Reinforcement value and fixed‐interval performance

The concept of reinforcement value summarizes the effect of different variables, such as reinforcement delay, reinforcement magnitude, and deprivation level, on behavior. In the present set of experiments, we evaluated the effect of reinforcement devaluation on performance under FI schedules. The literature on timing and reinforcement value suggests that devaluation generates longer expected times to reinforcement than the same intervals trained under control conditions. We devalued reinforcement with delay in Experiments 1A, 1B, and 2, and diminished deprivation in Experiments 3A and 3B. Devaluation reduced response rates, increased the number of one‐response intervals, and lengthened postreinforcement pauses, but had inconsistent effects on other timing measures such as quarter life and breakpoint. The results of delayed reinforcement and diminished deprivation manipulations are well summarized as reinforcement devaluation effects. These results suggest that devaluation may reduce stimulus control. In addition, we argue that the process by which delayed reinforcement affects behavior might also explain some effects observed in other devaluation procedures through the concept of reinforcement value.     

The effects of fixed‐interval schedules on variability of pigeons' pecking location

Many studies that have investigated performance under reinforcement schedules have measured response rate or interresponse time, which reflect the temporal dimension of responding; however, relatively few studies have examined other dimensions. The present study investigated the effects of fixed‐interval schedules on the location of pigeons' pecking response. A circular response area 22.4 cm in diameter was used so that the pecking responses were effective over a wide range. Pigeons were exposed to a fixed‐interval schedule whose requirement was systematically varied between conditions. Response location moved closer to the location of the last reinforced response as time elapsed in each trial. Additionally, as the fixed‐interval duration requirement increased, response locations shifted to the border of the response area and the variability of response locations increased. These results suggest that fixed‐interval schedules systematically control response location.     

Cooperative responding in rats maintained by fixed‐ and variable‐ratio schedules

The present study investigated the effects of fixed‐ratio (FR) and variable‐ratio (VR) reinforcement schedules on patterns of cooperative responding in pairs of rats. Experiment 1 arranged FR 1, FR 10, and VR 10 schedules to establish cooperative responding (water delivery depended on the joint responding of two rats). Cooperative response rates and proportions were higher under intermittent schedules than under continuous reinforcement. The FR 10 schedule generated a break‐and‐run pattern, whereas the VR 10 schedule generated a relatively high and constant rate pattern. Experiment 2 evaluated the effects of parametric manipulations of FR and VR schedules on cooperative responding. Rates and proportions of cooperative responding generally increased between ratio sizes of 1 and 5 but showed no consistent trend as the ratio increased from 5 to 10. Experiment 3 contrasted cooperative responding between an FR6 schedule and a yoked control schedule. Coordinated behavior occurred at a higher rate under the former schedule. The present study showed that external consequences and the schedules under which the delivery of these consequences are based, select patterns of coordinated behavior.     

On the limitations of fixed‐step‐size adaptive methods with response confidence

The family of (non‐parametric, fixed‐step‐size) adaptive methods, also known as ‘up–down’ or ‘staircase’ methods, has been used extensively in psychophysical studies for threshold estimation. Extensions of adaptive methods to non‐binary responses have also been proposed. An example is the three‐category weighted up–down (WUD) method (Kaernbach, 2001) and its four‐category extension (Klein, 2001). Such an extension, however, is somewhat restricted, and in this paper we discuss its limitations. To facilitate the discussion, we characterize the extension of WUD by an algorithm that incorporates response confidence into a family of adaptive methods. This algorithm can also be applied to two other adaptive methods, namely Derman's up–down method and the biased‐coin design, which are suitable for estimating any threshold quantiles. We then discuss via simulations of the above three methods the limitations of the algorithm. To illustrate, we conduct a small scale of experiment using the extended WUD under different response confidence formats to evaluate the consistency of threshold estimation.     

New heterogeneous test statistics for the unbalanced fixed‐effect nested design

When the underlying variances are unknown or/and unequal, using the conventional F test is problematic in the two‐factor hierarchical data structure. Prompted by the approximate test statistics (Welch and Alexander–Govern methods), the authors develop four new heterogeneous test statistics to test factor A and factor B nested within A for the unbalanced fixed‐effect two‐stage nested design under variance heterogeneity. The actual significance levels and statistical power of the test statistics were compared in a simulation study. The results show that the proposed procedures maintain better Type I error rate control and have greater statistical power than those obtained by the conventional F test in various conditions. Therefore, the proposed test statistics are recommended in terms of robustness and easy implementation.     

A Monte Carlo evaluation of masked visual analysis in response‐guided versus fixed‐criteria multiple‐baseline designs

We developed masked visual analysis (MVA) as a structured complement to traditional visual analysis. The purpose of the present investigation was to compare the effects of computer‐simulated MVA of a four‐case multiple‐baseline (MB) design in which the phase lengths are determined by an ongoing visual analysis (i.e., response‐guided) versus those in which the phase lengths are established a priori (i.e., fixed criteria). We observed an acceptably low probability (less than .05) of false detection of treatment effects. The probability of correctly detecting a true effect frequently exceeded .80 and was higher when: (a) the masked visual analyst extended phases based on an ongoing visual analysis, (b) the effects were larger, (c) the effects were more immediate and abrupt, and (d) the effects of random and extraneous error factors were simpler. Our findings indicate that MVA is a valuable combined methodological and data‐analysis tool for single‐case intervention researchers.     

Concurrent nonindependent fixed‐ratio schedules of alcohol self‐administration: Effects of schedule size on choice

Choice behavior was studied under concurrent nonindependent fixed‐ratio fixed‐ratio (nFR) schedules of reinforcement, as these schedules result in frequent changeover responses. With these schedules, responses on either operandum count toward the completion of the ratio requirements of both schedules. Five monkeys were subjects, and two pairs of liquid reinforcers were concurrently available: 16% (w/v) and 0% ethanol or 16% and 8% ethanol. For each pair of reinforcers, the nFR sizes were systematically altered across sessions while keeping the schedule size equal for both liquids. Responding varied as a function of reinforcer pair and nFR size. With the 16% and 0% pair, higher response rates were maintained by 16% and were an inverted U‐shape function of nFR size. With 16% and 8%, a greater number of responses initially occurred on the schedule that delivered 8% ethanol. However, as nFR size increased, preference reversed such that responses that delivered 16% ethanol were greater. When the nFR size was subsequently decreased, preference reverted back to 8%. Number of responses emitted per delivery was a dependent variable and, in behavioral economic terms, was the price paid for each liquid delivery. With 16% and 0%, changeover responses initially increased and then decreased as schedule size became larger. In contrast, with the 16% and 8% pair, changeover responses increased directly with schedule size. Responding under nFR schedules is sensitive to differences in reinforcer magnitude and demonstrates that relative reinforcing effects can change as a function of schedule size.     

Comparing fixed‐amount and progressive‐amount DRO Schedules for tic suppression in youth with chronic tic disorders

Chronic tic disorders (CTDs) involve motor and/or vocal tics that often cause substantial distress and impairment. Differential reinforcement of other behavior (DRO) schedules of reinforcement produce robust, but incomplete, reductions in tic frequency in youth with CTDs; however, a more robust reduction may be needed to affect durable clinical change. Standard, fixed‐amount DRO schedules have not commonly yielded such reductions, so we evaluated a novel, progressive‐amount DRO schedule, based on its ability to facilitate sustained abstinence from functionally similar behaviors. Five youth with CTDs were exposed to periods of baseline, fixed‐amount DRO (DRO‐F), and progressive‐amount DRO (DRO‐P). Both DRO schedules produced decreases in tic rate and increases in intertic interval duration, but no systematic differences were seen between the two schedules on any dimension of tic occurrence. The DRO‐F schedule was generally preferred to the DRO‐P schedule. Possible procedural improvements and other future directions are discussed.     

Children's preference for mixed‐ versus fixed‐ratio schedules of reinforcement: A translational study of risky choice

Laboratory research has shown that when subjects are given a choice between fixed‐ratio and bi‐valued mixed‐ratio schedules of reinforcement, preference typically emerges for the mixed‐ratio schedule even with a larger ratio requirement. The current study sought to replicate and extend these findings to children's math problem completion. Using an ABCBC reversal design, four fourth‐grade students were given the choice of completing addition problems reinforced on either a fixed‐ratio 5 schedule or one of three mixed‐ratio schedules; an equivalent mixed‐ratio (1, 9) schedule, a mixed‐ratio (1, 11) schedule with a 20% larger ratio requirement, and an equally lean mixed‐ratio (5, 7) schedule without the small fixed‐ratio 1 component. This was followed by a reversal back to the preceding phase in which preference for the mixed‐ratio schedule had been observed, and a final reversal back to the mixed‐ratio (5, 7) phase. Findings were consistent with previous research in that all children preferred the mixed‐ratio (1, 9) schedule over the equivalent fixed‐ratio 5 schedule. Preference persisted for the leaner mixed‐ratio (1, 11) schedule for three of the four children. Indifference or preference for the fixed‐ratio 5 alternative was observed in phases containing the mixed‐ratio (5, 7) schedule. These results extend previous research on risky choice to children's math problem completion and highlight the importance of a small ratio component in the emergence of preference for bi‐valued mixed‐ratio schedules. Implications of these results for arranging reinforcement to increase children's academic responding are discussed.     

Single‐limit interval estimates as reference points

People often describe uncertain quantities by suggesting a lower or upper limit of an uncertainty interval, rather than the complete range. Five studies are reported, which demonstrate how interval limits function as provisional reference points (PRP), conferring evaluative meanings to the target objects, by suggesting downward or upward comparisons. Thus, a price above X appears expensive, whereas a price below Y appears cheap, even when Y > X. This can give rise to framing effects: a purchase can appear to be recommended or advised against, and a seller can appear as optimistic or pessimistic, and, more generally, an estimate can indicate abundance or scarcity, depending upon which boundary (upper or lower) that is selected. Furthermore, inclusive lower bounds (minimum, at least) and upper bounds (maximum, at most) differ from exclusive lower (more than, above) and upper bounds (less than, below), by suggesting possible (likely) rather than implausible (unlikely) values. Copyright © 2006 John Wiley & Sons, Ltd.     

Concurrent variable‐interval variable‐ratio schedules in a dynamic choice environment

Most studies of operant choice have focused on presenting subjects with a fixed pair of schedules across many experimental sessions. Using these methods, studies of concurrent variable‐ interval variable‐ratio schedules helped to evaluate theories of choice. More recently, a growing literature has focused on dynamic choice behavior. Those dynamic choice studies have analyzed behavior on a number of different time scales using concurrent variable‐interval schedules. Following the dynamic choice approach, the present experiment examined performance on concurrent variable‐interval variable‐ratio schedules in a rapidly changing environment. Our objectives were to compare performance on concurrent variable‐interval variable‐ratio schedules with extant data on concurrent variable‐interval variable‐interval schedules using a dynamic choice procedure and to extend earlier work on concurrent variable‐interval variable‐ratio schedules. We analyzed performances at different time scales, finding strong similarities between concurrent variable‐interval variable‐interval and concurrent variable‐interval variable‐ ratio performance within dynamic choice procedures. Time‐based measures revealed almost identical performance in the two procedures compared with response‐based measures, supporting the view that choice is best understood as time allocation. Performance at the smaller time scale of visits accorded with the tendency seen in earlier research toward developing a pattern of strong preference for and long visits to the richer alternative paired with brief “samples” at the leaner alternative (“fix and sample”).     

Effects of post‐cue interval on intentional forgetting

This study examined the effect of post‐cue interval on directed forgetting and suppression. Experiments 1 and 2 used the item method of directed forgetting. The interval between the cue to remember/forget (R/F) and the presence of the next item was manipulated. As the post‐cue interval increased, the rates of hits and ‘remember’ responses on the recognition test also increased not only for R items but also for F items, suggesting that participants did not stop processing F items after the F cue. Experiment 3 manipulated both the number of response/suppression attempts and the duration of response/suppression for each word pair during the response/suppression phase. The results showed that increasing the number of suppression attempts led to worse recall in the subsequent memory test. However, increasing the duration of suppression reduced the suppression effect. These results provide insights into a key factor for successful intentional forgetting and suppression.     

On sample size calculation for 2×2 fixed‐effect ANOVA when variances are unknown and possibly unequal

The factorial 2 × 2 fixed‐effect ANOVA is a procedure used frequently in scientific research to test mean differences between‐subjects in all of the groups. But if the assumption of homogeneity is violated, the test for the row, column, and the interaction effect might be invalid or less powerful. Therefore, for planning research in the case of unknown and possibly unequal variances, it is worth developing a sample size formula to obtain the desired power. This article suggests a simple formula to determine the sample size for 2 × 2 fixed‐effect ANOVA for heterogeneous variances across groups. We use the approximate Welch t test and consider the variance ratio to derive the formula. The sample size determination requires two‐step iterations but the approximate sample sizes needed for the main effect and the interaction effect can be determined separately with the specified power. The present study also provides an example and a SAS program to facilitate the calculation process.     

The effects of reinforcer magnitude in the preceding and upcoming ratios on between‐ratio pausing in multiple,mixed, and single fixed‐ratio schedules

Hens responded under multiple fixed‐ratio schedules with equal response requirements and either a 1‐s or a 6‐s reinforcer. Upcoming reinforcer size was indicated by key color. Components were presented in a quasirandom series so that all four component transitions occurred. Postreinforcement pauses were affected by the upcoming and preceding reinforcer size, with longer pauses after large reinforcers followed by small reinforcers than when followed by large ones, and longer pauses after small reinforcers that were followed by small reinforcers rather than large ones. Pauses increased with fixed‐ratio size and the effects of reinforcer size were larger the larger the ratio. When reinforcer size was not signaled—mixed fixed‐ratio schedules—pauses were shorter after small than after large reinforcers. Signalling the upcoming reinforcer attenuated the effect of the previous reinforcer size on pause duration when small was followed by small and when either small or large by large, but enhanced the effect when large was followed by small. There was no effect of reinforcer size on pause duration when single fixed‐ratio schedules were arranged. The effects of reinforcer size on pauses depends on the size and range of the fixed ratios as well as the exact procedures used in the study.     

Mini‐breaks: the use of escape on a fixed‐time schedule to reduce unauthorized breaks from vocational training sites for individuals with brain injury

This study evaluated mini‐breaks with three individuals who were traumatically brain injured and engaged in unauthorized breaks. The vocational instructors reported that the three participants were having problems staying at their scheduled vocational training sites (walking away without permission). Following baseline, participants were placed on mini‐breaks; that is, participants were given a ten‐minute mini‐break every hour. Thus, mini‐breaks were given without regard to unauthorized breaks. Unauthorized breaks decreased to zero levels for all three participants when mini‐breaks commenced. Following 1 month of the mini‐breaks, two of the participants were put back on a regular break schedule (one 15‐minute AM break and one 15‐minute PM break and a 30‐minute lunch break). The third participant was placed in supported work. The effects of the mini‐breaks were maintained. Copyright © 1999 John Wiley & Sons, Ltd.     

CDF‐quantile distributions for modelling random variables on the unit interval

This paper introduces a two‐parameter family of distributions for modelling random variables on the (0,1) interval by applying the cumulative distribution function of one ‘parent’ distribution to the quantile function of another. Family members have explicit probability density functions, cumulative distribution functions and quantiles in a location parameter and a dispersion parameter. They capture a wide variety of shapes that the beta and Kumaraswamy distributions cannot. They are amenable to likelihood inference, and enable a wide variety of quantile regression models, with predictors for both the location and dispersion parameters. We demonstrate their applicability to psychological research problems and their utility in modelling real data.