The Psychological Record, 2004, 54,173-186
THE GENERALIZATION AND RETENTION OF EQUIVALENCE
RELATIONS IN ADULTS WITH MENTAL RETARDATION
RUTH ANNE REHFELDT and SHANNON ROOT
Southern Illinois University
The purpose of this experiment was to investigate the
generalization and long-term retention of equivalence relations in
individuals with mental retardation . To date, the generalization of
equivalence relations to a range of novel stimuli has only been
demonstrated among verbally competent adults. The responding
of many individuals with mental retardation often fails to come
under control of relevant stimulus features and fails to generalize
to novel stimuli. Thus, we assessed whether the generalization of
stimulus equivalence would occur in the absence of remedial
training for 4 adults with mild or moderate mental retardation.
Subjects learned 6 conditional discriminations and were tested for
the emergence and generalization of 3 symmetry and 3
equivalence relations . Subjects were also tested for their retention
of the relations approximately 1-4 months following their last
laboratory session. All subjects showed the emergence and
generalization of all of the relations in the absence of remedial
training, and most showed the long-term retention of the relations.
Accuracy improved during the retention test as a function of
repeated testing for some subjects.
The generalization of equivalence relations to a range of novel stimuli
has been reported a number of times in studies utilizing verbally competent,
adult human subjects (e.g., Fields, Adams, Buffington, Yang, & Verhave,
1996; Fields & Reeve, 2001; Fields, Reeve, Adams, Brown, & Verhave,
1997; Fields, Reeve, Adams, & Verhave, 1991; Rehfeldt, 2003; Rehfeldt &
Hayes, 2000; Rehfeldt, Hayes, & Steele, 1998). This body of research has
revealed that equivalence relations may generalize to dimensional variants
that are physically similar along some dimension to an original training
stimulus. For example, if a subject is taught conditional discriminations
This project was supported by a New Faculty/Creative Research Grant awarded to
Ruth Anne Rehfeldt by the Office of Research Development and Administration at Southern
Illinois University. We thank Specialized Training and Adult Rehabilitation (S.T.A.R.T.) in
Murphysboro, IL, and Lanny Fields and Simon Dymond for suggestions on an earlier
version . Address correspondence to Ruth Anne Rehfeldt, Ph.D., Rehabilitation Services
Program , Rehabilitation Institute, Mailcode 4609 , Southern Illinois University, Carbondale,
IL 62901 -4609. (E-mail:[email protected]).
174
REHFELDT AND ROOT
between stimuli A 1 and B1 and A 1 and C1, he or she will likely demonstrate
an equivalence relation between B1 and C1, in the absence of direct
training. Furthermore, dimensional variants of stimulus B1 are likely to
occasion the selection of C1 in the absence of training, with this likelihood
decreasing as the physical disparity between the dimensional variants and
stimulus B1 increases (Fields et aI., 1997). Because this finding has been
replicated a number of times with verbally competent human subjects, it is
reasonable to infer that the generalization of equivalence is adaptive. The
physical environment is variable and dynamic, with virtually no limit to subtle
similarities and differences between stimuli. The ability to accurately
categorize and partition the environment may be crucial to an organism's
survival (Sidman, 1994).
Although the stimulus equivalence paradigm has been used in
instructional settings for individuals with developmental disabilities such as
mental retardation and autism (e.g., Sidman, 1971; Stromer & Mackay,
1992), no study has reported the generalization of equivalence relations to
a range of dimensional variants among persons with such disabilities. The
generalization of equivalence relations by individuals with mental retardation
and related disabilities may be of critical importance in adjusting to the
demands of everyday life. Labor-intensive teaching strategies are often
employed to establish equivalence relations among such individuals (see
Saunders & Williams, 1998). If the relations do not generalize to a range of
novel stimuli, the value of such teaching is limited. However, stimulus
overselectivity is a frequently observed obstacle for individuals with mental
retardation and related disorders (e.g., Wilhelm & Lovaas, 1976; Rincover &
Ducharme, 1987), as well as transfer of stimulus control failures more
generally (Sulzer-Azaroff & Mayer, 1991). For example, Dube and Mcllvane
(1999) showed that subjects with mental retardation were unable to
accurately match two simultaneously presented sample stimuli to matching
comparisons in a delayed match-to-sample task. This overselective
responding was reduced when subjects were taught to make differential
observing responses in the presence of each of the sample stimuli. Thus,
whether adults with mental retardation will demonstrate the generalization of
stimulus equivalence relations under the same circumstances as verbally
competent, adult subjects is not known. Also not known is the training history
necessary and sufficient to facilitate the generalization of equivalence.
It is not only important that equivalence relations generalize, but also
that they are maintained in an individual's repertoire in the absence of
retraining. If they cannot be shown to be relatively stable over time, the
advantages offered by stimulus equivalence relations is uncertain. One
study to date has demonstrated the stability over time of equivalence
relations among subjects with developmental disabilities (Saunders,
Wachter, & Spradlin, 1988). In this study, subjects were tested for the
long-term stability of equivalence relations consisting of auditory and
visual stimuli 2 to 5 months following their original laboratory experience.
Of 4 subjects, 3 performed with at least 90% accuracy, while the 4th
subject eventually demonstrated 100% accuracy after additional test
GENERALIZED EQUIVALENCE
175
sessions (Saunders et aI., 1988; see also Spradlin, Saunders, &
Saunders, 1992). Another study demonstrated the long-term retention of
generalized equivalence relations in adult subjects without
developmental disabilities (Rehfeldt & Hayes, 2000). In this study, the
generalization of equivalence relations to a range of novel dimensional
variants was assessed, and subjects were tested for their ability to
demonstrate the generalized relations 2 to 3 months following their
original laboratory experience. Of 8 subjects, 2 showed criterion
performance on all symmetry and equivalence relations, while most
subjects demonstrated the retention of some, but not all, of the relations.
Findings from these two studies suggest that equivalence relations and
generalized equivalence relations are remarkably stable over time.
An investigation of the long-term retention of generalized equivalence
relations in individuals with cognitive deficits may be of value. It is
important to know the extent to which dimensional variants of original
training stimuli will continue to function as members of equivalence
relations, and what amount of retraining or repeated testing is necessary
to reestablish the generalized relations. Although the long-term retention
of generalized equivalence relations has been reported (Rehfeldt &
Hayes, 2000), systematic replication is necessary to ascertain the
generalizability of the reported effects across subjects and experimental
conditions (see Hayes, Barlow, & Nelson-Gray, 1999; Johnston &
Pennypacker, 1993). Moreover, because some individuals with mental
retardation and related disorders have been suggested to lack a
generalized categorization repertoire (Fields, Reeve, Matneja, Varelas,
Belanich, Fitzer, & Shamoun, 2002), a systematic replication with this
population is important.
The purpose of the reported experiment was to assess the
generalization and long-term retention of equivalence relations among
subjects with mild or moderate mental retardation. If generalization did
not occur, we questioned what remedial strategies might produce it. Four
adults with mild or moderate mental retardation were taught a total of six
conditional discriminations. They were then tested for the emergence and
generalization of three symmetry and three equivalence relations.
Subjects' retention of the relations was examined at least 1 month
following their last laboratory experience.
Method
Participants
Subject 1 was a 25 year-old female who was diagnosed with mild
mental retardation. She had an 10 of 67. Subject 2 was a 42 year-old
female who was diagnosed with mild mental retardation. She had an 10
of 73. Subject 3 was a 30 year-old female who was diagnosed with
moderate mental retardation and speech impairment. An 10 score was
not available for Subject 3, but an ICAP (Inventory for Client & Agency
Planning) assessment completed by staff at her vocational training
REHFELDT AND ROOT
176
agency suggested that she was functioning at the age equivalent of 8
years, 3 months. Subject 4 was a 33 year-old male diagnosed with
moderate mental retardation. He had an IQ of 47. None of the subjects
took medication throughout the duration of the study. None of the
subjects had known conditions of color blindness.
An experimental session lasted no longer than 45 min for each
subject, and each subject completed up to 10 sessions. Subjects were
compensated with $8 per session.
Apparatus and Stimulus Materials
Stimulus presentation and data collection were computer controlled.
The experiment was controlled by an IBM-compatible laptop, equipped
with a color monitor and a two-button mouse. Experimental sessions
were conducted in a quiet, nondistracting room in the residences of
Subjects 1 and 2, a secluded laboratory in a university setting for Subject
3, and in a secluded, nondistracting room at a developmental training
center for Subject 4. In all settings the computer was centered on a table
of approximately at least 2 ft x 2 ft. The experiment was programmed in
Microsoft PowerPoint® by both authors. The nine stimuli that were used
in the experiment are shown in Figure 1. As the figure shows, the stimuli
represented naturally occurring objects, but the relationships that were
trained between the stimuli were arbitrary. The three stimuli designated
as stimuli A 1, A2, and A3 were black and white objects, and the three
stimuli designated as C1 , C2, and C3 were gray boxes numbered "1," "2,"
and "3" with black lettering. The three stimuli designated as B1, B2, and
B3 were green, blue, and purple paintbrushes, which were identical
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Figure 1. The six stimuli used in the experiment. Stimuli B1, B2, and B3 were green, blue,
and purple, and their dimensional variants, presented during Phases 2 and 3, varied
between those hues.
GENERALIZED EQUIVALENCE
177
except for their hue. Depictions of naturally occurring stimuli were chosen
to sustain the attention and interest of the subjects.
Eight dimensional variants of the "B" stimuli were also utilized in the
experiment. These stimuli were identical to the "B" stimuli except that they
varied along the dimension of hue. The hue of stimuli B1, B2, and B3, as
created in Microsoft PowerPoint, was 120, 170, and 220, respectively.
The hue of the four dimensional variants along the continuum of hue
between B1 and B2 were 130, 140, 150, and 160 (varying shades of
green-blue), and the hue of the four dimensional variants along the
continuum of hue between B2 and B3 were 180, 190, 200, and 210
(varying shades of blue-purple), respectively.
Procedure
The experiment consisted of three phases. All trials throughout the
experiment contained sample stimuli that were presented in the top
center of the screen. Subjects were required to click the mouse upon the
sample stimulus in order to initiate the display of three comparison stimuli
below the sample stimulus. Comparison stimuli were evenly spaced
across the bottom of the screen, with the left, right, and center positions
of the comparison stimuli randomized across trials. Subjects selected a
comparison stimulus by clicking the computer mouse upon it. The onset
of each new trial was marked by the presentation of a sample stimulus.
For trials that occasioned feedback, correct matches were followed by a
5-s display of visual animation accompanied by sound (i.e., bursting
fireworks accompanied by a "whoosh"). All incorrect matches during
Phase 1 led to a repetition of the same trial. All trials were separated by
a 1-s intertrial interval throughout all phases.
Prior to the experiment, subjects were told that they were going to be
playing a matching game, and that it was their job to figure out the correct
way to make matches. Using stimuli that would not be utilized in the
actual experiment, the experimenter modeled three correct conditional
discriminations. This consisted of clicking the mouse upon the sample
stimulus to produce three comparison stimuli and selecting a comparison
stimulus by clicking the mouse upon it. The experimenter also modeled
incorrect conditional discriminations. Correct responses were followed by
5 s of animation accompanied by sound, and incorrect matches produced
a repeat of the same trial. The stimuli used during practice were naturally
occurring and the relations between stimuli were nonarbitrary (i.e., a
snowflake and a snowman). Subjects were allowed to practice making
conditional discriminations with the extraexperimental stimuli.
Phase 1: Matching-to-sample training. Six conditional discriminations
were established during Phase 1 (A 1-B1, A2-B2, A3-B3, A 1-C1, A2-C2,
and A3-C3). The A-B relations were trained first. Training was conducted
in blocks that contained nine trials. During the first block of training,
sample stimulus A 1 was presented on the first three trials, sample
stimulus A2 was presented on the second three trials, and sample
stimulus A3 was presented on the third three trials. Following the first
178
REHFELDT AND ROOT
block, the order of sample stimulus presentations was random within a
nine-trial block. The positioning of the comparison stimuli was randomly
determined across all trials. A-B training was complete when subjects
demonstrated a mastery criterion of 8/9, or 89% correct per block. The
first block did not count toward this criterion. The A-C relations were
trained next. The training of the A-C relations was identical to that of the
A-B relations. A mixed phase of A-B and A-C conditional discrimination
training then followed . This phase consisted of two blocks, one in which
the A-B relations were trained and one in which the A-C relations were
trained. The order of trials was random, and subjects were required to
demonstrate 16/18, or 89%, accuracy.
Phase 2: Symmetry, equivalence, & generalization test. During
Phase 2, the emergence and generalization of three symmetry (B1-A 1,
B2-A2, and B3-A3) relations and the emergence and generalization of
three equivalence (B1-C1, B2-C2, and B3-C3) relations was assessed.
Reinforced training trials were interspersed within the test trials, on a ratio
of approximately one training trial per every 3 to 4 test trials. Subjects
were first evaluated for the emergence of the symmetry relations followed
by the emergence of the equivalence relations. Each symmetry and
equivalence relation was assessed three times each. The generalization
of each of the three symmetry relations to eight dimensional variants of
the "B" stimuli was examined next. On test trials assessing the
generalization of the B-A relations, a dimensional variant was presented
as a sample stimulus instead of stimuli B1, B2, or B3. Each dimensional
variant was presented five times. The generalization of each of the three
equivalence relations to eight dimensional variants of the "B" stimuli was
examined last. On test trials probing the generalization of the B-C
relations, a dimensional variant was presented as a sample stimulus
instead of stimuli B1, B2, or B3. Each dimensional variant was presented
five times. All test trials were presented under extinction, with a 3-s
"blackout" (a gray, blank screen) following each test trial.
Phase 3. Retention test. This phase was identical to Phase 2 and was
conducted at least 1 month following subjects' completion of Phase 2. No
intervening laboratory experience occurred between Phases 2 and 3.
Subjects were not given any instructions prior to this phase.
Results
The 4 subjects all demonstrated mastery of the A-B and A-C
conditional discriminations during training. Shown in Table 1 is the
number of trial blocks required for each subject to attain criterion for each
set of conditional discriminations. Subjects required 1 to 6 blocks to
master the individual conditional discriminations and 1 to 14 blocks to
demonstrate maintenance of all baseline conditional discriminations.
GENERALIZED EQUIVALENCE
179
Table 1
Number of Training Blocks Required to Attain Mastery Criterion
for A-B, A-C, and Mixed A-B and A-C Conditional Discriminations
Training Phase
8ubject
A-B
A-C
Mix
81
82
3
1
2
3
3
1
6
4
14
1
4
1
83
84
Emergence and Generalization of Symmetry and Equivalence Relations
Symmetry relations were held to have emerged if a subject
performed with 100% accuracy on test trials assessing their emergence.
Likewise, equivalence relations were held to have emerged if a subject
performed with 100% accuracy on test trials assessing their emergence.
The panels on the left side of Figures 2-5 show the proportion of
symmetry and equivalence test trials responded to accurately by each
subject during Phase 2. Shown is the proportion of selection responses
for stimuli A 1, A2, and A3 occasioned by the "B" stimuli on symmetry test
trials, and for stimuli C1 , C2, and C3 on equivalence test trials. Figures 2
and 3 show that Subjects 1 and 2 demonstrated the emergence of all
symmetry and equivalence relations. Figure 4 shows that Subject 3
demonstrated the emergence of all symmetry and equivalence relations
with the exception of the B1-C1 equivalence relation. Figure 5 shows that
Subject 4 demonstrated all symmetry and equivalence relations with the
exception of the B1-C1 and B2-C2 equivalence relations.
The symmetry and equivalence relations were held to have
generalized if dimensional variants most similar in hue to stimulus B1
occasioned the selection of comparison stimuli A1 or C1 on at least 80%
of the test trials, if dimensional variants most similar in hue to stimulus B2
occasioned the selection of comparison stimuli A2 or C2 on at least 80%
of the test trials, and if dimensional variants most similar in hue to
stimulus B3 occasioned the selection of comparison stimuli A3 or C3 on
at least 80% of the test trials. The panels on the left side of Figures 2-5
show the proportion of selection responses for stimuli A 1, A2 , A3, and C1,
C2, and C3 occasioned by the dimensional variants of the "B" stimuli
during Phase 2. Figures 2 and 3 show that Subjects 1 and 2
demonstrated the generalization of all of the symmetry and equivalence
relations, as the dimensional variants most similar in hue to stimulus B1
occasioned the selection of comparison stimuli A 1 and C1 on at least
80% of the test trials, the dimensional variants most similar in hue to
stimulus B2 occasioned the selection of comparison stimuli A2 and C2 on
at least 80% of the test trials, and the dimensional variants most similar
in hue to stimulus B3 occasioned the selection of comparison stimuli A3
and C3 on at least 80% of the test trials. Figure 4 shows that Subject 3
demonstrated the generalization of all of the symmetry and equivalence
180
REHFELDT AND ROOT
relations with the exception of the B1-C1 equivalence relation . Figure 5
shows that Subject 4 demonstrated the generalization of all of the
symmetry and equivalence relations, with the exception of the B2-C2
equivalence relation. The figure shows that although Subject 4 did not
demonstrate the emergence of the B1-C1 equivalence relation, the two
dimensional variants most similar in hue to stimulus B1 occasioned the
selection of comparison stimulus C1 on at least 80% of the test trials.
Retention of Symmetry and Equivalence Relations
The same criteria used to infer the emergence of symmetry and
equivalence relations during Phase 2 was used to infer the retention of
those relations during Phase 3. Symmetry and equivalence relations
were held to have been retained if a subject performed with 100%
accuracy on test trials assessing their retention. The panels in the right
columns of Figures 2-4 and the middle and right columns of Figure 5
show the proportion of symmetry and equivalence test trials responded to
accurately by each subject during Phase 3, after at least 1 month had
elapsed following their completion of Phase 2. Figu re 2 shows that
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Figure 2. Proportion of symmetry and equivalence test trials responded to accurately by
Subject 1 during Phase 2 (left panel) and Phase 3 (right panel) . Shown is the proportion of
selection responses for stimuli A 1, A2, and A3 occasioned by the "8" stimuli on symmetry
test trials, and for stimuli C1, C2, and C3 on equivalence test trials.
Subject 1 retained the B2-A2 and B3-A3 symmetry relations and the B1C1 and B3-C3 equivalence relations , 102 days following her completion
of Phase 2. Figure 3 shows that Subject 2 retained the B1-A1 and B3-A3
symmetry relations and the B 1-C1 and B3-C3 equivalence relations, 71
days following her completion of Phase 2. Figure 4 shows that Subject 3
retained all of the symmetry relations and the B2-C2 equivalence relation,
64 days following her completion of Phase 2. Figure 5 shows that Subject
GENERALIZED EQUIVALENCE
181
4 demonstrated the retention of all of the symmetry and equivalence
relations the first and second time he completed Phase 3, 49 days
following his completion of Phase 2.
Retention of Generalized Symmetry and Equivalence Relations
The same criteria used to infer the generalization of the symmetry
and equivalence relations during Phase 2 was used to infer the retention
of the generalized symmetry and equivalence relations during Phase 3.
The generalized symmetry and equivalence relations were held to have
been retained if dimensional variants most similar in hue to stimulus B1
occasioned the selection of comparison stimuli A 1 or C1 on at least 80%
of the test trials, if dimensional variants most similar in hue to stimulus B2
occasioned the selection of comparison stimuli A2 or C2 on at least 80%
of the test trials, and if dimensional variants most similar in hue to
stimulus B3 occasioned the selection of comparison stimuli A3 or C3 on
at least 80% of the test trials. The panels in the right columns of Figures
2-4 and the middle and right columns of Figure 5 show the proportion of
selection responses for stimuli A 1, A2, A3, and C1, C2, and C3
occasioned by the dimensional variants of the "B" stimuli during Phase 3.
Figure 2 shows that Subject 1 demonstrated the retention of all of the
generalized symmetry and generalized equivalence relations 102 days
following her completion of Phase 2. The figure shows that although
Subject 1 did not retain the B 1-A 1 symmetry relation or the B2-C2
equivalence relation, the dimensional variants most similar in hue to
stimuli B 1 and B2 occasioned the selection of comparison stimulus A 1
and comparison stimulus C2 on at least 80% of the test trials. Figure 3
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Figure 3. Proportion of symmetry and equivalence test trials responded to accurately by
Subject 2 during Phase 2 (left panel) and Phase 3 (right panel). Shown is the proportion of
selection responses for stimuli A 1, A2, and A3 occasioned by the "8" stimuli on symmetry
test trials, and for stimuli C1 , C2, and C3 on equivalence test trials.
REHFELDT AND ROOT
182
shows that Subject 2 showed the retention of the B1 -A1
generalized symmetry relations and the B1-C1 generalized
relation 71 days following her completion of Phase 2.
Figure 4 shows that Subject 3 retained all of the
symmetry relations and all of the generalized equivalence
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Figure 4. Proportion of symmetry and equivalence test trials responded to accurately by
Subject 3 during Phase 2 (left panel) and Phase 3 (right panel). Shown is the proportion of
selection responses for stimuli A 1, A2, and A3 occasioned by the "8" stimuli on symmetry
test trials, and for stimuli C1 , C2, and C3 on equivalence test trials.
days following her completion of Phase 2. The figure shows that although
Subject 3 did not retain the B1-C 1 or B3-C3 equivalence relations, the
dimensional variants most similar in hue to stimuli B1 and B3 occasioned
the selection of comparison stimuli C1 and C3 on at least 80% of the test
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Figure 5. Proportion of symmetry and equivalence test trials responded to accurately by
Subject 4 during Phase 2 (left panel) and Phase 3 (middle and right panels) . Shown is the
proportion of selection responses for stimuli A 1, A2, and A3 occasioned by the "8" stimuli on
symmetry test trials, and for stimuli C1, C2, and C3 on equivalence test trials.
GENERALIZED EQUIVALENCE
183
trials. Figure 5 shows that Subject 4 showed the retention of all of the
generalized symmetry and equivalence relations the first time he
completed Phase 3, but because dimensional variants on the continuum
in hue between stimuli B1 and B2 reliably occasioned the selection of
comparison stimulus A3, Subject 4 repeated Phase 3 and demonstrated
the retention of all of the generalized symmetry and equivalence relations
49 days following his completion of Phase 2.
Discussion
This experiment demonstrated the generalization of equivalence
relations to a range of novel dimensional variants by 4 adults with known
intellectual or cognitive deficits. None of the subjects required remedial
training. These results extend the growing body of literature (e.g., Fields et
aI., 1996; Fields & Reeve, 2001; Fields et aI., 1997; Fields et aI., 1991;
Rehfeldt, 2003; Rehfeldt & Hayes, 2000; Rehfeldt et aI., 1998) illustrating the
generalization of equivalence to a range of novel stimuli to individuals with
mental retardation, a population of persons whose responding often fails to
come under control of relevant stimulus features and generalize to novel
stimuli. Importantly, the physical similarity between novel stimuli and an
original training stimulus appears to be one condition under which many
stimuli enter into equivalence relations. Thus, the training and test
procedures of this study were sufficient for producing generalized
equivalence relations in the 4 subjects.
It is important to point out that the B stimuli and their dimensional
variants varied along one dimension only. Subjects could not have
mastered the A-B conditional discriminations had their responding been
under the control of any dimension other than hue. Whether individuals
with mental retardation and similar disorders will show the generalization
of equivalence to novel stimuli when the stimuli vary along more than one
dimension remains to be seen. Moreover, post-hoc tests for the degree of
discriminability between the "B" stimuli and their dimensional variants
were not conducted. Generalization patterns, then, could have been
attributable to subjects' failures to discriminate between the stimuli.
Subjects' performances on generalization test trials during the first
test were largely consistent with their performance on symmetry and
equivalence test trials. That is to say, relations were only shown to have
generalized if they had also been shown to have emerged. Measures of
generalization might thus be regarded as supplemental indices of the
strength of emergent equivalence relations (see Dymond & Rehfeldt,
2001; Pilgrim & Galizio, 1996). For Subject 2 the B2-A2 and B2-C2
relations did not generalize to dimensional variants that were evenly
distributed to both sides of B2. Rather, the gradients for the B3-A3 and
B3-C3 relations were relatively wide. This may be attributable to this
subject's extraexperimental history with the particular hues used in this
experiment. Another interesting observation was that 2 of the 4 subjects
performed with higher accuracy on symmetry test trials than on
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REHFELDT AND ROOT
equivalence test trials during the first test. Accuracy, therefore , was an
inverse function of the nodal distance between stimuli. This observation
is consistent with other findings (e.g., Fields, Landon-Jimenez,
Buffington, & Adams, 1995; Fields & Verhave, 1987).
Results from the retention test showed that the generalized equivalence
relations were, for the most part, quite stable in subjects' repertoires, as the
subjects retained the relations anywhere from approximately 1 to 4 months
following their last laboratory session. Performance on generalization test trials
did not always overlap with performance on symmetry and equivalence test
trials , however. Some subjects showed the retention of a particular
generalized relation but did not demonstrate that the relation itself was intact.
However, an equivalence relation would not be expected to generalize if it was
not of sufficient strength in a subject's repertoire. One possibility is that
because the symmetry and equivalence test trials were conducted prior to the
generalization test trials, a period of time was necessary for the relations to
reemerge (e.g., Lazar, Davis-Lang, & Sanchez, 1984). Because training trials
were interspersed within the test trials, more exposure to the reinforced
baseline conditional discriminations may have been necessary to reestablish
the relations for some of the subjects. Fewer symmetry and equivalence test
trials were conducted than was the case for generalized symmetry and
equivalence test trials; this too may account for the discrepancy between
subjects' retention performances across the test trial types. A second
possibility is that the relations were intact, and the generalization test trials
provided supplemental information regarding the strength of the relations that
symmetry and equivalence test trials alone could not provide. It is also
important to note that retention of the relations did not appear to be an inverse
function of the nodal distance between stimuli, as was observed during the first
generalization test: The symmetry relations were not necessarily more stable
over time than were the equivalence relations (see Rehfeldt & Hayes, 2000).
Subject 4 showed unusual generalization patterns the first time he
completed the retention test (dimensional variants on the continuum in hue
between stimuli B1 and B2 reliably occasioned the selection of comparison
stimulus A3), but when he was retested, he showed the retention of all of the
relations. That this subject simply needed additional test sessions is
consistent with other findings which showed that stability was positively
influenced by repeated testing (Saunders et aI., 1988). In effect, the repeated
testing may have functioned as a form of retraining. This finding is also
consistent with the notion of delayed emergence (Lazar et aI., 1984). Efforts
to retest Subject 2, who showed the retention of only two generalized
symmetry relations and one generalized equivalence relation may have also
resulted in improved performance, but it was not possible to conduct
additional test sessions with this subject.
Future research should explore the generalization of equivalence among
individuals with more severe cognitive deficits than the subjects used in this
particular study. Generalization of equivalence should also be examined
among such individuals with stimuli that vary along more than one dimension.
Finally, the limits on the long-term stability of generalized equivalence
relations should be explored.
GENERALIZED EQUIVALENCE
185
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