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Effects of Immediate Tests on the Long-Term Maintenance of Stimulus Equivalence Classes.

Procedures used to study stimulus equivalence involve the establishment of sets of conditional discriminations and the assessment of stimulus equivalence within these stimulus classes. When establishing these stimulus classes in matching-to-sample (MTS) procedures, selecting specific discriminative stimuli referred to as comparisons in the presence of specific conditional stimuli known as samples in line with experimenter-defined four-term contingencies is reinforced. Stimulus equivalence classes are said to be established if performance have the properties of reflexivity, symmetry, and transitivity. These properties are commonly assessed using MTS procedures similar to those used during conditional discrimination training, although no programmed consequences for responding is included in this test. Reflexivity refers to consistently selecting comparison stimuli that are identical to the samples. Symmetry refers to the class consistent selection of comparisons that previously appeared as samples when samples that previously appeared as comparisons are presented. Finally, transitivity involves the class consistent selection of comparisons in the presence of samples that have only been indirectly related to the comparison via one or more trained conditional discriminations. For example, if the conditional discriminations AB and BC are trained (where A, B, and C refer to different stimuli), transitivity is evident if participants select the C comparisons of the same class when the A stimuli are presented as samples (Sidman, 1994; Sidman & Tailby, 1982).

Stimulus equivalence has been suggested to be a viable behavioral approach to the study of language and symbolic behavior because both stimulus equivalence classes and language involve arbitrary relations among stimuli and generative performance (Malott, 2003; Place, 1995-1996; Wilkinson & Mcllvane, 2001). The acquisition of a given language category, such as a spoken word/written word/referent relationship, is normally considered to be a more or less permanent change in the behavioral repertoire of an individual. For stimulus equivalence to be a considered a plausible behavioral approach to language, stimuli involved in stimulus equivalence classes must then be shown to exert appropriate control over behavior over longer periods of time, such as weeks, months, or years. In experimental settings, however, the assessment of stimulus equivalence typically takes place only immediately after prerequisite conditional discriminations have been established.

Some studies have investigated the long-term maintenance of stimulus equivalence performance without further exposure to the reinforcement contingencies of the prerequisite conditional discriminations. These studies have investigated the retention of stimulus equivalence classes over days (Billinger & Norlander, 2011 ; Eilifsen & Arntzen, 2015; Fienup & Dixon, 2006), weeks (Arntzen & Hansen, 2011; Arntzen, Petursson, Sadeghi, & Eilifsen, 2015; Camargo & Haydu, 2015; Doughty, Brierley, Eways, & Kastner, 2014; Eilifsen & Arntzen, 2015; Fienup & Dixon, 2006; Rehfeldt & Dixon, 2005), and months (Arntzen, Halstadtro, Bjerke, Wittner, & Kristiansen, 2014; Rehfeldt & Hayes, 2000; Rehfeldt & Root, 2004). Although a majority of studies have at least one example of stimulus equivalence performance that is maintained over time, all the studies also included participants whose performance showed a decline of experimenter-defined correct stimulus control over time. These studies are, however, difficult to compare because they involve procedural differences that can potentially influence the maintenance of stimulus equivalence classes. Some studies included tasks in addition to stimulus equivalence tests in an MTS format involving stimuli used in the stimulus equivalence tests, both in temporal proximity of the initial training and testing and the retention tests. Tasks include primary generalization tests and card sorting tasks (Arntzen et al., 2015a; Rehfeldt & Hayes, 2000; Rehfeldt & Root, 2004). In addition, several studies employed stimuli that may have already functioned as discriminative stimuli for the participants prior to the start of the experiment, such as commonly encountered smells, textual stimuli, and pictures of concrete objects (Arntzen et al, 2014; Arntzen et al. 2015a; Billinger & Norlander, 2011; Camargo & Haydu, 2015; Doughty et al., 2014; Fienup & Dixon, 2006; Rehfeldt & Dixon, 2005; Rehfeldt & Root, 2004). Such members of extraexperimental stimulus classes may affect performance both during conditional discrimination training and stimulus equivalence tests. Stimuli involved in these classes may also be encountered and interacted with between stimulus equivalence establishment and maintenance tests, which can potentially influence performance on these retention tests (for more on "meaningful" stimuli and stimulus equivalence, see Arntzen, Nartey, & Fields, 2015; Fields, Arntzen, Nartey, & Eilifsen, 2012; Nartey, Arntzen, & Fields, 2015a).

Experiment 2 in Eilifsen and Arntzen (2015) involved tests for trained conditional discriminations and stimulus equivalence presented 1 day, 2 weeks, and 4 weeks after conditional discrimination training and an immediately administered stimulus equivalence test. Results showed that participants who responded in accordance with stimulus equivalence immediately following conditional discrimination training continued to do so on maintenance tests, but participants who responded in line only with trained relations in the same initial test did not respond in line with any type of relation on later tests. Experience with successful performance on stimulus equivalence tests may have affected maintenance of trained conditional discriminations. One can then ask what effects the omission of a test for stimulus equivalence immediately following conditional discrimination training will have on the maintenance of trained and derived responding. That is, how does the opportunity to respond in accordance with stimulus equivalence immediately following the conditional discrimination training affect responding in accordance with stimulus equivalence over time? Even if stimulus equivalence tests are administered under extinction conditions, there may be events in testing that influence participant behavior, and these events may be crucial for test outcomes (Mcllvane & Dube, 1990; Spradlin, Saunders, & Saunders, 1992). Harrison and Green (1990) provided a particularly striking example of this type of behavior change under extinction conditions. In that study, adult and child participants experienced a two-choice MTS procedure without any programmed consequences involving trials that included one a consistent comparison choice given a specific sample along with several other comparison options. The majority of the participants responded in line with experimenter defined "conditional discriminations," and some participants also responded in line with the experimenter-defined classes in "transitivity/ equivalence" tests. As such, the study identified a source of stimulus control based on the consistency of sample-comparison pairs that generated responding similar to stimulus equivalence. Harrison and Green (1990) suggested that this type of stimulus control may occasionally occur in tests for stimulus equivalence. Such systematic responding in conditional discrimination procedures and stimulus equivalence tests not based on any reinforcement contingency set up by the experimenter has been referred to as conditional responding acquired by arbitrary assignment (de Rose, 1996). The phenomenon has also been referred to as responding in line with participant-defined classes (e.g., Arntzen et al., 2015a).

All previous studies on the long-term maintenance of stimulus equivalence classes have included a test for stimulus equivalence immediately following contact with the trained experimental contingencies. The current study investigated the effect of either including or omitting this stimulus equivalence test. First, conditional discriminations were trained using a one-to-many (OTM) training structure, a structure associated with a high probability of stimulus equivalence outcomes (Arntzen & Holth, 1997, 2000). Following this, some participants were given a stimulus equivalence test and others were not, and subsequently all participants were tested for trained conditional discriminations and stimulus equivalence approximately 2 and 4 weeks later. The effect of the immediate stimulus equivalence test was assessed by reporting the number of participants in each group who responded in accordance with stimulus equivalence, but data were also examined using several other types of analyses. First, it has been suggested that the number of conditional discrimination training trials completed may affect stimulus equivalence performance in several ways (e.g., Bortoloti, Rodrigues, Cortez, Pimentel, & de Rose, 2013; Dube & Mcllvane, 1996). As such, an analysis of possible systematic differences between the experimental groups on this parameter is warranted. Second, several studies have reported responding in line with the trained conditional discriminations or in line with symmetry and transitivity without responding in accordance with stimulus equivalence (e.g., Eilifsen & Arntzen, 2009). Reporting data from stimulus equivalence tests only as stimulus equivalence performance may not capture all trained and emergent performances resulting from experimental procedures, and, therefore, an analysis of responding in line with individual types of relations is warranted. Third, in several studies, stimulus equivalence responding has been shown to occur only after repeated exposure to stimulus equivalence test trials (e.g., Holth & Arntzen, 1998). This phenomenon has been referred to as the delayed emergence of stimulus equivalence (Sidman, 1994). It is of interest to see whether the probability of delayed emergence is altered by stimulus equivalence retention tests and whether the inclusion of a stimulus equivalence test following conditional discrimination training will affect such performance. Fourth, previous studies have shown evidence of responding in line with participant-defined classes. That is, systematic performance on stimulus equivalence tests not in line with experimenter-defined stimulus equivalence classes. (Fields et al., 2012). As with delayed emergence, it is of interest to see whether the probability of the development of participant-defined classes is affected by stimulus equivalence retention tests and whether the inclusion of a stimulus equivalence test immediately following conditional discrimination training will affect such performance.

Method

Participants

Twenty-seven participants between the age of 16 and 43 years were recruited through personal connections and at a community center for young adults. Fourteen participants were male, and 13 were female. Participants were assigned identification numbers from 5631 to 5657. The participants could choose to terminate their participation in the experiment at any time without any negative consequences; P5632 and P5655 did so during conditional discrimination training, and P5647 did not return for the second retention test. Twenty-four participants completed the experiment, and the subsequent presentation and discussion of data will be on the performance of these participants. All participants received 100 kroner (approximately 11 USD) per hour of participation. Upon arrival, the participants first read and signed a consent form that included information about anonymity, the right to withdraw from the experiment, the duration of the experiment, and the hourly pay rate. The participants were informed about stimulus equivalence and the purpose of the experiment as they exited the experimental setting.

Setting, Stimuli, and Apparatus

Participants sat in front of a table in an office cubicle situated in a larger room containing two identical cubicles and a chair and desk for the experimenter. One or both cubicles could be occupied at any given time, although participants did not interact with each other and were monitored by the experimenter throughout the experiment. Laptop computers placed on each table had purpose-built MTS software installed that presented stimuli and programmed consequences, collected data, and initiated experimental phase changes. Fifteen two-dimensional visual figures assumed to be unfamiliar to the participants were used as samples and comparisons. These stimuli were arbitrarily divided into three five-member classes in two different ways, with participants being randomly assigned across experimental conditions to experience the contingencies of one these two stimulus configurations. The stimulus sets are depicted in Fig. 1, and which participants received Stimulus Set 1 or Stimulus Set 2 is shown in the second column of Table 1. In experimental phases that included programmed consequences, words such as excellent, good, and other synonyms followed experimenter-defined correct comparison choices, and the word wrong followed experimenter-defined incorrect comparison selections.

Experimental Design

Participants were randomly assigned to one of two experimental conditions differing only by whether the stimulus equivalence test followed the establishment of prerequisite conditional discriminations was included. The test was omitted for the 12 participants in Group 1 and included for the 12 participants in Group 2. Subsequently, all participants experienced two retention tests assessing trained conditional discriminations and stimulus equivalence approximately 2 and 4 weeks after the initial conditional discrimination training.

Response Criteria for Relational Types, Stimulus Equivalence, and the Delayed Emergence of Stimulus Equivalence

If the participant made experimenter-defined correct comparison choices on at least 90% of trials assessing a particular type of relation, that relation (i.e., trained conditional discrimination, symmetry, or transitivity/equivalence) was considered present in the participant's behavioral repertoire. If the comparison selections were consistent with the experimenter-defined stimulus equivalence classes on at least 90% of trials assessing each of the three types of relations, responding was considered to be in accordance with stimulus equivalence. If this criterion was met only in the latter half of trials assessing trained conditional discriminations, symmetry, or transitivity/ equivalence, performance was considered an instance of delayed emergence of stimulus equivalence. If delayed emergence by this definition was seen in tests for stimulus equivalence following stimulus equivalence performance on earlier tests, the response pattern is labeled delayed reemergence of stimulus equivalence.

Procedure

The experiment started with the participant entering one of the office cubicles where the following instructions were displayed on a computer screen:
   A stimulus will appear in the middle of the screen. Click
   on the stimulus by using the computer mouse. Three
   other stimuli will appear. Choose one of these by using
   the computer mouse. If you select the stimulus we have
   defined as correct, words such as good, excellent, and so
   on will appear on the screen. If you press a wrong stimulus,
   the word wrong will appear on the screen. A tally
   of the number of correct responses you have made is
   shown at the bottom of the screen. In some stages of
   the experiment, the computer will not tell you if you
   made the correct or incorrect choice. However, based
   on what you have learned, it is possible to do all the
   tasks correctly. Please do your best to get everything
   right. Good luck! Please press the start button to begin
   the experiment.


Upon pressing the start button, the sample of the first trial appeared in the middle of the screen. Clicking on this using the computer mouse led to the appearance of three comparison stimuli presented randomly in three corners of the screen, leaving one corner blank. Both the sample and the comparisons remained on the screen until the participant made a comparison choice with the computer mouse. Following the selection of a comparison, a programmed consequence of positive or negative valence, depending on the response of the participant, appeared in the middle of the screen. The programmed consequence remained on the screen for 500 ms with a tally of the number of correct responses the participant had made throughout the conditional discrimination training displayed at the bottom right corner of the screen. A blank-screen 500-ms intertriai interval followed the programmed consequence.

Figure 2 illustrates the phases of the experiment for both experimental groups. Each box presents an experimental phase and includes the alphanumeric codes for the trial types included in the phase, with numbers indicating class membership and letters indicating different members of a class. In Phases 1-4, AB, AC, AD, and AE conditional discriminations were established and maintained. A block of trials involved the presentation of all trial types five times, resulting in blocks of 60 trials. Within a block, trial types were presented randomly. A new experimental phase was introduced if the participant selected the experimenter-defined correct comparisons on at least 54 (approximately 90%) of trials within a block. Fewer than 54 comparison selections conforming to the experimenter-defined classes led to the presentation of a block of trials with identical parameters, although with a new randomization of the trial types. In Phase 1, the conditional discrimination establishment phase, programmed consequences followed all comparison selections. In Phases 2, 3, and 4, the conditional discrimination maintenance phases, programmed consequences were delivered with a probability of 75%, 25%, and 0%, respectively. On trials without programmed consequences, a blank screen replaced the consequence in the 500ms period following comparison selection. Responding in line with the experimenter-defined classes in Phase 4 led to the introduction of Phase 5, the only phase of the experiment that differed for the two experimental groups. Participants in Group 1 continued to Phase 5A, where 36 conditional discrimination training trials without programmed consequences or a mastery criterion were presented in order to equalize the number of presentation of such trials types for both groups. Due to software limitations, the participants had to leave the office cubicle they were sitting in for about a minute, as the experimenter initiated the start of this phase. Group 2 continued to Phase 5B, a test for stimulus equivalence, which was automatically launched by the MTS software. The test for stimulus equivalence consisted of three repetitions of each trial type presented randomly. Thirty-six trials assessed trained conditional discriminations (AB, AC, AD, and AE relations), 36 trials assessed symmetry (BA, CA, DA, EA relations), and 108 trials assessed transitivity/ equivalence (BC, BD, BE, CB, CD, CE, DB, DC, DE, EB, EC, ED relations). No programmed consequences appeared following comparison selections in this phase. With the exception of the trial types presented, test trials were identical to the conditional discrimination training trials.

Upon the completion of Phase 5A or 5B, a time and date was set for the participant to return for Phase 6 two weeks later. Phase 6 consisted of a test for stimulus equivalence test that was identical to Phase 5B for participants in both groups. Following the completion of Phase 6, a time and date was set for the participant to return for Phase 7, after an additional 2 weeks. Phase 7 was also identical to Phase 5B. If possible, arrangements for the participants' return for retention tests was made exactly two weeks after the conditional discrimination training, and subsequently exactly two weeks after the first retention test. However, this was not always possible. Table 2 shows the number of days between Phase 5 and Phase 6 and between Phase 6 and Phase 7 for each participant, as well as group averages and ranges.

Results

Figure 3 summarizes the stimulus equivalence performances for participants in both experimental groups on all tests. In Group 1, in which participants did not experience a stimulus equivalence test immediately following conditional discrimination establishment, three of the 12 participants responded in accordance with stimulus equivalence on the 2-week test, and four participants did so on the 4-week test. In Group 2, 10 of the 12 participants responded in accordance with stimulus equivalence during the immediate test. None of the participants in Group 2 responded in accordance with stimulus equivalence on the 2-week test, and four participants did so on the 4-week test. Data on conditional discrimination and stimulus equivalence performance will be presented below in further detail.

Conditional Discrimination Training

Phase 1: Conditional Discrimination Establishment for Both Groups Table 1 reports the number of training trials for all participants in both groups in the third column. The median number of trials used to complete Phase 1 was 360 for Group 1 (range: 120-960) and 450 for Group 2 (range: 240-2,460). An unpaired t test showed no significant difference between Group 1 and 2 on this measure, t(22) = 0.6098, p = .5483. Participants receiving Stimulus Set 1 used a median of 420 trials to complete the conditional discrimination training (range: 120-960). The median number of trials was also 420 for participants receiving Stimulus Set 2 (range: 2402,460). An unpaired / test showed the difference in the number of training trials for participants receiving different stimuli sets not to be significant, t(22) = 0.2523, p = 0.8031.

Phases 2, 3, and 4: Conditional Discrimination Maintenance for Both Groups All participants completed the conditional discrimination maintenance phases in the minimum number of trials possible (180), except for P5640, who needed 540 trials to complete these phases.

Phase 5A: Additional Conditional Discrimination Maintenance for Group 1 With two exceptions, all participants made experimenter-defined correct comparison choices on all 36 trials in this phase. The exceptions were P5640, who made 32 experimenter-defined correct comparison choices and P5641, who made 34 such selections.

Detailed Analysis of Stimulus Equivalence Test Performance

Table 1 shows responding on trials assessing individual relational types in the immediate stimulus equivalence test for each participant in Columns 4-6. Corresponding data for the 2-week and 4-week stimulus equivalence tests are shown in Columns 7-9 and 10-12, respectively. Table 3 shows responding on trials assessing all relational types for the first and second half of the stimulus equivalence tests for the five participants showing delayed emergence or delayed reemergence of stimulus equivalence. Table 3 shows only results from the immediate and 2-week stimulus equivalence tests for participants in Group 2, as delayed emergence or delayed reemergence of stimulus equivalence was not seen for any participants in Group 1 or in the 4-week test for any participants in either group.

Phase 5B: Immediate Testing for Stimulus Equivalence for Group 2 In this test, experienced only by participants in Group 2, 10 of 12 participants responded in accordance with stimulus equivalence. The two remaining participants, P5645 and P5652, responded in line with the trained conditional discriminations and symmetry, but did not meet the criterion set for transitivity/equivalence. Both participants did, however, respond in accordance with delayed emergence of stimulus equivalence. Taking delayed emergence in account, all 12 participants in Group 2 responded in accordance with stimulus equivalence.

Phase 6: Two-Week Retention Test

Group 1 Three of 12 participants, P5633, P5656, and P5657, responded in accordance with stimulus equivalence. In addition, P5631 responded in line with the trained conditional discriminations and transitivity/equivalence but did not respond in line with symmetry. This participant did, however, respond in accordance with delayed emergence of stimulus equivalence. The remaining eight participants did not respond in accordance with either immediate or delayed emergence of stimulus equivalence, nor did they respond in line with any relational type

Group 2 None of the 12 participants responded in accordance with stimulus equivalence. However, four of the 12 participants, P5635, P5636, P5638, and P5645, responded in line with the trained conditional discriminations. P5638 also responded in line with symmetry, but not transitivity/ equivalence, and P5636 responded in line with transitivity/equivalence, but not with symmetry. Three of these four participants, P5635, P5636, P5638 did respond in accordance with delayed reemergence of stimulus equivalence. The remaining eight participants did not respond in accordance with either immediate or delayed emergence of stimulus equivalence, nor did they respond in line with any single relational type.

Phase 7: Four-Week Retention Test

Group 1 The three participants who responded in accordance with stimulus equivalence in the 2-week retention test, P5633, P5656, and P5657, continued to do so in the 4-week test. In addition, P5631, who responded in accordance with delayed emergence of stimulus equivalence in the 2-week test, now responded in accordance with stimulus equivalence. The remaining eight participants did not respond accordance with either immediate or delayed emergence of stimulus equivalence, nor did they respond in line with any single relational type

Group 2 All four participants who responded in line with one or more of the relational types and/or in accordance with delayed reemergence of stimulus equivalence in the 2-week retention test (P5635, P5636, P5638, and P5645), now responded in accordance with stimulus equivalence. The remaining eight participants did not respond accordance with either immediate or delayed emergence of stimulus equivalence, nor in line with any single relational type.

Analysis of Performance on Individual Trial Types in Stimulus Equivalence Tests

Figure 4 illustrates three distinct response patterns seen in tests for stimulus equivalence for participants in Group 1, and Fig. 5 illustrates three similar response patterns for participants in Group 2. Figure 4 shows the responding of P5637, P5633, and P5643, and Fig. 5 shows the responding of P5654, P5638, and P5652. Taken together, these six patterns are representative for all participants in the experiment, and the depiction of the participants shown could be substituted with other participants. In Fig. 4, the three matrices on the left depict responding in the 2-week stimulus equivalence test (Phase 6), and the three matrices to the right depict responding in the 4-week test (Phase 7). In Fig. 5, the three matrices to the left depict responding in the immediate test for stimulus equivalence (Phase 5B), the middle three matrices show responding in the 2-week stimulus equivalence test (Phase 6), and the matrices to the right depict the responding in the 4-week test (Phase 7). The vertical axis of each matrix shows the alphanumeric codes for samples, and the horizontal axis shows the codes for comparisons. Each cell illustrates the number of times a participant selected a comparison given a specific sample. Black cells indicate the maximum of three comparison selections given a specific sample, and gray cells, cells with diagonal lines, and white cells indicate two, one, or zero comparison selections, respectively, conditional upon a sample. For example, the second top cell from the left in the left matrix depicting the responding of P5637 in Fig. 4 illustrates that when Al was presented as the sample, the participant responded by selecting comparison B1 two times. Similarly, if looking three cells to the right, the black color in the cell directly below the El label illustrates that the participant chose the El comparison in the presence of the A1 sample three times. Note that the figures include an illustration of the untested reflexive relation, shown as a diagonal intersection of black cells through each matrix. For example, the cell in the top left corner of the left matrix depicting the responding of P5637 in Fig. 4 illustrates the hypothetical responding of choosing Al as a comparison in the presence of Al as a sample the maximum of three times. Experimenter-defined correct reflexive responding is taken as a given without being tested, as it is in the majority of studies on stimulus equivalence with human participants.

Group 1 The depiction of Pattern 1 at the top of Fig. 4 is characterized by gray cells and cells with diagonal lines distributed throughout the width of each matrix. This shows that responding on most trial types was not consistently allocated to specific comparisons, and, as such, indicates unstable and unknown stimulus control. The responding of P5637 serves as an example of this pattern in Fig. 4, but P5640, P5641, P5646, P5651, and P5653 also responded in a similar manner. The depiction of Pattern 2 in the middle of Fig. 4 consists of mostly black cells organized in three boxes running diagonally through the matrices. This shows that comparison selections were in line with the experimenter-defined stimulus equivalence classes. The responding of P5633 is shown in the figure, but P5631, P5656, and P5657 also displayed similar response patterns. The illustration of Pattern 3 at the bottom of Fig. 4 shows black cells clustered in the upper left part of the matrix, but the middle and the bottom parts are dominated by gray cells and cells with diagonal lines distributed throughout the width of the matrix. This indicates responding in line with the experimenter-defined classes on trial types assessing relations in Stimulus Class 1 and a lack of known stimulus control on trial types involving the two other stimulus classes. The right bottom matrix in Fig. 4, depicting the 4-week test, shows consistent responding on all trial types, illustrated by all black and white cells. For Stimulus Class 1, this performance is still in line with the experimenter-defined class, but this is not the case for the two remaining stimulus classes. The pattern is the result of responding in line with one experimenter-defined (A1B1C1D1E1) and two participant-defined classes (A2B3C2D2E2 and A3B2C3D3E3), including symmetric and transitive responding within these classes. The responding of P5643 is shown in Fig. 4, but P5634 also responded in line with both participant-defined classes (A1B1C2D1E1 and A2B2C1D2E2) and an experimenter-defined class (A3B3C3D3E3). The top half of Table 4 shows the number of comparison selections in line with the combinations of experimenter- and participant-defined classes for P5634 and P5643 in the first and second half of trials assessing each type of relation at both retention points. If considering 90% consistency on all relational types as responding in line with the specific combinations of experimenter- and participant-defined classes, P5634 responded in such a manner at both retention points. For P5643, such responding was seen in the latter half of the 2-week test and for the entire 4-week test.

Group 2 In all the patterns depicted in Fig. 5 nearly all responses to comparisons were in were line with the experimenter-defined classes in the test for stimulus equivalence administered immediately following conditional discrimination training. This is illustrated by a majority of black cells organized in three boxes running diagonally through the three matrices on the left of the figure. However, in the two retention tests, patterns similar to the ones described for participants in Group 1 are seen. The illustration of Pattern 4, shown at the top of Fig. 5, involves a large proportion of grey cells and cells with diagonal lines distributed throughout the width of the matrix in both retention tests, indicating unstable and unknown stimulus control. The responding of P5654 is shown in the figure, but P5639, P5648, and P5650 responded in a similar manner. The illustration of Pattern 5 in the middle of Fig. 5 involves mostly black cells in a three-box diagonal pattern in all three matrices, showing that responding was mostly consistent with the experimenter-defined classes on all stimulus equivalence tests. The responding of P5638 is shown in the figure, but P5635, P5636, and P5645 responded in a similar manner. The matrices illustrating Pattern 6 is dominated by black and white cells. However, the black cells are not contained to three squares, and as such, illustrates responding in line with participant-defined classes. The performance of P5652, who responded in line with the participant-defined classes A1B1C1D3E1 and A3B3C3D1E3 and the experimenter-defined class A2B2C2D2E2, is illustrated in Fig. 5, but P5642, P5644, and P5649 responded in a similar manner. P5642 responded in line with the participant-defined classes A1B1C2D1E1, A2B2C3D2E2, and A3B3C1D3E3. P5644 responded in line with the participant-defined classes A1B1C2D1E1 and A2B2C1D2E2, and the experimenter-defined class A3B3C3D3E3, and P5649 responded in line with the experimenter-defined class A1B1C1D1E1 and the participant-defined classes A2B2C2D3E2 and A3B3C3D2E3. The bottom half of Table 4 shows the number of comparison selections in line with the combinations of experimenter- and participant-defined classes for these four participants in the first and second half of trials assessing each relational type at both retention points. If considering 90% consistency on all relational types as responding in line with the combinations of experimenter- and participant-defined classes, P5644 and P5649 shows such responding in both the 2- and 4-week test. P5642 and P5652 responds in such a manner only in the 4-week test.

Summary of Response Patterns in Stimulus Equivalence Tests

Figure 6 summarizes the performance of all participants in both groups on all tests. Bars illustrate the number of participants responding in line with (1) stimulus equivalence, (2) delayed emergence or delayed reemergence of stimulus equivalence, (3) participant-defined classes, or (4) delayed emergence of participant-defined classes. In the immediate test (for participants in Group 2), all 12 participants showed either immediate or delayed emergence of stimulus equivalence. In the 2-week test, three participants in Group 1, who did not receive a stimulus equivalence test immediately following conditional discrimination training, responded in accordance with stimulus equivalence, and one additional participant showed evidence of delayed emergence. An additional participant displayed a consistent response pattern partly based on participant-defined classes. Another participant also responded consistently line with partly participant-defined classes in the latter half of the 2-week test. In Group 2, three of the 12 participants showed evidence of delayed reemergence of stimulus equivalence in the 2-week test, and two other participants displayed consistent responding within partly participant-defined classes. In the 4-week test, four participants in Group 1 responded in accordance with stimulus equivalence and two participants showed consistent responding within partly participant-defined classes. In Group 2, four participants responded in accordance with stimulus equivalence and four participants showed consistent responding within partly participant-defined classes in the 4-week test.

Discussion

Twenty-four participants received conditional discrimination training and were subsequently tested for maintenance of conditional discriminations and stimulus equivalence approximately 2 and 4 weeks later. Twelve participants were also immediately tested for stimulus equivalence following conditional discrimination training, whereas 12 different participants were not. Only a minority of participants in both groups responded in accordance with stimulus equivalence at retention points. No difference in performance was detected as a function of experimental group. Several participants displayed a consistent pattern of responding at retention points in line with stimulus classes partly or completely defined by the participant. Within these partly self-defined classes, participants responded in a manner similar to symmetry and transitivity/ equivalence.

In the current study, the procedure for establishing the conditional discriminations prerequisite for stimulus equivalence was conducted in a way similar to many other studies from our laboratory. Blocks of trials consisted of five repetitions of each trial type, the criterion for advancing through the conditional discrimination training phases and to the stimulus equivalence test was 90% experimenter-defined correct performance, and several phases in which performance was maintained with programmed consequences gradually being thinned were included. It can be argued that this training procedure and the performance criteria are relatively extensive and strict, respectively, both in comparison to other studies on the retention of stimulus equivalence classes and to studies on stimulus equivalence in general. As such, it seems unlikely that the lack of retention of the stimulus equivalence classes over time seen for many participants was caused by weak stimulus control or the lack of fluency of performance at the end of conditional discrimination training.

Several studies have successfully applied stimulus equivalence procedures to establish various useful skills in a wide variety of populations (e.g., Daar, Negrelli, & Dixon, 2015; Dixon & Lemke, 2007; Fields et al., 2009). Such studies have normally not included assessment of the maintenance of performance over time. Although all the participants in the current study who were tested for stimulus equivalence immediately following conditional discrimination training responded in accordance with stimulus equivalence, only a few did so at retention tests. This finding seems to pose a problem for the utility of stimulus equivalence as a technology for socially valid behavior change, as it is normally desirable for such change to last over time. However, procedures commonly used in the experimental analysis of stimulus equivalence, such as the procedure of the current experiment, may not be a particularly good analogue to situations in which stimulus equivalence technology is applied. Nonapplied stimulus equivalence procedures commonly utilize only abstract stimuli that are assumed to be unfamiliar to the participant prior the stimulus equivalence experiment. An applied analogue to the stimulus equivalence procedures commonly used for research purposes would, for example, involve teaching a person without any skills related to a set of semantic concepts the relations between the pictures, written words, and spoken words of these concepts. Such studies do exist with persons with learning disabilities, but then only with procedures involving extensive prompting and other variables that differ from those employed in the current study (e.g., Sidman & Cresson, 1973; Wilkinson, Rosenquist, & Mcllvane, 2009). Most applied studies have, however, included stimuli that were almost certainly familiar to the participants, such as text or pictures, as one or more of the stimuli in the stimulus equivalence classes. Participant familiarity with stimuli greatly increases the probability of successful stimulus equivalence performance (Arntzen et al., 2015a; Fields et al., 2012; Nartey, Arntzen, & Fields, 2015b) and may also affect the retention of stimulus equivalence classes. Future experiments should explore the effect of the inclusion of familiar stimuli on the retention of stimulus equivalence classes.

In the 4-week stimulus equivalence test, two of 12 participants in Group 1 and four of 12 participants in Group 2 responded in systematic manner not consistent with the experimenter-defined stimulus classes. This response pattern included responding in line with symmetric and transitive relations, but within classes only partly related to the conditional discrimination training. Such responding was not derived from any known reinforcement contingency and is apparently not an instance of stimulus equivalence (Sidman, 2000). Spradlin et al. (1992) suggested that experimenter-defined correct responding on some trial types may influence responding on other trials and be responsible for the delayed emergence of stimulus equivalence classes. If indeed this process occurs, such influence across trial types may also be a plausible part of the explanation of the responding of participants fonning self-defined classes as seen in the current experiment. As shown in Table 4, one participant responded in a manner that can be described as delayed emergence of participant-defined classes in the 2-week retention test, and two participants responded in line with participant-defined classes in the 4-week test, but not in the 2-week test. The responding of these three participants is compatible with a notion that responding on some trial types could influence responding on other trial types, eventually leading to a systematic pattern of responding. Three other participants, however, display participant-defined response patterns from the start of the first retention test they experienced. As such, the current results do not clearly indicate that experience with previous trials influenced later performance in such a manner that it led to responding in line with participant-defined classes.

One possibility is that the experimental setting, including stimulus presentation by the MTS software, served as a contextual cue indicating that a specific pattern of responding was scheduled for reinforcement. The novel responding similar to symmetry and transitivity/equivalence observed in the retention tests may then be regarded as a higher order or generalized operant, not unlike, for example, generalized identity matching (e.g., Jackson & Peigram, 1970). That is, contextual cues may promote responding in line with reflexivity, symmetry, and transitivity/equivalence. Such response patterns are apparently the result of reinforcement for similar responding in the past and may be the effect of multiple exemplar training. Multiple exemplar training is central to some accounts of the origins of stimulus equivalence, relational frame theory perhaps being the most notable (Stewart & Roche, 2013). Indeed, previous stimulus equivalence test experience may provide a potential explanation of the responding of the participants in Group 2 who responded in line with participant-defined classes after previously responding in accordance with stimulus equivalence. However, multiple exemplar training cannot easily explain the similar performance of participants in Group 1, who did not have previous stimulus equivalence test experience. For the latter group, it is possible to invoke extraexperimental experience with stimulus equivalence classes as an explanation for the response pattern, although such an explanation would be speculative. In addition, for the participants in Group 2 who previously responded in accordance with stimulus equivalence, it is difficult to explain why stimulus control generating a response pattern partly unrelated to previous reinforcement contingencies should take precedence over the stimulus control in line with experimenter-defined stimulus equivalence classes previously seen. Finally, an explanation invoking previous test experience does not address why particular patterns of responding in line with participants-defined classes, unique for each participant, were observed.

The results of the current experiment do not indicate that an immediate test for stimulus equivalence following conditional discrimination training enhances stimulus equivalence performance after a delay of several weeks. The results do, however, show that stimulus equivalence classes can be difficult to maintain over longer periods of time. As such, future studies should attempt to uncover variables that secure continued stimulus control in accordance with experimenter-defined stimulus equivalence classes over time. Such work will involve exploring the effects of manipulating both variables involved in the initial establishment of stimulus equivalence classes and variables involved in the tests for such classes over time.

DOI 10.1007/s40732-017-0247-y

Acknowledgements Parts of this manuscript have previously been presented at the 41st annual conference of the Association for Behavior Analysis International in San Antonio. TX. May 2015.

Funding for this study was provided by the Oslo and Akershus University College, where both authors are employed.

The manuscript has not been submitted elsewhere and the authors declare no conflicts of interest regarding the manuscript.

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national [Norwegian] research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent was obtained from all individual participants included in the study.

Compliance with Ethical Standards

Conflict of Interest The manuscript has not been submitted elsewhere and the authors declare no conflicts of interest regarding the manuscript.

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Christoffer Eilifsen (1) (iD) * Erik Arntzen (1)

Published online: 27 June 2017

[mail] Christoffer Eilifsen

christoffer.eilifsen@hioa.no

(1) Department of Behavioral Sciences, Oslo and Akershus University College, P.O. Box 4, St. Olavs plass, 0130 Oslo, Norway

Caption: Fig. 1 Illustration of the stimuli used as samples and comparisons in the experiment. The top half of the figure depicts Stimulus Set 1, which was used for 12 participants, and the bottom half of the figure depicts Stimulus Set 2, which was used for the other 12 participants. The numbers at the top of each half of the figure indicate class membership

Caption: Fig. 2 Phases of the experimental procedure for both groups. From the top to the bottom of the figure, phases are shown in the order they were introduced to the participants. Alphanumeric codes indicate the sample and the experimenter-defined correct comparison for each trial type

Caption: Fig. 3 Number of participants responding in accordance with stimulus equivalence in the immediate test for stimulus equivalence, the 2-week retention test, and the 4-week retention test

Caption: Fig. 4 Illustration of responding on all trial types in both tests for P5637, P5633, and P5643 in Group 1. Black cells indicate that three selections were allocated to a specific comparison given a specific sample, and gray cells, cells with diagonal lines, and white cells indicate two, one, or zero response allocations, respectively, to a comparison given a specific sample (see the text for further details)

Caption: Fig. 5 Illustration of responding on all trial types in all three tests for P5654, P5638, and P5652 in Group 2. Black cells indicate that three selections were allocated to a comparison given a specific sample, and gray cells, cells with diagonal lines, and white cells indicate a two, one, and zero response allocations, respectively, to a comparison given a specific sample (see the text for further details)

Caption: Fig. 6 Number of participants responding in line with experimenter- and participant-defined classes, either in the first half (immediate emergence) or second half (delayed emergence or delayed reemergence) of the test in the immediate test for stimulus equivalence, the 2-week retention test, and the 4-week retention test. IE = immediate emergence; DE = delayed emergence
Table 1 Stimulus set, number of
conditional discrimination
training trials, and stimulus
equivalence test results for
participants in both experimental
groups

P#      Stimuli   #TT    Immediate test        Two-week test

                         TCD   SYM   TRA/ EQ   TCD   SYM   TRA/ EQ

5633     Set 1    960    NA    NA    NA        36#   36#   99#
5656     Set 1    360    NA    NA    NA        36#   36#   102#
5657     Set 2    240    NA    NA    NA        35#   34#   102#
5631     Set 2    240    NA    NA    NA        36#   32    104#
5634     Set 2    180    NA    NA    NA        30    30    74
5637     Set 1    780    NA    NA    NA        16    18    31
5640     Set 1    960    NA    NA    NA        19    21    41
5641     Set 1    360    NA    NA    NA        13    14    31
5643     Set 1    120    NA    NA    NA        27    31    66
5646     Set 2    600    NA    NA    NA        18    11    31
5651     Set 1    960    NA    NA    NA        7     7     38
5653     Set 2    360    NA    NA    NA        26    26    50
5636     Set 2    600    36#   36#   107#      35#   31    100#
5638     Set 1    240    36#   36#   107#      34#   34#   94
5635     Set 2    2460   36#   36#   108#      35#   30    87
5645     Set 2    420    35#   35#   97        35#   32    97
5639     Set 2    420    36#   34#   104#      13    15    45
5642     Set 2    660    36#   35#   105#      22    18    35
5644     Set 2    420    36#   35#   107#      29    28    73
5648     Set 1    240    36#   36#   108#      18    21    46
5649     Set 1    300    36#   36#   104#      29    32    73
5650     Set 1    480    36#   36#   108#      20    18    50
5654     Set 1    780    36#   35    102#      21    19    50
5652     Set 2    540    35#   36#   96        27    25    60

P#      Four-week test

        TCD   SYM   TRA/ EQ

5633    36#   36#   108#
5656    36#   36#   107#
5657    36#   36#   107#
5631    36#   36#   107#
5634    30    30    69
5637    15    12    25
5640    11    14    39
5641    8     10    35
5643    30    30    72
5646    12    13    36
5651    13    12    36
5653    24    22    49
5636    36#   35#   107#
5638    36#   35#   106#
5635    36#   36#   105#
5645    35#   35#   106#
5639    11    13    45
5642    26    27    50
5644    30    30    72
5648    22    19    42
5649    29    29    72
5650    22    22    57
5654    20    16    55
5652    29    30    70

Note. The results for Group 1 are shown in the top half of the table
and those for Group 2 are shown in the bottom half of the table. P# =
participant number; #TT = number of training trials; TCD = trained
conditional discrimi/nations; SYM = symmetry; TRA/EQ = transitivity/
equivalence; and NA = not applicable. The stimulus equiva/lence tests
included 36 trials assessing TCD, 36 trials assessing SYM, and 108
trials assessing TRA/EQ. Numbers shown in bold indicate that the
participant responded in line with a particular relational type

Note. Numbers shown in bold indicate that the participant
responded in line with a particular relational type are indicated
with #.

Table 2 Number of days between stimulus equivalence tests for
participants in both experimental groups

p#         Days since last experimental session

           Two-week test   Four-week test

5631       14              14
5633       23              12
5634       22              14
5637       20              14
5640       15              14
5641       14              14
5643       14              14
5646       12              14
5651       16              16
5653       14              14
5656       15              14
5657       13              14
Mean       16.0            14.0
Range      12-23           12-16

5635       15              14
5636       14              13
5638       14              16
5639       14              14
5642       14              14
5644       14              14
5645       16              14
5648       17              14
5649       14              14
5650       14              13
5652       17              18
5654       16              14
Mean       14.9            14.3
Range      14-17           13-18

Note. The number of days between stimulus equivalence tests is shown
for Group 1 in the top half of the table and for Group 2 in the bottom
half. P# = participant number

Table 3 Number of experimenter-defined correct responses in the first
and second half of trials assessing each relational type in the
immediate test and 2-week test for participants showing delayed
emergence or delayed reemergence of stimulus equivalence

P#      Part of test   Immediate test       Two-week test

                       TCD   SYM   TRA/EQ   TCD   SYM   TRA/EQ

5635    First Half     18#   18#   54#      17#   12    33
        Last Half      18#   18#   54#      18#   18#   54#

5636    First Half     18#   18#   53#      17#   14    50#
        Last Half      18#   18#   54#      18#   18#   50#

5638    First Half     18#   18#   54#      16    16    41
        Last Half      18#   18#   53#      18#   18#   53#

5645    First Half     18#   18#   45       17#   16    48
        Last Half      17#   17#   52#      18#   16    49#

5652    First Half     17#   18#   43       13    13    33
        Last Half      18#   18#   53#      14    12    27

Note. Numbers shown in bold indicate that the participant responded
be in line with a particular relational type. Only participants in
Group 2 showed delayed emergence or delayed reemergence of stimulus
equivalence, and then only in the immediate or the 2-week test.
P# = participant number, TCD = trained conditional discriminations,
SYM = symmetry, and TRA/EQ = transitivity/equivalence

Note. Numbers shown in bold indicate that the participant responded
be in line with a particular relational type is indicated with #.

Table 4 Number of class consistent responses in the first and second
half of trials assessing each relational type in the immediate,
2-week, and 4-week tests for participants responding in line with
participant-defined classes

P#      Classes         Part of test   Immediate test

                                       TCD   SYM   TRA/EQ

5634    ED A1B1C1D1E1   First Half     NA    NA    NA
        PD A2B3C2D2E2   Last Half      NA    NA    NA
        PD A3B2C3D3E3   All Trials     NA    NA    NA

5643    PD A1B1C2D1E1   First Half     NA    NA    NA
        PD A2B2C1D2E2   Last Half      NA    NA    NA
        ED A3B3C3D3E3   All Trials     NA    NA    NA

5642    PD A1B1C2D1E1   First Half     15    16    30
        PD A2B2C3D2E2   Last Half      12    12    26
        PD A3B3C1D3E3   All Trials     27    28    56

5644    PD A1B1C2D1E1   First Half     13    14    42
        PD A2B2C1D2E2   Last Half      17    17    41
        ED A3B3C3D3E3   All Trials     30    31    83

5649    ED A1B1C1D1E1   First Half     14    14    40
        PD A2B2C2D3E2   Last Half      16    16    36
        PD A3B3C3D2E3   All Trials     30    30    76

5652    PD A1B1C1D3E1   First Half     14    16    30
        ED A2B2C2D2E2   Last Half      15    14    34
        PD A3B3C3D1E3   All Trials     29    30    64

P#      Classes         Two-week test        Four-week test

                        TCD   SYM   TRA/EQ   TCD   SYM   TRA/EQ

5634    ED A1B1C1D1E1   17#   17#   48       18#   18#   48
        PD A2B3C2D2E2   18#   18#   54#      18#   18#   54#
        PD A3B2C3D3E3   35#   35#   102#     36#   36#   102#

5643    PD A1B1C2D1E1   14    15    40       18#   18#   54#
        PD A2B2C1D2E2   17#   18#   51#      18#   18#   54#
        ED A3B3C3D3E3   31    33#   91       36#   36#   108#

5642    PD A1B1C2D1E1   16    12    39       17#   18#   49#
        PD A2B2C3D2E2   15    15    41       18#   18#   54#
        PD A3B3C1D3E3   31    27    80       35#   36#   103#

5644    PD A1B1C2D1E1   17#   16    54#      18#   18#   54#
        PD A2B2C1D2E2   18#   18#   54#      18#   18#   54#
        ED A3B3C3D3E3   35#   34#   108#     36#   36#   108#

5649    ED A1B1C1D1E1   18#   16    48       17#   17#   54#
        PD A2B2C2D3E2   17#   18#   54#      18#   18#   54#
        PD A3B3C3D2E3   35#   34#   102#     35#   35#   108#

5652    PD A1B1C1D3E1   13    14    37       17#   18#   51#
        ED A2B2C2D2E2   18#   14    47       18#   18#   54#
        PD A3B3C3D1E3   31    28    84       35#   36#   105#

Note. Numbers shown in bold indicate that the participant responded
in line with a particular relational type. Participants from Group 1
are shown in the top half of the figure, and those from Group 2 are
shown in the bottom half. P# = participant number, ED = experimenter/
defined, PD = participant/defined, TCD = trained conditional
discriminations, SYM = Symmetry, and TRA/EQ = transitivity/equi
valence

Note. Numbers shown in bold indicate that the participant responded
in line with a particular relational type is indicated with #.
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Author:Eilifsen, Christoffer; Arntzen, Erik
Publication:The Psychological Record
Article Type:Author abstract
Date:Dec 1, 2017
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