A further Experimental Step in the Analysis of Hierarchical Responding

Full reference: Gil, E., Luciano, C., Ruiz, F. J., & Valdivia-Salas, S. (2014). A further experimental step in the analysis of hierarchical responding. International Journal of Psychology and Psychological Therapy, 14(2), 137-153.

Study type: Laboratory experiment / Translational research on learning and cognition

Background and objectives

The study addresses the question of the conditions under which hierarchical classification of stimuli is established, a fundamental process in human cognition and categorization. From the perspective of Relational Frame Theory (RFT), the authors propose that hierarchical classification emerges from training in contextually controlled relational responding patterns that involve multiple exemplars and common perceptual features. The work is positioned within a sustained effort (including prior studies by the authors in 2009 and 2012) to understand how hierarchical networks are established and how stimulus functions are transformed within these networks.

The central research question is: how do functions acquired by stimuli in one part of a hierarchical network transfer to other members of the network through indirect relations? The previous study (Gil et al., 2012) demonstrated the transformation of functions in bidirectional hierarchical networks but with methodological limitations. The present experiment improves upon these findings by establishing unidirectional hierarchical networks that are clearer and isolating specific derived relations more effectively.

Method

Participants

Eight graduate and undergraduate students (4 females and 4 males; age range: 17-39 years) from diverse disciplines (psychology, journalism, computer science) volunteered to participate. Participants were recruited through bulletin board announcements and personal contacts. None had previous experience with the experimental procedures employed. All participants completed the study without monetary compensation. Upon completion of the tasks, participants were fully debriefed.

Experimental design

The design included five sequential experimental phases, each with specific objectives:

Phase 1: Training of relations among four arbitrary stimuli (A1, B1, C1, D1) through contextually controlled relational cues: INCLUDES, BELONGS TO, SAME, and DIFFERENT.

Phase 2: Training of three four-member equivalence classes (bottom-level classes) using matching-to-sample procedures (MTS): Class 1 (A1-B1-C1-D1), Class 2 (A2-B2-C2-D2), Class 3 (A3-B3-C3-D3).

Phase 3: Training of the middle and top levels of the hierarchy through INCLUDES and BELONGS TO relations among the equivalence classes. Two novel stimuli (X and Y) were trained as the most inclusive contexts.

Phase 4: Establishment of specific functions in stimuli X.1, D2, and C3 using pairing and MTS training procedures.

Phase 5: Critical test of function transformation across the entire hierarchical network, testing derived and untrained functions.

The dependent variables were: number of trials required to reach learning criteria, percentage of correct responses, and performance on the critical test of function transformation.

Materials and apparatus

The experiment was conducted in a quiet room equipped with a table, chair, and laptop computer. A computer program designed in Visual Basic 6.0 presented all stimuli and recorded participant responses. The stimuli were the same as those used in the prior study by Gil et al. (2012). All stimuli were presented in black and white on the screen. Arbitrary relational symbols in the upper position served as relational cues: INCLUDES (or IS FORMED BY), BELONGS TO (or IS A PART OF), SAME, and DIFFERENT. Thirteen sets of visual stimuli (including drawings and photographs of known objects) were used to train relational relations.

Procedure

The general procedure consisted of two brief breaks (at the end of Phases 2 and 3), all of which were conducted in a single session lasting between 65 and 90 minutes. Participants were instructed through instructions presented on the screen. The complete experiment included five phases.

Phase 1: Training of the relational cues (INCLUDES, BELONGS TO, SAME, and DIFFERENT). The purpose of this phase was to establish four arbitrary stimuli as different relational cues. Multiple-exemplar training (MET) was used with arbitrary stimuli as cues (Sets 1 to 10). Trials had the following characteristics: (a) there were two types of trials: stimulus-selection trials (e.g., stages 1 to 4) and cue-selection trials (e.g., stages 4 and 5); (b) each relational cue was trained across multiple trials among multiple stimulus sets; (c) the order of trial presentation was fixed and kept constant across participants; (d) participants responding incorrectly on the first presentation of a trial in the sequence was followed by repetition of the same trial. Consequently, mastery criterion was achieved when participants responded correctly to the last trial in the sequence. Additionally, (d) new sets were introduced to test the four relational functions trained during this phase.

Phase 2: Training and testing of three four-member equivalence classes (bottom level of the hierarchies). This phase was identical to that employed by Gil et al. (2012). Three four-member equivalence classes were trained using one-to-many matching-to-sample (MTS) procedures: Class 1 (A1-B1-C1-D1), Class 2 (A2-B2-C2-D2), Class 3 (A3-B3-C3-D3). Training consisted of stimulus-selection trials only, where an A stimulus served as sample, B, C, or D stimuli served as comparisons, and SAME served as comparisons. Training was conducted in two ways: first A2-C2, then A3-C3, and finally A1-C1. Training blocks containing all relations were presented until 100% correct responses were produced within a block. Participants who did not meet testing criteria within five test-retrain cycles were dismissed from further participation. During the break, participants remained in an adjacent room and were offered beverages.

Phase 3: Training of the middle and top levels of the hierarchies. During this phase, stimuli A and B were used, along with the new stimulus shown at the bottom of Figure 1. Relational cues (e.g., X includes X1/X2; Y includes Y1) were used in matching-to-sample procedures. For example, an image of a brain appeared in the upper position in the middle of the screen, and the four SAME, DIFFERENT, INCLUDES, and BELONGS TO stimuli appeared at the bottom of the screen in 2 parts of Figure 3. In various trials during this phase, using the cue-selection stimulus format, a brain image appeared in the upper position on screen, followed by an image on screen middle, and then three figures at the bottom of the screen (the correct response was highlighted). Multiple trials were presented in this phase using the cue-selection stimulus format according to the procedures described for Phase 1. For example, a brain image appeared in the upper position on the screen, followed by an image in the middle of the screen, and then three figures at the bottom of the screen. Subsequently, three relations were presented in blocks of six trials (two per relation) in which the order of presentation was randomized among all trials followed by one block of nine testing trials. If participants produced 100% correct responses in the block, equivalence stimuli were presented; otherwise, they were presented with an additional 9-trial retraining block.

Phase 4: Establishment of X.1, D2, and C3 as cold, heavy, and sweet, respectively. Stimulus pairing and MTS procedures were used as follows. First, two consecutive stimulus-pairing trials were presented for each stimulus for a total of six trials. In each trial, a stimulus appeared centered in the left half of the screen; 0.5 s later, the expression "is cold" appeared centered in the right half of the screen. MTS trials were then presented in blocks of five trials containing five trials per stimulus until participants produced 100% correct responses within a block. In a given trial, one of the stimuli appeared centered at the top of the screen, followed 0.5 s later by the expression "is" centered in the middle of the screen, and 1 s later by four comparison options with "correct" at the bottom. The position of comparisons was balanced across trials. Feedback (i.e., CORRECT or WRONG) followed participants' responses.

Phase 5: Critical Test of transformation of functions within hierarchical relations. This phase started immediately after Phase 4. Participants read the following instructions: "The arrangement of stimuli on the screen will now be different. Please respond according to what you have learned throughout the procedure. Pay close attention to the response options and select the MOST CORRECT one. Sometimes the computer will tell you whether your choice is correct or not." Feedback was never provided during these test trials. Transformation of functions was tested with two stimuli from the top or most inclusive context of the hierarchies (X and Y), one stimulus from the middle level of the two-branch hierarchy (X.2), three stimuli from the bottom level of both hierarchies (C1, C2, and D3), and one negative comparison stimulus (M). The latter was used for experimental control purposes.

Data analysis

Data were analyzed by recording the number of trials required to reach learning criteria in each phase, the percentage of correct responses in each phase, and performance on the critical test (number of trials answered correctly out of seven trials presented). The computer software automatically recorded all responses and reaction times (although reaction times are not reported here).

Results

All participants met the test criterion in Phase 1 except P6, who was dismissed from further participation. The number of trials required to reach criterion varied from 105 (P1) to 127 (P8), and the percentage of correct responses ranged from 85.8% (P8) to 100% (P1).

All remaining participants except P3 met the training criteria for the formation of three four-member equivalence classes (see Table 3, Phase 2). The range of trials required to complete the training and percentage of correct responses was, respectively, from 66% (P4) to 75% (P1) and from 88.6% (P2) to 95.4% (P4). Equivalence classes were retested twice, at the beginning and end of Phase 3.

The remaining six participants met the training criterion. The number of trials required to reach criterion varied from 82 (P7) to 96 (P1) and participants showed a range of correct responses from 93.8% (P4) to 100% (P7).

In order to pass the Test of Transformation of Functions, participants had to respond correctly to stimuli X (i.e., "X has a part that is cold and heavy") and Y (i.e., "Y is sweet" or "has a part that is sweet"), and to four of the five remaining stimuli to meet the training criterion during Phases 1 to 3. The number of correct responses to the test of transformation of functions during Phase 5 varied from 3 to 7 trials per stimulus (see Table 3, Phase 5).

Specifically, five of the six participants exposed to this test passed it (see Table 3). Of the six participants who completed the Critical Test procedure, five responded according to the arbitrary relations established among the stimuli. More specifically, they responded that D3 was sweet, by virtue of its relational relation to C3 that was directly established as sweet. They also correctly responded that X.2 was heavy (or had a part that was heavy) by virtue of its derived hierarchical relation to D2 that was directly established as heavy. Finally, they correctly responded that category X had a cold part and a heavy part, by virtue of its direct hierarchical relations to X.1 (directly established as cold) and X.2, the latter in a derived hierarchical relation with D2 heavy.

Some notable limitations of the study merit mention. Transformation of functions was tested with seven stimuli and the test included seven trials, one per stimulus. The test structure itself might have influenced the likelihood that participants produced correct responses randomly. However, the strict test criterion (six correct responses out of seven trials with elevated numbers of response options per trial) was intended to rule out such possibility. Additionally, future studies may consider increasing the number of test trials per stimulus.

Discussion and conclusions

The present study replicates and improves upon the findings reported in a previous preliminary study (Gil et al., 2012). Four stimuli were trained as different relational cues (INCLUDES, BELONGS TO, SAME, and DIFFERENT). Subsequently, two three-level hierarchical networks were trained using the previously established relational cues. Three different functions were then provided to three different stimuli in the hierarchical networks (i.e., X.1 is cold, D2 is heavy, and C3 is sweet). Finally, transformation of functions was tested with the two stimuli at the top or most inclusive context of the hierarchies (X and Y), with stimuli at the middle level of the two-branch hierarchy (X.2), three stimuli from the lower level of both hierarchies (C1, C2, and D3), and one negative comparison stimulus (M).

Compared to the findings of Gil et al. (2012), the present results present several advantages. First, in Gil et al. (2012), the hierarchical relations were trained in both directions (e.g., X includes X.2, and X.2 belongs to X) and, consequently, the derived relations were not clearly isolated. In the present experiment, however, the most inclusive hierarchical context of the hierarchical relational networks was established in only one direction (e.g., X includes X.2). Consequently, the present findings constitute a more robust demonstration of stimulus function transformation according to hierarchical relation.

A second way in which the present findings advance with respect to Gil et al. (2012) is that the response options in the present study isolated a more precise transformation of untrained or inclusive stimulus features of hierarchy X. In the previous study, the correct response when testing for the functions of X was "X is always cold and heavy," which might be misleading in that it might indicate that all properties of each subcategory or member enter into the definition of hierarchy features. In the present experiment, the word "always" was eliminated and the cue "part of" was added in the Critical Test to better isolate the transformation of functions from the lower to the upper level of the hierarchy. Specifically, the inclusion of the expression "part of" allowed responding to X as in the animals example (i.e., some are scary and some are friendly).

Participant performance during the critical tests was functionally equivalent to the example presented in the Introduction. That is, in the same way that when the child chooses a parrot because he likes birds, our participants derived that C1 was cold because it was a member of X.1, which was previously established as cold. In this way, given that X.1 was established as cold, D2 as heavy, and C3 as sweet, when it was tested that X with X.2 as members of X, and when it was tested that Y with C3 as a member of Y.1, participants responded correctly. This demonstrates the conditions under which functions might transfer top-down from subordinate to superordinate members in the function hierarchy.

Some limitations of the present study merit mention. Transformation of functions was tested with seven stimuli and the test included seven trials, one per stimulus. The test structure itself might have influenced the likelihood that participants produced correct responses randomly. However, the strict test criterion (six correct responses out of seven trials with elevated numbers of response options per trial) was intended to rule out such possibility. Additionally, future studies may consider increasing the number of test trials per stimulus. Other future studies might also consider replacing the response option "is..." with the stimulus previously trained as an arbitrary relational cue (i.e., the relational cue SAME instead of "is...," and the relational cue INCLUDES instead of "has a part that is..."). In this way, one could minimize the influence of the pre-experimental functions of the words used during the training sessions of the relational cues and thus identify the function relevant to the critical test.

As has been noted (Slattery & Stewart, 2014), research on this difficult behavior is still far from providing a clean procedure for the derived transformation of stimulus functions in hierarchical frameworks. This has been the case with other types of relational responding (e.g., Barnes-Holmes, Barnes-Holmes & Smeets, 2004; Berens & Hayes, 2007; Cassidy, Roche & Hayes, 2011; Luciano, Gómez, & Rodríguez, 2007; Luciano et al., 2009; Stewart, Barnes-Holmes & Weil, 2009).

Significance and contribution

This study significantly contributes to the functional analysis of human hierarchical responding by providing an improved demonstration of how stimulus functions consistently transform within unidirectional hierarchical networks. By improving the methodological design of the prior study (Gil et al., 2012), this work provides more robust evidence that functions established at higher levels of a hierarchy transform predictably to members at lower levels. The findings have theoretical implications for understanding how stimulus properties are acquired and transformed through multiple and hierarchically organized relations, and suggest procedures for future investigations of function transformation in other relational frames.