Increasing the Probability of Stimulus Equivalence With Adults Wi

7/27/2019 Increasing the Probability of Stimulus Equivalence With Adults Wi

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The Psychological Record , 2004 , 54, 423-435

INCREASING THE PROBABILITY OF STIMULUS EQUIVALENCEWITH ADULTS WITH MILD MENTAL RETARDATION

RICHARD R. SAUNDERS and JULIE E . MCENTEEUniversity of Kansas

In Experiment 1 , 6 adults with mild mental retardation weretaught 3 overlapping conditional discriminations in a linea r seriesstructure , establishing the possibility of the emergence of 2stimulus equivalence classes of 4 stimuli per class. Trainingemployed balanced trial types in which the discriminative stimuliwere presented in fixed pairs across conditional discriminations(e .g ., 81 and 82, C1 and C2) . No participant .showed theemergence of equivalence classes in initial testing ; 1 participantshowed the establishment of classes with repeated testing ,including tests for symmetry alone. In Experiment 2, 6 additionaladults with mild mental retardation were similarly trained , with onemethodological modification : Prior to testing, each comparisonstimulus (e.g. , 81) was presented in some trials w ith everystimulus from the opposing class (i.e., A2, 82 , C2, and D2). Withthis modification , 4 of 6 participants showed the establishment ofequivalence classes during initial testing . The results supporthypotheses about the essential role of simple discriminationacquisition in equivalence class establishment.

A stimulus equivalence class may be defined as a set of stimuli thatare interchangeable or substitutable in certain contexts, such as inconditional discriminations (Spradlin, Cotter, & Baxley , 1973). Onecommon method of presenting conditional discriminations is matching -tosample (MTS) training with reinforcement contingencies (Green &Saunde rs , 1998). A now common outcome is that training with only asmall number of interrelated MTS conditional discriminations results inemergence of numerous untrained conditional discriminations (e.g., R . R.Saunders, Wachter, & Spradlin, 1988) . In mapping how conditionaldiscriminations might be interrelated to produce this effect, Fields and

Development of this paper was supported in part by National Institute of Child Healthand Human Development Grants HD18955 and HD02528 to the Schiefelbusch Institute forLife Span Studies , University of Kansas. Portions of this paper were presented at the 25thMeeting of the Association for Behavior Analysis , Chicago, IL. Requests for reprints shouldbe addressed to Richard R . Saunders , Schiefelbusch Institute for Life Span Studies , 1000Sunnyside Ave. , 1052 Dole , Lawrence, KS 66045 . (E-mail: rrsaun @ku ..edu).


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Verhave (1987) described four parameters relevant to the organization ofequivalence classes . The parameters were (a) number of stimul i perclass , (b) number of nodes , (c) the dist ribution of non nodal stimuli amongnodal stimuli, and (d) directionality of training. Node, perhaps the keyparameter , refers to a stimulus that participates in two or more conditionaldiscriminations , thus providing for their interrelation or overlap .Directionality of training refers to whether the nodes serve as conditionalstimul i (i.e., samples in MTS problems), discr iminative stimuli (i.e .,comparison stimuli in MTS p roblems) , or both during training .

Training in which nodal stimuli serve as sample stimuli in some MTSconditional d iscriminations and as comparison stimuli in others has beenreferred to as a linear series (LS) training structure (K. J . Saunders,Saunders, W illiams , & Spradlin , 1993). The LS structure has been usedfrequently in experiments on stimulus equivalence w ith normal child renand adults with mixed results (e.g ., Annett & Leslie , 1995 ; Arntzen &Holth , 1997, 2000b; Fields, Landon-Jimenez, Buffington , & Adams, 1995;Fields, Newman, Adams, & Verhave, 1992; Holth & Arntzen, 1998, 2000;Lazar , Davis-Lang , & Sanchez, 1984 ; Michael & Bernstein , 1991;Spradlin , Saunders , & Saunders, 1992).

R. R. Saunders and Green (1999) postulated that the failure toproduce equivalence class establishment with the LS structure could becaused by a difference in the simple discriminations required duringtraining versus testing. In LS training , some of the possible simplediscriminations among stimuli are not required for problem solution , butthese discriminations are essential for solving the conditionaldiscriminations that comprise the tests for equivalence. For example,given training leading to two potential stimulus classes of four stimuli each(i.e., train AB, BC, CD) there will have been no training trial containing anA stimulus and a D stimulus. One of the trial types that tests for theproperty of trans itivity, however, w ill be Stimulus A 1 as sample and theStimuli D1 and D2 as comparison stimuli. In training two Classes of fourstimuli , for example, R. R. Saunders and Green fixed the number ofdiscriminations unrequired by training, but essential in tests , at 12 . Otherinvestigators have concurred generally with this analysis, concluding thatif each stimulus in the training set is not discriminated from the remainingstimuli , negative outcomes on tests for stimulus equivalence classes arelikely (see Mcllvane & Dube , 1996 ; K. J. Saunders et aI. , 1993 ; Sidman,1986, 1994; Spradlin & Saunders , 1986) . Although discriminations amongstimuli in an experiment may arise as a function of var iables other than

the formal elements of the training (e.g. , stimulus naming), the datasuggest that these other variables are not always at work.Research with participants with mental retardation has produced data

consistent with R. R. Saunders and Green's analysis with structures otherthan LS. Across several early experiments, adolescents and adults withmental retardation were trained with minimal instructions in either sampleas-node (SaN) or comparison-as-node (CaN) structures leading potentiallyto 2 four- or five-member equivalence classes (Drake & Saunders , 1987 ,


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cited in K. J. Saunders et aI. , 1993; K. J. Saunders et aI., 1993 ; R. R.Saunders , Saunders, Kirby , & Spradlin , 1988; R. R. Saunders , Wachter , et al.

1988; Spradlin & Saunders , 1986). Across these studies , equivalenceclasses were established in only 1 of 7 participants trained with SaNprocedures , but in 14 of 15 participants trained with CaN procedures. SaNstructures are hypothesized to share the same problem as LS, with respectto unrequired discriminations (R . R. Saunders & Green , 1999). In contrast,CaN requires all test -essential discriminations. More recently , R. R.Saunders , Drake , and Spradlin (1999) reported similar results with youngchildren with mental ages presumed to be similar to the mental ages of theparticipants with mild mental retardation. Four of 5 CaN-trained preschoolchildren showed equivalence class establishment while only 2 of 6 SaNtrained children had similar test performances.

To date , scant research on the establishment of classes with the LSstructure has been conducted with participants with mental retardation .We hypothesized that if R. R. Saunders and Green's (1999) analysis isaccurate, results with a LS structure should lead to results more similar toprevious findings with SaN structures than findings with CaN structures .Further , we hypothesized that modifications to typical train ing methodswith the LS structure might lead to results more similar to prior resultswith CaN structures . That is , if training in the LS structure were conductedsuch that discrimination of each stimulus from every othe r stimulus wasmore likely during training , then equivalence class establishment shouldbe more probable than when such discriminations are not enabled. Twoexperiments were designed to test these hypotheses.

Experiment 1

Method

ParticipantsAll participants in this study were consumers of services in state- and

community-operated agencies . Each pa rticipated at times that did notinterfere with important daily activities . Each participated under informedconsent procedures required by the human rights committees of therespective agencies and of the University of Kansas. In Experiment 1, 6adults with mild mental retardation (based on results of most recentformal testing) served as participants . Ages ranged from 23-48 yearsacross the 3 ma le and 3 female participants.

ApparatusParticipants sat at a desk in an office cubicle facing a computer

monitor. Sessions were presented using a Macintosh LCIII computerwith an ArtMedia 14 in. Trinitron CRT (Model TC1564). The monitor hada touchscreen operating with Troll Touch Software (Version 1 .8.8). Asoftware program was used to program stimulus display sequences andresponse consequences.


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The experimental stimuli are shown in the training structure schematicdepicted in Figure 1. To establish the conditional discriminations depicted, asample stimulus appeared in the middle of the screen to begin a trial; a touchto the sample resulted in the concurrent display of two-choice stimuli, belowand on either side of the sample. A touch to either comparison resulted inthe programmed consequence(s), temporary removal of all stimuli(approximately 2 s), and presentation of the next sample. On trials withconsequences, an experimenter-designated correct response produced anauditory jingle from the computer; incorrect responses produced a"raspberry" sounding buzz. The participants were paid at the end of eachsession, in cash, for each experimenter-designated correct response. Eachcorrect response equaled 1 cent.

ProceduresArbitrary MTS training. Training and testing occurred in a linear-series

structure leading potentially to two c lasses of four stimuli each, as shownin Figure 1. Training began with the first conditional discrimination (AB) in

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Figure 1. Schematic of the training structure and stimuli employed. Solid arrows indicatetrained relations. The vertical arrows on dashed lines indicate symmetry tests . Thehorizontal arrows connected with dashed lines indicate tests for transitivity and symmetrictransitivity and are labeled as equivalence tests.

sessions of 32 trials each. When the participant's performance metcriterion on AB , training on BC commenced , followed by training on CD .Training continued first with all three conditional discriminations mixed inthe same sessions with trial-by-trial feedback, sessions with feedbackreduced to 75% of the trials, and then in sessions without trial-by-trialfeedback. Testing began when the participant's performance on all thediscriminations could be maintained without feedback. The training andtesting in this experiment was conducted with "balanced" trial types(Green & Saunders, 1998; R. R. Saunders & Green, 1999). With balanced


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INCREASING PROBABILITY OF EQUIVALENCE 427

trial types, comparison stimulus B 1 , for example, was always presentedwith comparison stimulus B2 (never with C2 or 02). This arrangement intwo-choice MTS training also has been referred to as the "pairedcomparison " procedure (Sp radl in & Saunders , 1986) . The performancecriterion for each phase of this training was 100% correct for one sessionor two consecutive sessions at or above 90% correct. Participantscompleted up to four sessions per day , depending on their extraexperimental activity schedules.

Tests for the properties of equivalence . Test sessions contained sixtest trials unsystematically interspersed among 26 training trials. Testtrials never occurred consecutively . Responses on training trials and testtrials produced no programmed consequences during test sessions. Thetrial types in the test sessions consisted of tests for transitivity only (i.e .,the relations AC, BD, AD) and direct tests for symmetric transitivity orequivalence (i.e ., the relations CA , DB, DA). As these relations must betested for both potential classes , 12 test trials spread across two testsessions constituted a complete test that will be referred to as an"equivalence test. " Following training, the equivalence test wasadministered twice. Equivalence class establishment was judged to haveoccurred if each test administration produced at least 10 experimenterdesignated correct responses in the 12 test trials. If testing failed toproduce criterion-level performances , two test sessions with tests for theproperty of symmetry were conducted (BA , CB, DC). Symmetry testsessions consisted of six test tria ls and two symmetry test sessionsconstituted a symmetry test. The criterion for concluding that symmetrywas demonstrated was 10 of 12 experimenter-designated correctresponses . If symmetry testing demonstrated that the trained conditionalrelations had the property of symmetry, the equivalence test was againadministered twice . If, during any test sess ion of either type , training trialaccuracy fell below 90 %, training sessions without trial -by-trial feedback

were re-presented until accuracy again met criterion . Further, throughoutthe experiment, days in which test sessions were scheduled alwaysbegan with a training session (without feedback) to ensure that thetrained performances were at criterion prior to testing .

Results

The participants in Experiment 1 required between 7 and 63 trainingsessions (median = 23) to meet the criterion for testing for equivalence

classes. As shown in Figure 2, no participant met the criterion forequivalence class establishment in the first two equivalence tests (EQ1and EQ2) . Participant P4 received only one initial equivalence test priorto symmetry testing because he informed the experimenters of a changein his residence only 1 day prior to leaving. He and P1 , P2, and P3 passedthe symmetry tests. Each was retested for equivalence . Participant P4could be tested on ly once and therein showed no evidence of equivalenceclass establishment; P2 and P3 received two tests and neither met the


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428

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SAUNDERS AND MCENTEE

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Figure 2. Results of Experiment 1 for all participants on tests for equivalence (blackcolumns) and tests for symmetry (white columns), if applicable.

criterion of class establishment. Because P1 's fourth equivalence test(EQ4) produced 10 of 12 correct responses, she was given a fifth test inwhich she had 11 of 12 correct responses. Thus, P1 showed equivalenceclass establishment with repeated testing. Participant P5 did not pass thesymmetry test and was therefore not retested for equivalence; and P6 leftthe facility unexpectedly before additional testing could be conducted.

Figure 3 shows the median response latencies to comparison stimulifor training trials and test trials in the first equivalence test (two sessions)for each participant in Experiment 1. All had longer latencies or slowerresponse speeds on test trials than training trials. Participant P1, whoultimately demonstrated equivalence class establishment, had the largestdifference between training and test trial latencies.


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Increasing the Probability of Stimulus Equivalence With Adults Wi

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