analyses of response–stimulus sequences …descriptive analyses cannot be used to identify...

ANALYSES OF RESPONSE–STIMULUS SEQUENCES INDESCRIPTIVE OBSERVATIONS

ANDREW L. SAMAHA

UTAH STATE UNIVERSITY

TIMOTHY R. VOLLMER, CARRIE BORRERO, AND KIMBERLY SLOMAN

UNIVERSITY OF FLORIDA

CLAIRE ST. PETER PIPKIN

WEST VIRGINIA UNIVERSITY

AND

JASON BOURRET

NEW ENGLAND CENTER FOR CHILDREN

Descriptive observations were conducted to record problem behavior displayed by participantsand to record antecedents and consequences delivered by caregivers. Next, functional analyseswere conducted to identify reinforcers for problem behavior. Then, using data from thedescriptive observations, lag-sequential analyses were conducted to examine changes in theprobability of environmental events across time in relation to occurrences of problem behavior.The results of the lag-sequential analyses were interpreted in light of the results of functionalanalyses. Results suggested that events identified as reinforcers in a functional analysis followedbehavior in idiosyncratic ways: after a range of delays and frequencies. Thus, it is possible thatnaturally occurring reinforcement contingencies are arranged in ways different from thosetypically evaluated in applied research. Further, these complex response–stimulus relations can berepresented by lag-sequential analyses. However, limitations to the lag-sequential analysis areevident.

DESCRIPTORS: conditional probability, descriptive analysis, developmental disabilities,lag-sequential analysis

_______________________________________________________________________________

Much has been learned in recent years aboutthe role of reinforcement in the maintenance ofsevere problem behavior. For example, func-tional analysis methods developed by Iwata,Dorsey, Slifer, Bauman, and Richman (1982/1994) have shown that severe behavior disordersare usually learned operant behavior. Functional

analyses usually involve the arrangement ofreinforcement contingencies that specify areinforcer delivery following the target response(i.e., the probability of a reinforcer given anoccurrence of problem behavior is 1.0) but noreinforcer delivery if the target response doesnot occur (i.e., the probability of a reinforcergiven no response is 0). A reinforcer has beenidentified when response rates are higher in onecondition than in other conditions.

Recently, in descriptive analysis research,potential reinforcement contingencies havebeen examined in naturally occurring humaninteractions (Borrero & Vollmer, 2002;Thompson & Iwata, 2001, 2007; Vollmer,Borrero, Wright, Van Camp, & Lalli, 2001).

Portions of this article were supported by the NationalInstitute of Child Health and Human Development,HD38698. We thank Brian Iwata and David Smith fortheir comments on an earlier version of this manuscriptand Gene P. Sackett for a helpful e-mail exchange.

Address correspondence to Andrew L. Samaha, Depart-ment of Special Education and Rehabilitation, Utah StateUniversity, 2865 Old Main Hill, Logan, Utah 84322-2865 (e-mail: [email protected]).

doi: 10.1901/jaba.2009.42-447

JOURNAL OF APPLIED BEHAVIOR ANALYSIS 2009, 42, 447–468 NUMBER 2 (SUMMER 2009)

447

Because no experimental manipulation is made,descriptive analyses cannot be used to identifyreinforcers. However, there are other potentialuses of descriptive analyses. First, descriptiveanalyses might help to operationally defineappropriate or inappropriate behavior. Second,descriptive data might shed light on the baselinerate, latency, duration, or intensity of targetbehavior. Third, descriptive analyses might beused to identify common behavioral consequenc-es. For example, Thompson and Iwata (2001)demonstrated that self-injury emitted by individ-uals with developmental disabilities was predic-tive of subsequent delivery of attention by staff.Fourth, descriptive analyses can be useful whenobserving how reinforcers interact with behaviorunder ordinary circumstances. For this use ofdescriptive analysis, a functional analysis shouldbe conducted to identify reinforcers. The de-scriptive data can then be used to describerelations between reinforcement and behavior innatural interactions. For example, Borrero andVollmer related descriptive data to the matchinglaw after identifying reinforcers via functionalanalysis. It is important to note that this use ofdescriptive analysis is not necessarily for thepurpose of clinical assessment. Rather, thisapproach might be used to better understandhow contingencies of reinforcement work innatural interactions. It is this usage of descriptiveanalysis that is the focus of the current study.

One method of data analysis for descriptivedata involves the use of conditional probabilities(e.g., Lerman & Iwata, 1993). Conditionalprobabilities reflect the probability of observingone event (e.g., a putative reinforcer, such asattention) given the occurrence of another event(e.g., a response, such as self-injury). Suchcomparisons can be used to describe relationsbetween events that happen after responses andthose events that happen either independent of,before, or in the absence of responses.

One advantage of conditional probabilityanalyses is that they can be used to interpretdata in light of a conceptualization of contin-

gency, such as that described by Catania (1998).Catania accounted for reinforcement effects asthe result of interactions between two condi-tional probabilities: the probability of a rein-forcer given a response and the probability of areinforcer given no response. For example, in agiven environment, the probability of attentiongiven self-injury might be .8, and the probabil-ity of attention given the nonoccurrence of self-injury might be .2. If self-injury is shown tooccur primarily in the attention condition of afunctional analysis and is shown to persist in the.8 versus .2 conditional probability arrangementin the natural environment, it suggests that thereinforcement contingency that maintains prob-lem behavior has been described.

Vollmer et al. (2001) examined naturallyoccurring interactions using conditional proba-bilities. They tracked the delivery of potentialreinforcers such as attention, access to materials,and escape from demands. Many of theinteractions they examined involved whatappeared to be a blend of response-dependentand response-independent events; that is, rein-forcers were likely to occur following behavioras well as in the absence of behavior. Thus, theauthors used a conceptualization of contingencysimilar to that of Catania (1998) to interpretthe data. More specifically, they empiricallydistinguished possible positive, negative, andneutral contingencies by comparing the prob-ability of observing an event following behaviorto the unconditional or background probabilityof that event (the probability of observing thatevent following randomly selected points duringthe observation). Positive contingencies werethose in which the conditional probability of anevent was higher than the unconditionalprobability. Negative contingencies were thosein which the conditional probability of an eventwas lower than the unconditional probability.One limitation of the study was that afunctional analysis was not conducted todetermine the stimulus functions of the eventstracked during the descriptive analysis.

448 ANDREW L. SAMAHA et al.

Emerson, Thompson, Reeves, Henderson,and Robertson (1995) analyzed naturally oc-curring contingencies using a method called lag-sequential analysis. They compared the proba-bility of putative reinforcers following targetbehavior to the probability of observing thoseevents independent of behavior (unconditionalprobability). Traditional methods of calculatingconditional probability usually produce one testvalue and one comparison value per observa-tion. Conversely, lag-sequential analyses canproduce conditional probabilities for everysecond before and after a target response. Thismethod allows more precise descriptions of howthe probability of observing an event changesbefore and after some point of reference (usuallyoccurrences of the target response).

Functional analysis methods can provideempirical support for the reinforcing functionsof events observed during a descriptive analysis.To date, Emerson et al. (1995) is the onlypublished examination of lag-sequential analy-ses that was informed by functional analyses.However, the functional analyses in that studywere limited because they were conducted inconjunction with an existing treatment protocolthat consisted of delivery of a mild reprimandand diversion following severe self-injury andaggression.

Another way to address response–stimulusrelations in the natural environment is to usemultiple evaluations of contingency on the sameset of data. Multiple evaluations are importantfor at least two reasons: (a) No single statisticcan appropriately summarize the degree towhich a given environment might supportbehavior, and (b) the best measures of contin-gency strength are not yet known. Therefore, abroader picture of the relations in effect wouldat least increase the chances that investigatorscontact the important ones.

The purpose of the current study was toexamine and evaluate how reinforcement con-tingencies that support severe problem behaviormight work in the natural environment.

Initially, data were collected using a descriptiveanalysis. Following the descriptive analysis, afunctional analysis was conducted to provideempirical demonstrations of the stimulus func-tions of events observed during the descriptiveanalysis. Then, multiple measures of contin-gency, including lag-sequential analyses, weretaken from the descriptive analysis data sets andinterpreted.

METHOD

Participants and Settings

Four adolescents who had been referred forthe assessment and treatment of severe problembehavior participated. Two had been admittedto an inpatient facility, and 2 attended a schoolfor individuals with developmental disabilities.These individuals participated in some or all ofa series of three descriptive analysis studies,including the present study (the other studieswere Sloman et al., 2005, and St. Peter et al.,2005). However, different features of thedescriptive data were used in all of the studies,and the data were used for different purposes.The ages listed below reflect participant status atthe beginning of data collection.

Alice was a 14-year-old girl who had beendiagnosed with childhood disintegrative disor-der. She engaged in aggression and disruption,which consisted of hitting people and throwingitems. Greg was an 8-year-old boy who hadbeen diagnosed with autism and mild mentalretardation and engaged in screaming. Amy wasa 14-year-old girl who had been diagnosed withmoderate mental retardation and engaged inself-injury. Jasmine was a 14-year-old girl withno formal diagnosis who engaged in aggressionand disruption, which consisted of slappingpeople and throwing items, respectively.

Descriptive Analysis

Descriptive observations were conductedduring interactions between participants andtheir care providers (parents or teachers) usingthe methods described by Vollmer et al. (2001).

EVALUATIONS OF CONTINGENCY 449

Observers used a computerized data-collectionsystem to simultaneously record environmentalevents and instances of problem behavior.Environmental events were divided into twoclasses: those that may serve as potentialreinforcers (attention, absence of instructions,and access to tangible items) and those that mayserve as potential establishing operations (EOs;low attention, instruction presentation, andrestricted access to materials). Environmentalevents were scored as duration measures. Specif-ically, observers pressed a key on the computer ortouch screen to indicate the onset of the event andagain after termination of the event.

Environmental events were operationally de-fined in mutually exclusive and exhaustivecategories such that when the potential reinforcerfor one kind of event was observed and recorded,its corresponding potential EO was turned off.For example, observers turned off the low-attention key and turned on the attention keyduring a transition from low attention to thedelivery of attention. Having data collectorsrecord both the occurrence and nonoccurrenceof environmental events independently allowedus to be more confident about the state of a givenevent without having to make inferences giventhe absence of behavior on the part of theobserver. It also allowed us to correct or omiterrors based on inconsistencies in the data (e.g.,having both a potential EO key and itscorresponding reinforcer off at the same time).This procedure is described in more detail underthe section on Data Preparation.

It was possible for more than one potential EOor reinforcer to be scored at the same time. Forexample, periods of low attention and restrictedaccess to materials could overlap. However,periods of EOs could not overlap with theircorresponding reinforcers; periods of low atten-tion could not be scored at the same time asperiods of attention (i.e., low attention andattention were mutually exclusive categories).

Observers scored ‘‘task on’’ at the occurrenceof the first instruction (academic or otherwise)

since ‘‘task off’’ was last scored. An instructionwas defined as a spoken command to initiate,continue, or complete a preacademic, academic,vocational, life-skill, or self-care activity. Ob-servers continued to score ‘‘task on’’ until eitherthe task materials (and prompts from thetherapist) were withdrawn, the caregiver turnedaway, or 10 consecutive seconds passed withoutthe presentation of additional instructions.‘‘Task off’’ was scored at the cessation of ‘‘taskon.’’ ‘‘Attention on’’ was scored at the occur-rence of any spoken statement by the caregiverdirected to the participant or physical contactbetween the caregiver and participant. Thismeant that nearly all initiations of demands or‘‘task on’’ were accompanied by ‘‘attention on.’’However, there were many situations in which‘‘attention on’’ could have been scored without‘‘task on’’ (e.g., brief or extended socialinteractions or praise). ‘‘Attention on’’ contin-ued to be scored until 3 consecutive secondspassed without either a spoken statement orphysical contact by the caregiver, at which point‘‘attention off’’ was scored. ‘‘Access to materi-als’’ was scored when toys, food items, or playmaterials were currently being manipulated bythe participant, were within reach of theparticipant when seated, or were no longerbeing manipulated but had not been restrictedby a caregiver. ‘‘Restricted access’’ was scoredduring all other times.

For Amy and Jasmine, instructions tended tooccur during circle time (e.g., ‘‘Point to todayon the calendar,’’ or ‘‘Point to the picture withmore money’’) or unstructured time (e.g., ‘‘pickthat up’’ or ‘‘sit down’’). For Greg and Alice,instructions often involved self-care tasks (e.g.,‘‘get dressed’’ or ‘‘brush your teeth’’). Thenature of the instructions meant that most werenot accompanied by the simultaneous deliveryof play items. Therefore, it was usually notnecessary to distinguish between the delivery ofplay materials and the delivery of workmaterials because the latter rarely happened.When demands were accompanied by the


delivery of materials (e.g., if the caregiverhanded the participant a block and an emptycontainer and said, ‘‘Put the block in thebucket’’), observers were instructed to err on theside of not scoring the delivery of materials.

Problem behavior included aggression, disrup-tion, and self-injurious behavior. Aggression wasdefined as throwing objects within 1 m ofanother person or hitting, kicking, pushing,pulling, biting others, or attempts to do so.Disruption was defined as throwing objects (butnot within 1 m of another person); climbing onfurniture; forceful contact of the hand or feet withtables, walls, or floors; and property destruction,including tearing of books or magazines, breakingwriting instruments, and drawing on walls. Self-injury was defined as forceful contact with thehead or hand and hard surfaces, self-pinching,self-choking, and hair pulling.

For Alice and Greg and their parents,descriptive observations were conducted on aninpatient unit that specialized in the treatment ofsevere problem behavior. Observations wereconducted in hospital rooms that contained asofa, chairs, and table. Additional materials (e.g.,toys, books, magazines, videocassettes, television)were also available in the room. Observationswere conducted over a period of 1 to 7 weeks, andthe total observation time summed to 100 and110 min, respectively. Individual observationperiods lasted between 10 and 20 min, depend-ing on the activity. For these participants, initialobservations were unstructured; however, after itbecame apparent that both caregivers had atendency to avoid situations that evoked problembehavior, we prompted caregivers to create thosesituations. Specifically, we asked Alice’s caregiverto ‘‘show us what happens when you’re busy andcan’t talk to Alice,’’ and we asked both caregiversto ‘‘show us what happens when Alice [Greg]cannot have something she [he] wants.’’ Theenvironment was not physically arranged by theexperimenter prior to these sessions, but thecaregiver was free to use any of the materialsalready present in the room.

For Amy and Jasmine and their teachers,observations were conducted in their class-rooms. Classrooms typically contained chairs,desks, and a sofa. Additional materials (e.g.,toys, books, magazines, work materials) werealso present. In addition to the participant andthe teacher, one or more aides and severalstudents were present. Observations were con-ducted over a period of 2 to 3 weeks, and thetotal observation time summed to 130 and190 min, respectively. Individual observationslasted between 10 and 30 min, depending onthe activity. Observations conducted in theclassrooms were unstructured, because problembehavior was readily apparent and because itwas considered too intrusive to the ongoingclassroom activities for the teacher to interruptplanned activities.

An effort was made to conduct descriptiveanalyses until at least five instances of problembehavior were observed over at least 180 min ofobservation. However, a high frequency andseverity of problem behavior necessitated move-ment toward functional analysis and treatmentearlier than planned for Alice, Greg, and Amy.

Functional Analysis

Following the descriptive analysis, a func-tional analysis was conducted using proceduressimilar to those described by Iwata et al. (1982/1994). The same data-collection system usedduring the descriptive analysis was also usedduring the functional analysis. In addition,attempts were made to incorporate attention,demands, and preferred items similar to thoseobserved during the descriptive analysis. Func-tional analyses were conducted in a vacanthospital room on the unit for Alice and Gregand in a spare classroom for Amy and Jasmine.All functional analysis sessions lasted 10 min.Four test conditions and one control conditionwere alternated in a multielement design.During the control condition, participants wereprovided with access to preferred materials andcontinuous attention. Occurrences of problem


behavior resulted in no programmed conse-quences.

An attention condition was implemented totest whether problem behavior was reinforcedby therapist attention. During the attentioncondition, participants had access to preferredmaterials, as identified by a free-operantpreference assessment (Roane, Vollmer, Ring-dahl, & Marcus, 1998) while the therapistpretended to work. Occurrences of problembehavior produced 30 s of access to attention,which consisted of a brief reprimand, state-ments of comfort, and physical contact.

A tangible condition was implemented to testwhether problem behavior was reinforced byaccess to preferred materials. During the tangiblecondition, participants were provided withcontinuous attention while the therapist interact-ed with the participants’ preferred materials.Occurrences of problem behavior produced 30 sof access to the preferred materials.

An escape condition was implemented to testwhether problem behavior was reinforced byescape from demands. Instructional tasks ordemands were selected on the basis of interviewswith primary care providers and observationsconducted during the descriptive analysis.During the escape condition, each participantsat at a table with work tasks. The therapistguided the participant through the tasks using agraduated, three-prompt sequence (Horner &Keilitz, 1975). The sequence consisted of averbal prompt, a model of the appropriateresponse, and physical guidance to complete theappropriate response. Compliance resulted inbrief praise and immediate presentation of thenext demand. If the participant did not complywithin 10 s, the next step in the sequence wasinitiated. Occurrences of problem behaviorproduced a 30-s break from demands.

Alone and no-consequence conditions wereconducted to test whether problem behaviorwould persist in the absence of social conse-quences (automatic reinforcement). No-conse-quence conditions were conducted for Amy, and

alone conditions were conducted for Alice. Onlyone alone session was conducted for Gregbecause he rarely engaged in problem behavioroutside social contexts, and he attempted to leavethe room during the session (data not included).A no-consequence condition was considered forJasmine, but it would have been difficult tocontrol for therapist reactions (i.e., flinching) toJasmine’s aggression. During either condition,toys and all other potentially preferred materialswere removed from the room, and therapistattention was restricted. The only differencebetween the no-consequence and alone condi-tions was whether or not adults were present.No-consequence conditions were conducted atthe school sites, where it was required that adultsremain in the room with students at all times.Alone conditions were conducted on the inpa-tient unit where one-way windows were avail-able. Occurrences of problem behavior duringeither condition resulted in no programmedconsequences.

Interobserver Agreement

To calculate interobserver agreement forbehavior, data from both observers were dividedinto consecutive 10-s bins, and the smallernumber of events recorded by one observer wasdivided by the larger number of events recordedby the other observer (Iwata, Pace, Cowdery, &Miltenberger, 1994). For behavior and envi-ronmental events scored using a durationmeasure, the smaller number of seconds wasdivided by the larger number of seconds withinthe 10-s bins, and the obtained values wereaveraged for the entire session for all durationmeasures. In the case in which both observersagreed that zero responses occurred, the intervalwas scored as 100% agreement. The samecalculation methods were used in both thedescriptive and functional analyses.

A second independent observer simulta-neously and independently scored 36% ofobservations during the descriptive analysis.Mean interobserver agreement for problembehavior was 96% (range, 90% to 99%). Mean


interobserver agreement for relevant environ-mental events was 86% (range, 82% to 91%).

A second observer recorded data for 58%,41%, 46%, and 91% of Alice’s, Greg’s, Amy’s,and Jasmine’s functional analysis sessions,respectively. Mean agreement for problembehavior was 98% (range, 93% to 100%) forAlice, 90% (range, 79% to 100%) for Greg,95% (range, 65% to 100%) for Amy, and 98%(range, 96% to 100%) for Jasmine.

Data Preparation

Prior to conducting the lag-sequential analysis,the descriptive analysis data were reviewed forerrors that were then either corrected or omitted.Three kinds of errors were identified in the data.First, there was often a delay between thebeginning of a session and the time during whichthe first event or occurrence of problem behaviorwas recorded. These delays ranged between 0 and4 s (median, 2 s). This was corrected for bysubtracting the delay to the first key from thesession duration and the start and stop times ofevery event or occurrence of problem behavior inthe session. Second, keys for EOs and theircorresponding reinforcers were sometimes scoredin such a way that the events overlapped. Forexample, the key for ‘‘attention on’’ may not havebeen turned off until 2 s after ‘‘attention off’’ wasturned on, meaning that both were on at the sametime (which, according to their mutually exclu-sive definitions, was impossible). This wascorrected for by setting the offset time of theformer key to the onset time of the latter. Third,the data contained periods of time during whichneither an EO key nor its correspondingreinforcer was scored. If the time during whichneither key was scored was greater than 10 s, thenthat session was omitted from the analysisrelevant to those keys. This resulted in onesession being removed from the no-demandanalysis for Alice and one session being removedfrom the no-demand analysis for Jasmine. Thesechanges had only minor effects on the subsequentanalyses and resulted in no changes to conclusionsbased on the data.

Lag-Sequential Analysis

A lag-sequential analysis is a procedure usedto identify repeated sequences of events and hasbeen used to analyze complex social interactions(Emerson et al., 1995; Sackett, 1979). Time-based lag-sequential analysis allows the calcula-tion of conditional probabilities both backwardsand forwards in time relative to a criterion event(G. P. Sackett, personal communication, Oc-tober 26, 2005). Lag-sequential analyses wereconducted by first organizing the data accordingto each participant and then performing theanalysis for each putative reinforcer.

In this study, conditional probabilities (theprobability of a potential reinforcer given aninstance of problem behavior) were calculatedfor the 120 s before and the 120 s followinginstances of problem behavior. Conditionalprobabilities of potential reinforcers were cal-culated by dividing the number of times thepotential reinforcer was observed at that specifictime (with respect to problem behavior) by thenumber of opportunities there were to observepotential reinforcers at that specific time. Thenumber of opportunities was equal to thenumber of times problem behavior occurredminus the number of observations that wouldhave fallen outside the session. For example, if100 instances of problem behavior occurred andattention occurred 20 times in the first secondafter problem behavior, the conditional proba-bility would have been .20. Suppose (for thepurposes of describing these calculations) that25 of those 100 instances of problem behavioroccurred during the last second of the observa-tion. Under those conditions, there would havebeen 25 fewer opportunities to observe atten-tion in the second following problem behavior.Therefore, the number of opportunities wouldhave been 75 instead of 100 and the conditionalprobability would have been .27 (20 of 75).This description for the calculation of condi-tional probabilities entails that each obtainedprobability is an aggregate. Specifically, it is theproportion of observations (at a specific point in


time in relation to the occurrence of problembehavior) in which a potential reinforcer wasobserved.

Several window sizes were informally evalu-ated prior to the study. This evaluationdetermined that window sizes could be in-creased to span up to 240 s and still clearlydepict changes in probability within the 10 simmediately surrounding behavior. Therefore, atotal window size of 240 s was chosen tocapture as large a sample as possible. (Readerswho wish to consider only more immediatechanges can easily do so by obscuring the endsof the figures using a sheet of paper.)

Conditional probabilities were calculated forenvironmental events surrounding each instanceof problem behavior, independent of interveninginstances of problem behavior. This meant thatthe observation windows overlapped if two ormore instances of behavior occurred within 120 sof each other. For example, if problem behavioroccurred at Seconds 200 and 215, conditionalprobabilities were calculated for the first instancefrom Second 80 to Second 320 and for thesecond instance from Second 95 to Second 335.Therefore, the conditional probability should beinterpreted to mean the proportion of instancesof problem behavior that were either preceded orfollowed by a potential reinforcer (at the specifictime in question). An alternative method couldhave been to calculate conditional probabilitiesfor each second before and after problembehavior until another instance of problembehavior was observed. However, we believedthat results from such an approach would havebeen more difficult to interpret and containedimplicit assumptions about the effects of inter-vening occurrences of problem behavior onreinforcers rather than simply a description ofthe temporal relation between behavior andpotential reinforcers.

Conditional probabilities of potential rein-forcers were also calculated for the nonoccur-rence of problem behavior. This calculation wasidentical to the lag-sequential analysis described

above, with one exception. The probability ofobserving potential reinforcers was calculatedfor each of the 120 s before and after everysecond that did not contain problem behavior.This is in contrast to the previous calculationthat examined each of the 120 s before and aftereach instance of problem behavior.

Unconditional probabilities of potential rein-forcers were also calculated. This calculation wasidentical to the above analyses, with oneexception. The probability of observing potentialreinforcers was calculated for each of the 120 sbefore and after every second in the observation.

The lag-sequential analysis calculations de-scribed above were altered slightly to produce ameasure called within-EO (Vollmer et al.,2001). For within-EO lag-sequential analysiscalculations, instances of problem behavior wereincluded only if they occurred during theabsence of the putative reinforcer. For example,when calculating the within-EO lag-sequentialanalysis of attention given problem behavior,instances of problem behavior were includedonly when they occurred during the absence ofantecedent attention (i.e., during ‘‘attentionoff’’). Suppose 30 instances of problem behav-ior were recorded during a given observation. If20 of those instances of problem behavioroccurred in the presence of an EO, only those20 were used to calculate the conditionalprobability of a potential reinforcer. Thecalculations for conditional probability giventhe nonoccurrence of behavior and uncondi-tional probability were conducted by evaluatingthe probability of potential reinforcers 120 sbefore and after seconds without problembehavior and every second, respectively, whilethe EO was in place. For all of the within-EOcalculations, the observation window was free tofall outside the EO. The probability of apotential reinforcer can only increase followingbehavior; therefore, the useful comparison isbetween the conditional probability of apotential reinforcer following behavior and theunconditional probability or the probability of a


potential reinforcer following the nonoccur-rence of behavior.

Custom software was written by the firstauthor to conduct the lag-sequential analyses.The software was initially written in VisualBasic; however, running the analysis requiredmore than 20 hr of computation for a singledata set using a Pentium IV 2-Ghz processor.Subsequently, the software was rewritten in Cand required less than a minute to compute asingle data set. Validation of the software wasperformed by repeatedly comparing the outputsof both programs to sets of lag-sequentialanalysis data that were calculated by hand.

All contingencies were identified using visualinspection of the plotted lag-sequential analysisdata. We did not conduct statistical tests ofsignificance because we could not find compel-ling evidence that a statistically significantdifference (between the comparison conditionalprobability values) was a necessary condition toobserve reinforcement effects. In addition, itseemed intuitive that problem behavior couldbe maintained in the absence of a statisticallysignificant difference. For example, Skinner(1956) showed that even a single instance of areinforcer presentation was sufficient to main-tain behavior.

RESULTS

Functional Analysis

Figure 1 shows the functional analysis resultsfor Alice, Greg, Amy, and Jasmine. Results forAlice showed the highest levels problembehavior in the attention and escape conditions,suggesting that her problem behavior wasreinforced by attention and escape. Results forGreg showed the highest levels of problembehavior in the tangible condition. Thissuggested that his problem behavior wasreinforced by access to tangible items. Resultsfor Amy showed higher rates of problembehavior during tangible and escape conditionsthan in the control. This suggested that herproblem behavior was reinforced multiply by

access to tangible items and escape fromdemands (note that the functional analysisresults for Amy were previously reported bySt. Peter et al., 2005, but are reproduced herefor convenience). Results for Jasmine showedhigh rates across every test condition. Thus, herproblem behavior was multiply reinforced byaccess to tangible items, access to attention, andescape from demands.

Descriptive Analysis

Alice, Greg, Amy, and Jasmine were observedwhile interacting with their caregivers forapproximately 100, 110, 130, and 190 min,respectively. During that period, Alice emitted40 instances of problem behavior. In addition,her caregivers implemented approximately67 min of attention, 91 min of access to toys,and 81 min of breaks from tasks (rounded tothe nearest minute). During Greg’s observa-tions, he emitted 33 instances of problembehavior. His caregivers implemented approxi-mately 86 min of attention, 53 min of access totoys, and 81 min of breaks from tasks. DuringAmy’s descriptive analysis, she emitted 469instances of problem behavior. Her caregiversimplemented approximately 44 min of atten-tion, 108 min of access to toys, and 101 min ofbreaks from tasks. During Jasmine’s descriptiveanalysis, she emitted 25 instances of problembehavior. Her caregivers implemented approx-imately 37 min of attention, 81 min of accessto toys, and 170 min of breaks from tasks.

Lag-Sequential Analyses

The purpose of the study was to examine thepattern of environmental events most similar toreinforcers identified via the functional analysis.Therefore, only lag-sequential analyses of eventsidentified as reinforcers by the functionalanalysis are presented below. In the interest ofspace, only Jasmine’s lag-sequential analysis ofno demands and Amy’s lag-sequential analysisof access to tangible items are presented. Inaddition, Jasmine’s within-EO lag-sequentialanalysis was removed because only one instance


Figure 1. Functional analysis results for Alice, Greg, Amy, and Jasmine.


of problem behavior occurred while demandswere being presented. The remaining analysesmay be obtained from the first author.

Initial examination of the data revealed novisible differences between the data pathsdepicting the unconditional probability ofpotential reinforcers and the conditional prob-ability of potential reinforcers given the nonoc-currence of behavior for any of the participantsand analyses. Therefore, the results for theunconditional probability of potential reinforc-ers will not be discussed below.

The names given to potential reinforcers inthe following section do not attempt todifferentiate between the onset of an event(e.g., a potential EO or a reinforcer) and itscontinued presentation. For example, the wordsno demands refer to both the transition from aperiod of demands to the withdrawal ofdemands (escape) and the continued absenceof demands. However, for the sake of clarity,both are referred to as no demands. The same isalso true for access to toys and attention.

Figures 2 through 7 show the relationbetween occurrences of problem behavior andan event similar to those identified as areinforcer (via functional analyses) for thatbehavior for each participant. Seconds beforeand after problem behavior are depicted alongthe x axis, and the probability of observing theputative reinforcer is depicted along the y axis.

Figure 2 shows the results of Alice’s lag-sequential analysis for attention. The top panelshows two data paths: the probability of attentiongiven the occurrence of problem behavior and theprobability of attention given the nonoccurrenceof problem behavior. These data paths show twopositive contingencies. The first positive contin-gency is indicated by an increase in theprobability of attention given an occurrence ofproblem behavior starting 3 s after occurrences ofproblem behavior. This increase shows thatattention was more likely to be observed afterproblem behavior than before. The secondpositive contingency is indicated by the difference

between the probability of attention given anoccurrence of problem behavior and the proba-bility of attention given the nonoccurrence ofproblem behavior. This difference shows thatattention was more likely to be observedfollowing problem behavior than following anyother second of the observation during whichproblem behavior was not observed.

The bottom panel of Figure 2 shows twodata paths: the within-EO probability ofattention given the nonoccurrence of behaviorand the within-EO probability of attentiongiven the occurrence of problem behavior.These data paths show a positive contingency.The positive contingency is indicated by thedifference between the probability of attentiongiven the nonoccurrence of behavior and theconditional probability of attention givenbehavior to the right of the vertical lineindicating occurrences of problem behavior.This shows that attention was more likely to beobserved following problem behavior (thatoccurred while attention was not delivered)compared to seconds during which problembehavior was not observed.

Figure 3 shows the results of Alice’s lag-sequential analysis for no demands. The toppanel shows two data paths: the probability ofno demands given the occurrence of problembehavior and the probability of no demandsgiven the nonoccurrence of problem behavior.The data show two negative contingencies andone positive contingency. The first negativecontingency is depicted in the decrease in theprobability of no demands (given an occurrenceof problem behavior) immediately before toimmediately after occurrences of problembehavior. This decrease shows that periodswithout demands were less likely to be observedjust after problem behavior than just beforeproblem behavior. In other words, demandswere more likely following problem behavior(e.g., if Alice engaged in throwing an item, hercaregivers might have instructed her to pick itup, which would produce an increase in the


Figure 2. The lag-sequential analysis of attention for Alice. The open diamonds show the probability of attention (E)given an occurrence of problem behavior (R). The solid line shows the probability of attention given the nonoccurrenceof problem behavior (R̄).


Figure 3. The lag-sequential analysis of no demands for Alice. The open diamonds show the probability of nodemands (E) given an occurrence of problem behavior (R). The solid line shows the probability of attention given thenonoccurrence of problem behavior (R̄).


Figure 4. The lag-sequential analysis of access to toys for Greg. The open diamonds show the probability of access totoys (E) given an occurrence of problem behavior (R). The solid line shows the probability of access to toys given thenonoccurrence of problem behavior (R̄).


Figure 5. The lag-sequential analysis of access to toys for Amy. The open diamonds show the probability of access totoys (E) given an occurrence of problem behavior (R). The solid line shows the probability of access to toys given thenonoccurrence of problem behavior (R̄).


Figure 6. The lag-sequential analysis of no demands for Amy. The open diamonds show the probability of nodemands (E) given an occurrence of problem behavior (R). The solid line shows the probability of no demands given thenonoccurrence of problem behavior (R̄).


probability of demands following problembehavior). The second negative contingency isindicated by the difference between the prob-ability of no demands given an occurrence ofproblem behavior and the probability of nodemands given the nonoccurrence of problembehavior. This difference shows that periods ofno demands were less likely to be observedfollowing problem behavior than following anysecond of the observation during which prob-lem behavior was not observed. The positivecontingency is indicated by the upward trend inthe conditional probability of no demands formost of the 120 s following behavior. As withall conclusions about functional relations basedon descriptive analyses, the presence of theupward trend may not have any effect onbehavior. Nonetheless, it is interesting toconsider the possibility that such a change in

the trend of no demands could produce areinforcement effect.

The bottom panel of Figure 3 shows twodata paths: the within-EO probability of nodemands given the nonoccurrence of behaviorand the within-EO probability of no demandsgiven the occurrence of problem behavior.These data show that demands were morelikely to have terminated within 10 s followingseconds in which problem behavior did notoccur compared to following seconds in whichproblem behavior did occur (a negative contin-gency). However, the probability of no de-mands following problem behavior continuedto increase at a rate higher than the probabilityof no demands following seconds withoutproblem behavior (a positive contingency). Thissuggests that although demands were neverterminated within the first 3 s following

Figure 7. The lag-sequential analysis of no demands for Jasmine. The open diamonds show the probability of nodemands (E) given an occurrence of problem behavior (R). The solid line shows the probability of no demands given thenonoccurrence of problem behavior (R̄).


problem behavior, they were more likely to haveended between 12 and 45 s after problembehavior than after seconds without problembehavior. Furthermore, this disparity was alsopresent from 58 s to 101 s and again from107 s to 120 s.

Figure 4 shows the results of Greg’s lag-sequential analysis for access to toys. The datadisplayed in the top panel suggest a negativecontingency. This is indicated by the differencebetween the probability of toys given anoccurrence of problem behavior and theprobability of toys given the nonoccurrence ofa problem behavior. This difference shows thattoys were less likely to be available followingproblem behavior than following any othersecond of the observation during which prob-lem behavior was not observed.

The lower panel of Figure 4 shows two datapaths: the within-EO probability of access totoys following the nonoccurrence of problembehavior and the within-EO probability ofaccess to toys following the occurrence ofproblem behavior. Similar to the within-EOno-demands data for Alice, these data showalternating periods of negative, neutral, andpositive contingencies. The probability ofhaving access to toys was higher during thefirst 22 s following seconds in which problembehavior did not occur. The probability ofhaving access to toys was comparable from 23 sto 41 s following problem behavior andfollowing seconds not containing problembehavior. Conversely, the probability of havingaccess to toys from 42 s to 58 s was higherfollowing seconds containing problem behavior.At greater delays, a negative contingency waspresent from 59 s to 101 s, and a positivecontingency was present from 102 s on.

Figure 5 shows the results of Amy’s lag-sequential analysis for access to toys. The toppanel shows two data paths: the probability ofaccess to toys given the occurrence of problembehavior, and the probability of access to toysgiven the nonoccurrence of problem behavior.

These data paths show two positive contingen-cies. The first positive contingency is indicatedby a subtle increase in the probability of accessto toys following problem behavior over time(from .8507 to .8850). This suggests that accessto toys became more likely as more time passedfollowing problem behavior. However, it wasnot simply the case that the probability of accessto toys increased throughout the sessionindependent of behavior, because the probabil-ity of access to toys following seconds in whichproblem behavior did not occur actuallydecreased slightly (from .8042 to .7972). Thesecond positive contingency is indicated by thedifference between the probability of access totoys given an occurrence of problem behaviorand the probability of access to toys given thenonoccurrence of problem behavior. Thisdifference shows that Amy was more likely tohave access to toys following problem behaviorthan following any other second of theobservation during which problem behaviorwas not observed.

The bottom panel of Figure 5 shows two datapaths: the within-EO probability of access to toysfollowing the nonoccurrence of problem behaviorand the within-EO probability of access to toysgiven the occurrence of problem behavior. Thesedata paths indicate that access to toys was morelikely to occur within 77 s following periods notcontaining problem behavior compared to sec-onds containing problem behavior (a negativecontingency). However, that relation flips whendepicting the period from 78 s to 120 s (apositive contingency).

Figure 6 shows the results of Amy’s lag-sequential analysis for no demands. The toppanel shows two data paths: the probability of nodemands given the occurrence of problembehavior, and the probability of no demandsgiven the nonoccurrence of problem behavior.The probability of no demands did not increasefollowing behavior compared to before behavior(indicating a neutral contingency). However, theprobability of no demands did increase following


behavior from 34 s to 85 s and from 96 s to120 s compared to following seconds withoutproblem behavior (a positive contingency).

The bottom panel of Figure 6 shows twodata paths: the within-EO unconditional prob-ability of no demands and the within-EOprobability of no demands given the occurrenceof problem behavior. These data paths show anegative contingency. The negative contingencyis indicated by the difference between theprobability of no demands following thenonoccurrence of problem behavior comparedto the probability of no demands following theoccurrence of problem behavior. This showsthat periods of no demands were less likely to beobserved following problem behavior thatoccurred during the presentation of a taskcompared to seconds without problem behavior(while tasks were still being presented).

Figure 7 shows the results of Jasmine’s lag-sequential analysis for no demands. The datashow a positive contingency. The positivecontingency is indicated by the differencebetween the probability of no demands given anoccurrence of problem behavior and the proba-bility of no demands given the nonoccurrence ofproblem behavior. This difference shows thatperiods of no demands were more likely to beobserved following problem behavior than fol-lowing any other second of the observation duringwhich problem behavior was not observed.

DISCUSSION

This study detailed a method of data analysiscalled lag-sequential analysis to examine therelations between severe problem behavior emit-ted by adolescents and the behavior of theircaregivers. The stimulus functions of commonantecedents and consequences (e.g., attention,escape from demands, and delivery of toys) wereevaluated for each participant using functionalanalysis methods similar to those described byIwata et al. (1982/1994). Lag-sequential analyseswere then performed on data collected duringinteractions between caregivers and adolescents

with severe problem behavior. Potential rein-forcement contingencies were found to followone or more of three basic patterns: (a)Conditional probabilities (of putative reinforcingevents) were higher following problem behaviorthan before problem behavior, (b) conditionalprobabilities were higher following problembehavior than were conditional probabilitiesgiven no problem behavior (and unconditionalprobability), and (c) problem behavior wascorrelated with a change in the trend ofconditional probabilities (e.g., although theconditional probability of no demands for Alicewas not initially high following problem behav-ior, problem behavior was correlated with achange in trend from decreasing to increasingprobability). To our knowledge, this is the firstdemonstration of momentary fluctuations inprobability of events after identifying reinforcersvia functional analysis. Thus, the present methodrepresents a tentative step forward to examinepotential reinforcement contingencies that oper-ate in the natural environment.

It is important to emphasize that the currentapplication of descriptive analysis was notintended to replace the role of a functionalanalysis. This study did not involve a compar-ison between functional analysis and descriptiveanalysis methods. Instead, the approach wasdesigned, in a sense, to take a snapshot ofbehavior and environmental events and then toevaluate the snapshot after reinforcers had beenidentified via functional analysis. The idea isthat it may be useful to understand how, and inwhat relation to behavior, events similar tothose identified in the functional analysisactually occur during adult–child interactions.Thus, the approach was not presented as aclinical assessment procedure and should not beconstrued as such. Specifically, we do notrecommend that a lag-sequential descriptiveanalysis be inserted into a functional assessmentregimen. Rather, it is hoped that the informa-tion obtained from the study might be useful toapplication and in future applied research.


One way the study might influence futureapplication is by emphasizing the complexity ofreinforcement contingencies. Although it isperhaps not surprising for behavior analysts, theresults suggest that potentially reinforcing eventsmight exert influence over behavior even whenthey occur in very subtle ways. For example, inAlice’s case, the negative contingency present inthe first 11 s following problem behavior suggeststhat her caregivers were implementing somethingakin to brief differential reinforcement of otherbehavior. However, the data also show a positivecontingency between Seconds 12 and 45. FromAlice’s perspective, it may be that althoughproblem behavior did not immediately producea break from demands, her caregivers were morelikely to provide escape after a brief delay. Such apattern could be missed by a casual observation oreven the calculation of conditional probabilities10 s following problem behavior. To address this,specific training could be provided to Alice’scaregivers to continue implementing demands for1 min following problem behavior.

A second way that the study might influencefuture research is from its emphasis thatdescriptive research should continue not neces-sarily for the purpose of identifying methods assuitable replacements for a functional analysisbut rather for the purpose of identifying thekinds of potential reinforcement contingenciesthat should be evaluated in both basic andapplied research. For example, although re-search on descriptive analysis has focused on theidentification of positive contingencies betweenbehavior and environmental events, it ispossible that in some cases behavior couldpersist in the presence of a negative or neutralcontingency. An individual with an extensivereinforcement history might continue to engagein problem behavior in the face of a treatmentinvolving differential reinforcement of otherbehavior. It is possible that, under suchconditions, the occasional mistake of deliveringa reinforcer following problem behavior couldserve to maintain behavior, despite the overrid-

ing negative contingency in place. We arecurrently evaluating negative contingencies andhistory effects in our animal operant laboratory(Samaha, Vollmer, & Osteen, 2005), and wehope to extend that research to severe behaviordisorders. For example, how negative does anew contingency need to be in order to suppressbehavior previously reinforced by strong posi-tive contingencies?

The specific approach used in this study, lag-sequential analysis, has advantages over otherdata-summary approaches (e.g., it allows mo-ment-to-moment evaluations of probability),but it also has clear disadvantages. In somecases, the lag-sequential analysis provided aplausible description of behavior and reinforce-ment in the natural environment. Alice’sattention data (Figure 2, top) are perhaps theclearest, reflecting a clear change in theconditional probability of attention before andafter problem behavior and following problembehavior compared to following seconds with-out problem behavior. In other cases, differentcontingency measures provided contradictoryinformation. Amy’s access to materials data(Figure 5, top) reflect hardly any discerniblechange in the probability of access before andafter problem behavior, but a clear difference inthe comparison between conditional probabil-ities given problem behavior and secondswithout problem behavior. In other cases,results of the lag-sequential analysis failed todescribe any plausible reinforcing relation.Greg’s access to materials data (Figure 4) showthe largest obtained difference between theprobability of a potential reinforcer followingproblem behavior compared to following sec-onds without problem behavior, yet in adirection opposite than that expected for thereinforcement of problem behavior. In fact, anexamination of the session-by-session datasuggested no clear relation between the poten-tial reinforcer and problem behavior. A within-session analysis showed that he had undisruptedaccess to materials prior to and during problem


behavior during the session in which he engagedin the highest rates of problem behavior. Onepossible explanation for the failure to identify aplausible reinforcing relation is that the rein-forcer for Greg’s problem behavior was notpresented (contingent on behavior) during thedescriptive analysis. If so, problem behaviormay have been reinforced in some otherenvironment and occurred during the descrip-tive analysis as a result of generalization orinduction. This problem raises a larger ques-tion: How much descriptive data are needed toprovide a representative sample of events?

In addition to concerns about the lag-sequential approach itself, there are otherlimitations to the current study that are perhapsinherent to descriptive research. Supposedlysimilar events were delivered as consequencesduring the functional and descriptive analyses.For example, the attention delivered by thetherapists during functional analysis sessionsmay have been functionally different than theattention delivered by caregivers during thedescriptive analysis. Similarly, it is not knownwhether periods without demands functionsimilarly to periods of transition from demandto no demand (i.e., a true escape contingency).Attempts were made to incorporate similarforms of attention, preferred materials, anddemands into the functional analysis that wereobserved in the descriptive analysis; however, noclaim is made that the events were exactly thesame. Future research might attempt to increasethe similarities between functional and descrip-tive analyses by having caregivers serve astherapists during the functional analysis sessionsor by attempting to assess the relative reinforc-ing efficacy of events as delivered by caregiversand therapists.

In conclusion, a method for identifyingpossible reinforcement contingencies was eval-uated. It was necessary to conduct a functionalanalysis to identify the stimulus functions ofpossible reinforcers. In future work, functionalanalyses could be conducted using contingency

arrangements similar to those found in thedescriptive analysis. Perhaps these analyses willallow more to be learned about the nature ofreinforcement.

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Received March 2, 2006Final acceptance August 30, 2007Action Editor, Jennifer McComas


analyses of response–stimulus sequences …descriptive analyses cannot be used to identify...

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