files.eric.ed.gov · Key words: delay discounting, self-control, choice, behavioral economics, assessment ... This equation proposes a discounting function in which the subjective

TEMPORAL DISCOUNTING PREDICTS STUDENT RESPONSIVENESSTO EXCHANGE DELAYS IN A CLASSROOM TOKEN SYSTEM

DEREK D. REED AND BRIAN K. MARTENS

SYRACUSE UNIVERSITY

Typical assessments of temporal discounting involve presenting choices between hypotheticalmonetary outcomes. Participants choose between smaller immediate rewards and larger delayedrewards to determine how the passage of time affects the subjective value of reinforcement. Fewstudies, however, have compared such discounting to actual manipulations of reward delay. Thepresent study examined the predictive validity of a temporal discounting procedure developed foruse with children. Forty-six sixth-grade students completed a brief discounting assessment andwere then exposed to a classwide intervention that involved both immediate and delayedreinforcement in a multiple baseline design across classrooms. The parameters derived from twohyperbolic models of discounting correlated significantly with actual on-task behavior underconditions of immediate and delayed exchange. Implications of temporal discountingassessments for behavioral assessment and treatment are discussed.

Key words: delay discounting, self-control, choice, behavioral economics, assessment

_______________________________________________________________________________

Impulsivity is a defining feature of attentiondeficit hyperactivity disorder (ADHD) inchildren (Barkley, 1997, 1998). The presenceof impulsive behaviors in childhood has beenlinked to long-term unemployment, schoolmaladjustment, lack of occupational alterna-tives, and poor parenting as adults (Bloomquist& Schnell, 2002). Impulsivity (or conversely,deficits in self-control) may also be related tomore extreme problem behaviors such as eatingdisorders, substance abuse, and even suicide (seeWenar & Kerig, 2006).

Basic researchers interested in impulsive andirrational decision making have defined impul-sivity as a response profile favoring smallersooner rewards (SSRs) over larger later rewards(LLRs; Rachlin & Green, 1972), or what is

known as temporal discounting.1 Temporaldiscounting refers to the phenomenon in whichrewards lose their subjective value as the delay totheir receipt increases (Ainslie, 1974; Madden &Johnson, 2010). Mazur (1987) developed aprocedure for measuring temporal discountingin pigeons by investigating the point at which anSSR was chosen over an LLR within a titratingseries of comparison trials. Depending on thesubject’s choice each trial, the LLR was furtherdelayed when choice favored LLRs or deliveredmore immediately when choice favored SSRs.This procedure was used to determine the point(i.e., the indifference point or subjective value) atwhich the subject switched from an LLR to anSSR. Plotting the indifference points (i.e., thesubjectively discounted values of the LLR)against their delays revealed a hyperbolic func-tion conforming to the model:

Vi~Ai

1zkD, ð1Þ

where V is the subjective value of a specific

Correspondence concerning this article should beaddressed to Derek D. Reed, who is now at theDepartment of Applied Behavioral Science, Dole HumanDevelopment Center, 1000 Sunnyside Ave., Room 4048,Lawrence, Kansas 66045 (e-mail: [email protected]).

doi: 10.1901/jaba.2011.44-1

1 The reader will note the use of the term reward ratherthan reinforcer. In discussions of hypothetical choices,typically employed in discounting research, consequencesare not typically delivered as part of the choice paradigm.Thus, we cannot be certain that the choice produces anactual increase in behavior.

This study was conducted by the first author in partialfulfillment of the requirements for the PhD degree inschool psychology at Syracuse University. We thankFlorence D. DiGennaro-Reed, Tanya L. Eckert, MartinJ. Sliwinski, Lauren Axelrod, and Lauren McClenney fortheir assistance throughout the duration of this project.

JOURNAL OF APPLIED BEHAVIOR ANALYSIS 2011, 44, 1–18 NUMBER 1 (SPRING 2011)

1

reward, A is the actual amount of the reward, D isthe delay until the reward is obtained, and k isthe derived scaling constant of the hyperbola.This equation proposes a discounting function inwhich the subjective value of a reward increasesas its amount increases, but decreases as ahyperbolic function of the waiting time until itis obtained.

In analyses of discounting, relatively higher kvalues translate to relatively higher degrees ofimpulsive responding, as the hyperbolic curveaccelerates downward more rapidly acrossincreasing delays. Figure 1 shows two hypo-thetical discounting functions, one characteris-tic of self-control (values discounted less withincreases in delay, producing a lower k value)and one characteristic of impulsivity (valuesdiscounted more with increases in delay,producing a higher k value). According to themodel depicted in the equation above, a trade-off exists between the value of a reinforcer andthe delay until its receipt. It is important to notethat the hyperbolic function depicted byEquation 1 also permits analysis of data patternsthat feature preference reversals (i.e., when a

participant chooses the LLR after choosing theSSR at previous delays).

Investigators have typically used hypotheticalmonetary choice trials to examine the discount-ing phenomenon with humans. For example,Green, Fry, and Myerson (1994) asked 12sixth-grade children, 12 college students, and 12older adults to choose between an SSR and anLLR (each framed as hypothetical monetaryrewards) across a series of trials using a titratingprocedure adapted from Rachlin, Raineri, andCross (1991). Specifically, participants werepresented with two sets of cards with printedmonetary amounts. One set of 30 cardscontained the SSR values that varied from0.1% to 100% of the LLR comparison values.The second set contained the LLR values. Eightdelay values were used for each monetary valueof the LLR: 1 week, 1 month, 6 months, 1 year,3 years, 5 years, 10 years, and 25 years. Delayswere presented in both progressively ascendingand descending orders. Equation 1 was appliedto the obtained indifference points, calculated asthe average switch point (i.e., when theparticipant shifted preference from the LLR tothe SSR) for each delay between the ascendingand descending reward conditions. With anLLR value of $1,000, k values for the children,young adults, and older adults were .618, .075,and .002, respectively. The relatively higher kvalues suggest more rapidly decreasing slopes(i.e., greater discounting) for the children’sdiscounting plots, suggesting more impulsiveresponding than the two older groups. Varianceaccounted for (R2) was .995 for the children,.996 for the young adults, and .995 for theolder adults.

Temporal discounting has been used toconceptualize impulsive decisions, such as drugabuse (e.g., Madden, Petry, Badger, & Bickel,1997), cigarette smoking (e.g., Bickel, Odum,& Madden, 1999), and gambling (e.g., Dixon,Marley, & Jacobs, 2003), as resulting from thelowered subjective value of rewards associatedwith self-control. This in turn has suggested

Figure 1. Hypothetical discounting plot depictingboth steep discounting (higher k, dashed curved line;

i.e., impulsivity) and less steep discounting (lower k, solidcurved line; i.e., self-control).

2 DEREK D. REED and BRIAN K. MARTENS

procedures for reducing impulsive tendencies bygradually shaping the delay associated with theself-control response. For example, Neef, Bi-card, and Endo (2001) examined the relativeinfluence of response effort and reinforcer rate,quality, and immediacy on choice responding ofthree children with ADHD. Immediacy was themost influential reinforcer dimension in eachcase, followed by quality and then rate. Duringsubsequent self-control training, delay to receiptof high-quality or high-rate reinforcers wasreduced and then systematically increased to thebaseline value of 24 hr. By the end of training,all three children exhibited self-control bychoosing the reinforcer dimension that com-peted with immediacy.

Some evidence suggests that results ofdiscounting assessments that use hypotheticalrewards, as in Green et al. (1994), are predictiveof choices that involve real rewards in laboratorysettings (e.g., Johnson & Bickel, 2002; Mad-den, Begotka, Raiff, & Kastern, 2003; Maddenet al., 2004). Moreover, the hypotheticalmonetary choice trial paradigm has demon-strated adequate reliability as an assessmentmethod for college-aged participants at 3-day(Lagorio & Madden, 2005), 1-week (Simpson& Vuchinich, 2000), 3-month (Ohmura,Takahashi, Kitamura, & Wehr, 2006), and 6-month (Beck & Triplett, 2009) test–retestintervals. Despite promising results in labora-tory research, the extent to which discountingassessments are predictive of human behavior ineducational settings remains untested. Critch-field and Kollins (2001) have proposed thattemporal discounting assessments may beespecially advantageous in such settings becausethey involve behaviors for which consequencesare far removed in time or which are indicativeof self-control deficits that interfere withcontingency learning (e.g., as in children withADHD). More specific to the current study,because the rewards delivered in educationalsettings are often delayed (e.g., grades, feedbackon performance, token exchanges for primary

reinforcers), a better understanding of therelation between discounting and responsive-ness to delayed reinforcers would be beneficialto clinicians and researchers.

The primary goal of this study was toexamine the relation between children’s re-sponses on hypothetical monetary choice trialsand their subsequent responsiveness to bothimmediate and delayed rewards as part of anindependent group-oriented classroom contin-gency. A secondary goal was to evaluate theconsistency of obtained discounting scoresacross a 1-week interval. In so doing, we soughtto determine if a temporal discounting assess-ment for children demonstrated adequate test–retest reliability and yielded coefficients ofstability similar to those found with adultpopulations (e.g., Beck & Triplett, 2009;Lagorio & Madden, 2005; Ohmura et al.,2006; Simpson & Vuchinich, 2000). Finally,we sought to determine the efficacy of anadapted discounting procedure for children thatincorporated shorter delays and smaller rewardvalues. This was done to make the hypotheticalchoices more similar to the kinds of temporalsequences and monetary amounts with whichchildren may have experience.

METHOD

Participants and Setting

Students from three sixth-grade classrooms(21, 17, and 8 students from Classrooms 1, 2,and 3, respectively) were recruited for partici-pation (n 5 46) from a rural public elementaryschool in the northeast United States. Ages ofparticipants ranged from 11 years 5 months to12 years 7 months (M 5 12.1, SD 5 0.3).Screening criteria for inclusion in the studywere (a) the absence of any formal disabilityclassification, (b) English proficiency, and (c)the ability to read, each of which was evaluatedthrough teacher interviews. Consent from thestudents’ primary caregivers, as well as verbalassent from the students themselves, wasobtained prior to participation.

DISCOUNTING PREDICTS CLASSROOM BEHAVIOR 3

During the first phase, participants complet-ed a brief temporal discounting assessment (seebelow) individually in the hallway outside theirclassrooms. During the second phase, theexperimenter implemented a classwide inter-vention in the participants’ math class. For eachof the three classrooms, the interventionoccurred during the same math class with thesame math teacher (i.e., students rotated fromtheir home classroom to this math classroom).

Response Measurement

Temporal discounting assessment. The partic-ipants were asked to indicate their preferencebetween two hypothetical choices: one rewardthat was smaller in magnitude but availableimmediately (SSR) and a larger reward availableafter some delay (LLR). During each choicetrial, the SSR and LLR were presented oppositeone another on a magnetic board (see below).Participants were asked to touch the rewardthey most preferred during each trial. Thereward that the participant touched wasconsidered the preferred choice for that trial(there was never a need for the experimenter toprompt a participant to point or to prompt aparticipant to point to only one value). Theexperimenter recorded all choices across all trialson data sheets that displayed all possible choicesfor each of the eight delay values assessed.

Classwide intervention. On-task behaviorrequired that the student have his or her bodyoriented toward work materials (adapted fromMartens, Bradley, & Eckert, 1997). Percentageof intervals scored on task served as thedependent variable across all conditions. On-task behavior was recorded using a 5-s time-sampling procedure, cued by a MotivAidervibrating timer device. Observers began byobserving the participant located in one cornerof the classroom and moving to the peeradjacent to him or her at the end of each 5-sinterval. The observation round was finishedafter the sequence of observations was complet-ed (i.e., observers recorded data once for eachparticipant using the momentary time-sampling

procedure). Only participants seated at his orher assigned desk at the moment of the timesample were observed. It should be noted thatparticipants usually remained seated in theirassigned desks during the duration of theobservations. During a 20-min period, observ-ers completed approximately 10 rounds ofobservation (i.e., obtained approximately 10time samples per participant).

Stimulus Preference Assessment

A group-administered pictorial-choice pref-erence assessment (adapted from Fisher et al.,1992; see Reed & Martens, 2008) identifiedpreferred academic-related items (pens, pencils,stickers, and erasers) for use as rewards. Thestimulus picked most often by the group in eachclassroom was considered highly preferred, andthe stimulus picked least often was consideredleast preferred. The remaining two items wereconsidered moderately preferred. For Class-rooms 1 and 2, pens were highly preferred,with pencils and erasers moderately preferred.For Classroom 3, pencils were highly preferred,and pens and erasers were moderately preferred.For all three classrooms, stickers were the leastpreferred items.

Temporal Discounting Assessment

The experimenter used a magnetic board(26.2 cm by 35.8 cm) that stood upright on aneasel to present hypothetical choices to theparticipants. Participants sat across the tablefrom the experimenter, with the temporaldiscounting display board in front of them onthe table. Reward values and delays until rewardwere displayed on magnets (2.6 cm by 10.2 cm)that were placed in their respective positions onthe display board. Specifically, amounts dis-played on the magnets were in accordance witha titrated series of forced-choice amounts. Theexperimenter read the following directions tothe participants:

Today, we are going to play a pretend game aboutmaking choices about money. Since we are onlypretending, you will not actually get the money that


you choose. But I want you to pretend that the gameis real, so please take your time to decide whichamount of money you would really want. Ourpretend game will be done with this board. The leftside [points to left side] of the board will show acertain amount of money you can pretend to haveright now [stress ‘‘right now’’]. On the right side ofthe board [points to right side] is the amount ofmoney you can wait [stress ‘‘wait’’] to have instead. Iam going to ask you a lot of pretend decisions tomake. When I place the money amounts on theboard, I will ask you to pick the one you want themost. If you want to choose the money on the leftside, simply point to that side. If you decide that youwant to wait to have the money on the right side,simply point to the right side. Let’s practice. Wouldyou rather have $1 now [puts up $1 magnet on left],or $1,000 in 10 minutes [puts up $1,000 and10 minutes magnets on right]. Great! You chose —.Now you know how to play. Do you have anyquestions before we start?

The experimenter manipulated the amountof the SSR at different LLR delay values todetermine the points at which each participantchanged his or her preference from the LLR(always a hypothetical $100) to the SSR. EightLLR delay values were assessed: 1 day, 5 days,1 month, 2 months, 6 months, 9 months,1.5 years, and 4 years. These delays remainedconstant for a block of trials. Within each trialblock, the value of the SSR varied depending oneach choice made by the participant (see below).Eight indifference points (one at each delayvalue) were used to fit the hyperbolic curve foreach participant. All participants began with the1-day LLR delay and continued through theseries of delays in the same order, from shortestto longest.

The experimenter began each block of trialsby asking the participant to choose between $50available immediately and $100 available after adelay of X, where X represented the value of theLLR delay during that respective block of trials.If a participant chose the $50 available now, thenext trial pitted an even smaller amount ofmoney available now against $100 available atthe given delay. However, when the participantopted for the $100 available at the given delay,the experimenter asked the participant tochoose between a larger immediate monetary

amount (i.e., SSR) and the delayed $100 on thenext trial. This rapid titration procedurecontinued until the participant demonstratedpreference for the LLR after previously switch-ing to the SSR after an initial LLR choice (orvice versa; see Critchfield & Atteberry, 2003,for a visual depiction). After two such prefer-ence reversals, a final trial was conducted todetermine the indifference point. If a partici-pant demonstrated exclusive preference foreither the LLR or SSR across five consecutivetitrations, the discounting assessment trials forthat delay value were concluded. The subjectivevalue of the $100 (i.e., the indifference point)then was derived by averaging the SSR value onthe previous trial and the value of the SSRduring this final choice trial. This adjustingprocedure allowed an estimation of the indif-ference point (i.e., the averaged SSR valueconverted to a percentage of LLR; also referredto as the subjective value) of the $100 across theeight delay values in terms of smaller amountsof money available immediately (ranging from0.1% to 99.9% of the value of the delayedmonetary amount, or $100) at each delay (seeCritchfield & Atteberry, 2003).

The assessment occurred twice during thecourse of the study, with the two administra-tions of the assessments separated by 1 week.Repeated administration of the assessmentallowed an examination of test–retest reliabilityover a 1-week interval.

Classwide Intervention

One to 2 days following the second admin-istration of the discounting assessment, theexperimenter implemented a classwide inter-vention targeting on-task behavior in eachclassroom. Only one session was conductedeach day, 5 days per week, during the baselineand sooner reward conditions. During thedelayed reward condition, sessions were con-ducted once per day, Monday through Thurs-day. The experimenter was present on Friday todeliver rewards earned on Thursday, but noobservations were conducted, nor could stu-


dents earn rewards on Fridays during thedelayed reward condition. This proceduralvariation was necessary to ensure that a 24-hrexchange delay was in effect throughout thiscondition. All sessions lasted 20 min.

Baseline. Participants were observed duringteacher-led instructional time when the studentswere expected to be seated at their desks. Noprogrammed reinforcement contingencies werein place for on-task behavior.

Sooner reward. Procedures were identical tobaseline except that participants could earn apreferred item immediately following theobservation. Prior to all intervention sessions,participants were reminded of the classroomtoken system. The experimenter deliveredfeedback via a token board to all participantscoded as on task during the first, third, fourth,sixth, and eighth rounds of observations. Thus,tokens were delivered immediately followingapproximately half of the time-sample observa-tions throughout the session. We chose todeliver feedback on an intermittent schedule toreduce the likelihood of reactivity from thestudents’ recognition of the time-samplingintervals. The experimenter provided feedbackto participants observed to be on task by placinga token next to the student’s name on a displayboard located on the chalkboard in front of theclassroom. Immediately after the observation,participants observed to be on task during allfive feedback rounds could choose between onehighly preferred item and two moderately orleast preferred items. Participants observed to beon task during three or four feedback roundscould choose one moderately preferred item,and participants observed to be on task forfewer than three feedback rounds (but morethan zero) could choose one least preferreditem. No participant was ever observed to be offtask for all five observations.

Delayed reward. Procedures were identical tothose in the sooner reward condition except thattokens were exchanged for back-up reinforcersat the beginning of the next day’s session,

approximately 24 hr after the tokens had beenearned. We selected a 24-hr exchange delay toavoid adventitious reinforcement (i.e., exchang-ing Monday’s tokens on Wednesday couldadventitiously reinforce responding on Tues-day).

Design. The effects of the classwide interven-tion on on-task behavior were evaluated using amultiple baseline design across classrooms. Thedesign began with three baseline sessions in thefirst classroom followed by five sessions of thesooner reward condition. After stable data wereobserved via visual inspection of classroomaggregated data, five sessions of the delayedreward condition occurred for Classroom 1 andseven sessions occurred for Classrooms 2 and 3.

Procedural Fidelity and Interobserver Agreement

During both temporal discounting assess-ments and the classwide intervention, a secondindependent observer was present for at least33% of each assessment and classroom obser-vation sessions to monitor the fidelity ofadherence to the research protocol. During thetemporal discounting assessment, the fidelityobserver recorded whether the researcher pre-sented the discounting choices in the expectedsequence based on participant responses. Devi-ations from the protocol were scored as adisagreement for that particular block of trials(with a constant large-reward delay) in thetemporal discounting assessment. Similarly,procedural fidelity for the classwide interven-tion was assessed by having a second observerrecord token and back-up reinforcer delivery.Specifically, the second observer was given a listof participants who met the various reinforce-ment criteria. This observer then recorded thenames of students who obtained reinforcersfrom the experimenter, as well as those studentswho did not, along with the number and typeof rewards they obtained. This list was cross-referenced with the original list of eligibleparticipants to assess fidelity of both tokenand reinforcer delivery. In all instances, proce-dural fidelity was calculated by dividing the


number of instances of agreement (i.e., appro-priate implementation of the treatment proto-col) by the number of agreements plusdisagreements (i.e., instances of deviations fromthe treatment protocol), multiplied by 100%.For both discounting assessments, as well asduring each condition of the classwide inter-vention, fidelity was 100% for all threeclassrooms.

A second independent observer was presentfor at least 33% of the sessions in eachclassroom to collect data for the purpose ofcalculating interobserver agreement during eachtemporal discounting assessment and eachcondition of the classwide intervention. Duringthe temporal discounting assessment, the sec-ond observer recorded the participant’s choiceon every trial using the same data sheets as theexperimenter. Similarly, interobserver agree-ment for the classwide intervention was assessedby having a second observer independentlyrecord student behavior on a classwide inter-vention data sheet. In all instances, agreementwas calculated by dividing the number ofinstances of agreement by the number ofagreements plus disagreements, multiplied by100%. Interobserver agreement was 100% forall three classrooms for both discountingassessment. During baseline of the classwideintervention, mean agreement was 97% forClassroom 1, 99.6% for Classroom 2, and 97%for Classroom 3. During the sooner rewardcondition for the three classrooms, meanagreement was 99% for Classroom 1, 99% forClassroom 2, and 100% for Classroom 3.Finally, during the delayed reward condition,mean agreement was 99% for Classroom 1,99.7% for Classroom 2, and 99% for Class-room 3.

Data Analysis

It has been proposed that adding anadditional free parameter (superscript s in theequation below) to the equation described byMazur (1987) may account for individualdifferences in organisms’ sensitivity to delay

(i.e., organisms’ responses controlled more byreward delay than reward amount; Logue,Rodriguez, Pena-Correal, & Mauro, 1987;Rachlin, 1989). Inclusion of the additional freeparameter s results in the following two-parameter hyperboloid discounting model(Myerson & Green, 1995):

Vi~Ai

(1zkDi)s : ð2Þ

By definition, the inclusion of s improves thegoodness of fit of the discounting model to adata set relative to Equation 1. Many contem-porary studies of discounting use this two-parameter hyperboloid model (Equation 2)rather than the simple hyperbolic model inEquation 1 or more complex models ofdiscounting (see McKerchar et al., 2009).Because the field has not conclusively demon-strated superiority of one equation over another,we analyzed our data using both hyperbolic(Equation 1) and hyperboloid (Equation 2)discounting equations. With regard to the useof the hyperboloid model, we examinedwhether the additional free parameter s in thetwo-parameter hyperbolic discounting modeloffered any advantage over assuming a value of1 for the students in our sample. This findingwould provide further evidence of the robust-ness of the hyperboloid discounting equation intheoretical discussions of quantitative modelsand further demonstrate that the findings inbasic experimental studies may be translated toelementary-aged students.

Discounting parameters (i.e., k values andR2) were obtained by fitting the mean of eachparticipant’s indifference points from the twoassessment sessions to Equations 1 and 2 usingthe PROC NONLIN function in the SASstatistical software program. This mean scorewas used to control for any fluctuations thatmay have occurred in response patterns betweenthe initial test session and the 1-week retest. Themean across temporal discounting assessmentswas taken as an estimate of the true score andwas used for analyses of the psychometric


properties of the temporal discounting assess-ment.

Myerson, Green, and Warusawitharana(2001) proposed that, in addition to quantita-tive models of discounting, researchers alsoreport the area under the discounting curve.Area under the curve (AUC) is a nontheoreticalapproach to evaluating the degree of discount-ing, measured by plotting indifference points(i.e., the delay value at which smaller rewardsbecome more preferred than larger rewards) onthe ordinate with delays to the larger reward onthe abscissa. When thus plotted, low AUCvalues correspond with high k values, becausethe hyperbolic function drops rapidly. Typical-ly, AUC estimates are calculated using thetrapezoidal method based on the equation,

AUC~X

(x2{x1)(y1zy2)

2

� �, ð3Þ

where x1 and x2 are successive delays and y1 andy2 are the subjective value of those delays. Thismethod of analysis was used to provide atheoretically neutral quantification of discount-ing. Due to the skewed distribution (i.e.,variance was not a normally distributed bellcurve) of the participants’ discounting data,nonparametric Spearman’s rho (rs) correlationswere conducted to determine the coefficient ofstability for participants’ indifference pointsacross the 1-week test–retest window.

For all participants, the mean of his or herindividual percentage of intervals with on-taskbehavior during the delayed condition wassubtracted from the mean of his or herpercentage of intervals on task during thesooner condition to yield a difference score.Correlations then were computed betweenparticipants’ individual discounting parameters(from Equations 1 and 2 as well as AUC) andtheir difference scores from the classwideintervention to determine the degree to whichthe results of the temporal discounting assess-ment predicted the differential effectiveness ofdelayed or immediate consequences in the

classwide reinforcement system (i.e., a proxyto predictive validity). Specifically, Spearman’srho correlations were used to determine if thoseindividuals with higher difference scores hadlower AUC and higher k parameters.

RESULTS

Temporal Discounting Assessment

To determine whether increasing delays wereassociated with discounted reward values in thehypothetical choices presented to participants, acriterion adapted from Dixon, Jacobs, andSanders (2006) was employed. Under thiscriterion, a participant was considered to showa discounting effect if the mean of theindifference points from the three shortest delayconditions exceeded the mean of the indiffer-ence points from the three longest delayconditions, with no more than one instance ofan increase in indifference points across succes-sive delays (i.e., preference reversal). However,considering the exploratory nature of thecurrent study, this criterion was amended toallow up to two instances of increasingindifference points across successive delays inan effort to maximize the number of partici-pants for analysis. In total, only 26 of the 46(56%) participants met this inclusionary crite-rion. It is estimated that discounting studieswith adults exclude up to 15% of their data dueto invalid patterns (i.e., multiple preferencereversals; Critchfield & Atteberry, 2003).Therefore, all analyses and data presented arespecific to those participants whose data met theinclusionary criteria. For seven of the 26participants, we could not fit Equation 2 tothe data due to extreme variability in choice.

In strict discounting, each successive delayshould feature a lower subjective value (i.e.,lower indifference point) than the previous (i.e.,a strict monotonically decreasing trend). In thepresent study, only five participants (P6, P12,P13, P16, and P22) featured such a pattern.However, 16 (61%) of the 26 participantsdemonstrated a more liberal monotonically


decreasing trend in which each successive delayfeatured a subjective value that was either lessthan or equal to the subjective value at theprevious delay. The remaining 10 participants(38%) were those individuals with either one ortwo preference reversals. (Each participant’sindifference points across all eight delays fromAssessments 1 and 2 are available from the firstauthor.)

Table 1 presents the best fitting values takenby the parameters of Equations 1 and 2 (thediscounting models typically employed indiscounting studies; see Critchfield & Kollins,2001; Myerson et al., 2001), as well as the meanAUC and the difference score derived from theclasswide intervention, for each of the 26participants whose data were analyzed (recallthat participants with more than two instances

of increasing indifference points as delaysincreased were excluded from these analy-ses).The median k value and R2 for Equation1 were .03 (i.e., moderate discounting) and .98(i.e., 98% of the variance was accounted for bythe discounting model) for the 26 participantswhose data were analyzed, respectively. Simi-larly, for Equation 2, the median k value was.02 and the median R2 was .98. As notedpreviously, Equation 2 could not be fit to sevenparticipants’ data due to multiple preferencereversals. For these participants, only Equation1 and AUC parameters are reported in Table 1.

Through the use of Equation 2 (i.e., thehyperboloid model), fitting each participant’sdata to the statistical model not only derived kand R2 values but also an exponent value (s) thatis considered to be a sensitivity-to-delay param-

Table 1

Derived k Values for Equations 1 and 2, Proportions of Variance Accounted for by Equations 1 and 2 (R2), Derived s

Values for Equation 2, Mean Area under the Curve (AUC), and Derived Difference Score from the Classwide

Intervention for Each Participant

Participant

Equation 1 Equation 2

Mean AUC Diff scorek R2 k S R2

P1a 0 1.00 20.14 1.29 .16 .97 .11P2 0 .99 .69 2.05P3 0 .98 .65 .14P4 0 1.00 .44 .04P5 0 .94 20.16 1.73 .31 .36 .03P6a 0.01 .99 0.01 0.02 1.00 .30 .01P7 0.01 .98 .26 .05P8 0.02 .95 20.13 1.23 .36 .24 .13P9a 0.02 .98 20.13 1.02 .47 .21 .05P10 0.01 .99 0.01 0 .99 .17 .16P11 0.01 .98 0.01 0.11 .99 .16 .06P12 0.03 .99 0.02 0.07 .99 .12 .10P13 0.01 .98 0.01 0 .98 .12 2.05P14 0.02 .98 20.13 0.93 .56 .11 2.01P15 0.07 .97 0.04 0.16 .98 .09 .18P16 0.05 .86 0.02 0.37 .96 .08 .18P17 0.05 1.00 0.05 0 .99 .07 .07P18a 0.15 .99 0.16 20.01 .99 .02 .21P19a 0.67 .90 .01 .24P20 1.84 1.00 1.54 0.17 1.00 .01 .22P21a 0.76 .96 0.23 0.48 1.00 .01 .25P22 0.93 .99 5.73 21.31 1.00 .01 .37P23 1.78 .83 0.15 1.01 .97 .01 .06P24 0.73 .98 1.21 20.28 .98 .01 .12P25 0.87 .96 0 .09P26 0.61 .86 0 .08

a Participant included as an exemplar in Figure 3.


eter. If the exponent is not found to besignificantly different than 1 given the standarderror of the fitted parameter, Equation 2reduces to Equation 1. In the current study,the derived exponents in the hyperboloid model(Equation 2) were indeed significantly differentthan 1, suggesting that the participants weremore sensitive to shorter delays than whatwould be expected in the hyperbolic model(Equation 1), t(17) 5 23.65, p , .01. Thus, ahyperboloid model was necessary to bestdescribe the patterns of responding observedin the discounting assessment for the 19participants with one or fewer preferencereversals. However, for the seven participantswho demonstrated two preference reversals, thehyperbolic model was necessary due to theinability of the hyperboloid model to fit theirdata.

AUC was calculated using Equation 3 foreach of the 26 participants using the data fromboth Assessments 1 and 2. As describedpreviously, the AUC discounting metric is ameasure of discounting that is independent ofany theoretical model (e.g., hyperbolic vs.hyperboloid). Moreover, AUC ensures that adiscounting parameter can be calculated andused to make relative comparisons amongparticipants, even if data do not suggestadherence to discounting assumptions. Thus,AUC may be considered an exact measurementof discounting, unlike the estimations used inEquations 1 and 2. For Assessments 1 and 2,AUC ranged from 0 to .99 and 0 to 1,respectively. These data indicate that our samplewas comprised of participants with extremediscounting tendencies (AUC near 0), as well asextremely self-controlled response patterns(AUC near 1).

Test–Retest Reliability

To investigate test–retest reliability for thetemporal discounting assessment, a coefficientof stability (i.e., a correlation coefficient ofreliability estimated through the stability ofindifference points) was computed for each of

the eight delays, in addition to the AUC valuesfor Assessments 1 and 2. Figure 2 displays thescatterplots of the aggregate indifference pointsfrom Session 1 and Session 2, along with theSpearman’s rho coefficient of stability (rs), foreach of the eight delay values. Specifically, thehighest coefficients of stability were found forthe following delays: 9 months (rs 5 .90),6 months (rs 5 .87), 5 days (rs 5 .86), and1.5 years (rs 5 .82). The lowest degree ofreliability was observed at the 1-day delay (rs 5

.68). All other delays had reliability coefficientsof .81. Thus, adequate levels of test–retestreliability (i.e., .80 and above) were obtained forseven of the eight (87.5%) delay values.Moreover, each of the coefficients at the variousdelays across all 26 participants was significantat p , .01. Reliability was assessed for the AUCdiscounting metric to determine the stability ofpreferences at the eight delay values across the1-week test–retest interval. The AUC statisticwas also found to be significantly reliable acrossthe 1-week test–retest interval, rs(24) 5 .88, p, .01.

Classwide Intervention

Results of the classwide intervention arepresented in Figure 3 (left) for six students,consistent with the multiple baseline designacross classrooms (Classrooms A, B, and C).These exemplars were selected based on thecriterion that the participant demonstratedeither high or low AUC scores relative to otherstudents in the classroom. The multiple baselinedesign figures in Figure 3 (right) depict dis-counting plots for Testing Times 1 and 2 aswell as AUC estimates for each assessment.Exemplar students with lower AUC scores (thesecond student in each pair) were considered tobe more impulsive, and those with higher AUCscores (the first student in each pair) wereconsidered to be less impulsive than his or herpeers (see the discounting plots in the rightpanels of Figure 3).

As seen in Figure 3 (left), relatively higherlevels of on-task behavior were observed during


Figure 2. Scatterplots of aggregate indifference points for each of the eight delays, across Sessions 1 and 2. Each panel

represents an individual delay value and provides the Spearman’s rho correlation for that delay value, along with adiagonal line that indicates the slope of a perfect correlation. Double asterisks indicate that the correlation is significant atthe .01 alpha level.


baseline for participants who had higher AUCvalues via the discounting task (Figure 3, right).Increases in on-task behavior during the soonerreward condition relative to baseline weregreater for those participants with lower AUCvalues than for participants with higher AUCvalues, with P19 having the largest relative

increase (i.e., from approximately 60% on taskin baseline to 100% in the sooner rewardcondition). For two of the three participantswith higher AUC values (P1 and P6), onlymodest improvements were observed in levels ofon-task behavior. However, it should be notedthat on-task behavior in baseline was relatively

Figure 3. Results of the classwide intervention for on-task behavior in concurrent multiple baseline format for sixexemplar students, along with his or her derived difference score between the reinforcement conditions. Filled circles in

the left panels represent data for exemplar impulsive students, and open circles represent data for exemplar self-controlstudents. Dashed gray lines represent mean levels of on-task behavior in each condition. Panels to the right of the time-series figures show discounting plots for Testing Times 1 and 2 as well as AUC estimates for each assessment.


high. For example, P6 had 100% on-taskbehavior in baseline, so any potential changesduring the reinforcement conditions could onlybe in a negative direction. For all threeparticipants with higher AUC values, transi-tioning from the sooner reward condition to thedelayed reward condition produced only negli-gible differences in on-task behavior. However,for all three participants with lower AUC, on-task behavior substantially decreased as theytransitioned from the sooner to the delayedconditions. Comparing these differences inlevels of on-task behavior across reward delayconditions to the AUC scores in Figure 3(right) illustrates these relations.

Difference scores for all 26 participantsranged from 2.05 to .37, with a median of.10 (see Table 1). In this case, lower scoressuggested less difference between immediateand delayed contingencies (or in the case of anegative number, higher percentages in thedelayed condition than in the sooner condi-tion), with higher scores indicating morepercentage of intervals on task during thesooner condition. Positive difference scoreswere found for 23 of the 26 cases, suggestinga consistent effect across participants. Thesedifference scores were calculated for use inanalyses of the validity of the temporaldiscounting assessment.

Validity Analyses

Correlations were computed between pairs ofthe three discounting parameters (i.e., k inEquation 1, k in Equation 2, and AUC) todetermine their degree of correspondence. Thecorrelation between Equation 1 k and AUC wassignificant and highly negative, rs(24) 5 2.94, p, .01, as was the correlation between Equation 2k and AUC, rs(17) 5 2.92, p , .01, using thecriterion set forth by Cohen (1988). Thus,higher k values were indeed associated withlower AUC values. In addition, the correlationbetween the discounting parameters Equation 1k and Equation 2 k was significant and highlypositive, rs(17) 5 .90, p , .01.

Figure 4 shows three scatterplots that depictthe relation between participants’ discountingparameters and decreases in students’ on-taskbehavior due to reinforcement delay (i.e., thedifference score). Each plot features the Spear-man’s rho linear regression line to describequantitatively the correlations between thesevariables. As Figure 4 indicates, the rank-ordercorrelation between each of the three discount-ing parameters and difference scores wasmoderate and significant: for Equation 1 kand the difference score, rs(24) 5 .58, p , .01;for Equation 2 k and the difference score, rs(17)5 .66, p , .01; for AUC and the differencescore, rs(24) 5 2.50, p , .01, indicatingadequate levels of predictive validity. That is,delayed rewards were less effective than imme-diate rewards for increasing on-task behavior ofstudents with higher discounting scores fromthe temporal discounting assessment (and lowerAUC values), consistent with the data inFigure 3.

DISCUSSION

Delay of reward is inevitable in most settings.Undoubtedly, no organism experiences imme-diate contact with rewards at all times. Despitethis, many questions remain regarding theanalysis of delayed reinforcement (Critchfield& Kollins, 2001). The present study attemptedto answer several questions posed by Critchfieldand Kollins regarding the use of temporaldiscounting assessments, thereby replicatingand extending previous discounting research.First, does the preference for hypotheticalrewards in standard temporal discountingassessments translate to or predict observablebehaviors that are reinforced with actualrewards? Similar to previous research (Kirby &Marakovic, 1996; Richards, Zhang, Mitchell, &de Wit, 1999), the present study foundadequate levels of predictive validity between apaper-and-pencil discounting assessment forchildren and their responsiveness to immediateand delayed classroom rewards.


Second, are the findings from temporaldiscounting assessments adequately stable overtime? Similar to the previous studies onreliability (Beck & Triplett, 2009; Lagorio &Madden, 2005; Ohmura et al., 2006; Simpson& Vuchinich, 2000), this investigation foundadequate test–retest reliability across a 1-weekinterval for both indifference points and AUCestimates. Thus, the current study suggestedthat the temporal discounting assessment maybe reliable for many children.

Third, are children similar to adults in thatthey exhibit negative decelerating discountingfunctions such that the subjective value of theLLR decreases more rapidly at small delays thanat longer delays (recall the example in Fig-ure 1)? The present study replicated thefindings from Barkley, Edwards, Laneri, Fletch-er, and Metevia (2001) and Green et al. (1994)with a majority, albeit a slim one, of respondingconforming to general models of discounting.Unlike previous research with children, thisstudy used an adapted assessment (i.e., shorterdelays and smaller values) in an effort to makethe procedures more applicable to these youngparticipants. Although these efforts were per-haps a step in the right direction, more

adaptations may be warranted given that only56% of our sample met the discountingcriterion adapted from Dixon et al. (2006). Inaddition, analysis of the additional free param-eter s in Equation 2 found that, similar toadults, the students’ sensitivity to delay wassignificantly different from 1 (specifically,significantly less than 1), directly replicatingthe findings of Myerson and Green (1995).Thus, these data suggest that the theoreticalmodels of discounting derived in the basicliterature are robust across age groups. Specif-ically, these data indicate that, similar to adults,children are more sensitive to shorter delays(relative to longer ones) than what is predictedby the simple hyperbolic model of discounting(i.e., Equation 1).

Finally, implications of the present findingsmay extend beyond the assessment of temporaldiscounting. The results obtained from theclasswide token system offer an interestinginsight into the role of token exchange delaysin the management of classroom behavior. Pastresearch into exchange delays has suggested thatorganisms tend to value rewards that areavailable sooner rather than later (Hackenberg& Vaidya, 2003; Hyten, Madden, & Field,

Figure 4. Scatterplots of discounting parameters and derived difference scores from the classwide intervention. Eachpanel represents an individual discounting parameter and provides the Spearman’s rho correlation for that parameterwith the difference score, along with a best fit linear regression line. Double asterisks indicate that the correlation is

significant at the .01 alpha level.


1994; Jackson & Hackenberg, 1996). To date,these findings have not been replicated inapplied settings. The present study showed thatstudents’ levels of on-task behavior weresensitive to token exchange delays as part of aclasswide token economy. From a clinicalstandpoint, token-exchange procedures for stu-dents with low AUC values (which suggestsgreater levels of impulsivity) were more likely tobe efficacious when exchange delays wererelatively brief. The behavior of students withrelatively high AUC values improved even whenexchange delays were relatively long.

A second implication of these findings is thepotential importance of training behaviorconsistent with self-control when using class-room reinforcement programs. For example,one might establish control over appropriatebehavior by immediately delivering large mag-nitude reinforcers and then gradually increasingthe delay across sessions. This approach hasbeen reliably successful for individuals withADHD (e.g., Binder, Dixon, & Ghezzi, 2000),developmental disabilities (e.g., Vollmer, Bor-rero, Lalli, & Daniel, 1999), and brain injury(e.g., Dixon, Horner, & Guercio, 2003). Asimilar fading process might be incorporatedinto a choice paradigm in which one or morepreferred reinforcer dimensions are manipulat-ed to initially bias responding in favor of thedelayed alternative, as in Neef et al. (2001).Whether such procedures would ultimately shiftindifference points and produce lower k valuesduring a temporal discounting assessment is aquestion worthy of future investigation.

A number of procedural limitations compro-mise the external validity of our findings.Specifically, only 26 of the 46 participantsmet Dixon et al.’s (2006) criterion for dis-counting (i.e., consistent decrease in thesubjective value of the LLR as delay increaseswith minimal preference reversals across delays),suggesting a number of future research direc-tions. First, the current methodology employedonly hypothetical choices, and our sample of

sixth-grade students may have had little to noprior experience with such choices. Futureinvestigations should examine whether actualreward choice and hypothetical reward choicesproduce consistent outcomes for this age group.Second, this assessment examined maximumdelay values of up to 4 years and maximumreward values of $100. It seems plausible thatreducing these maximum values would havemade the hypothetical choices more similar tothe actual choices that the participants werelikely to have experienced in their day-to-daylives. Thus, more research with children isnecessary to isolate the delay and reward valuesthat yield data consistent with discountingassumptions for the majority of participants.

Third, the test–retest reliability of the hypo-thetical monetary reward task was assessed foronly a 1-week interval. The extent to whichdiscounting in children would remain stable overlonger time periods given intervening experienc-es or developmental gains in cognition remainsunknown. Fourth, the hypothetical monetarychoices in the discounting assessment werequalitatively different from the academic-relatedrewards used in the classwide intervention,possibly compromising the assumption thatone kind of reward could serve as a proxy foranother. Fifth, we did not randomize the relativeposition (left or right) of the SSR, which maypossibly confound results if a position bias haddeveloped. (It should be noted that none of theparticipants was suspected of demonstratingresponse bias during the assessment [e.g., alwayschoosing the stimulus on the left].) Finally, withthe exception of the 1-day delay, the currentinvestigation did not use equivalent delay lengthsbetween the discounting assessment and theexchange delays in the intervention. Futurestudies that compare subjective values fromdiscounting assessments’ delay values to equiv-alent delay values in actual behavior-changeprocedures should provide a more direct com-parison between hypothetical discounting andactual responsiveness to delayed reinforcement.


In addition to the possible limitations of thetemporal discounting assessment, several proce-dural characteristics of the classwide interven-tion also limit interpretations of the presentfindings. First, no reinforcer assessment wasconducted to validate the results of thepreference assessment due to the large numberof students in this study and practical con-straints. Thus, we relied on the verbal report ofthe participants that these rewards were pre-ferred and therefore would function as rein-forcers in the classwide token economy. Had wedocumented that these preferred stimuli wereindeed reinforcers, our classroom interventionmay have yielded better differentiation acrossconditions. Second, during baseline of theclasswide intervention, levels of on-task behav-ior for most participants were relatively high,leaving little room to demonstrate effects of theintervention. With such a ceiling effect, wecannot be certain of the potential differencesregarding the effectiveness of our delayed andimmediate reward conditions.

Third, we did not include formal tokentraining, nor did students in these classroomshave prior experience with token systems.Fourth, all classrooms proceeded through thedesign in the same order (i.e., baseline, soonerreward, delayed reward). It is possible that ordereffects may have contributed to the observedchanges in behavior during the delayed condi-tion. In addition, the absence of within-subjectreplication limits the degree to which we couldattribute behavior change to the exchange delaysalone. This should be addressed in futureresearch. Fifth, the 24-hr delay in the delayedreward condition was arbitrarily chosen in aneffort to make the contingencies salient withouthaving additional observations precede thedelivery of back-up reinforcers for previoussessions. A longer exchange delay may haveproduced larger differences between the soonerand delayed reward conditions. Parametricanalyses of differing delay values or the use ofprogressive exchange delays in actual classroom

interventions would better translate the basicresearch on discounting and exchange delays.

The limitations of the current study not-withstanding, this investigation demonstratedthat a hypothetical monetary-choice temporaldiscounting assessment can yield estimatesregarding the degree to which delay of a rewarddevalues it in a choice task. The study extendsprevious research in this area by (a) evaluatingthe psychometric properties of a child-adaptedtemporal discounting assessment procedure, (b)experimentally manipulating exchange delays toderive predictive validity estimates, and (c)demonstrating that greater degrees of discount-ing (i.e., relatively more impulsive responding)were correlated with reduced efficacy of delayedback-up reinforcers in a token economy. Thisinvestigation suggests that intervention agentsmay indeed benefit from consideration of thediscounting phenomenon in the design andimplementation of applied behavior-changeprocedures.

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Received March 6, 2008Final acceptance March 19, 2010Action Editor, William Ahearn


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files.eric.ed.gov · Key words: delay discounting, self-control, choice, behavioral economics, assessment ... This equation proposes a discounting function in which the subjective