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# «EVALUATIONS OF DELAYED REINFORCEMENT IN CHILDREN WITH DEVELOPMENTAL DISABILITIES By JOLENE RACHEL SY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL ...»

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Thus, if stimuli were present on the screen for 5 s prior to a “correct” response, then response rate for that particular delay was considered to be 12 responses per min (one response divided by 5 s, multiplied by 60 s). Within each session, response rates for each delay were averaged, even if reinforcers were not delivered at the end of the delay. Thus, if a “correct’ response was followed by an “incorrect” response, the delay would be equal for these responses, even though a reinforcer would only be delivered following the “correct” response. In these cases, response rates were calculated separately and then averaged. Response rates were then averaged across sessions as a function of each delay. It should be noted that more response rates were averaged into mean response rates during the smaller delays. This is because subjects did not contact high delays during sessions with low breakpoints. Thus, for Vlade, 11 sessions of data were averaged into each mean response rate for delays between 5 s and 60 s, 6 sessions of data were averaged into each mean response rate for delays between 65 s and 80 s, and 5 or fewer sessions of data were averaged into each mean response rate for delays between 90 s and 120 s. For Alice, 14 sessions of data were averaged into each mean response rate for delays between 10 s and 100 s, and 12 sessions of data were averaged into each mean response rate for 110-s and 120-s delays. For Walden, 25 sessions of data were averaged into each mean response rate for delays between 10 s and 60 s, 24 sessions of data were averaged into each mean response rate for delays between 70 s and 80 s, 23 sessions of data were averaged into each mean response rate for 90- to 110-s delays, and 21 sessions of data were averaged into the mean response rate for the 120-s delay. The relationship between mean response rate and delay to reinforcement was quantified using a modified version of Mazur’s (1987)

hyperbolic delay discounting equation:

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Reilly and Lattal (2004) used this equation to predict response rate (B) as a function of each delay (D). The equation contains two free parameters, BI and k, which represent estimated rate of responding under immediate reinforcement and estimated degree of discounting due to increasing delays to reinforcement, respectively. BI and k were estimated using Microsoft® Excel, which minimized the sum of squared deviations between the obtained values and the predicted curve.

Percent “correct” data for all 3 subjects are presented in Figure 2-3. Percentage of “correct” responses was calculated by dividing the number of “correct” responses by the total number of responses. Responses from the first 10 forced-exposure trials were not included in these calculations. Vlade selected the “correct” response an average of 94.38% during the delayed reinforcement condition (range, 91% - 100%) and an average of 92.29% during the immediate reinforcement condition (range, 78% - 100%).

Alice selected the “correct” response 89.57% (range, 54.5% - 100%) and 81.98% (range, 18.2% - 100%) during the delayed reinforcement and immediate reinforcement conditions, respectively. Walden was initially more likely to select the “correct” response during the immediate reinforcement condition. However, he eventually selected the “correct” response almost exclusively during both delayed reinforcement (89.85%;

range, 53.33% - 100%) and immediate reinforcement (98.66%; range, 90.9% - 100%) conditions. Figure 2-4 presents mean percent “correct” data as a function of each delay to reinforcement. For all 3 subjects, percent “correct” remained fairly stable across increasing delays to reinforcement.

Figure 2-5 presents breakpoints obtained during the chained FR 1 – PT schedule in Experiment 1A. Breakpoints were defined as the last delay contacted prior to meeting the session termination criteria. The maximum possible delay that subjects could contact was 120 s. In general, breakpoints varied from session to session. Vlade’s mean breakpoint was 85.7 s (range, 60 - 120 s), Alice’s mean breakpoint was 117.14 s (range, 110 – 120 s), and Walden’s mean breakpoint was 110.77 s (range, 60 - 120 s).

For Alice and Walden, there was a negative relationship between the k value estimated using the modified version of Mazur’s hyperbolic delay discounting equation and mean breakpoint. In other words greater degrees of discounting due to the delay were associated with lower breakpoints, which suggests that k was an accurate representation of discounting due to the delay for these subjects.

In summary, Experiment 1A evaluated the effects of delayed reinforcement on the behavior of children with DD using a chained schedule of reinforcement. The removal of stimuli in the terminal component of the chained schedule ensured that programmed delays matched obtained delays because subjects could not emit the target response during the terminal component. Additionally, the removal of stimuli was programmed following both “correct” and “incorrect” responses, thus degrading the relationship between the removal of stimuli and reinforcement. The results from Experiment 1A suggests that signaled, delayed reinforcement can maintain responding by individuals with DD, even when the signal is degraded. In addition, results suggest that adding a delay between a response and a reinforcer will not produce decreases the percent of “correct” responses made by the subjects. Results also suggest that individuals with DD will continue to respond, even as delays to reinforcement increase. However, these findings might be specific to the reinforcement schedule programmed (FR 1 schedule).

Thus, the purpose of Experiment 1B was to examine the effects of delayed reinforcement using a VI schedule.

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During Experiment 1B, subjects were again exposed to two experimental conditions. During the delayed reinforcement condition, a chained VI 15- or 30-s – PT schedule of reinforcement was in effect. Relative to the FR 1 schedule programmed in Experiment 1A, this schedule was programmed to allow for greater response variability in the initial component. The VI 15-s schedule consisted of 20 intervals (range, 0.38 to

59.94 s) generated using a Fleshler and Hoffman (1962) progression, while the VI 30-s schedule consisted of 20 intervals (range, 0.76 to 119.87 s) generated using the same progression. All subjects were initially exposed to the chained VI 30-s – PT schedule of reinforcement. However, Walden’s low percent “correct” appeared to be the result of interval strain, so for him the initial component was switched to a VI 15-s schedule for Experiments 1B and 1C. During the delayed reinforcement condition, the position of stimuli was randomized following each response that occurred before the interval had elapsed. Stimuli were removed from the screen contingent on the first response after the interval had elapsed and remained absent for the duration of the PT component, which increased by a fixed amount (i.e., 5 or 10 s) following successive reinforcer deliveries. At the end of the terminal component, a tone was sounded and reinforcers were delivered if the response that initiated the terminal component had been “correct.” If this response had been “incorrect,” a tone was not sounded and reinforcers were not delivered. Following the completion of each terminal link, stimuli were represented on the screen following a 3-s or 30-s ITI. This ITI was programmed to allow subjects to consume the reinforcer.

During the immediate reinforcement condition, a yoked VI schedule of reinforcement was in effect. Again, this schedule was chosen to keep the response requirement relatively similar to that programmed in the delayed reinforcement condition, while at the same time equating reinforcement rate to that obtained during each previous delayed reinforcement session. In the yoked VI schedule, the intervals were yoked to the obtained IRI of each previous delay session. The duration of each immediate reinforcement session was yoked to the duration of each previous delayed reinforcement session. During each session in the immediate reinforcement condition, responses that occurred prior to the end of the interval resulted in the randomized repositioning of stimuli on the screen, and the first response after the interval requirement elapsed either resulted in the immediate presentation of a tone and a reinforcer (if the response had been “correct”) or an absence of differential consequences (if the response had been “incorrect”).

–  –  –

At the start of each session, subjects’ responses during the first 10 trials generally suggested that discriminations were acquired. Vlade selected the “correct” response 95.21% (range, 60% - 100%) of the time during the last five trials prior to each delayed reinforcement session and 94.78% of the time (range, 40% - 100%) during the last five trials prior to each immediate reinforcement session. Alice selected the “correct” responses 88% of the time (range, 20% - 100%) during the last five trials prior to each delayed reinforcement session and 91% of the time (range, 60% - 100%) during the last five trials prior to each immediate reinforcement session. Although Alice’s level of percent “correct” was low during some of these sets of trials, there was not a relationship between levels of percent “correct” during the last five trials and levels of percent “correct” during subsequent delayed reinforcement (R2 =.02) or immediate reinforcement (R2 =.03) sessions. Walden selected the “correct” response 87.14% of the time (range, 40% - 100%) during the last five trials prior to each delayed reinforcement session and 92.86% of the time (range, 60% - 100%) prior to each immediate reinforcement session. For Walden, there was not a relationship between levels of percent “correct” during the last five trials and levels of percent “correct” during subsequent delayed reinforcement (R2 =.02) or immediate reinforcement (R2 =.01) sessions.

Figure 2-6 displays response rate data from Experiment 1B. Response rates were calculated in a manner similar to Experiment 1A, with the total number of “correct” responses following the first 10 forced-exposure trials divided by the total amount of time in which it was possible to make a response. Response rates were again slightly elevated during immediate reinforcement condition relative to the delayed reinforcement condition. Vlade engaged in an average of 4.38 responses per min during the immediate reinforcement condition (range, 1.22 – 13.41 responses per min) and an average of 3.27 responses per min in the delayed reinforcement condition (range, 0.75 – 12.43 responses per min). Alice engaged in an average of 4.48 responses per min during the immediate reinforcement condition (range, 2.62 – 6.60 responses per min) and an average of 3.06 responses per min in the delayed reinforcement condition (range, 1.15 – 5.98 responses per min). Walden engaged in an average of 3.08 responses per min in the immediate reinforcement condition (range, 1.25 – 8.64 responses per min) and an average of 3.92 responses per min during the VI 30-s component of the delayed reinforcement condition (range, 1.65 – 8.57 responses per min) and 1.56 responses per min during the VI 15-s component of the delayed reinforcement condition (range, 1.00 – 2.62 responses per min).

Figure 2-7 depicts mean response rates as a function of each delay and curves predicted by the modified version of Mazur’s (1987) hyperbolic delay discounting equation. Calculations of mean response rates were similar to those computed during Experiment 1A: The number of “correct” responses made prior to each delay were divided by the total amount of time in which it was possible to make a response since the last trial. Once again, more response rates were averaged into mean response rates during the smaller delays. For Vlade, at least 20 sessions of data were averaged into each mean response rate for delays between 5 s and 40 s, at least 10 sessions of data were averaged into each mean response rate for delays between 45 s and 60 s, and 7 or fewer sessions of data were averaged into each mean response rate for delays between 65 s and 120 s. For Alice, at least 10 sessions of data were averaged into each mean response rate for delays between 10 s and 60 s, but 8 or fewer sessions of data were averaged into each mean response rate for delays between 70 s and 90 s.

For Walden, 7 sessions of data were averaged into each mean response rate for delays between 10 s and 30 s, but only 5 or fewer sessions of data were averaged into each mean response rate for delays between 40 s and 70 s. Walden’s data only include data from the VI 15-s component. For Vlade and Alice, mean response rates decreased as delays to reinforcement increased. For Walden, mean response rates remained fairly stable as delays to reinforcement increased.

In general, percent “correct” did not differ across conditions. Percent “correct” was again calculated by dividing the number of “correct” responses made after the first 10 forced-exposure trials by the total number of “correct” and “incorrect” responses made after the first 10 forced-exposure trials. These data are depicted in Figure 2-8. Vlade selected the “correct” response an average of 82.45% during the delayed reinforcement condition (range, 40% - 100%) and an average of 80.27% during the immediate reinforcement condition (range, 55.55% - 100%). Alice selected the “correct” response an average of 71.15% during the delayed reinforcement condition (range, 50% and an average of 67.81% during the immediate reinforcement condition (range, 41% - 91.67%). Walden selected the “correct” response an average of 64.72% during the VI 30-s component of the delayed reinforcement condition (range, 51.32% an average of 61.45% during the VI 15-s component of the delayed reinforcement condition (range, 48.57% - 75%), and an average of 67.55% during the immediate reinforcement condition (range, 49.21% - 82.76%). Figure 2-9 presents mean percent “correct” data as a function of each delay to reinforcement. For all 3 subjects, percent “correct” remained fairly stable across increasing delays to reinforcement.

Figure 2-10 displays breakpoints obtained when a chained VI - PT schedule of reinforcement was programmed. Mean breakpoints were 39.89 s (range, 10 s – 85 s),

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