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Asymmetries in the bidirectional associative strengths between events in cue competition for causes and effects
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Asymmetries in the bidirectional associative strengths between events in cue competition for causes and effects
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Content
ASYMMETRIES IN THE BIDIRECTIONAL ASSOCIATIVE STRENGTHS
BETWEEN EVENTS IN CUE COMPETITION FOR CAUSES AND EFFECTS
Copyright 2003
by
Deanah K. Kim
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF ARTS
(PSYCHOLOGY)
December 2003
Deanah Kim
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UMI Number: 1420374
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UNIVERSITY OF SOUTHERN CALIFORNIA
THE GRADUATE SCHOOL
UNIVERSITY PARK »
LOS ANGELES, CALIFORNIA 90089-1695
This thesis, written by
under the direction o f ht C thesis committee, and
approved by all its members, has been presented to and
accepted by the Director o f Graduate and Professional
Programs, in partial fulfillment of the requirements fo r the
degree o f
'irector
Date D ecem ber 1 7 s 2 0 0 3
Thesis Committee
Chair
...........T y — —
yif
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ii
Table of Contents
List of Tables iii
List of Figures iv
Abstract v
Introduction 1
Cue Competition in Associative Models 4
Cue Competition in Causal Model Theory 1
Cue Competition in Contiguity Models 9
Cue competition in Neural Network Models 11
Study 1 19
Overview 19
Method 20
Results and Discussion 23
Study 2 28
Overview 28
Method 29
Results and Discussion 32
General Discussion 39
References 44
Appendix A 48
Appendix B 53
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List of Tables
Table 1. Mean initial and final ratings and differences for test questions
by experimental condition.
Table 2. Mean ratings and differences in cue competition for Effects
by experimental condition.
Table 3. Mean ratings and differences in cue competition for Causes
by experimental condition.
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Iv
Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
List of Figures
A structural model of the feed forward network
for cue competition between effects.
A structural model of the recurrent network
for cue competition between effects.
Final activation values demonstrating cue competition
for causes after Phase 1 and 2 training
(but not after Phase 2 only training) in the recurrent
neural network model simulation, where A and B are
the multiple causes and X is the common effect.
Final activation values demonstrating cue competition
for effects after Phase 1 and 2 training
(but not after Phase 2 only training) in the recurrent
neural network model simulation, where A is the common cause
and X and Y are the multiple effects.
Mean final ratings for cue competition for effects
in the AXY (control) and AX-AXY (experimental) conditions
in Study 1, where A is the common cause,
and X and Y are the two competing effects.
Mean final ratings for cue competition for effects
in the AXY (control) and AX-AXY (experimental) conditions
in Study 2, where A is the common cause,
and X and Y are the two competing effects.
Mean final ratings for cue competition for causes
in the ABX (control) and AX-ABX (experimental) conditions
in Study 2, where A and B are the competing causes,
and X is the common effect.
13
14
16
18
26-27
35
37
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V
Abstract
Two experiments using social stimuli tested a recurrent neural network model’s
predictions for cue competition for causes and effects. The delta rule-based model
predicts the presence of cue competition for causes as well as for effects as a result
of an asymmetry in the bidirectional associative strengths between the relevant cue-
outcome pairs. Results support the model’s prediction for the presence o f cue
competition for causes and for effects. However, the observed asymmetry in the
bidirectional associative strengths between the common cause and the redundant
outcome in cue competition for effects was in the opposite direction of that predicted
by the recurrent network model. Further, cue competition for causes did not exhibit
the predicted asymmetry in the bidirectional associative strengths between the
redundant cause and the common outcome. The implications these results have for
the various contingency learning models’ accounts of cue competition are discussed.
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1
Introduction
Detecting and assessing the strength o f contingent relationships between
events is essential for survival for animals and humans alike. This ability has further
implications for an organism’s survival beyond the realm of biological consequences
and extends to its success in correctly representing the relationships between
behavioral motivations and consequences in a social world. Understanding causes of
events allows us to predict future events as well as to retroactively explain why
certain events occurred. Causal knowledge also empowers us to control future events
by allowing us to plan actions to achieve goals. The importance o f causal knowledge
has long been recognized by philosophers and psychologists alike, and many models
have been postulated to explain how we acquire knowledge of cause-effect
relationships in our environment.
Since the launch of research in causal induction, beginning with Pavlovian
learning to human causal attribution, categorization and neural networks, many
researchers have focused their interest on causal models that explain the competitive
nature of learning of cues that predict or Indicate the occurrence o f an event (e.g.,
Rescorla & Wagner, 1972; Gluck & Bower, 1988; Shanks, 1991; Waldmann &
Holyoak, 1992). The associative model (e.g., Rescorla-Wagner, 1972) claims that
judgments o f cause come from the empirical contingency o f cues to causality, where
there is a regular succession of the effect following the cause, and there is a temporal
and spatial contiguity (Baker, Murphy & Vallee-Tourangeau, 1996). In other words,
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2
associations between cues are strengthened when the cues are contiguous and are
weakened when a cue occurs by itself. Some o f the advantages o f this model are its
computational simplicity and its ability to accommodate and predict competition
between cues. When multiple cues are present preceding an event, these cues
compete with each other for predictive strength, and thus results in the competitive
learning o f cues. A classic example of this competition between cues occurs in
blocking, where upon learning that stimulus A predicts outcome X during the first
training phase, there is a deficit of learning that stimulus B also perfectly predicts X
when AB are presented together preceding X in the second training phase.
Although cue competition of antecedent events (causes) is well established in
both animal and human causal learning literature, a somewhat newer question of
whether competition occurs when multiple cues are outcomes (effects) o f a common
event has produced somewhat inconsistent findings and has resulted in a heated
debate over the past decade (e.g., Shanks, 1991; Waldmann & Holyoak, 1992; Van
Hamme & Wasserman, 1993; Price & Yates, 1995; Matute, Arcediano & Miller,
1996; Shanks, & Lopez, 1996; Esmoris-Arranz, Miller & Matute, 1997). Cue
competition for effects describes a two-stage conditioning phenomenon where upon
first learning that outcome X perfectly indicates the occurrence of cause A during
Phase 1 of training, there is a deficit in learning that outcome Y also perfectly
indicates the occurrence of cause A when the XY compound is presented together
subsequently after the presentation of cause A during the Phase 2 training.
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While some researchers who have obtained cue competition for effects (e.g.,
Shanks, 1991; Shanks & Lopez, 1996; Price & Yates, 1993,1995; Cobos, Lopez,
Cano, Almarz & Shanks, 2002) are inclined to interpret the finding to be consistent
with associative learning theories, proponents o f the causal model theory (e.g.,
Waldmann and Holyoak 1992, 1997; Melz, Cheng, Holyoak & Waldmann, 1993;
Waldmann, 2000, 2001) suggest that causes compete whereas effects do not,
following from the argument that mere contiguity is not enough to confirm the causal
status of cues. Rather, they propose that human causality judgments are based on the
consideration o f what happens in the absence o f the cause as well, in addition to
taking into account the covariation o f the cause and the effect. Further, as part of the
causal learning and reasoning processes, people represent causal relationships with
the understanding that a cause imparts its effects. Thus, multiple cues as effects do
not compete with each other because they provide new information about the
consequences o f a common cause.
Other researchers who also have demonstrated cue competition between
outcomes (or effects) argue that neither associative nor causal model theories
adequately accommodate cue competition for effects (e.g., Matute et al., 1996;
Esmoris-Arranz et al., 1997; Miller & Matute, 1998); instead they assert that the
findings are more consistent with contiguity theory, which assumes that associations
are learned noncompetitively and bidirectionally through simple contiguity, and the
cue competition effects take place at the retrieval or judgmental stages.
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The goal o f this paper is to first describe the associative learning model,
causal model theory and contiguity theory’s accounts of contingency teaming and
their predictions for cue competition for causes as well as for effects. In addition, a
recurrent neural network model of contingency learning will be introduced, and its
predictions for cue competition between causes and effects will be discussed in
comparison with the other models. Next, two experiments designed to test the
different predictions for the occurrence of cue competition between effects will be
presented. These experiments use various social behaviors as target stimuli for cues
and outcomes in an attempt to extend the research in multiple cue contingency
learning beyond the traditional settings o f biological, physical or abstract events and
their consequences. Finally, the results of these experiments and the implications
they have for the various accounts of cue competition will be discussed.
Cue Competition in Associative Models
According to the associative view of contingency learning and judgment,
which is based on the Rescorla-Wagner model ofPavlovian conditioning (Rescorla
& Wagner, 1972), events become associated with each other after repeated pairings,
and the judgment o f the strength of the contingency between events is directly
related to the strength of the association. With respect to blocking and cue
competition, Rescorla-Wagner model is able to predict the associative consequences
of presenting multiple cues together, in that it “provides a trial-by-trial description of
how the associative status of a conditioned stimulus (CS) changes when the stimulus
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is paired with an unconditional stimulus (US) in the presence of other CSs” (Miller,
Barnet & Grahame, 1995, p.363). The Rescorla Wagner model is conceptually
related to the delta learning rule, where the change in the associative strength of a
cue on any given trial is directly proportional to the difference between the expected
status o f the outcome and the true status of the outcome. Formally stated, the
Rescorla-Wagner model assumes that
A V C s(n) ~~ C f-cs Pus(n) ( ^ us(n) ~ V total(n))?
where AVC S (n) is the change in the associative strength (V) o f CS as a result of a
pairing with US on trial n; ac s is the learning rate parameter (constant) of the CS;
Pus(n) is the learning rate parameter (constant) of the US on trial n; 1 us( n) is the
asymptote of learning or the maximum associative strength that the US can support
on trial n; and Vtota i(n ) is the sum of associative strengths o f all CSs present on trial n,
or the extent to which the US is predicted on trial n. The basic principle behind the
Rescorla-Wagner model is that associative learning is determined by the extent to
which an US is surprising. Surprise is represented in the model by the difference
between the US that is actually presented on trial n and the US that is expected on
the basis of the summed predictive value o f all the cues that are present on trial n.
Thus, cue competition is observed in blocking experiments because by the
end of Phase 1 training, the animal has learned that CSi perfectly predicts the US.
During Phase 2 training, when CSi and CS2 are presented together with the US, no
learning will occur for the compound CS1CS2 because changing the associative
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strength o f the CS2 cannot improve the already perfect predictability of the US.
Explained in terms of the equation, Phase 1 training with CSi elevates Vto tai so that
the term (X- Vto tai) is smaller for CS2 on the Phase 2 CS1CS2— » US trials than if CSi
had not been pretrained, thus resulting in a smaller AV. As stated earlier, this
competition of cues as antecedent events has been observed consistently in both
animal and human research (e.g., Matute et al., 1996; Esmoris-Arranz et el., 1997;
Denniston et a l, 1996; Shanks & Lopez, 1996).
However, the Rescorla-Wagner model is less adequate in predicting cue
competition between multiple effects of a common cause, because it is a predictive
model which assumes a cause-to-effect directionality in the learning associations. In
other words, the difference term (X- Vtotai) only applies to the predictability o f cue
(CS) to outcome (US), not outcome to cue. In fact, Matute et al. (1996) claim that the
Rescorla-Wagner model is rather silent with respect to diagnostic testing. On the
other hand, several researchers have obtained cue competition for effects and have
provided associative accounts for them (e.g., Shanks, 1991; Shanks & Lopez, 1996;
Price & Yates, 1995; Cobos, Cano, Lopez, Luque & Almaraz, 2000; Cobos et al,
2002). One explanation is that “for an associative account, the real-world
interpretation of the events is immaterial. If the subject is required to predict
outcomes from cues, the cues represent the input to the system and the outcome
represents the target to be predicted, regardless of causal order” (Shanks & Lopez,
1996, p.513). In other words, although the Rescorla-Wagner model predicts
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7
competition between antecedent events and no competition of subsequent events due
to it being a predictive model, it can accommodate cue competition of effects by
using a diagnostic learning model, where the multiple effects can be presented as
antecedent events, which is understood to occur after their cause, even though the
effects are presented prior to the cause. Thus the effects (antecedents) compete with
each other in predicting the cause. Consistent with this, Shanks & Lopez (1996)
showed that competition can be obtained both between multiple causes that are
trained and tested in the predictive, or cause-to-effect (CE), direction and between
multiple effects that are trained and tested in the diagnostic, or effect-to-cause (EC),
direction, where potential effects were always presented as antecedents o f a common
cause.
Cue Competition in Causal Model Theory
The underlying view in causal model theory is that people use abstract and
meaningful world knowledge about the basic characteristics o f causal relations, and
consists o f three assumptions: 1) that causal information is learned in the cause-to-
effect direction, even when information about the effect is presented before the
cause; 2) that the perceived causal strength between two events is based on the
contingency between the possible cause and the effect; and that 3) although the links
in the causal model are from cause-to-effect, people are still able to engage in both
predictive and diagnostic reasoning (Waldmann & Holyoak, 1992). In the causal
model, the associative terms cues and outcomes are replaced with causes and effects,
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8
which inherently imply the directionality o f the causal link. The causal model theory
uses a contingency rule to deal with a multiple cue situation, where the contingency
is the difference between the proportion o f cases in which the effect and cause co
occur and the proportion of cases in which the effect occurs in the absence of the
cause. When the causal model is predictive, cue competition between causes is
expected in the classic blocking paradigm because during Phase 2 training, the new
cue, Cue2, always co-occurs with first cue, Cuei. Thus, Waldmann and Holyoak
(1992) argue that because “it is impossible to determine whether the observed
unconditional contingency between Cue2 and the effect is genuine or spurious,” this
should lead to uncertainty, which should further lead to a lowered predictiveness of
Cue2, or partial blocking (p. 226). On the other hand, when the causal model is
diagnostic, Waldmann and Holyoak (1992) assert that effects do not compete with
each other, in that each effect, as well as any interaction between them, provides
further information about the cause. Therefore, the new effect, E2, is simply
integrated into the contingency that cause C causes the previously paired effect, Ei,
as well as E2 (Waldmann & Holyoak, 1992; Waldmann, 2000, 2001).
Waldmann and Holyoak (1992) conducted three experiments, which with the
exception of Experiment 2, found competition for causes but not for effects.
However, there are several problems with the methodology that have also been noted
by other researchers (e.g., Matute et al., 1996; Shanks & Lopez, 1996). First, they
always presented effects as antecedents to causes, and therefore, it is difficult to
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ascertain whether their results suggest a lack of cue competition between effects or a
lack o f cue competition between effects that are presented as antecedent events. Also,
competition between causes was always paired with predictive (CE) training, where
multiple causes are presented before the common effect, and competition between
effects was always paired with diagnostic (EC) training, where multiple effects are
presented before the common cause. Thus the direction o f training was confounded
with the competitiveness of causes and effects. Finally, the direction of testing was
also inconsistent. Whereas competition between causes was always tested in the CE
direction, competition between effects was tested in the CE direction in Experiment
1 and in the EC direction in Experiments 2 and 3. Although competition between
causes was always observed, competition between effects was only obtained in
Experiment 2. However, Waldmann and Holyoak (1992) discounted this effect as
being a result of the subjects’ relying on previous “concrete” knowledge pertaining
to the relationship between the stimuli used. This claim is problematic because
Shanks and Lopez (1996) replicated the cause and effect conditions used by
Waldmann and Holyoak (1992) while at the same time controlling for abstract and
concrete knowledge o f subjects, and observed cue competition for effects regardless
of the concrete or abstract status of the stimuli.
Cue Competition in Contiguity Models
Some researchers propose that a simple contiguity (or noncompetitive) theory
of learning may better accommodate these inconsistencies in demonstrating cue
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competition for effects (e.g., Matute et al., 1996; Esmoris-Arranz et a l, 1997). They
base this claim on several research findings. First Esmoris-Arranz et al. (1997)
obtained cue competition for effects by presenting effects as subsequent events,
rather than antecedent events, using rat subjects. This suggests that CE versus EC
direction of training is not a crucial factor in obtaining competition for effects. Next,
they found that the wording of test question moderates the observance o f cue
competition for effects (Matute et al., 1996). They point out that in all the previous
experiments that failed to obtain cue competition for effects, there was a procedural
asymmetry between the cause and effects conditions. Specifically, when the test
question was worded in terms of causality, regardless of being worded in the CE or
EC direction (i.e., is C the cause o f E? vs. is E the effect of C?), the question may
have fostered competition between causes in that it implicitly asked subjects to
comparep[E|C] withp[E|C’]. Thus, “the question may have become competitive
when several causes were present (cause condition), but it became noncompetitive
when only one possible cause was available (effect condition)” (Matute et al., 1996,
p .191). To support this hypothesis, Matute et al., (1996) obtained cue competition for
both causes and effects when they used test questions that implicitly probed the
conditional probability of an effect given a cause compared to its probability given
an alternative cause (p[E|C] with/?[E|C’j) in the cause condition, and the conditional
probability of a cause given an effect compared to its probability given an alternative
effect (p[C|E] with/?[C|E’]) in the effect condition. Further, they failed to obtain cue
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11
competition for either causes or effects when test questions were worded in terms of
contiguity, or actual co-occurrences, implying noncompetitive learning. Matute et al.
(1996) interpret these findings to suggest that cue competition takes place at the
retrieval or judgmental stages, and does not necessarily imply a deficit in the
learning of associations: “intact associations can flexibly be used as a function of
task demands during assessment,” and “may compete in some test conditions but not
in others, depending on whether test conditions encourage competition” (p. 192).
Cue competition in Neural Network Models
Adaptive neural networks models have their roots in associative learning and
animal conditioning, and range from simple one-layer networks connected by
unidirectional links to complex multilayered networks with bidirectional links that
back-propagate learning changes. Multilayer networks using the delta learning rule,
which is essentially the same as the Rescorla-Wagner (1972) model of associative
learning in animals, have been demonstrated to provide an accurate account of
human categorization and to learn many discriminations such as parity, exclusive-or,
and symmetry relationships (e.g., Sutton and Barto, 1981; McClelland and
Rumelhart, 1985; Gluck and Bower, 1988). The delta rule is an error-correcting
learning rule that says that the changes in weights, Awjj, from input node i to output
node j is given by the following equation:
A w %= q (tj- Oj) & i,
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12
where a is the activation on input node i, t is the target activation on output node j, o
is the observed or actual activation on output j, and r\ is the learning rate (constant).
In other words, the change in weight of the link between the input and output nodes,
Aw, depend on the extent to which the target activation of the output is discrepant
from the observed activation of the output. For example, if the network correctly
identifies the (t-o) term to be 0, there will be no update in weight. However, if the
network outputs an activation value o f -1 but the target value is 1, there will be an
increase in weight. Likewise, if the network outputs an activation value of 1 but the
desired value is -1, there will be a decrease in weight.
Gluck and Bower (1988) and Shanks (1991) were able to demonstrate that a
simple one-layer network using the delta rule correctly predicted competition of cues
(symptoms) for a common outcome (a rare disease). However, because they both
used a feed-forward network model as shown in Figure 1, the direction of training
was modeled with diagnostic learning, where the symptoms were represented as
input nodes and the disease was represented as a single node output. Thus, while
they were able to show that a neural network model can predict cue competition for
effects (symptoms) for a common cause (disease) with diagnostic learning, their
models cannot accommodate cue competition for effects with predictive learning
without using a separate, structurally different network.
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Figure 1.
Feed Forward Network
Symptom 2
Symptom 4
Symptom 3
Disease
Symptom 1
A structural model o f the feed forward network for cue competition between
effects.
More recently, Read (in an unpublished manuscript) demonstrated that a
recurrent network with bidirectional links between the input and output nodes using
the delta rule can predict blocking and cue competition for both causes and effects.
As shown in Figure 2, what is worthy of note is that unlike the feed forward model,
the recurrent model is able to acquire bidirectional links or associations between the
input and output nodes, and thus is able to accommodate both predictive and
diagnostic learning in the same model.
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Figure 2
Recurrent N etw ork
Effect 1
Cause
Effect 2
A structural model of the recurrent network for cue competition between
effects.
In addition, the strength of the bidirectional links between any given two nodes that
represent any given two events may differ as a function of the direction of the
association that is activated by the test stimuli. This possible asymmetry in the
associative strengths of the bidirectional links using delta rule learning can be
illustrated in the classic blocking paradigm, where upon if one first learns that cue A
causes outcome X, there is a deficit in subsequently learning that cue B also causes
outcome X, even though the AB compound are always paired together preceding X
during the second phase of learning. According to the recurrent model, the
observation of the blocking of cue B depends on the direction o f the associative link
between B and X that is activated because of the asymmetry in weight changes of
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15
these links that occurs during the Phase 2 training. The link from B-*X should
exhibit the effect o f competitive learning because, when B is activated, X is already
activated due to the simultaneous presence o f A, which already is a perfect predictor
o f X. In other words, there is very little weight change in the link from B— »X during
Phase 2 training because B does not provide any new information about the
predictability o f X. However, the link from X— »B should not exhibit cue competition
during Phase 2 training, as activating X does not necessarily increase the prediction
of B because B is not predicted by anything. Therefore, there is a great discrepancy
from the target activation of B and the actual activation of B, which results in a
greater weight change in the link from X— >B. The resulting asymmetry in the
strength of associations between B— >X and X— >B will be such that the link from
X— »B will be stronger than the link from B— »X, suggesting that cue competition
should only be observed in the link from B— »X. As presented in Figure 3, Read was
able to demonstrate this asymmetry in weights between the links B— >X and X— >B in
a simulation using the recurrent network model, and the results reflect that cue
competition for causes occurs in the link from B— *X.
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Figure 3.
Phase 2 only: ABX
Phase 1 and Phase 2: AB-ABX
Final activation values demonstrating cue competition for causes after Phase
1 and 2 training (but not after Phase 2 only training) in the recurrent neural
network model simulation, where A and B are the multiple causes and X is
the common effect.
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17
Similarly, the recurrent model predicts cue competition for effects using the
same rule, where upon if one first leams that cause A leads to effect X, there is a
deficit in later learning that effect Y is also an effect o f A when the XY compound is
subsequently paired after A during Phase 2 training. Again, the model predicts an
asymmetry between the associative strengths of the links from A— »Y and Y— »A. The
associative link from Y— >A should exhibit competitive learning because when Y is
activated during Phase 2 training, A is already highly activated from the
simultaneous presence of X, which is already a perfect predictor o f A. Thus, there is
very little weight change in the link from Y— *A because Y does not add any new
information about the predictability of A. However, the link from A— »Y should not
exhibit a cue competition in learning because when A is activated during Phase 2
learning, it does not predict Y because Y is not predicted by anything. Therefore, the
discrepancy between the target activation of Y and the actual activation of Y is large,
resulting in a bigger weight change in the link from A— >Y. Thus, the model predicts
that the associative strength from A— »Y should be stronger than the associative
strength o f Y— »A, and that cues (or effects in this case) should only compete when
reasoning from Y— >A, but not when reasoning from A— >Y. Read was, again, able to
demonstrate the asymmetry in weights between the links A— and Y— »A in his
simulation, and the results, presented in Figure 4, reflect that cue competition for
effects occurs in the link from Y— >A.
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18
Figure 4.
Phase 1 only: AXY
< 1
N O
ON
NO
• 6?9
Phase 1 and Phase 2: AX-AXY
o
Final activation values demonstrating cue competition for effects after Phase
1 and 2 training (but not after Phase 2 only training) in the recurrent neural
network model simulation, where A is the common cause and X and Y are
the multiple effects.
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19
The purpose of this current paper is threefold. First, it will attempt to
contribute to the existing literature that suggests that cue competition for effects
indeed occurs. Second, it will demonstrate that this effect can be obtained by using
non-traditional stimuli that are social in nature. Finally, it will attempt to examine
and replicate the predictions of the recurrent network model for cue competition and
the asymmetry in the associative strengths of the bidirectional links between the cue
and the target outcome. This will be accomplished by asking the subjects to make
judgments about the associative strengths of each of the two possible directional
links between a cue and an outcome. It is expected that cue competition for effects
will be observed as well as the asymmetry in the associative strength of the two
possible links between the common cause and the target outcome. Further, it is
expected that the target outcome, Y, will compete with outcome, X, only when
reasoning backward from Y ^ A , but not when reasoning forward from A— >Y.
Study 1
Overview
Study 1 was designed to test the simulation results of Read’s recurrent neural
network model for cue competition between multiple effects in human behavioral
contingency learning and causal reasoning using social stimuli. The stimuli involved
were four unrelated behaviors that have no known preexisting relationship with each
other: breaking a glass (cause A); shaving one’s head (effect X); lighting a tree on
fire (effect Y); and meditating (filler effect Z). The directionality-of-training variable
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20
was controlled for by presenting all of the information simultaneously in list format
(as Van Hamme et al. (1993) and Matute et al. (1996) did) with a line break in
between the antecedent and subsequent events to separate the common cause from
the multiple effects. Finally, instead of using just CE or EC worded questions at
testing, questions probing the bidirectional associative strengths between all four
behaviors were used (A— »X; X— »A; A— »Y; Y— »A; X— »Y; Y— fX; A— >Z; Z— >A).
Method
Participants and Design. Ninety-three undergraduates from the
University o f Southern California Subject Pool volunteered for the study for a partial
course requirement credit. The study was a between subjects design with repeated
measures, where the experimental group received both Phase 1 and Phase 2 of
training, and the control group only received the Phase 2 portion of training.
Materials and Procedure. Upon arriving, the participants were randomly
assigned to the experimental or control group and were seated in front of a computer
terminal, on which the entire experiment was conducted. The cover story was
presented on the computer screen, and directed subjects to imagine that they were
anthropologists in the distant fixture traveling to a long lost human colony on a
faraway planet in order to study their culture and social customs. Specifically, they
were instructed that their goal was to leam the various behavioral patterns of the
colonists by observing the descriptions of individual instances of sets of behaviors.
Before seeing the actual descriptions of the behavioral sets, however, all subjects
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21
were asked to make some initial judgments about the extent to which the four
stimulus behaviors were related to each other in order to establish that they had no
known previously existing relationship with each other. Specifically, they were told
to indicate the extent to which the occurrence of one behavior affects the likelihood
of the occurrence o f another behavior on a scale from - 1 0 to 1 0 , where - 1 0 indicates
that the first behavior strongly inhibits the likelihood of the second behavior, 1 0
indicates that the first behavior strongly increases the likelihood of the second
behavior, and 0 indicates that the two behaviors are unrelated. Further, these
questions were identical to the test questions used after the training phase(s), and
thus involved making judgments about the four stimulus behaviors in all possible
directions of reasoning.
After the initial ratings, participants in the experimental condition were
presented with Phase 1 of training, where they saw 10 behavioral sets exhibited by
10 different individuals. Each behavioral set was presented individually on separate
screens along with the name of the individual exhibiting the behaviors. Each
behavioral set remained displayed on the screen until the subject pressed the space
bar to advance to the next behavioral set. Eight out of the 10 sets involved the
occurrence o f “breaking a glass” (Cause A) followed by “shaving one’s head” (effect
X); two of the 10 sets involved the occurrence of “breaking a glass” (cause A)
followed by “meditating” (filler effect Z). The order in which the 10 individual
behavioral sets were presented was randomized for each participant using Psyscope.
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22
After Phase 1 training, subjects were immediately presented with Phase 2 training,
where they saw 10 more behavioral sets exhibited by 10 new individuals. Eight out
o f the 10 sets involved the occurrence of “breaking a glass” (cause A) followed by
“shaving one’s head” (effect X) and “lighting a tree on fire” (effect Y). As in Phase 1,
two of the 10 sets involved the occurrence of “breaking a glass (cause A) followed
by “meditating” (filler effect Z). Participants in the control condition only received
Phase 2 portion of the training. The entire cover story and the training materials for
Study 1 are presented in Appendix A.
Immediately following the training, the subjects were asked to make final
judgments about the extent to which the occurrence o f one behavior affects the
likelihood o f the occurrence of another behavior for all four stimulus behaviors in all
possible directions of reasoning. The rating scale used for the final judgments was
the same one used earlier for initial judgments. Thus, subjects made judgments about
the extent to which “breaking a glass” affects the likelihood of “shaving one’s head”
(A— »X); “shaving one’s head” affects the likelihood o f “breaking a glass” (X— »A);
“breaking a glass” affects the likelihood of “lighting a tree on fire” (A— »Y); “lighting
a tree on fire” affects the likelihood o f “breaking a glass” (Y— »A); “shaving one’s
head” affects the likelihood of “lighting a tree on fire” (X— »Y); “lighting a tree on
fire” affects the likelihood o f “shaving one’s head” (Y— X ); “breaking a glass”
affects the likelihood of “meditating” (A— >Z); and “meditating” affects the
likelihood of breaking a glass” (Z— »A).
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23
Results and Discussion
The mean ratings for the initial and final test questions are presented in
Table 1. The mean of all eight initial ratings was -.62 for the experimental condition,
and -.49 for the control condition, indicating that the four stimulus behaviors had no
preexisting causal relationships between each other. The mean o f all eight final
ratings were 5.77 for the experimental condition, and 6.19 for the control condition,
demonstrating that subjects were able to learn the causal contingencies of stimulus
behaviors that were presented in list-format.
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Table 1.
Mean initial and final ratings and differences for test questions by experimental condition.
Initial f-test for Equality o f Means Final
Ratings Condition N Mean t df Sis. (2-tailed) Ratings Condition N Mean t df Sig.(2-tailed)
A— »X AXY
AX-AXY
48
45
-.98
-1.53
.642 91 .522 A— »X AXY
AX-AXY
48
44
7.46
7.86
-.632 90 .529
X— >A AXY
AX-AXY
47
45
-.15
-.58
.604 90 .547 X— »A AXY
AX-AXY
47
45
6.57
7.49
-1.383 90 .170
A— >Y AXY
AX-AXY
47
43
-.60
-.70
.130 8 8 .897 A— »Y AXY
AX-AXY
48
45
7.21
5.29
3.021 91 .003
Y— »A AXY
AX-AXY
48
44
.38
.91
-.764 90 Y— »A AXY
AX-AXY
48
45
6.90
6.84
.071 91 .944
X— >Y AXY
AX-AXY
48 -.75
-.91
.240 90 .811 X— »Y AXY
AX-AXY
48
45
7.13
6.16
1.303 91 .196
Y— >X AXY
AX-AXY
46 - . 2 0
- . 0 2
-.335 8 8 .739 Y— »X AXY
AX-AXY
48
44
7.50
6.16
.370 90 .712
A— >Z AXY
AX-AXY
48
4 4
. 1 0
.27
-.205 90 .838 A— >Z AXY
AX-AXY
48
45
4.15
4.78
-.742 89 .460
Z—* -A AXY
AX-AXY
47
44
-1.70
-2.52
.992 89 .324 Z— »A AXY
AX-AXY
48
44
2.77
.45
2.168 90 .033
AXY= control condition, where only Phase 2 training was administered; A X -A X Y - experimental condition, where both
Phase 1 and Phase 2 trainings were administered.
25
A repeated measures analysis for initial and final ratings by experimental
condition showed a main effect for the within-subject variable of initial and final
ratings for each of the initial and final rating pairs, with the exception of the pair
from effect Z to cause A (initial and final A— »X: F{\, 58) = 111.99, p = 00; initial
and final X-+A: F (l, 58) = 105.88,/? = .00; initial and final A-»Y: F (l, 56) = 81.44,
p = 00; initial and final Y— *A: F (l, 57) = 66.07,p =.00; initial and final X— »Y: F{1,
58) = 75.92, p =.00; initial and final Y— »X: F{1, 58) = 70.69,p =.00; initial and final
A— >Z: F{1, 57) = 10.82,/? =.00; and initial and final Z-^A: F (1, 58) = 1.54,/? = 21.
Given that effect Z was a filler item, this lack o f significance between the initial and
final ratings for Z— *A does not have a major impact on the critical variables under
current investigation. The interaction between the initial and final ratings and
experimental condition was not significant for any of the pre-post rating pairs.
Subjects with missing data were excluded casewise from the analysis.
A between-groups comparison by experimental condition for each of the
eight final ratings found all o f them to be non-significant with the exception of one.
Interestingly, the difference between the experimental and control Y— >A rating,
where cue competition was predicted to occur by the recurrent network, was non
significant, 1(91) = .071,/? =.944. Instead, the difference between experimental and
control final A— >Y rating was found to be highly significant, t{9\) = 3.02,/? = 003.
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26
As presented in Figure 5, the results show evidence for cue competition
between effects as a result of an asymmetry in the associative strengths of the
bidirectional links between Cause A and Effect Y.
Figure 5.
AXY
u >
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27
Figure 5 continued.
AX-AXY
O n
Mean final ratings for cue competition for effects in the AXY (control) and
AX-AXY (experimental) conditions in Study 1, where A is the common
cause, and X and Y are the two competing effects.
However, the asymmetry is in the opposite direction of that which is predicted by the
delta learning rule of the recurrent network. The model predicts that the difference in
the associative strengths between the experimental and control conditions should
occur for the final rating of Y-*A. Surprisingly, the results o f Study 1 indicate that
the difference in the associative strengths between the experiment and control
conditions occurs in the A— >Y direction of reasoning (5.29 for the experimental
condition vs. 7.21 for the control condition) and not in the predicted Y— >A direction
(6.84 for experimental vs. 6.90 for control).
In searching for a plausible explanation for the findings in Study 1, the clarity
o f the test questions in the experiment was called into question. After learning the
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28
behavioral contingencies, subjects were asked to make some “final estimates about
the extent to which the occurrence o f the first behavior affects the likelihood o f the
occurrence of the second behavior.” However, for the backward reasoning test
questions (e.g., X— »A, Y— »A, and Z— >A) the actual test questions asked subjects to
indicate the likelihood that an individual doing X (or Y or Z) had previously done A.
In other words, the task instructions implicitly asked subjects to make forward casual
judgments from the first listed behavior to the second, while the actual test questions
asked subjects to make backward causal judgments from the first listed behavior to
the second (at least for the backward reasoning questions). Thus, it is unclear as to
whether Study 1 was successful in truly measuring the bidirectional associative
strengths among the four stimulus behaviors in all possible directions.
Study 2
Overview
Due to the unexpected findings in Study 1, Study 2 was designed to replicate
the results of Study 1 with several changes. First, as there were some issues
regarding the clarity of the test questions in Study 1, the wording o f the test
questions was changed in Study 2 to reflect specific conditional probabilities.
Therefore, test questions probing the associative strength o f the link from A — »X
became P[X|A], X— >A became P[A|X], and so forth (The specific phrasing of the
new test questions is presented later in this section). Next, because the recurrent
network model also predicts cue competition for causes as a result o f asymmetrical
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29
associative strengths in the bidirectional links between the redundant cue and
outcome, the design used in Study 1 was used in Study 2 to investigate cue
competition for causes as well as for effects. For the Effects condition, the design
and stimulus behaviors (Cause A, Effects X, Y and Z) were identical to those of
Study 1. For the Causes condition, Cause A and Effect X remained the same with the
addition of a new redundant Cause B, (“ringing a bell”) in the Phase 2 training
portion, and changing the previous filler effect Z to filler cause Z. Finally, as the
design o f Study 1 allowed for the presentation of all the stimulus materials and the
data collection to be entirely on Psyscope, it lent itself to being easily translated into
a web-based study. Thus, Study 2 was conducted as an on-line study.
Method
Participants. One hundred and sixty adults ranging from ages 18 to 67
participated in this study. The mean age o f participants was 39.28 (SD = 12.792).
The mean ages o f subjects within the different conditions are as follows; control
Effects: 41.2, SD = 13.339; experimental Effects: 41.5, SD - 12.556; control Causes:
38, SD = 11.974; and experimental Causes: 36.09, SD = 13.422. Subjects were
participants in our previous on-line studies who indicated that they were interested in
participating in future on-line studies, and were recruited by email. Most of the
participants were residents o f the US, with the exception o f 3 who resided in Canada
and in the UK. In return for their participation, participants were entered into a
lottery of a $50 cash prize, with the odds of winning at 1/50. The study was a
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30
between subjects design with repeated measures, where as before, the experimental
groups for causes and effects received both Phase 1 and Phase 2 parts o f training,
and the control groups only received the Phase 2 portion o f training.
Materials and Procedure. Participants clicked on a link in their email that
directed them to the on-line study. Upon clicking on the button that initiated the
experiment, participants were randomly assigned to one of four conditions:
experimental and control conditions for Causes and experimental and control
conditions for Effects. Participants were presented with the same cover story as in
Study 1. Because Study 1 established that there were no known preexisting
relationships between the stimulus behaviors, the initial judgments were dropped for
Study 2. The procedure for the Effects condition was identical to that in Study 1,
where participants in the experimental group were first presented with Phase 1 of
training, during which they saw 1 0 behavioral sets exhibited by 1 0 different
individuals. Again, each behavioral set was presented individually on separate
screens along with the name o f the individual exhibiting the behaviors. Each
behavioral set remained displayed on the screen until the subject clicked on the
“continue” button to advance to the next behavioral set. Eight out o f the 10 sets
involved the occurrence of “breaking a glass” (Cause A) followed by “shaving one’s
head” (effect X); two of the 10 sets involved the occurrence of “breaking a glass”
(cause A) followed by a “meditating” (filler effect Z). The order in which the 10
individual behavioral sets were presented was randomized for each participant using
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31
a Javascript code. After Phase 1 training, subjects were immediately presented with
Phase 2 training, where they saw 10 more behavioral sets exhibited by 10 new
individuals. Eight out of the 10 sets involved the occurrence o f “breaking a glass”
(cause A) followed by “shaving one’s head” (effect X) and “lighting a tree on fire”
(redundant effect Y). As in Phase 1, two of the 10 sets involved the occurrence of
“breaking a glass (cause A) followed by “meditating” (filler effect Z). The order in
which Phase 2 sets of behaviors were presented was randomized for each participant
as well. Participants in the control condition only received Phase 2 portion of the
training. Also, unlike in Study 1, the order of the eight test questions were
randomized for each participant as well.
The procedure for the Causes condition was identical to that for Effects, with
the exception of changes in the stimulus behaviors. Participants in the experimental
group were presented with Phase 1 o f training, where they saw 10 behavioral sets
exhibited by 10 different individuals. Eight out of the 10 sets involved the
occurrence of “breaking a glass” (cause A) followed by “shaving one’s head” (effect
X); two of the 10 sets involved the occurrence of “meditating” (cause filler cause Z)
followed by a “shaving one’s head” (effect X). Next, they were presented with Phase
2 training, where they saw 1 0 more behavioral sets exhibited by 1 0 new individuals.
Eight out of the 10 sets involved the occurrence of “breaking a glass” (cause A) and
“ringing a bell” (redundant cause B) followed by “shaving one’s head” (effect X). As
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32
in Phase 1, two of the 10 sets involved the occurrence of “meditating (filler cause z)
followed by “shaving one’s head” (effect X).
Immediately following the training, the subjects were asked to make final
judgments about the extent to which the occurrence of one behavior affects the
likelihood o f the occurrence of another behavior in terms of conditional probabilities
for all four stimulus behaviors in all possible direction of reasoning. In the two
Causes conditions, they were asked to make judgments about P[A|X], P[X|A],
P[B|X], P[X|B], P[A|B], P[B|A], P[Z|A], and P[A|Z] and make their judgments using
a rating scale from 0 to 10, where 0 indicates “No chance”, 5 indicates “50-50”, and
10 indicates “Certain”. The test questions were phrased: for P[A|X], “Assuming that
someone shaves their head, how likely is it that they had broken a glass,” and for
P[X|A], “Assuming that someone has broken a glass, how likely is it that they will
shave their head?,” and so forth. In the two Effects conditions, subjects made
judgments about P[A|X], P[X|A], P[A|Y], P[Y|A], P[X|Y], P[Y|X], P[A|Z], and
P[Z|A]. Note that the stimulus behaviors for A and X, and the test questions for
P[A|X] and P[X|A] are the same for both Causes and Effects conditions. A complete
list of the test questions as well as the training materials for Study 2 is presented in
Appendix B.
Results and Discussion
The mean final ratings by experimental vs. control conditions for both Causes
and Effects conditions are presented in Tables 2 and 3.
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33
Table 2.
Mean ratings and differences in cue competition for Effects by experimental
condition.
Condition N Mean
f-test for Eauality of Means
t d f Sie. (2-tailed)
Effect A— >X AXY 28 6 . 8 6 -.592 70 .556
AX-AXY 44 7.16
Effect X— »A AXY 28 7.00 -1.037 70 .303
AX-AXY 44 7.70
Effect A— > Y AXY 28 7.36 3.752 70 . 0 0 0
AX-AXY 44 5.30
Effect Y— » A AXY 28 7.29 -.476 70 .635
AX-AXY 44 7.61
Effect X-»Y AXY 28 7.39 1.823 70 .073
AX-AXY 44 6.16
Effect Y— fX AXY 28 8.07 1.078 70 .285
AX-AXY 44 7.30
Effect A— »Z AXY 28 3.68 1.317 70 .192
AX-AXY 44 2.95
Effect Z— *A AXY 28 5.00 .171 70 .864
AX-AXY 44 4.84
AXY= control condition, where only Phase 2 training was administered; AX-AXY=
experimental condition, where both Phase 1 and Phase 2 trainings were administered.
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34
Table 3.
Mean ratings and differences in cue competition for Causes by experimental
condition.
Condition N Mean
t-test for Equality of Means
t df Sis. (2-tailed)
Cause A— »X ABX 47 8.04 -2.165 76 .034
AX-ABX 31 9.10
Cause X— »A ABX 47 6.68 -1.419 76 .160
AX-ABX 31 7.52
Cause B— »X ABX 47 7.70 2.573 76 .012
AX-ABX 31 5.97
Cause X— »B ABX 47 6.38 2.885 76 .005
AX-ABX 31 4.61
Cause A— »B ABX 47 8.36 5.948 76 .000
AX-ABX 31 5.16
Cause B— »A ABX 47 7.21 1.257 76 .213
AX-ABX 31 6.29
Cause Z— *X ABX 47 6.94 -.766 76 .446
AX-ABX 31 7.52
Cause X— >Z ABX 47 4.34 .610 76 .544
AX-ABX 31 3.97
ABX= control condition, where only Phase 2 training was administered; AX-ABX=
experimental condition, where both Phase 1 and Phase 2 trainings were administered.
As presented in Figure 6, the results for the Effects condition in study 2 replicate
those of Study 1.
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35
Figure 6.
AXY
AX-AXY
o\
Mean final ratings for cue competition for effects in the AXY (control) and
AX-AXY (experimental) conditions in Study 2, where A is the common
cause, and X and Y are the two competing effects.
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36
Between groups comparison of the final ratings for the experimental and control
conditions do not show a difference in the critical variable o f Y — >A rating, 1(70) = -
.47,p =.63, but instead in the A— >Y rating, 1(70) = 3.75, p =.00. In other words, cue
competition for effects is obtained due to the asymmetrical associative strengths of
the bidirectional links between Cause A and the redundant Effect Y. However, as In
Study 1, the asymmetry is in the opposite direction o f that which is predicted by the
delta rule of the recurrent network. Whereas the neural network model predicts that
the link from Y— >A should experience a deficit in acquiring associative strength in
the experimental condition and thus become weaker than the link from A— »Y, the
results of Study 2 indicate that the opposite is true. The difference in the associative
strengths between the experiment and control conditions occurs in the A— »Y
direction of reasoning (5.30 for the experimental condition vs. 7.36 for the control
condition) and not in the Y— »A direction (7.61 for experimental vs. 7.29 for control).
For the Causes condition, there is a significant difference between the
experimental and control groups for the critical variable of B— >X rating, 1(76) = 2.57,
p = 01. However, the between groups difference for the non-critical variable of
X— *B is also significant at 1(76) = 2.88, p = 00, as presented in Figure 7.
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37
Figure 7.
ABX
AB-ABX
'■ IQ .
N)
' 'P
ON
Mean final ratings for cue competition for causes in the ABX (control) and
AX-ABX (experimental) conditions in Study 2, where A and B are the
competing causes, and X is the common effect.
In other words, cue competition for causes is obtained, but it is not due to an
asymmetry in the associative links of the bidirectional links between the redundant
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38
Cause B and the common effect X (B— >X vs. X— »B). In fact, contrary to the network
model’s predictions that there should be a deficit in the acquisition o f associative
strength only in the link from B— »X in the experimental condition, there is no
asymmetry in the bidirectional associative strengths between Cause B and Effect X.
The difference in the associative strengths between the experiment and control
conditions occurs in both the B— >X direction of reasoning (5.97 for the experimental
condition vs. 7.70 for the control condition) as well as in the X— direction (4.61
for experimental vs. 6.38 for control).
Another interesting result is the difference in the overall pattern o f the
bidirectional associative links between the two control and the two experimental
groups in the Causes and Effects condition. In the Effects condition, the associative
strengths of the bidirectional links between each stimulus pairs are relatively equal in
the control group (A ^ X = 6.86 vs. X -»A = 7.00, A— >Y = 7.36 vs. Y->A = 7.29),
and this is similarly reflected in the experimental group (except for the deficit in the
link from A— >Y, which was explained earlier to be responsible for the cue
competition effect). However, for the Causes condition, there are asymmetries in the
associative strengths of the bidirectional links between each stimulus pairs in the
control group (A— >X = 8.04 vs. X— >A = 6.68, B— »X = 7.70 vs. X— >B - 6.38). This
pattern is also reflected in the experimental group, so that A— >X = 9.10 vs. X— »A =
7.52, B— »X = 5.7 vs. X — »B = 4.61. Thus, it appears that for the Causes condition,
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39
forward links from causes to effect have stronger associations than backward links
from effect to causes.
General Discussion
Taken together, the results of the present studies replicate the well-
established phenomenon of competition between causes (e.g., Van T F fa mme et al.,
1993; Waldman & Holyoak, 1992) as well as the more controversial presence of
competition between effects (Shanks, 1991; Price & Yates, 1993; Esmoris-Arranz et
al., 1995; Matute et al., 1996). Further, the present studies demonstrate that this
effect is not limited to the traditional context of biological, physical and abstract
events and can also be obtained within the context o f social behaviors.
Previous research in cue competition for causes and effects has typically
involved investigating the phenomenon using only one direction o f testing. In other
words, studies looking at cue competition for causes typically obtained judgments in
the cause to effect direction, and cue competition for effects was typically
investigated from the effect to cause direction of reasoning. The present study is the
first to investigate cue competition for causes and effects by systematically exploring
all possible directional links between causes and effects. In doing so, Study 1
demonstrated that cue competition between effects occurs when reasoning forward
from cause to the redundant effect (A— *Y), rather than when reasoning backward
from the redundant effect to cause (Y— >A). Similarly, Study 2 also showed that cue
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40
competition between effects occurs with forward reasoning but not with backward
reasoning, and that cue competition between causes occurs with both forward
reasoning from the redundant cue to effect (B— >X) as well as with backward
reasoning from effect to the redundant cue (X— »B).
The implications these results have for the various causal models are
enlightening yet somewhat ambiguous. The results clearly show no support for the
causal model theory, which states that causes compete and effects do not. There is no
evidence to support that people construct predictive vs. diagnostic causal models
which leads to the differential predictions for cue competition between causes and
effects.
One o f the main reasons for the emergence of the issue o f predictive vs.
diagnostic learning in cue competition research was because a diagnostic learning
model is the only way that the Rescorla-Wagner rule could predict cue competition
for effects. This has led to a long standing debate between the supporters of the
associative and the causal model views over whether or not cue competition for
effects can be obtained with diagnostic learning. As stated earlier, one o f the virtues
of the recurrent network model is that it allows one to obtain cue competition for
effects without having to use diagnostic learning because one can simultaneously
look at all possible directions of learning and reasoning regardless o f whether one is
investigating cue competition for causes or effects. Although the present study did
not investigate cue competition under the scope of predictive vs. diagnostic learning
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41
models, the results nonetheless contradict the causal model theory’s prediction for
the lack o f cue competition between effects.
As for the associative learning and the neural network models, on the one
hand, the results seem to support their prediction of competitive learning and the
presence o f cue competition between effects. On the other hand, the finding that cue
competition occurs when reasoning forward from common cause to the redundant
effect (and not when reasoning backward) for effects and when reasoning both
forward and backward between the common effect to the redundant cause for causes
is completely at variance with what is predicted by the delta learning rule. This
implies that the delta rule may not be the best way to model cue competition in
human causal learning and reasoning.
Proponents of the contiguity model of learning (e.g., Matute et al., 1996;
Esmoris-Arranz et al., 1997) propose that learning occurs noncompetitively, and that
cue competition occurs at the retrieval or judgment stages. Moreover, Matute et al.
(1996) only found cue competition when the test questions were phrased in terms of
conditional probabilities. The design o f the present studies does not allow us to tease
out whether cue competition occurs in the learning or the testing stage. However,
assuming that it occurs at the reasoning stage, the pattern o f results for cue
competition between effects in Studies 1 and 2 suggests that people may use a
process similar to calculating conditional probabilities when determining the
associative strengths o f the links between cues and outcomes. Specifically, the
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42
results o f the present studies show that cue competition between effects occurs when
reasoning from A— *Y and not from Y— >A after AX-AXY training. This makes sense
in terms of conditional probability, in that, taking all instances of the learning trials
into account, every time Y was presented, it was always preceded by A, and thus the
association from Y— >A is 100%. However, whenever A was presented, Y followed
A only half the time (during Phase 2), and thus the association from A— »Y is 50%.
Thus, cue competition between effects occurs when reasoning from A— »Y but not
when reasoning from Y— »A, demonstrating an asymmetry in the bidirectional links
between the cause and the redundant cue that is opposite o f that is predicted by the
delta learning rule.
However, with regard to cue competition for causes in Study 2, the same
logic does not seem to apply. According to conditional probability, after AX-ABX
training, every time B is presented, it is always followed by X, and thus the resulting
association from B— »X should be 100%. Likewise, whenever X is presented, B
precedes it only half the time, and thus the resulting association from X— »B should
only be 50%. Thus, cue competition between causes should occur only when
reasoning from X-^B and not when reasoning from B— >X. The present results for
cue competition between causes, however, do not fit this description. Instead, the
results indicate that there is no asymmetry in the bidirectional associative links
between the redundant cause and the common effect in cue competition between
causes; cue competition occurs when reasoning both from B— »X and from X— >B .
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43
This effect is puzzling in that there is no obvious explanation for why cue
competition for causes appears to be different from cue competition for effects, and
it is important that this effect be replicated in a future study. In the mean time, it may
be interpreted to suggest partial support for some of the assumptions of the causal
model theory, in that people represent information about multiple causes differently
than information about multiple effects. However, because the causal model theory
clearly states that cue competition for effects should not be obtained, it is far from
being adequate to reconcile the contradictory presence of cue competition for effects
in the current study. Likewise, the different contingency learning models discussed
above appear to provide only a partial explanation of the various aspects of the
results presented in this study. In trying to develop a more comprehensive theory of
contingency learning and reasoning, the results of the present study must first be
replicated. Further, it should also be seen whether a recurrent network model using a
different learning rule can predict the current findings. Finally, future studies in cue
competition should be designed to address and examine the various types of
reasoning processes participants may use to arrive at their judgments of contingency.
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44
References
Baker, A. G., Murphy, R. A., Vallee-Tourangeau, F. (1996). Associative and
normative models of causal induction: Reacting to versus understanding
cause. In D. R. Shanks, K., I. Holyoak, & d. L. Medin (Eds.), Causal
Learning (pp. 1-45). San Diego, CA: Academic Press, Inc.
Cobos, P. L., Cano, A., Lopez, F. J., Luque, J. L., & Almaraz, J. (2000). Does the
type of judgment required modulate cue competition? Quarterly Journal o f
Experimental Psychology, 53B, 193-207.
Cobos, P. L., Lopez, F. J., Cano, A., Almaraz, J. & Shanks, D. R. (2002).
Mechanisms o f predictive and diagnostic causal induction.. Journal o f
Experimental Psychology: Animal Behavior Processes, 28, 331-346.
Denniston, J. C., Miller, R. R., & Matute, H. (1996). Biological significance as a
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Esmoris-Arranz, F. J., Miller, R. R. & Matute, H. (1997). Blocking of subsequent
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Behavior Processes, 23, 145-156.
Gluck, M. A. & Bower, G. H. (1988). From conditioning to category learning: An
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Matute, BL, Arcediano, F. & Miller, R. R. (1996). Test question modulates cue
competition between causes and between effects. Journal o f Experimental
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learning rule? Comment on Shanks (1991). Journal o f Experimental
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Miller, R. R. & Matute, H. (1998). Competition between outcomes. Psychological
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Price, P. C. & Yates, J. F. (1995). Associative and rule-based accounts of cue
interaction in contingency j udgment. Journal o f Experimental Psychology:
Learning, Memory and Cognition, 21, 1637-1655.
Read, S. J. (Unpublished manuscript). An integrative model of causal learning and
causal reasoning using a feedback neural network.
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Rescola, R. A., & Wagner, A. R. (1972). A theory of Pavlovian conditioning:
Variations in the effectiveness of reinforcement and nonreinforcement. In A.
H. Black & F. Prokasy (Eds.), Classical conditioning II: Current theory and
research (pp. 64-99). New York: Appleton-Century-Crofts.
Shanks, D. R. (1991). Categorization by a connectionist network. Journal o f
Experimental Psychology, 37B, 1-21.
Shanks, D. R. & Lopez, F. J. (1996). Causal order does not affect cue selection in
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Sutton, R. S. & Barto, A.G. (1981). Toward a modem theory o f adaptive networks:
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Van Hamme, L. J. & Wasserman, E. A. (1993). Cue competition in causality
judgments: The role o f manner o f information presentation. Bulletin o f the
Psychonomic Society, 31, 457-460.
Waldmann, M. R. (2000). Competition among causes but no effects in predictive and
diagnostic learning. . Journal o f Experimental Psychology: Learning,
Memory and Cognition, 26, 52-76.
Waldmann, M. R. (2001). Predictive versus diagnostic causal learning: Evidence
from an overshadowing paradigm. Psychonomic Bulletin & Review, 8, 600-
608.
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Waldmann, M. R. & Holyoak, K. J. (1992). Predictive and diagnostic learning within
causal models: Asymmetries in cue competition. Journal o f Experimental
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Appendix A
Stimulus and Testing Materials fo r Study I.
Cover Story. Imagine that you are an anthropologist in the year 2780. In the last
500 years, our understanding o f astrophysics has advanced rapidly along with the
technology that enables humans to travel through space in any distance with efficient
speed. Concurrently, advances in the fields o f atmospheric and environmental
controls have also progressed at an accelerated rate, allowing mankind to resolve the
problem o f overpopulation on Earth by colonizing habitable planets in planetary
systems extending as far out as to the end of our galaxy.
Over hundreds of years, although most colonies have kept in close contact
with Earth, a few colonies on the outskirts of the Milky Way have lost touch with the
mother planet as well as with the other human colonies, and have mostly become
forgotten. As an anthropologist, you are greatly interested in traveling to these lost'
colonies to study the physical and cultural development, the social customs, and
beliefs of the human colonists. Your research team has recently discovered one such
colony on the planet Niobe-IV in the Niobe System. This colony has been out of
contact with Earth for almost 300 years, and you anticipate that these Niobians,
although human, to be quite different from humans on Earth in their culture and
social customs.
Once you have arrived at Niobe-IV, you and your team o f researchers have
been spending the last four months unobtrusively observing and documenting the
different behavioral patterns of Niobians. While categorizing a set of common
behaviors, you notice that some behaviors appear to be associated with the
occurrence o f other behaviors, whereas some do not. The relationships between any
particular set ofbehaviors do not seem to make any intuitive sense, at least in terms
of social and cultural customs on Earth. You conclude that the only way to
understand the behaviors and customs of the Niobians is to take each unfamiliar
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49
behavioral pattern, and study the individual cases in which the set ofbehaviors did or
did not occur.
Keeping this scenario in mind, your goal is to try to determine the causes and
effects for a certain set ofbehaviors of the Niobians. For this task, you will be given
a series of descriptions, each indicating the relationship between several behaviors:
one behavior occurs and is followed by either one or two behaviors.
On the following screens, you will see a total of 20 observations of situations
in which the behaviors you are interested occurred (10 in the control condition).
Then, you will be asked to make some estimates about the extent to which the
occurrence o f one behavior is likely to affect the likelihood of the occurrence of
another behavior.
Phase 1(AX) training stimuli (Experimental condition only).
John breaks a glass.
John shaves his head.
Susan breaks a glass.
Susan shaves her head.
Bob breaks a glass.
Bob shaves his head.
Jeff breaks a glass.
Jeff shaves his head.
Marie breaks a glass.
Marie shaves her head
Lisa breaks a glass.
Lisa shaves her head.
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Jose breaks a glass.
Jose shaves Ms head.
Noah breaks a glass.
Noah shaves his head.
Eve meditates.
Eve shaves her head.
Mike meditates.
Mike shaves his head.
Phase 2(AXY) training stimuli.
Shawn breaks a glass.
Shawn shaves his head. Shawn lights a tree on fire.
Ann breaks a glass.
Ann shaves her head. Ann lights a tree on fire.
Neal breaks a glass.
Neal shaves his head. Neal lights a tree on fire.
Bill breaks a glass.
Bill shaves his head. Neal lights a tree on fire.
Jenny breaks a glass.
Jenny shaves her head. Jenny lights a tree on fire.
Will breaks a glass.
Will shaves his head. Will lights a tree on fire.
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51
Adam breaks a glass.
Adam shaves his head. Will lights a tree on fire.
Amy breaks a glass.
Amy shaves his head. Will lights a tree on fire.
Hans breaks a glass.
Hans meditates.
Lena Hans breaks a glass.
Lena meditates.
Instructions. You have now finished seeing the 20 sets o f behavioral patterns of
Niobians (or 10 in the control condition). Using the rating scale below, please make
your final estimates about the extent to which the occurrence of the first behavior
affects the likelihood of the occurrence of the second behavior.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Initial and final rating items.
A — *X: Type in a number between -10 and 10 to indicate your estimate o f the extent
to which breaking a glass affects the likelihood o f shaving one’s head.
A— »Y: Type in a number between -10 and 10 to indicate your estimate of the extent
to which breaking a glass affects the likelihood o f lighting a tree on fire.
X— >A : Type in a number between -10 and 10 to indicate your estimate o f the
likelihood that an individual shaving one’s head had previously broken a
glass.
Y— »A: Type in a number between -10 and 10 to indicate your estimate of the
likelihood that an individual lighting a tree on fire had previously broken a
glass.
Inhibits the
Likelihood of
Second Behavior
The Two
Behaviors are
Unrelated
Increases the
Likelihood of
Second Behavior
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52
X— »Y: Type in a number between -10 and 10 to indicate your estimate o f the
likelihood that an individual who had shaved one’s head had also lit a tree on
fire.
Y— *X: Type in a number between -10 and 10 to indicate your estimate o f the
likelihood that an individual who had lit a tree on fire had also shaved one’s
head.
A— >Z: Type in a number between -10 and 10 to indicate your estimate o f the extent
to which breaking a glass affects the likelihood o f meditating.
Z— >A: Type in a number between -10 and 10 to indicate your estimate o f the extent
to which meditating affects the likelihood of breaking a glass.
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53
Appendix B.
Stimulus and Testing Materials fo r Study 2.
Cover story. The cover story is identical to that o f Study 1.
Effects Condition.
Phase 1 and 2 training stimuli. Stimulus training materials were
identical to those in Study 1.
Instructions. You have now finished seeing the 20 sets o f behavioral
patterns of Niobians (or 10 in the control condition). On the next several screens, we
would like for you to make some estimates about the extent to which the occurrence
o f one behavior affects the likelihood of the occurrence o f another behavior using the
following rating scale.
0 1 2 3 4 5 6 7 8 9 10
No Chance 50-50 Certain
Test items.
A— >X: Assuming that someone has broken a glass, how likely is it that he or she will
shave his or her head?
A— >Y: Assuming that someone has broken a glass, how likely is it that he or she will
light a tree on fire?
X— >A : Assuming that someone shaves his or her head, how likely is it that he or she
had broken a glass?
Y— >A : Assuming that someone lights a tree on fire, how likely is it that he or she had
broken a glass?
X— >Y: Assuming that someone shaves his or her head, how likely is it that he or she
will also light a tree on fire?
Y— »X: Assuming that someone lights a tree on fire, how likely is it that he or she
will also shave his or her head?
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54
A— »Z: Assuming that someone has broken a glass, how likely is it that he or she will
meditate?
Z— »A: Assuming that someone has broken a glass, how likely is it that he or she will
meditate?
Causes Condition.
Phase 1(AX) training stimuli (Experimental condition only).
John breaks a glass.
John shaves his head.
Susan breaks a glass.
Susan shaves her head.
Bob breaks a glass.
Bob shaves his head.
Jeff breaks a glass.
Jeff shaves his head.
Marie breaks a glass.
Marie shaves her head
Lisa breaks a glass.
Lisa shaves her head.
Jose breaks a glass.
Jose shaves his head.
Noah breaks a glass.
Noah shaves his head.
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55
Eve meditates.
Eve shaves her head.
Mike meditates.
Mike shaves his head.
Phase 2 (ABX) training stimuli.
Shawn breaks a glass. Shawn rings a bell.
Shawn shaves his head.
Ann breaks a glass. Ann rings a bell.
Ann shaves her head.
Neal breaks a glass. Neal rings a bell.
Neal shaves his head.
Bill breaks a glass. Bill rings a bell.
Bill shaves his head.
Jenny breaks a glass. Jenny rings a bell.
Jenny shaves her head.
Will breaks a glass. Will rings a bell.
Will shaves his head.
Adam breaks a glass. Adam rings a bell.
Adam shaves his head.
Amy breaks a glass. Amy rings a bell.
Amy shaves his head.
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56
Hans meditates.
Hans shaves Ms head.
Lena meditates.
Lena shaves her head.
Test items.
A— >X: Assuming that someone has broken a glass, how likely is it that he or she will
shave his or her head?
B— >X: Assuming that someone has rung a bell, how likely is it he or she will shave
his or her head?
X— > A: Assuming that someone shaves his or her head, how likely is it that he or she
had broken a glass?
X— »B: Assuming that someone shaves his or her head, how likely is it that he or she
had rung a bell?
A— »B: Assuming that someone breaks a glass, how likely is it that he or she will also
ring a bell?
B— >A: Assuming that someone rings a bell, how likely is it that he or she will also
break a glass?
A— »Z: Assuming that someone meditates, how likely is it that he or she will shave
his or her head?
Z— »A: Assuming that someone shaves his or her head, how likely is it that he or she
had mediated?
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Kim, Deanah K.
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Asymmetries in the bidirectional associative strengths between events in cue competition for causes and effects
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Psychology
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University of Southern California
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