subject (Experiment 2) and within-subject (Experiment 3). Mean reinforced IRTs were similar on both the VI+ and yoked VI schedules, but these values were more variable on the VI+ schedule. These results provided no evidence that rats are sensitive to the feedback function relating response rate to reinforcement rate on a VI+ schedule.     

Effect of a signalled delay between an action and outcome on human judgement of causality

Three experiments examined the influence of a stimulus inserted between an action (pressing the space bar of a computer) and an associated delayed outcome (a triangle lighting up on the screen) on ratings of the causal effectiveness of that action. In Experiment 1, subjects rated an action that produced an outcome immediately as more causally effective than an action that produced a delayed outcome. The rating of the causal effectiveness of an action that produced a delayed outcome in which the delay was filled by a stimulus was higher than the rating of actions that produced the outcome after an unsignalled delay. In Experiment 2, the effect of a stimulus presented uncorrelated with the action or the outcome was examined and found not to enhance the rating of causal effectiveness of an action that produced a delayed outcome. In Experiment 3, the degree of correlation between the stimulus and the consequence was examined. Ratings of the causal effectiveness of the action were greater the higher percentage of delay intervals that were signalled.     

Response rate viewed as engagement bouts: effects of relative reinforcement and schedule type.

The rate of a reinforced response is conceptualized as a composite of engagement bouts (visits) and responding during visits. Part I of this paper describes a method for estimating the rate of visit initiations and the average number of responses per visit from log survivor plots: the proportion) of interresponse times (IRTs) longer than some elapsed time (log scale) plotted as a function of elapsed time. In Part 2 the method is applied to IRT distributions from rats that obtained food pellets by nose poking a lighted key under various multiple schedules of reinforcement. As expected, total response rate increased as a function of (a) increasing the rate of reinforcement (i.e., variable-interval [VI] 4 min vs. VI 1 mi), (b) increasing the amount of the reinforcer (one food pellet vs. four pellets), (c) increasing the percentage of reinforcers that were contingent on nose poking (25% vs. 100%), and (d) requiring additional responses after the end of the VI schedule (i.e., adding a tandem variable-ratio [VR] 9 requirement). The first three of these variables (relative reinforcement) increased the visit-initiation rate. The tandem VR, in contrast, increased the number of responses per visit. Thus, variables that have similar effects on total response rate can be differentiated based on their effects on the componemts of response rate.     

Instrumental performance on negative schedules

Three experiments examined the performance of rats pressing a lever for food reinforcement on a schedule in which high rates of response resulted in lowered rates of reinforcement (i.e. a schedule with a negative component). In Experiment 1, rats responded on a variable interval (VI) schedule with a conjoint component such that every 30 responses a reinforcement programmed by the VI schedule was cancelled. These subjects generally emitted a lower response rate than rats responding on a VI schedule yoked to the former subjects with respect to the delivery of reinforcement, although response rate differences were sometimes not large. Similar response-rate effects were obtained in Experiment 2 using a within-subject yoking procedure. In Experiment 3, reinforced interresponse times were matched on negative and VI schedules yoked in terms of reinforcement rate, and the response rate emitted in these conditions were similar. These results give support to theories of instrumental conditioning that stress the strengthening and shaping properties of reinforcement.     

Human sensitivity to reinforcement feedback functions

Two experiments investigated human sensitivity to the temporally extended aspects of reinforcement schedules. Experiment 1 investigated human sensitivity to the extended and local aspects of three reinforcement schedules: variable ratio (VR), variable interval (VI), and variable-interval-plus-linear-feedback (VI+) schedules. Experiment 2 investigated this sensitivity on two reinforcement schedules: VI and VI+ schedules. In both experiments, there was evidence of sensitivity to the temporally extended aspects of the schedule: There were differences between the response rate on the VI+ and yoked-VI schedules, but no statistical difference in rates of response between the VR and VI+ schedules. The VI+ versus VI difference was much more pronounced when a lower response force needed to depress a lever was used. These results suggest that human subjects do show some sensitivity to temporally extended aspects of schedules of reinforcement.     

Response rate and sensitivity to the molar feedback function relating response and reinforcement rate on VI+ schedules of reinforcement

In 5 experiments, the author examined rats' sensitivity to the molar feedback function relating response rate to reinforcement rate on schedules of reinforcement. These studies demonstrated that, at lower rates of responding, rats' performance on variable ratio (VR), variable interval (VI), and variable interval with linear feedback loop (VI+) schedules was determined largely by reinforcement of interresponse times; response rates were faster on VR than on both VI and VI+ schedules. In contrast, when procedures were adopted to maintain high rates of response, rats showed sensitivity to the molar characteristics of the schedules; they responded as fast on a VI+ schedule as on a VR schedule and faster on both of these schedules than on a yoked VI schedule. When the variance of response rate was manipulated, this factor was noted as an important element in determining sensitivity to the molar characteristics of the schedule.     

Perception of causal relations in humans: Factors affecting judgments of response-outcome contingencies under free-operant procedures

In three experiments, college studients responded to and rated a range of positive, random, and negative response-outcome contingencies presented in free-operant formats. These experiments sought a paradigm that would yield sensitive and unbiased judgments of response-outcome relations and explored the role of time in the judgment of response-outcome covariation. In Experiment 1, the effects of making continuous and discrete responses on subjects' contingency judgments were compared. In Experiment 2, the effects of changing the temporal definition of discrete responses were examined as were the effects of the amount of exposure to contingency problems. In Experiment 3, the effects of temporal regularity in defining response occurrence and nonoccurrence were investigated. In all three experiments, subjects' judgments were strong linear functions of the programmed contingencies between telegraph key operation and the illumination of a brief light. This result shows free-operant scheduling of response-outcome contingencies to be a highly sensitive and unbiased method of investigating causal perception. Additionally, judgment accuracy was found to be higher for males than for females and to improve as the probability of the subject's making a recorded response rose from .00 toward .50. Finally, a correlational analysis of several possible judgment rules supported the conclusion that subjects rated response-outcome relations on the basis of the difference in the probability of an outcome given their having recently made or not made a response.     

Interlocking schedules: the relationship between response and time requirements.

Rats were exposed to an interlocking fixed-ratio 150 fixed-interval 5-minute schedule of food reinforcement and then to yoked variable-ratio schedules in which individual ratios corresponded exactly to the ratios of responses to reinforcement obtained on the interlocking schedule. After additional training with the interlocking schedule, the rats were exposed to yoked variable-interval schedules in which intervals corresponded to the intervals between successive reinforcements obtained on the second interlocking schedule. Response rates were highest in the yoked VR condition and lowest in the yoked VI, while intermediate rates characterized the interlocking schedule. Break-run patterns of responding were generated by the interlocking schedule for all subjects, while both the yoked VR and VI schedules produced comparatively stable local rates of responding. These results indicate that responding is sensitive to the interlocking schedule's inverse relationship between reinforcement frequency and responses per reinforcement.     

Effects of variable-interval value and amount of training on stimulus generalization.

In Experiment 1 pigeons pecked a key that was illuminated with a 501-nm light and obtained food by doing so according to a variable-interval (VI) schedule of reinforcement, the mean value of which differed across groups: either 30 s, 120 s, or 240 s. The pigeons in all three groups were trained for 10 50-min sessions. Generalization testing was conducted in extinction with different wavelengths of light. Absolute and relative generalization gradients were similar in shape for the three groups. Experiment 2 was a systematic replication of Experiment 1 using line orientation as the stimulus dimension and a mean VI value of either 30 s or 240 s. Again, gradients of generalization were similar for the two groups. In Experiment 3 pigeons pecked a key that was illuminated with a 501-nm light and obtained food reinforcers according to either a VI 30-s or a 240-s schedule. Training continued until response rates stabilized (> 30 sessions). For subjects trained with the 30-s schedule, generalization gradients were virtually identical regardless of whether training was for 10 sessions (Experiment 1) or until response rates stabilized. For subjects trained with the VI 240-s schedule, absolute generalization gradients for subjects trained to stability were displaced upward relative to gradients for subjects trained for only 10 sessions (Experiment 1), and relative generalization gradients were slightly flatter. These results indicate that the shape of a generalization gradient does not necessarily depend on the rate of reinforcement during 10-session single-stimulus training but that the effects of prolonged training on stimulus generalization may be schedule dependent.     

Behavioral economic analysis of activity choice in obese children

Evaluated children's choice for sedentary versus vigorous activity. Experiment 1 assessed the influence of percent overweight (less than 20%, 20% to 80%, greater than 80%) on choice of a moderately liked vigorous activity at a constant variable ratio (VR) 2 reinforcement schedule versus a highly liked sedentary activity with the schedule varied from VR2 to VR32. All children chose the sedentary choice when the schedules were VR2. As the cost for sedentary activity increased, lean and moderately obese children switched to the vigorous activity, but the very obese children still chose the sedentary activity. Experiment 2 compared moderately obese children's choice between easily accessible, highly or least liked vigorous activities (VR2) and highly liked sedentary activity with the schedule varied from VR2 through VR16. When the reinforcement schedules were equal, and sedentary activity and vigorous activity were rated as equally linked, children chose the sedentary activity. All subjects switched from the sedentary to the vigorous activity, but there were no differences in choice as a function of liking for vigorous activities.     

Collateral responding during differential reinforcement of low rates

Two pigeons were trained to peck either of two response keys for food, under two different variable-interval schedules. When responding stabilized, the schedule on the left key (reinforcement-key) was changed to a differential-reinforcement-of-low-rates schedule, and responses on the right key (extinction-key) were no longer reinforced. The mean interresponse time of responses on the reinforcement-key approximated the temporal requirement of the reinforcement schedule on that key. Collateral responding on the extinction-key was maintained by one of the birds. A “run” of these collateral responses was defined as a sequence of responses on the extinction-key occurring between two responses on the reinforcement-key. For this one bird, collateral behavior, measured by mean time per run and mean number of responses per run, was an increasing function of the temporal requirements of the reinforcement schedule on the reinforcement key, and it was strongly positively correlated with the mean interresponse time of responses on the reinforcement-key. However, from an analysis of the results, the collateral behavior did not appear to have mediated the temporal spacing of responses on the reinforcement-key.     

Frequency distribution of interresponse times during VI and VR reinforcement

A detailed analysis was made of the interresponse times (IRTs) of two rats under both a VI 40-sec and a VR 15-sec schedule. Except for the latency of the first response after a reinforcement, the mean IRTs of all further responses differed little. Similarly, the frequency distributions of the successive IRTs did not vary greatly, but were of no simple form. Sequential dependencies between successive IRTs were small, never accounting for more than 1% of the variance.     

More on concurrent interval-ratio schedules: a replication and review.

It has been suggested that the failure to maximize reinforcement on concurrent variable-interval, variable-ratio schedules may be misleading. Inasmuch as response costs are not directly measured, it is possible that subjects are optimally balancing the benefits of reinforcement against the costs of responding. To evaluate this hypothesis, pigeons were tested in a procedure in which interval and ratio schedules had equal response costs. On a concurrent variable time (VT), variable ratio-time (VRT) schedule, the VT schedule runs throughout the session and the VRT schedule is controlled by responses to a changeover key that switches from one schedule to the other. Reinforcement is presented independent of response. This schedule retains the essential features of concurrent VI VR, but eliminates differential response costs for the two alternatives. It therefore also eliminates at least one significant ambiguity about the reinforcement maximizing performance. Pigeons did not maximize rate of reinforcement on this procedure. Instead, their times spent on the alternative schedules matched the relative rates of reinforcement, even when schedule parameters were such that matching earned the lowest possible overall rate of reinforcement. It was further shown that the observed matching was not a procedural artifact arising from the constraints built into the schedule.     

Variable-ratio schedules as variable-interval schedules with linear feedback loops.

The mathematical theory of linear systems has been used successfully to describe responding on variable-interval (VI) schedules. In the simplest extension of the theory to the variable-ratio (VR) case, VR schedules are treated as if they were VI schedules with linear feedback loops. The assumption entailed by this approach, namely, that VR and VI-plus-linear-feedback schedules are equivalent, was tested by comparing responding on the two types of schedule. Four human subjects' lever pressing produced monetary reinforcers on five VR schedules, and on five VI schedules with linear feedback loops that reproduced the feedback properties of the VR schedules. Pressing was initiated by instructions in 2 subjects, and was shaped by successive approximation in the other 2. The different methods of response initiation did not have differential effects on behavior. For each of the 4 subjects, the VR and the comparable VI-plus-linear-feedback schedules generated similar average response rates and similar response patterns. The subjects' behavior on both types of schedule was similar to that of avian and rodent species on VR schedules. These results indicate that the assumption entailed by the VI-plus-linear-feedback approach to the VR case is valid and, consequently, that the approach is worth pursuing. The results also confute interresponse-time theories of schedule performance, which require interval and ratio contingencies to produce different response rates.