INCREASING THE PROBABILITY OF STIMULUS EQUIVALENCE WITH ADULTS WITH MILD MENTAL RETARDATION

The Psychological Record, 2004, 54, 423-435 INCREASING THE PROBABILITY OF STIMULUS EQUIVALENCE WITH ADULTS WITH MILD MENTAL RETARDATION RICHARD R. SAUNDERS and JULIE E. MCENTEE University of Kansas In Experiment 1, 6 adults with mild mental retardation were taught 3 overlapping conditional discriminations in a linear series structure, establishing the possibility of the emergence of 2 stimulus equivalence classes of 4 stimuli per class. Training employed balanced trial types in which the discriminative stimuli were presented in fixed pairs across conditional discriminations (e.g., 81 and 82, C1 and C2). No participant.showed the emergence of equivalence classes in initial testing; 1 participant showed the establishment of classes with repeated testing, including tests for symmetry alone. In Experiment 2, 6 additional adults with mild mental retardation were similarly trained, with one methodological modification: Prior to testing, each comparison stimulus (e.g., 81) was presented in some trials with every stimulus from the opposing class (i.e., A2, 82, C2, and D2). With this modification, 4 of 6 participants showed the establishment of equivalence classes during initial testing. The results support hypotheses about the essential role of simple discrimination acquisition in equivalence class establishment. A stimulus equivalence class may be defined as a set of stimuli that are interchangeable or substitutable in certain contexts, such as in conditional discriminations (Spradlin, Cotter, & Baxley, 1973). One common method of presenting conditional discriminations is matching-tosample (MTS) training with reinforcement contingencies (Green & Saunders, 1998). A now common outcome is that training with only a small number of interrelated MTS conditional discriminations results in emergence of numerous untrained conditional discriminations (e.g., R. R. Saunders, Wachter, & Spradlin, 1988). In mapping how conditional discriminations might be interrelated to produce this effect, Fields and Development of this paper was supported in part by National Institute of Child Health and Human Development Grants HD18955 and HD02528 to the Schiefelbusch Institute for Life Span Studies, University of Kansas. Portions of this paper were presented at the 25th Meeting of the Association for Behavior Analysis, Chicago, IL. Requests for reprints should be addressed to Richard R. Saunders, Schiefelbusch Institute for Life Span Studies, 00 Sunnyside Ave., 52 Dole, Lawrence, KS 66045. (E-mail: rrsaun @ku.. edu).

424 SAUNDERS AND MCENTEE Verhave (1987) described four parameters relevant to the organization of equivalence classes. The parameters were (a) number of stimuli per class, (b) number of nodes, (c) the distribution of non nodal stimuli among nodal stimuli, and (d) directionality of training. Node, perhaps the key parameter, refers to a stimulus that participates in two or more conditional discriminations, thus providing for their interrelation or overlap. Directionality of training refers to whether the nodes serve as conditional stimuli (i.e., samples in MTS problems), discriminative stimuli (i.e., comparison stimuli in MTS problems), or both during training. Training in which nodal stimuli serve as sample stimuli in some MTS conditional discriminations and as comparison stimuli in others has been referred to as a linear series (LS) training structure (K. J. Saunders, Saunders, Williams, & Spradlin, 1993). The LS structure has been used frequently in experiments on stimulus equivalence with normal children and 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 to produce equivalence class establishment with the LS structure could be caused by a difference in the simple discriminations required during training versus testing. In LS training, some of the possible simple discriminations among stimuli are not required for problem solution, but these discriminations are essential for solving the conditional discriminations 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 an A stimulus and a D stimulus. One of the trial types that tests for the property of transitivity, however, will be Stimulus A 1 as sample and the Stimuli D1 and D2 as comparison stimuli. In training two Classes of four stimuli, for example, R. R. Saunders and Green fixed the number of discriminations unrequired by training, but essential in tests, at. Other investigators have concurred generally with this analysis, concluding that if each stimulus in the training set is not discriminated from the remaining stimuli, negative outcomes on tests for stimulus equivalence classes are likely (see Mcllvane & Dube, 1996; K. J. Saunders et ai., 1993; Sidman, 1986, 1994; Spradlin & Saunders, 1986). Although discriminations among stimuli in an experiment may arise as a function of variables other than the formal elements of the training (e.g., stimulus naming), the data suggest 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 other than LS. Across several early experiments, adolescents and adults with mental retardation were trained with minimal instructions in either sampleas-node (SaN) or comparison-as-node (CaN) structures leading potentially to 2 four- or five-member equivalence classes (Drake & Saunders, 1987,

INCREASING PROBABILITY OF EQUIVALENCE 425 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, equivalence classes were established in only 1 of 7 participants trained with SaN procedures, but in 14 of 15 participants trained with CaN procedures. SaN structures are hypothesized to share the same problem as LS, with respect to 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 young children with mental ages presumed to be similar to the mental ages of the participants with mild mental retardation. Four of 5 CaN-trained preschool children 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 LS structure has been conducted with participants with mental retardation. We hypothesized that if R. R. Saunders and Green's (1999) analysis is accurate, results with a LS structure should lead to results more similar to previous findings with SaN structures than findings with CaN structures. Further, we hypothesized that modifications to typical train ing methods with the LS structure might lead to results more similar to prior results with CaN structures. That is, if training in the LS structure were conducted such that discrimination of each stimulus from every other stimulus was more likely during training, then equivalence class establishment should be more probable than when such discriminations are not enabled. Two experiments were designed to test these hypotheses. Experiment 1 Method Participants All participants in this study were consumers of services in state- and community-operated agencies. Each participated at times that did not interfere with important daily activities. Each participated under informed consent procedures required by the human rights committees of the respective agencies and of the University of Kansas. In Experiment 1, 6 adults with mild mental retardation (based on results of most recent formal testing) served as participants. Ages ranged from 23-48 years across the 3 male and 3 female participants. Apparatus Participants sat at a desk in an office cubicle facing a computer monitor. Sessions were presented using a Macintosh LCIII computer with an ArtMedia 14 in. Trinitron CRT (Model TC1564). The monitor had a touchscreen operating with Troll Touch Software (Version 1.8.8). A software program was used to program stimulus display sequences and response consequences.

426 SAUNDERS AND MCENTEE The experimental stimuli are shown in the training structure schematic depicted in Figure 1. To establish the conditional discriminations depicted, a sample stimulus appeared in the middle of the screen to begin a trial; a touch to the sample resulted in the concurrent display of two-choice stimuli, below and on either side of the sample. A touch to either comparison resulted in the programmed consequence(s), temporary removal of all stimuli (approximately 2 s), and presentation of the next sample. On trials with consequences, an experimenter-designated correct response produced an auditory jingle from the computer; incorrect responses produced a "raspberry" sounding buzz. The participants were paid at the end of each session, in cash, for each experimenter-designated correct response. Each correct response equaled 1 cent. Procedures Arbitrary MTS training. Training and testing occurred in a linear-series structure leading potentially to two classes of four stimuli each, as shown in Figure 1. Training began with the first conditional discrimination (AB) in..,. I I 001 r----:l... I I!...If. I" I II Ill!,, /I II J Figure 1. Schematic of the training structure and stimuli employed. Solid arrows indicate trained relations. The vertical arrows on dashed lines indicate symmetry tests. The horizontal arrows connected with dashed lines indicate tests for transitivity and symmetric transitivity and are labeled as equivalence tests. sessions of 32 trials each. When the participant's performance met criterion on AB, training on BC commenced, followed by training on CD. Training continued first with all three conditional discriminations mixed in the same sessions with trial-by-trial feedback, sessions with feedback reduced to 75% of the trials, and then in sessions without trial-by-trial feedback. Testing began when the participant's performance on all the discriminations could be maintained without feedback. The training and testing in this experiment was conducted with "balanced" trial types (Green & Saunders, 1998; R. R. Saunders & Green, 1999). With balanced

INCREASING PROBABILITY OF EQUIVALENCE 427 trial types, comparison stimulus B 1, for example, was always presented with comparison stimulus B2 (never with C2 or 02). This arrangement in two-choice MTS training also has been referred to as the "pairedcomparison" procedure (Spradlin & Saunders, 1986). The performance criterion for each phase of this training was 0% correct for one session or two consecutive sessions at or above 90% correct. Participants completed up to four sessions per day, depending on their extraexperimental activity schedules. Tests for the properties of equivalence. Test sessions contained six test trials unsystematically interspersed among 26 training trials. Test trials never occurred consecutively. Responses on training trials and test trials produced no programmed consequences during test sessions. The trial types in the test sessions consisted of tests for transitivity only (i.e., the relations AC, BD, AD) and direct tests for symmetric transitivity or equivalence (i.e., the relations CA, DB, DA). As these relations must be tested for both potential classes, test trials spread across two test sessions constituted a complete test that will be referred to as an "equivalence test." Following training, the equivalence test was administered twice. Equivalence class establishment was judged to have occurred if each test administration produced at least experimenterdesignated correct responses in the test trials. If testing failed to produce criterion-level performances, two test sessions with tests for the property of symmetry were conducted (BA, CB, DC). Symmetry test sessions consisted of six test trials and two symmetry test sessions constituted a symmetry test. The criterion for concluding that symmetry was demonstrated was of experimenter-designated correct responses. If symmetry testing demonstrated that the trained conditional relations had the property of symmetry, the equivalence test was again administered twice. If, during any test session of either type, training trial accuracy fell below 90%, training sessions without trial-by-trial feedback were re-presented until accuracy again met criterion. Further, throughout the experiment, days in which test sessions were scheduled always began with a training session (without feedback) to ensure that the trained performances were at criterion prior to testing. Results The participants in Experiment 1 required between 7 and 63 training sessions (median = 23) to meet the criterion for testing for equivalence classes. As shown in Figure 2, no participant met the criterion for equivalence class establishment in the first two equivalence tests (EQ1 and EQ2). Participant P4 received only one initial equivalence test prior to symmetry testing because he informed the experimenters of a change in his residence only 1 day prior to leaving. He and P1, P2, and P3 passed the symmetry tests. Each was retested for equivalence. Participant P4 could be tested only once and therein showed no evidence of equivalence class establishment; P2 and P3 received two tests and neither met the

428 SAUNDERS AND MCENTEE U PI 8 8 U 8 8 6 4 2 o P4 P2 8 8 6 i!: 2 o o P5 8 8 6 4 2 o P3 U 8 8 P6 Figure 2. Results of Experiment 1 for all participants on tests for equivalence (black columns) and tests for symmetry (white columns), if applicable. criterion of class establishment. Because P1 's fourth equivalence test (EQ4) produced of correct responses, she was given a fifth test in which she had 11 of correct responses. Thus, P1 showed equivalence class establishment with repeated testing. Participant P5 did not pass the symmetry test and was therefore not retested for equivalence; and P6 left the facility unexpectedly before additional testing could be conducted. Figure 3 shows the median response latencies to comparison stimuli for training trials and test trials in the first equivalence test (two sessions) for each participant in Experiment 1. All had longer latencies or slower response speeds on test trials than training trials. Participant P1, who ultimately demonstrated equivalence class establishment, had the largest difference between training and test trial latencies.

INCREASING PROBABILITY OF EQUIVALENCE 429 CI) "'0 0 <..> (],) 6 C/l 4.-< "'0 (],) ::s 2 I'. Trainig Trials 8 Test Trials 0. - ---- _.. ---._------'-' PI P2 P3 P4 P5 P6 Figure 3. Median latencies of responses to comparison stimuli for training trials and test trials in the first two equivalence tests for each participant in Experiment 1. Experiment 2 Method Participants and Apparatus For Experiment 2, 6 new participants were recruited: 4 males and 2 females with mild mental retardation ranging in age from 18-47 years. The same apparatus and stimuli were employed with these participants. Procedures The training procedures in Experiment 2 were the same as in Experiment 1 until the participants met the Experiment 1 criterion for equivalence testing. The requirement for testing was one session at 0% correct or two consecutive sessions at >90% correct in sessions with no trial-by-trial feedback for responses. When that criterion was met, each participant was trained in additional sessions wherein trials with unpaired comparisons (e.g., A1 as sample, B1 and D2 as comparisons or A1 as sample, B1 and A2 as comparisons) were intermixed with trials with paired comparisons (e.g., with A1 as sample, B1 and B2 as comparisons) (see Kennedy, 1991, and Fields, Adams, Verhave, & Newman, 1990, for prior use of unpaired comparisons). Each version of unpaired comparisons (e.g., B1 with C2) was presented 1 or 2 times with each respective sample stimulus (e.g., A 1) within each session. Position of the correct comparison was counterbalanced across trials. A minimum of two sessions at >90% correct without feedback and with unpaired comparisons was required to commence equivalence testing. Testing was conducted as described for Experiment 1: two equivalence tests, a symmetry test if needed, and two equivalence tests if symmetry was

430 SAUNDERS AND MCENTEE passed. In Experiment 2 equivalence tests, test trials were intermixed with training trials with paired and unpaired comparisons, but all test trials contained paired comparisons. Thus, the test trial types in Experiment 2 were identical to those used in Experiment 1. Results Exposure to the unpaired comparisons did not significantly disrupt responding in 5 participants prior to testing. One participant could not maintain >90% correct responding with unpaired comparisons, however, and was replaced with an additional participant. With the exception of the replaced participant, two to five sessions with unpaired comparisons were required to meet the criterion for testing (median = 2). The eventual 6 participants in Experiment 2 required to 23 training sessions (median = 15) to meet the criteria for testing. Figure 4 shows that P7 and P8 had of correct responses in each of the first two equivalence tests. Participant P9 was correct of and 11 of times across these tests and P scored out of in each test. Paricipants P11 and P did "til u 1) "til 0 8 0 u P7 u 8 PIO 0; 6 -;;; 6 4 4 2 2 0 0 <;;J & "til u <;;J <;;J 0 u 8 P8 u -;;; 6 c f- 4 4 2 2 0 0 1) 0 8 PII & v.,&.s\ & cl' <;;J <;;J <;;J "til 0 8 0 u P9 u 8 PI2 6 '" 4 u 2 f- f- 0 0 & v.,&, > & cl' <;;J <;;J <;;J Figure 4. Results of Experiment 2 for all participants on tests for equivalence (black columns) and tests for symmetry (white columns), if applicable. 1) <;;J & <o.t' <o.t' <;;J <;;J <;;J <;;J

INCREASING PROBABILITY OF EQUIVALENCE 431 not meet the criterion for equivalence class establishment; each subsequently passed the symmetry test, and each again failed to show class establishment in the third and fourth equivalence tests. Figure 5 shows the median response latencies to comparison stimuli for the participants in Experiment 2 in the first two equivalence tests. All have longer latencies on test trials than on training trials. For P7 and P8, who were 0% correct on equivalence tests, the differences are small. For P9 and P, who met the criterion for equivalence class establishment but not errorlessly, the latency differences are large, as seen with P1 (who ultimately passed) in Experiment 1. (f) "0 8 I::::: 0 u 6 if)... 4 "0 2 0 P7 P8 P9 PI0 Pll P Figure 5. Median latencies of responses to comparison stimuli for training trials and test trials in the first two equivalence tests for each participant in Experiment 2. Discussion R. R. Saunders and Green (1999) concluded that training in LS and SaN structures does not require certain simple discriminations that are essential for passing subsequent tests for equivalence. Their conclusions were predicated on the assumption that training in these structures utilized paired comparisons, as employed in Experiment 1. As hypothesized, the participants in Experiment 1 produced overall results more comparable to previous results with SaN training structures than CaN training structures. Only 1 of 6 participants had test results indicative of equivalence class establishment and then, only after repeated testing. The present results are also similar to those reported across four studies reported by Arntzen and Holth, in which only 15 of 59 normal adult participants showed equivalence class establishment following LS training leading to three classes of three stimuli each (Arntzen & Holth, 1997, 2000b, Holth & Arntzen, 1998, 2000). Also as hypothesized, the participants in Experiment 2 produced

432 SAUNDERS AND MCENTEE overall results more similar to previous results with CaN training structures. Of 6 participants, 4 had initial test results indicative of equivalence class establishment. A tentative inference is that the unpaired comparison procedure used in Experiment 2 required acquisition of the simple discriminations not required by a paired comparison procedure. Presumably, acquiring these discriminations prior to testing led to the higher proportion of participants showing equivalence class formation. The results from P11 and P demonstrate, however, that acquisition of these discriminations alone is not sufficient for equivalence-indicative performances. A reasonable question to ask of the results is whether variables other than presentations of comparison stimuli can account for the differences. One possibility is that exposure to a few sessions of unpaired comparisons overtrains the conditional discriminations and such overtraining affects equivalence class establishment. If overtraining reliably produced equivalence class establishment, however, we would expect to see it occur in the participants in both experiments who underwent symmetry testing and repeated equivalence testing. By the end of the fourth equivalence test (EQ4), they had received additional training trial exposure, including the first session of each day, which always was a training review session. Another possibility is that the participants in Experiment 2 differed from those in Experiment 1, perhaps along some dimension of competence with conditional discriminations. As a group, the participants in Experiment 2 required fewer training sessions to meet the criterion for testing than did the Experiment 1 group. However, P3 required only seven training sessions in Experiment 1 to reach equivalence testing (six is the minimum possible), but did not show class establishment despite repeated testing. Similarly, P11 required but 11 sessions prior to testing in Experiment 2, including exposure to the unpaired comparisons for 2 sessions, and he likewise did not show equivalence class establishment. Because sessions to criterion also has not been a reliable predictor of class establishment in prior research with people with mental retardation (e.g., R. R. Saunders, Wachter, et ai., 1988), the present data support a discrimination explanation. The latency data, showing longer latencies on test trials than training trials, replicates findings by other researchers (Arntzen & Holth, 1997, 2000a, 2000b; Holth & Arntzen, 2000; Spencer & Chase, 1996). The latency data from the two experiments also parse the participants into three groups. Participants P7 and P8 showed little difference between training trial and test trial latencies, with both medians near 2 s. The lack of disparity between training and test trial latencies may reflect a high degree of discrimination among the stimuli. Participants P1, P9, and P showed equivalence class establishment, but with some test trial errors. These participants showed the largest disparity between training and test trial latencies, with median differences of 6 to 7 s. The remaining participants who did not show equivalence class establishment had

INCREASING PROBABILITY OF EQUIVALENCE 433 median differences of about 2 s. Thus, the latency data and test results parse the participants into the same subgroups. It is unclear what this means; the number of participants in each subgroup is too small for drawing any firm conclusions. Future research might include latency analysis, however, to determine if this pattern will be replicated or whether it extends to results with other training structures. In MTS training, sample/s+ or sample/s- control of responding can arise (Carrigan & Sidman, 1992). Sample/S- control refers to responses to the experimenter-designated correct comparison as a function of rejection of the incorrect comparison. Thus, the incorrect comparison controls the correct i response. The quintessence of sample/s- control arises from the structure employed in the present study: two potential LS classes of four stimuli established in two-choice MTS (Johnson & Sidman, 1993). Carrigan and Sidman explained how consistent sample/s- control leads to 33% overall correct responding on tests in this structure. Under sample/s- control, the performances on all one-node tests (two-thirds of the test trials; AC, BD, CA, DB) will be incorrect and performances on two-node tests will be correct (AD, DA). The test performances observed in Experiment 1 do not reflect this pattern or overall percentage correct. Thus, we infer that sample/s- control during training was not the reason equivalence classes were established with only 1 participant. A similar conclusion can be drawn for P11 and P in Experiment 2. We speculate, however, that the participant that was replaced in Experiment 2 may have experienced difficulty with the unpaired comparisons as a function of a history of sample/s- control when the comparisons were paired. The replacement of the incorrect comparison with a new incorrect comparison would likely disrupt established control by the former incorrect comparison. This possibility prompts an analysis regarding the test performances of P7 and P8 versus P11 and P. If responding during initial training were under exclusive sample/s+ control, the introduction of unpaired comparisons might have no effect. Indeed, the substitution might go undetected because the stimulus control of responding was already established and was not reliant on the negative comparisons. In that case, the planned-for discrimination between the correct comparison and the substituted incorrect comparison might not arise. This failure to discriminate could explain the results of P11 and P. In contrast, if a combination of sample/s+ and sample/s- control was operational during the early training of P7 and P8, then (a) the sample/s+ control would act to prevent complete disruption of responding and (b) the substitution would disrupt sample/s- control sufficient to produce attention to and discrimination between the newly paired stimuli. In future research, one might employ limited or selective substitution to tease out the relative contributions of control. For example, one might employ the A stimuli as negative comparisons in BC training trials as the only substitutions made to unpair the comparisons. Would this contribute to correct responses on CA and AC tests, while leaving AD, DA, BD, and DB trials uninfluenced?

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