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Cue competition effects in human causallearningEdgar H. Vogel

a, Jacqueline Y. Glynn

b& Allan R. Wagner

b

aFacultad de Psicologa, Universidad de Talca, Talca, Chile

b

Department of Psychology, Yale University, New Haven, CT, USAPublished online: 17 Mar 2015.

To cite this article:Edgar H. Vogel, Jacqueline Y. Glynn & Allan R. Wagner (2015): Cue competitioneffects in human causal learning, The Quarterly Journal of Experimental Psychology, DOI:10.1080/17470218.2015.1014378

To link to this article: http://dx.doi.org/10.1080/17470218.2015.1014378

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Cue competition effects in human causal learning

Edgar H. Vogel1, Jacqueline Y. Glynn2, and Allan R. Wagner2

1Facultad de Psicologa, Universidad de Talca, Talca, Chile2Department of Psychology, Yale University, New Haven, CT, USA

(Received 6 March 2014; accepted 21 January 2015)

Five experiments involving human causal learning were conducted to compare the cue competitioneffects known as blocking and unovershadowing, in proactive and retroactive instantiations.Experiment 1 demonstrated reliable proactive blocking and unovershadowing but only retroactive uno-

vershadowing. Experiment 2 replicated the same pattern and showed that the retroactive unoversha-dowing that was observed was interfered with by a secondary memory task that had no demonstrableeffect on either proactive unovershadowing or blocking. Experiments 3a, 3b, and 3c demonstrated

that retroactive unovershadowing was accompanied by an inated memory effect not accompanyingproactive unovershadowing. The differential pattern of proactive versus retroactive cue competitioneffects is discussed in relationship to amenable associative and inferential processing possibilities.

Keywords: Cue competition; Blocking; Unovershadowing; Retrospective revaluation.

Cue competition effects are robust in human causallearning (HCL) as they are in Pavlovian condition-ing. For example, when a compound of stimulisignals a reinforcing outcome (AX+), the added

experience with one of the stimuli alone also signal-ling reinforcement (A+) can lead to a decrease inthe response to X (so-called blocking), whereasexperience with A alone without reinforcement(A) can increase the response to X (so-calledrelease from overshadowing, or unovershadowing),when compared to no A-alone experience(Dickinson, Shanks, & Evenden, 1984; Wagner,1969).

A major difference in the particulars of the cuecompetition effects in the two situations is in

their degree of dependence on the order of theexperiences described. In Pavlovian conditioning,the aforementioned inuence of A training, in con-junction with AX+, was initially seen to depend

heavily upon the A trials preceding the AX+trials (e.g., Kamin, 1968,1969; but see Kaufman& Bolles,1981), and the common associative the-ories developed to explain the effects (e.g.,

Mackintosh, 1975; Pearce, 1987; Pearce & Hall,1980; Rescorla & Wagner, 1972; Wagner, 1981)have been built around this feature. In contrast, inHCL the inuence of A experience is less depen-dent upon its order with respect to the AX+ trials(e.g., Shanks, 1985), and the theories offered toexplain the effects in this circumstance have empha-sized this fact (e.g., Cheng, 1997; Dickinson &Burke, 1996; Le Pelley & McLaren, 2001; VanHamme & Wasserman,1994).

Given the empirical and theoretical importance

of this difference in the cue competition effectsobserved in HCL versus Pavlovian conditioning,it is understandable that considerable research hadbeen devoted to the explicit comparison of the

Correspondence should be addressed to Edgar H. Vogel, Universidad de Talca, Facultad de Psicologa, Talca, Chile. E-mail:[email protected]

Part of this work was supported by Fondecyt [grant number 1120265].

2015 The Experimental Psychology Society 1

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proactive inuence (i.e., when A trials precedeAX+) and the retroactive inuence (i.e., when Atrials follow AX+) of the cue competition inHCL. Some of what is known is the following.

First, although there are more robust retroactivecue competition effects in HCL than expected on

the basis of Pavlovian conditioning observationsand theories (e.g., Luque & Vadillo, 2011;Shanks, 1985), it has been most common toobserve lesser retroactive than proactive effects(e.g., Chapman,1991; Lovibond, Been, Mitchell,Bouton, & Frohardt,2003; Melchers, Lachnit, &Shanks, 2004, 2006; Mitchell, Lovibond,Minard, & Lavis,2006).

Second, the lesser retroactive versus proactivecue competition effects have been most evident incomparisons of retroactive versus proactive blocking

rather than comparisons of retroactive versus proac-tive unovershadowing. Although there is someevidence of retroactive blocking (e.g., Hannah,Crump, Allan, & Siegel, 2009; McCormack,Butterll, Hoerl, & Burns,2009; Vadillo, CastroMatute, & Wasserman, 2008; Wasserman &Castro, 2005), Chapman (1991) offered a directcomparison of retroactive versus proactive blockingto show the former to be less. Likewise, Lovibondet al. (2003) and Mitchell et al. (2006) showedthat retroactive blocking was less robust than proac-

tive blocking. There is no similar systematic evi-dence on whether retroactive unovershadowing isalso less than proactive unovershadowing.

Third, there is some evidence that retroactivecue competition is more susceptible to concurrentprocessing interference than is proactive cue com-petition. It has been demonstrated that the proac-tive blocking effect can be diminished by therequirement of a concurrent task (De Houwer &Beckers,2003; Experiment 2), so that such inter-ference is not unique to retroactive cue competition.

However, Aiken, Larkin, and Dickinson (2001)employing a design in which AX+ trials were con-trasted with either A or A+ trials, showed thatthedifferentialcue competition was more interferedwith by a secondary task when the A alone trialsfollowed, rather than preceded, the compoundtrials. Since this study did not include comparisonconditions that could isolate separate blocking

versus unovershadowing effects, it could notcomment on whether the greater interference wasa result of diminished retroactive versus proactiveblocking, diminished retroactive versus proactiveunovershadowing, or both.

Fourth, there is evidence that retroactive cue

competition is dependent upon within-compoundassociations in a way that proactive cue competitionis not. Two relevant studies are those by Dickinsonand Burke (1996) and Larkin, Aitken, andDickinson (1998), which manipulated the consist-ency of the stimulus pairings during compoundtraining. Wasserman and Berglan (1998) andWasserman and Castro (2005) further demon-strated that retroactive unovershadowing and retro-active blocking occurred only in participants whoremembered which cues were trained in compound.

Likewise, Melchers et al. (2004,2006), Mitchell,Killedar, and Lovibond (2005), and Vandorpe,De Houwer, and Beckers (2007; Experiment 1)demonstrated that cue competition was correlatedwith memory of the compounds in the retroactiveorder, but not in the proactive order. In addition,Luque, Flores, and Vadillo (2013) reported thatretroactive blocking and retroactive unovershadow-ing were facilitated when the compounds consistedof high preexperimental associates, as compared tolow preexperimental associates, whereas proactive

blocking and proactive unovershadowing were notsimilarly inuenced.

The present series of experiments was designedto provide further comparisons of retroactive andproactive cue competition effects, with appropriatecomparison conditions, to be able to speak to theseparable blocking and unovershadowing inu-ences that appear to be involved.

In Experiment 1, we conducted an independentassessment of proactive blocking, proactive unover-shadowing, retroactive blocking, and retroactive

unovershadowing, each in comparison to an appro-priate null treatment. The results indicated less ret-roactive than proactive cue competition, due todiminished retroactive as compared to proactiveblocking, without diminished retroactive as com-pared to proactive unovershadowing.

Experiment 2 replicated the results ofExperiment 1 on proactive and retroactive cue

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competition effects, again showing retroactive uno-vershadowing without retroactive blocking, withthe further assessment of the effects of a concurrentmemory task. The concurrent processing task inter-fered with retroactive unovershadowing more thanwith either proactive unovershadowing or proactive

blocking. Since retroactive blocking was notobserved, the experiment was silent on whether itwould be equally diminished.

Experiments 3a, 3b, and 3c provided evidenceconsistent with the supposition that the presen-tation of A after AX+ in a retroactive unoversha-dowing design produced recall of the compoundAX, a consequence that it did not have as a resultof proactive unovershadowing training.

The conclusions are that while blocking andunovershadowing occur in proactive cue compe-

tition, retroactive cue competition is more restrictedto unovershadowing, and that the retroactive uno-vershadowing that does occur is more susceptibleto concurrent interference and more involving ofmemory retrieval than is forward unovershadowing.The implications for theoretical interpretation areaddressed in the General Discussion.

EXPERIMENT 1

Whereas there is considerable evidence that retro-active cue competition effects are less robust thanproactive effects, it is less clear whether this differ-ence is peculiar to retroactive blocking or is equallytrue of retroactive unovershadowing. Experiment 1was designed to compare proactive and retroactiveblocking, as well as proactive and retroactive uno-vershadowing when separately contrasted withappropriate control conditions.

The experimental situation was similar to that ofVan Hamme and Wasserman (1994) and Castro

and Wasserman (2007) and consisted of askingparticipants to suppose they are allergists whohave to learn which foods produce an allergic reac-tion in actitious patient, Mr. X. Participants werepresented with a sequence of slides in which a Mr.X was reported to have eaten a particular food orpair of foods and then to have experienced an aller-gic reaction or not. After viewing the experiences of

Mr. X, participants were asked to rate the extent towhich the foods of experimental interest caused anallergic response.

The experiment involved four different trainingconditions: Proactive blocking, retroactive block-ing, proactive unovershadowing, and retroactive

unovershadowing. One group of participants wastrained with the proactive and retroactive blockingconditions, in counterbalanced orders, and anotherwith the proactive and retroactive unovershadowingconditions.

Table 1summarizes the particulars of trainingand testing. In the proactive blocking condition,the participants received six trials in which foodA was always paired with an allergic reaction(A+), and food I was not (I). Subsequently,there were two compounds of interest, AB+,

which had been preceded by the reinforcement ofone of the elements, and CD+, which was not sopreceded. Some buffer trials (IJand KL) wereincluded to force participants to discriminatebetween reinforced and nonreinforced compounds.In test, the focus was on the participants nalevaluation of the comparable untreated elementsB versus D. In order to reduce variability, ratherthan relying in a single test of each target cue, par-ticipants were asked to rate B and D, each alone,and in compound with the previously nonrein-

forced cues J and L. The case of retroactive block-ing involved the same experiences, but with theelement training (E+ M) and compound train-ing (EF+, GH+, MN, and OP) in the oppo-site order (with tests of the target cue, F, and thecontrol cue, H, alone and in compounds with thepreviously nonreinforced N and P). All subjectswere evaluated on both comparisons, in balancedorders.

The second group received the unovershadow-ing conditions. As seen inTable 1, in the proactive

unovershadowing condition one of the compounds(AB+) was preceded by nonreinforced trials withone of its components (A), whereas the othercompound (CD+) was not so preceded. The retro-active unovershadowing condition involved thesame experiences, but in the opposite orderthatis, training with EF+, GH+, MN, and OPfollowed by E and M+. The testing with

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B versus D in the proactive case and F versus H inthe retroactive case was identical to that in theblocking conditions.

Method

ParticipantsA total of 32 undergraduate psychology students atYale University participated in the experiment forcourse credit. They were tested individually andhad no previous experience in similar research.The participants were randomly assigned to ablocking group (n= 16) or an unovershadow-inggroup (n= 16).

MaterialsThe stimuli were presented and data collected witha personal computer connected to a 15-inch colourscreen and programmed with the E-prime software(Version 1.1; Psychology Software Tools, Inc.,Pittsburgh, PA). The stimuli were the pictures of16 different foods (apple, avocado, banana, broc-coli, carrots, coffee, eggs, grapes, ice-cream,lemon, mushroom, meat, peppers, strawberry,toast, and tomato).

ProcedureThe major features of the task and the program-ming environment were patterned after Castroand Wasserman (2007). The full instructions,which are presented in the SupplementalMaterial, asked the participants to learn, throughinformation presented on the computer screen,

which foods or combinations of foods caused aller-gic reactions to actitious patient.

The proper task began with a block of 36 train-ing trials presented to the participant. At the begin-

ning of each trial, the sentence Mr. X ateappeared on the top-left portion of the screen sim-ultaneously with the picture of a food or a pair offoods. The presentation of the stimuli was followed2 s later by the phrase, Do you think Mr. X willhave an allergic reaction?, and the participantswere required to answer yes or no by clickingthe respective buttons. After the participantentered a response, feedback was provided on thebottom of the screen for 3 s. The feedback con-sisted of the words CORRECT orINCORRECT

, in yellow, over the sentence

Allergic reaction, in red, for the reinforced (+)trials, or No allergic reaction, in green, for thenonreinforced () trials. The top panel of Figure1 exemplies the presentation of a pair of foodsand the middle panel the modication that wouldoccur if the subjects responded that the pair was fol-lowed by an allergic reaction, and that this was, infact, the programmed relationship. The trial termi-nated with a new screen of 1-s duration reportingthe cumulative percentage of correct responses.

Upon completion of the

rst block of 36 trainingtrials, the participants were presented with the fol-lowing message: Now we would like you to rate thelikelihood that each food or each combination of foodscauses Mr. X to have an allergic reaction. Duringthis phase, the picture of a food or pair of foodsappeared in the top centre of the screen, and theparticipants were asked to rate to what extent does

Table 1. Design of Experiments 1 and 2

Proactive Retroactive

Group Phase 1 Phase 2 Test Phase 1 Phase 2 Test

Blocking group A+ (6)

I

(6)

AB+ (6) CD+ (6)

IJ

(6) KL

(6)

B, BJ, BL, D, DJ,

DL, J, L

EF+ (6) GH+ (6)

MN

(6) OP

(6)

E+ (6)

M

(6)

F, FN, FP, H, HN,

HP, N, PUnovershadowing

groupA (6)I+ (6)

AB+ (6) CD+ (6)IJ(6) KL (6)

B, BJ, BL, D, DJ,DL, J, L

EF+ (6) GH+ (6)MN (6) OP (6)

E (6)M+ (6)

F, FN, FP, H, HN,HP, N, P

Note:Letters AP represent different foods that could be followed (+) or not followed () by an allergic reaction in a hypotheticalpatient. The numbers in parenthesis indicate the frequency of each trial type.



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(do) this (these) food (foods) cause an allergic reactionin Mr. X? The participant entered his or herrating by clicking over one number from 0 to 100in an 11-point scale. The bottom panel ofFigure

1depicts an example of one test trial. The partici-pants were required to rate eight foods or pairs offoods.

Next, the participants were presented with thefollowing sentence: You have nished the rstpart of the experiment. Please take a few moments

to relax. The instructions for the second part arethe same as in the beginning. They will be displayedagain when you continue. Then, the instructionswere repeated, and the participants receivedanother block of 36 training trials and eight testingtrials, involving an entirely new set of foods.

For every subject, one block of 36 training trialsand eight testing trials represented a proactive con-dition, and the other block represented a retroactivecondition. For half of the participants in each groupthe proactive condition was presented rst, and for

the other half the retroactive condition was pre-sented rst.

The assignment of specic foods to the con-ditions AP was partially counterbalanced acrossparticipants of each group by means of their differ-ent allocation in one of four subgroups, each with adifferent assignment of foods as AP. This coun-terbalancing ensured that the critical compoundsAB, CD, EF, and GH were composed equallyoften by the same pairs of foods. The position(right vs. left) of the pictures of foods forming a

compound was equated across the experiment.That is, in half of the trials the stimuli were pre-sented in one position (e.g., EF), and in the otherthe relative position was reversed (e.g., FE). Theorder of testing of the various elements and com-pounds was independently determined for eachparticipant by a random order generator.

The experiment was run in two replications,each consisting of 16 participants distinguishedby assignment to one of the two cue competitioncontingencies, blocking or unovershadowing, and

within each such group to one of the two ordersof experience with the proactive and retroactiveconditions and the four different food assignments.

Statistical analysisThe blocking and unovershadowing effects wereexamined by computing the mean causal valuesassigned by each subject to the test trials involving

Figure 1. Example of the screens presented to the participants during

training (top and middle panels) and testing (bottom panel) inExperiment 1.



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the target cue (i.e., B, BJ, and BL in the proactiveorder and F, FN, and FP in the retroactive order)and to the test trials involving the control cue(i.e., D, DJ, and DL in the proactive order and H,HN, and HP in the retroactive order). FollowingVandorpe and De Houwer (2005, 2006) the depen-

dent variable was examined through a cue compe-tition index. In the case of blocking, the indexwas computed as the mean causal rating for com-pounds involving the control cues (D/H) minusthe mean causal ratings for compounds involvingthe target cues (B/F). In the case of unovershadow-ing, the index was computed as the mean causalrating for compounds involving the target cues(B/F) minus the mean causal ratings for compoundsinvolving the control cues (D/H.) The statisticalreliability of the effects was assessed by a 2 (contin-

gency: blocking vs. unovershadowing) 2 (order:proactive vs. retroactive) 2 (replications) mixed-design analysis of variance (ANOVA).

Results and discussion

Figure 2 presents the mean causal ratings to thetarget and control cues in the blocking (top plots)and unovershadowing (bottom plots) groups foreach of the proactive (left-hand plots) and retroactive(right-hand plots) orders. The top plots indicate that

there was a noticeable proactive blocking effect inthe form of lower ratings to the target cue than tothe control cue (left-hand plot), but no evident retro-active blocking in similar comparison (right-handplot). Accordingly, the cue competition index forthe proactive blocking condition (M= 22.081,SEM= 6.380) was substantially higher thanthe index for the retroactive blocking condition(M=0.225, SEM= 7.407). Conversely, thebottom plots indicate that there was a clear unover-shadowing effect in the form of an enhancement

of responding to the target cue as compared tothe control cue in both the proactive condition(left-hand plot) and the retroactive condition(right-hand plot). Consequently, the cue compe-tition index was similar and substantial in both theforward (M= 18.969,SEM= 4.735) and backward(M= 25.631, SEM= 7.767) unovershadowingconditions.

The statistical analyses using the cue compe-tition index conrmed that blocking and unover-shadowing were differentially dependent on theorder of training: The ANOVA revealed a reliableContingency Order interaction, F(1, 28)=4.419, p= .049, 2p= .131. Subsequent compari-

sons indicated that the difference between proactiveand retroactive blocking was reliable,t(30)= 2.237,p= .033, Cohens d= 0.817, while the differencebetween proactive and retroactive unovershadow-ing was not reliable, t(30)= 0.668, p= .510,Cohens d= 0.244. Likewise, the difference inthe magnitude of the blocking and unovershadow-ing was reliable in the retroactive case, t(30)=2.385; p= .024, Cohens d= 0.871, but not inthe proactive case, t(30)= 0.382; p= .706,Cohens d= 0.139. Furthermore, the cue compe-

tition index was signicantly greater than zero inthe case of proactive blocking, t(15)= 3.461,p= .03, Cohens d= 1.787, proactive unoversha-dowing, t(15)= 4.006, p= .001, Cohens d=2.069, and retroactive unovershadowing, t(15)=3.300, p= .005, Cohens d= 1.704, but not inthe case of retroactive blocking, t(15)=0.30,p= .976, Cohensd= 0.155.

In summary, Experiment 1 demonstrated bothproactive blocking and proactive unovershadow-ing, whereas, in contrast, only retroactive unover-

shadowing was observed. These results are inagreement with several other studies that haveshown that whereas the incremental retroactiveunovershadowing resulting from A was sub-stantial and reliable, any decremental retroactiveblocking resulting from A+ was not observed(Beckers, Vandorpe, Debeys, De Houwer, 2009;Larkin et al., 1998; Le Pelley & McLaren,2001). Several additional studies (Chapman,1991; Lovibond et al., 2003; Mitchell et al.,2006) have reported retroactive blocking, but

have been consistent with the observation ofExperiment 1 that it was less robust than wasproactive blocking.

In contrast to the available evidence of dimin-ished retroactive as compared to proactive blocking,Experiment 1 found relatively equivalent retroac-tive and proactive unovershadowing. This suggeststhat the observation that there is less retroactive



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than proactive cue competition effect, in designs inwhich blocking and unovershadowing are com-pared with each other, rather than to appropriatecontrols (e.g., Melchers et al., 2004,2006), couldbe due to the fragility of retroactive blocking andless attributable to diminished retroactive than toproactive unovershadowing.

EXPERIMENT 2

There is some evidence that retroactive cue compe-tition effects are more susceptible to being inter-fered with by competing task demands than aresimilar proactive effects (Aitken, Larkin, &

Dickinson,2001). However, the available ndings,like the aforementioned studies of Melchers et al.(2004,2006), have involved comparisons of block-ing and unovershadowing treatments and have notprovided assessments of whether the separateeffects of either blocking or unovershadowing (orboth) are more susceptible to interference in a ret-

roactive than in a proactive sequence. Experiment 2involved a replication of the design of Experiment 1with and without a companion competing task. Itwas designed to investigate the effects of a concur-rent memory task on proactive and retroactive uno-vershadowing, both of which were substantial inExperiment 1, and potentially allowed similarassessments under conditions of proactive and

Figure 2. Mean causal ratings in trials involving the target and control cues during testing in Experiment 1. The top plots depict the data of theproactive (left-hand plot) and retroactive (right-hand plot) blocking comparisons and the bottom plots the data of the proactive (left-hand plot)and retroactive (right-hand plot) unovershadowing comparisons. Regarding statistical analyses, see the text for means and standard errors of themeans of the cue competition indexes.



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retroactive blocking, although retroactive blockingwas not observed in Experiment 1.

In Experiment 2, some participants were askedto remember a three-digit number and report itupon demand, after which the number was replacedby another to be remembered, and reported, in con-

tinuous fashion. Otherwise the comparisons ofproactive and retroactive blocking and unoversha-dowing were exactly like those described inExperiment 1.

Method

ParticipantsA total of 32 undergraduate psychology students atYale University participated in the experiment forcourse credit. They were tested individually and

had no previous experience in similar research.The participants were randomly assigned to oneof four groups (n= 8): blocking load, blocking noload, unovershadowing load, unovershadowing noload.

Materials and procedureThe contingencies involved in the causal learningtask of Experiment 2 were identical to those ofExperiment 1, as summarized in Table 1. Thatis, in one condition the participants were trained

and tested on proactive and retroactive blockingin counterbalanced orders, and in another con-dition they were trained in proactive and retroac-tive unovershadowing in similar counterbalancedorders. The critical difference was the introductionin each condition of a load group, in which theparticipants performed a digit-remembering taskconcurrently with the causal leaning task, inaddition to a no-load group equivalent to that inExperiment 1.

At the beginning of the experiment, participants

in the load groups were introduced to the digitremembering task as described in theSupplemental Material, which was followed bythe instructions for the causal learning task, whichwere identical to those of Experiment 1.

At the beginning of each trial, the computer pre-sented a screen saying Remember the followingnumber:Then a three-digit number selected from

a list of randomized numbers was added to thescreen for 1 s. After 3 s of blank screen, thefood for that trial was presented, and the participantmade a prediction and received feedback in a manneridentical to that in Experiment 1. Immediatelythereafter, a new screen appeared with the text

Type the number you were remembering and pressRETURN to move to the next trial, and the partici-pant had an opportunity to report the three-digitnumber. Participants in the load groups also wereasked to perform the digit remember task duringtesting. Apart from this, the procedure for the loadgroup and that for the respective no load group wasidentical.

Statistical analysisAs in Experiment 1, the blocking and unoversha-

dowing effects were examined by computing themean values assigned by each subject to the testtrials involving the target cue (i.e., B, BJ, and BLin the proactive orders and F, FN, and FP in theretroactive orders) versus the test trials involvingthe control cue (i.e., D, DJ, and DL in the proactiveorders and H, HN, and HP in the retroactiveorders). The dependent variable for the statisticalanalyses was the same cue competition index,based upon the difference between the responseto the target and control cues, as that used in

Experiment 1. The statistical reliability of theblocking and unovershadowing effects was assessedseparately by a 2 (order: proactive vs. retroactive) 2 (load condition: no load vs. load) mixed-designANOVA.


Blocking effectsThe main results of the blocking contingency aredepicted inFigure 3. The top plots indicated that

in the no-load groups there was an observed proac-tive blocking effect, in the form of less respondingto the test compounds involving the target cue thanto the test compounds involving the control cue,but no retroactive blocking effect, replicating thendings concerning the similar comparisons inExperiment 1. Likewise, the bottom plots showthat in the load groups the comparisons of



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responding to the target and control stimuli yieldeda similar proactive blocking effect and absence of

retroactive blocking effect. These observationswere conrmed by the statistical analyses with thecue competition index, which showed a reliablemain effect of order, F(1, 14)= 10.133, p= .007,2p= .420, and no reliable effect of load, F(1,

14), 1, nor Load Order interaction, F(1,14), 1. The main effect of order and the absenceof Load Order interaction suggest that the

presence of proactive blocking and the absence ofretroactive blocking that was observed in

Experiment 1 are relatively insensitive to the loadmanipulation. The essential nding was that thecue competition index was reliably greater thanzero in the proactive order (M= 35.625, SEM=9.020), t(15)= 3.950, p= .001, Cohens d=2.039, but not in the retroactive order (M=3.958, SEM= 6.953), t(15)=0.569, p= .578,Cohensd= 0.298.

Figure 3. Mean causal ratings in trials involving the target and control cues during testing in the blocking group of Experiment 2. The top plotsdepict the data of the proactive (left-hand plot) and retroactive (right-hand plot) blocking comparisons for theno cognitive loadgroup and thebottom plots the corresponding data for thecognitive loadgroup. Regarding statistical analyses, see the text for means and standard errors ofthe means of the cue competition indexes.



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Unovershadowing effectsThe more interestingndings involving the unover-shadowing effects are depicted inFigure 4. The topplots indicate that, as in Experiment 1, with no cog-nitive load, there was an evident unovershadowingeffect in the form of greater responding to the

target than to the control cues in both the proactiveand retroactive conditions. In comparison, thebottom plots show that with the memory loadthere was still substantial proactive unovershadowing,with greater responding to the target than to the

control cues, but no apparent retroactive unoversha-dowing. The statistical analysis with the cue compe-tition index indicated a reliable Load Orderinteraction,F(1, 14)= 13.719,p= .002, 2p= .495.Given this interaction, further analysis revealed that(as in Experiment 1) there was no reliable difference

between the cue competition index of the proactiveand retroactive conditions in the no load group,t(14)= 0.333, p= .774, Cohens d= 0.178. Incontrast, in the load group the cue competitionindex was reliably greater in the proactive condition

Figure 4. Mean causal ratings in trials involving the target and control cues during testing in the unovershadowing group of Experiment2. The top plots depict the data of the proactive (left-hand plot) and retroactive (right-hand plot) unovershadowing comparisons for theno cognitive loadgroup and the bottom plots the corresponding data for the cognitive loadgroup. Regarding statistical analyses, see thetext for means and standard errors of the means of the cue competition indexes.



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than in the retroactive condition, t(14)= 4.905,p, .001, Cohens d= 2.622. Furthermore, the cuecompetition index was reliably greater than zero inthe proactive no-load (M= 22.085,SEM= 7.069),t(7)= 3.124,p= .017, Cohens d= 2.362, retroac-tive no-load (M= 24.999, SEM= 5.774), t(7)=

4.330, p= .03, Cohens d= 3.273, and proactiveload (M= 37.501, SEM= 12.372), t(7)= 3.031,p= .019, Cohens d= 2.291, conditions, but didnot differ reliably from zero in the retroactiveload condition (M=5.418, SEM= 13.815),t(7)=0.392,p= .707, Cohensd= 0.296.

In conclusion, whereas proactive unovershadow-ing and proactive blocking were not degraded bythe concurrent memory task employed inExperiment 2, the retroactive unovershadowingthat was observed in the no-load conditions in

Experiment 1 and Experiment 2 was not observedin the load condition of Experiment 2. Since therehave been some reports of cognitive interferencewith proactive cue competition (De Houwer &Beckers, 2003; Liu & Luhmann, 2013), perhapsthe most secure conclusion at this point is thatproactive effects appear to be less susceptible tointerference than retroactive effects. The presentdata are consistent with the ndings of Aitken,Larkin, and Dickinson (2001) who found that aconcurrent secondary task that did not interfere

with proactive blocking did interfere with a non-specic retroactive cue competition effect. SinceExperiment 2 provided independent assessmentsof proactive and retroactive blocking and unover-shadowing, the data allow the more specic con-clusion that retroactive unovershadowing appearsto be more susceptible to interference than is thecorresponding proactive unovershadowing.

EXPERIMENT 3A

There is substantial evidence that retroactive cuecompetition effects are more dependent upon thememorial relationship between the manipulatedcue and the compound in which it was trainedthan are corresponding proactive effects (e.g.,Melchers et al.,2004,2006; Mitchell et al.,2005;Vandorpe et al., 2007). Experiment 3a provides

further evidence of this fact, via a variation on aninated-memory assessment employed byJohnson and her colleagues in which participantsare asked to judge the frequency of occurrence ofitems that have previously been presented differentnumbers of times, but also imagined different

numbers of times (e.g., Johnson, Raye, Wang, &Taylor, 1979, Johnson, Taylor, & Raye, 1977).The striking result of Johnsons studies is that thejudgements of the frequency of occurrence ofitems increased not only as a function of thenumber of presentations of the item but also as afunction of the number of times that the item wasprovoked into memory by a retrieval cue. Basedon these ndings, we reasoned that if the retroac-tive unovershadowing effect observed inExperiments 1 and 2 was dependent upon the uno-

vershadowing stimulus, E, provoking a retrieval ofthe memory of the compound, EF, in which thetarget stimulus, F, previously occurred, it mightbe expected that the participants would show aninated judgement of the frequency of occurrenceof the compound, EF, relative to an equally pre-sented comparison compound.

Thus, Experiment 3a employed a retroactiveunovershadowing treatment as in Experiments 1and 2, but also required posttraining judgementsof the frequency with which different compounds

occurred. To evaluate whether subjects retrievedthe memory of the compound involved in retroactiveunovershadowing, Experiment 3a repeated the basicprocedure, in which the two compounds of interest(EF+ and GH+) occurred six times each, but in thecompany of other compounds, which occurred fromtwo to 10 times (seeTable 2), followed by a phase oftraining in which Ewas presented six times alone.After training, participants were asked not only tojudge how likely the target and control elements, Fand H, were to cause an allergic reaction, but also

how frequently the various compounds containingthem and other stimuli had occurred.

Method

ParticipantsA total of 16 undergraduate psychology students atYale University participated in the experiment for



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course credit. They were tested individually andhad no previous experience in similar research.

Materials and procedureThe materials and procedure were essentially thesame as those for the retroactive unovershadowingcondition of Experiment 1. As seen in Table 2,

the procedure of Phase 1 involved training withtwo reinforced compounds, EF+ and GH+, andone nonreinforced compound, MN-, which wereexperienced six times, as in Experiment 1, in thecompany of several other compounds that wereexperienced fewer or more times, AB+ (2 times),IJ (4 times), KL (8 times), and CD+ (10times), as well as two single stimuli, O+ and P,each presented three times. The second phase wasidentical to Experiment 1 with six trials of eachof E and M+. The most critical difference was

the addition of a

frequency judgement testinter-posed between training and the regular causal jud-

gement test. The instructions for the frequencyjudgement test were as follows: Now we wouldlike you to provide us with some additional infor-mation about what Mr. X ate during his allergytests. Mr. X did not have the chance to eat all of the

foods in equal combination with each other. Please,

indicate how often you observed Mr. X to have eatenthe following combinations. Then the picture of apair of foods appeared in the top centre of thescreen and the participants were asked to rateHow many times did Mr. X eat these foods together?The participant entered his or her rating by clickingover one number from 0 to 10 in an 11-point scale.

The participants were required to rate the com-pound EF (which was the target compound) andGH (which was the equally occurring comparison)as well as the compounds AB, IJ, KL, and CD, inrandom orders. Upon completion of the frequencyjudgement test, the participants received exactlythe same causal judgements test as that ofExperiment 1.

The experiment was conducted in four identicalreplications of four participants each. The four par-ticipants in each replication received the same fourbalanced food assignments of cues AP as inExperiment 1.

Statistical analysisThe unovershadowing effect was evaluated as inExperiments 1 and 2 by computing a cue compe-tition index based on the differential causalratings assigned by the participants to the target

Table 2. Designs of Experiments 3a, 3b, and 3c

Training Test

Experiment Phase 1 Phase 2 Frequency ratings Causal ratings

Experiment 3a EF + (6) GH+ (6) E (6) EF, GH, AB, IJ, MN,

KL, CD

F, FN, FP, H, HN,

HP, N, PRetroactive unovershadowing AB+

(2) O+

(3)P (3) IJ(4) M+

(6)

MN (6) KL(8)CD+ (10)

Experiment 3b E (6) EF + (6) GH+ (6) EF, GH, AB, IJ, MN,KL, CD

F, FN, FP, H, HN,HP, N, PProactive unovershadowing M+ (6) AB+(2) O+ (3)

P(3) IJ(4)MN(6) KL(8)

CD+ (10)

Experiment 3c EF + (6) GH+ (6) E (6) M+ (6) EF, GH, AB, CD, MN,OP, IJ, KL

F, H, B, D, N, PRetroactive & proactive

unovershadowingA (6) O+ (6)

MN (2) IJ (10)AB+ (6) CD+ (6)OP (2) KL (10)

Note:Letters AP represent different foods that could be followed (+)or not followed () by an allergic reaction in a hypotheticalpatient. The numbers in parentheses indicate the frequency of each trial type.



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and control cues, F and H, respectively, and stat-istically analysed by a one-sample t-test. In orderto examine whether the participants were sensitiveto the different frequencies with which the differentcompounds were presented during training, a trendanalysis was conducted on the judged frequencies of

occurrence of the control compounds that wereexperienced 2 (AB), 4 (IJ), 6 (GH), 8 (KL), and10 (CD) times. The frequency effect of specialinterest was evaluated through an inated fre-quency index, computed as the judged frequencyto compound EF minus the judged frequency tocompound GH, and was analysed by a one-samplet-test.

Results and discussionThe left-hand plot ofFigure 5 depicts the meancasual ratings to the target and control cues intesting. There was a retroactive unovershadowingeffect, as in Experiments 1 and 2, in the form ofgreater responding to the target than to thecontrol cue. This was conrmed by the observationthat the cue competition index was reliably greater

than zero (M= 36.875, SEM= 6.875), t(15)=5.364,p,.001 Cohensd= 2.780.

The important additional observations aredepicted in the right-hand plot of Figure 5. Asmay be seen, the participants were appropriatelysensitive to the frequency with which the com-

pounds had occurred. Specically, the participantsassigned a monotonically increasing judged fre-quency of occurrence to the control compounds,as their actual frequency increased from 2 to 10,which was conrmed by the reliability of thelinear trend, F(1, 12)= 74.983, p, .05. In con-trast, the compound in which the target cue wasincluded (EF) was judged to have occurred with agreater frequency than the equally experiencedcontrol compound, GH, and numerically greaterthan the next more frequently occurring control

compound. The inated frequency index was sig-nicantly different from zero (M= 1.250,SEM= 0.536), t(15)= 2.331, p= .034, Cohensd= 1.204.

These results appear to present a novel indi-cation of the retroactive inuence of the E- trainingon the memory of the previously experiencedEF+ compound. The compound, in addition to

Figure 5. The left-hand plot presents the mean causal ratings to the target and control cues during the causal judgement test of Experiment 3a.The right-hand plot presents the mean judged frequency of occurrence of target and control compounds as a function of their actual frequency ofoccurrence in Experiment 3a. Regarding statistical analyses, see the text for means and standard errors of the means of the cue competition andinated frequency indexes.



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containing a component, F, of increased causalvalue, appeared to have an inated frequency ofoccurrence. It is quite possible, however, that theinated judged frequency of EF was due to a con-ating of the remembered number of occurrencesof the compound and the subsequent occurrences

of the component, E. The participants may haveestimated how frequently food resembling E andEF occurred, not just EF. Experiment 3b wasdesigned to discriminate between these alternatives.

EXPERIMENT 3B

If the subjects in Experiment 3a judged the targetcompound EF to have occurred more frequentlythan the control compound GH, because they con-ated the number of EF+ and the number ofE occasions, one would expect the same error ofjudgement if the E occasions occurred prior tothe EF occasions, as well as after the EF occasions.Alternatively, if the subjects in Experiment 3ajudged the target compound, EF, to have occurredmore frequently, because the E occasions recalledthe previously experienced EF compound intomemory, a similar inated memory effect shouldbe precluded if EF is not experienced, and retrieva-ble, until after E is presented. To test these

alternatives, Experiment 3b was designed exactlylike Experiment 3a (seeTable 2), but to involve aproactive, rather than a retroactive, overshadowing,comparison, with E experience prior to that ofEF+.

Method

ParticipantsA total of 16 undergraduate psychology students atYale University participated in the experiment forcourse credit. They were tested individually andhad no previous experience in similar research.

Materials and procedureAll of the materials, procedure, and statisticalanalysis were identical to those of Experiment 3a,except that the two training phases involving E

and EF+were reversed, so as to emulate a proactiveunovershadowing condition (seeTable 2).


The left-hand plot ofFigure 6 depicts the mean

casual ratings to the target and control cues intesting. In agreement with Experiments 1 and 2,there was a substantial proactive unovershadowingeffect in the form of more responding to thetarget than to the control cue. Statistical compari-son showed again that the cue competition indexwas reliably different from zero (M= 24.375,SEM= 7.410), t(15)= 3.263, p= .005, Cohensd= 1.685.

The data from the frequency test depicted in theright-hand plot of Figure 6 indicate that, as in

Experiment 3a, the judged frequency of thecontrol compounds increased monotonically withtheir programmed frequency of occurrence, whichwas conrmed by a reliable linear trend, F(1,12)= 142.116,p, .05. Although there was some-what greater frequency judged to the EF compoundthan to the GH compound, unlike Experiment 3a,the inated frequency index did not differ signi-cantly from zero (M= 0.375, SEM= 0.427),t(15)= 0.878,p= .394, Cohensd= 0.453.

The nding of a reliable inated memory effect

in Experiment 3a, but not in Experiment 3b, isconsistent with the supposition that retroactiveunovershadowing and proactive unovershadowingdiffer in that the former, but not the latter, isaccompanied by memorial retrieval of the com-pound by its manipulated component.

EXPERIMENT 3C

Although the results of Experiments 3a and 3b are

congruent with the hypothesis of differentialmemory of the target compound in the retroactiveas compared with the proactive unovershadowingcondition, they would be more convincing if thedifferential frequency judgement were observedafter direct comparison of the proactive and retro-active conditions in the same experiment.Therefore, in Experiment 3c we examine the



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inated memory effect through a within-subjectsdesign involving both retroactive and proactiveunovershadowing conditions. The design of theexperiment is outlined in Table 2. As can beseen, the experiment is a within-subjects instantia-tion of Experiments 3a and 3b, so that for each par-ticipant the compound phase of retroactive

unovershadowing coexisted with the elementphase of proactive unovershadowing, and, sub-sequently, the element phase of retroactive unover-shadowing coexisted with the compound phase ofproactive unovershadowing. A further differencefrom Experiments 3a and 3b is that in thepresent experiment there were only two ller com-pounds to contrast numerically with the criticalcompounds, presented either 2 times (MN andOP, for the retroactive and proactive orders,respectively) or 10 times (IJ and KL, for the retro-

active and proactive orders, respectively).

Method

ParticipantsA total of 32 undergraduate psychology students atYale University participated in the experiment for

course credit. They were tested individually andhad no previous experience in similar research.

Materials and procedureAll of the materials, procedure, and statisticalanalysis were identical to those of Experiments

3a and 3b, except for the following. First, theexperiment is a within-subjects design, asdescribed above (see Table 2). Second, the orderof the test trials was partially counterbalancedacross participants to control the relative positionsof the compounds and components of comparativeinterest. Specically, in Subgroup 1 the order was:IJ, MN, EF, GH, KL, OP, AB, and CD in thefrequency judgement test and N, F, H, P, B,and D in the causal judgement test. Subgroup 2was identical to Subgroup 1 except that the

order of presentation of each target compoundand component (e.g., EF and F) in relationshipto its respective control (e.g., GH and H) wasreversed. In Subgroup 3 the respective orderswere: KL, OP, AB, CD, IJ, MN, EF, and GH,and P, B, D, N, F, and H. Subgroup 4 was iden-tical to Subgroup 3 except that the order of testingof each target compound and component in

Figure 6. The left-hand plot presents the mean causal ratings to the target and control cues during the causal judgement test of Experiment 3b.

The right-hand plot presents the mean judged frequency of occurrence of target and control compounds as a function of their actual frequency ofoccurrence in Experiment 3b. Regarding statistical analyses, see the text for means and standard errors of the means of the cue competition andinated frequency indexes.



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relationship to its control was reversed. Theseveral orders ensured that each target and itsrespective control were always tested in contiguoustrials and that the sequential position of the targetand control cues of the proactive and retroactiveorders was counterbalanced. Third, the causal jud-

gements test was simplied, so that target andcontrol cues were only tested alone. Since therewere four different food assignments (as inExperiments 3a and 3b) and four test orders,there were a total of 16 different participant con-ditions. The experiment was conducted in tworeplications of these conditions.


The left-hand plot ofFigure 7depicts the mean

casual ratings to the target and control cues intesting. In agreement with Experiments 3a and3b (as well as Experiments 1 and 2), there wasa clear proactive and retroactive unovershadow-ing effect in the form of more responding tothe target than to the control cue in eachcondition. The mean cue competition indexwas signicantly greater than zero in both

the retroactive (M= 36.563, SEM= 4.130),t(31)= 8.853, p, .001, Cohens d= 3.180, andproactive (M= 37.500, SEM= 3.045), t(31)=12.314, p, .001, Cohens d= 4.423, orders,with a 2 (order) 2 (replication) ANOVAshowing no reliable difference between the two,

F(1, 30), 1.The data from the frequency test depicted in

the right-hand plot of Figure 7 indicate that, asin Experiments 3a and 3b, the judged frequencyof the control compounds increased monotonicallywith their programmed frequency of occurrence inthe retroactive as well as in the proactive orders.More importantly, the target compound wasjudged with higher frequency than its control inthe retroactive order (which is consistent withExperiment 3a) but not in the proactive order.

ANOVA revealed that the inated frequencyindex was reliably greater in the retroactive casethan in the proactive case, F(1, 30)= 5.516,p= .031,2p= .147, with no reliable effect of repli-cation, F(1, 30)= 2.174, p= .151, 2p= .068, orOrder Replication interaction, F(1, 30), 1.Further analyses compared the judged frequencyof the target compounds from the retroactive

Figure 7. The left-hand plot presents the mean causal ratings to the target and control cues during the causal judgement test of Experiment 3c.The right-hand plot presents the mean judged frequency of occurrence of target and control compounds as a function of their actual frequency ofoccurrence in Experiment 3c. Regarding statistical analyses, see the text for means and standard errors of the means of the cue competition andinated frequency indexes.



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versus the proactive treatments across the 32 par-ticipants. In agreement with the differentialresults of the inated frequency indexes, thismeasure was also reliable (M= 0.81, SEM=0.278), t(31)= 2.919, p= .006, Cohens d=1.049, attesting to the greater judged frequency

of the target compound in the retroactive than inthe proactive orders.

The overall results of Experiments 3a, 3b, and3c provide reasonable evidence for an inatedmemory effectthat is more evident in associationwith a retroactive unovershadowing contingencythan with a similar proactive contingency. Thedata, to our knowledge, are the rst to make useof the inated memory evaluation in investigationof causal learning, but are congruent with thend-ings of Johnson et al. (1979,1977) in showing that

an inated memory of an item can occur when theitem may be assumed to be provoked in memoryby a retrieval cue (Experiments 3a and 3c), dis-tinguishable from other similar treatments thatdo not support such retrieval (Experiments 3band 3c). The observations of Experiment 3 addanother dimension to the ndings that distinguishretroactive and proactive cue competition effectson the basis of the importance of effectivewithin-compound associations (Dickinson &Burke,1996; Larkin et al., 1998; Melchers et al.,

2004, 2006; Mitchell et al., 2003; Vandorpeet al., 2007; Wasserman & Berglan, 1998;Wasserman & Castro, 2005). It needs to beacknowledged that there are other possible expla-nations of the inated memory effect observedin Experiment 3 that the employed designscannot rule out. For example, it can be arguedthat there was amore accuratejudgement of the fre-quency of the target compound in the proactivecondition than in the retroactive conditionbecause the frequency test occurred more immedi-

ately after the compound training and more separ-ated from the potentially confusing elementtraining. We did not see evidence of differentialaccuracy in the frequency test with the controland ller compounds that were differentially separ-ated from training, but this and other possibilitiesremain open to future research.

GENERAL DISCUSSION

The experiments that we have reported all demon-strated retroactive as well as proactive cue compe-tition effects. The notable contrast is that theretroactive cue competition effects were more

restricted and differentially associated with otherevidence of memorial processing than were therelated proactive cue competition effects.Experiments 1 and 2 showed that whereas proac-tive cue competition may be independently seenin both blocking and unovershadowing, retroactivecue competition was largely (if not solely) attribu-table to unovershadowing, and not to detectableblocking. Experiment 2 demonstrated that retroac-tive unovershadowing, as observed in Experiment1, was vulnerable to interference by a concurrent

memory task, whereas similar proactive unoversha-dowing was not detectably diminished by the sametask. Experiment 3 observed that an AX+/Asequence that produced retroactive unovershadow-ing, as in Experiments 1 and 2, also led subjects tooverestimate the frequency of AX occurrences,whereas an A/AX+ sequence that producedproactive unovershadowing did not demonstrablydo so. The severalndings hold a number of impli-cations for candidate theories of human causallearning.

The cue competition effects, such as blocking(Kamin, 1968) and release from overshadowing(Wagner, 1969), that were observed in Pavlovianconditioning importantly inspired modern theoriesof associative learning (e.g., Mackintosh, 1975;Pearce & Hall, 1980; Rescorla & Wagner, 1972;Wagner,1981). In turn, these models, by anticipat-ing that there might be similar cue competitioneffects in human causal learning, substantiallyencouraged investigation in this domain(Dickinson et al., 1984; Gluck & Bower, 1988;

Shanks & Dickinson,1987).The RescorlaWagner model exemplies theaforementioned theory type. It assumes that thetrial-by-trial increase in associative strength to anyconditioned stimulus (CS) is computed as V=(V), where Vis the aggregate associativestrength of all of the cues present on that trial, and



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and are learning rate parameters representingthe salience of the CS and the unconditionedstimulus (US), respectively. The rule made itunderstandable that increasing the associativestrength of A by reinforced A+ trials wouldincrease the V on subsequent AX+ trials and

thus diminish VXthat is, lead to blocking.Likewise, decreasing any associative strength thatA might have (by virtue of prior training or by gen-eralization from other stimuli) through nonrein-forced A trials would decrease the V onsubsequent AX+ trials and thus increase VXthat is, lead to unovershadowing.

The Sometimes Opponent Processes (SOP)model (Wagner,1981) deals with cue competitionin a more complex, but related, manner. It assumesthat stimulus presentation activates a sequence of

representative nodes, Al followed by A2, with therelationship that the A2 node recurrently inhibitsactivity in the A1 node, making it transiently lesssusceptible to activation by its normally initiatingstimulus. The learning assumption is that the tem-poral contiguity of CS and US can produce bothexcitatory and inhibitory CSUS associationsdepending on the overlapping nodal activities:Excitatory CSUS association is assumed to beproportional to the momentary product of the con-current A1CSand A1USactivity; inhibitory CSUS

association is assumed to be proportional to themomentary product of the concurrent A1CS andA2US activity. The consequence of an acquiredassociative tendency is subsequently to allowinitial A1 activity of the CS to provoke some A2activity in the US node, or to suppress other associ-ative activation of the A2 node of the US, depend-ing upon the sign and magnitude of the association.By these assumptions, blocking results from thefact that A+ training causes A to become capableof activating the A2 node of the US upon AX+

occasions, leading to diminished activation of theA1 node of the US and, thus, to both diminishedexcitatory learning as well as increased inhibitorylearning to X. By the same token, if A is renderedless excitatory by previous nonreinforcement, sub-sequent AX+ training should produce more excit-atory learning (and less inhibitory learning) to Xthan in situations in which A is not so pretreated.

These trial-by-trial associative models yield thestrong prediction, previously well documented(e.g., Chapman, 1991; Lovibond et al., 2003;Melchers et al., 2004,2006; Mitchell et al., 2006)and conrmed in the present studies, that cue com-petition effects should be greater following proac-

tive than following retroactive treatment.However, neither the RescorlaWagner modelnor SOP, as described, anticipates that the trainingof A alonefollowingthe training of AX+ will haveanyinuence on the tested response to X. The the-ories are designed to capture the facts of proactivecue competition, but do not anticipate the retroac-tive cue competition in human causal learning asobserved by Shanks (1985) among others, and asreported here.

Van Hamme and Wasserman (1994) and

Dickinson and Burke (1996) proposed modi-cations to the RescorlaWagner and the SOPmodels, respectively, that were calculated toaccount for the nding of retroactive cue compe-tition in human causal learning. The alterationsboth involved the supposition that on the occasionsof A training after AX+ training, a representationof the absentX stimulus that might be retrievedfrom memory would be decremented or incremen-ted in associative strength, opposite in direction tothe consequences for the A stimulus that was

present. As amended, both the modiedRescorlaWagner model and the modied SOPmodel predict some measure of retroactive cuecompetition, but, notably, the modied SOPmodel predicts less robust retroactive than proactivecue competition, due, specically, to retroactiveblocking being less robust, than retroactive unover-shadowing, as was the pattern observed inExperiments 1 and 2 (Larkin et al., 1998).Whether these modied models will prove moreuseful than their original versions will surely

depend on their abilities to cope as well withinthe domain of Pavlovian conditioning, as incoping with the facts of retroactive cue competitionin human causal learning. In the present context,the more immediate challenge is that, althoughthey can accommodate to various degrees the rela-tive amounts of proactive and retroactive blockingand overshadowing reported in Experiments 1



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and 2 (Larkin et al. 1998; Wasserman & Castro,2005), they do not provide a natural account ofthe distractor and inated memory effects reportedin Experiments 2 and 3.

The major alternative to such associative modelsare rule-based models in which the effective com-

putation is assumed to occur at the time of judge-ment, based upon the aggregate informationavailable at the time. The probabilistic contrastmodel proposed by Cheng and Novick (1990,1992) is a good example, addressed to cue compe-tition effects. The approach begins from theassumption that causal judgement is related to acomparison of the experienced probability of aneffect in the presence versus the absence of agiven candidate cause, or P (Jenkins & Ward,1965), but further species that causal judgement

is not thereby sufciently determined. In situationswith multiple possible causes, as in cue competitionexperiments, it is supposed that the effective causalstrength of a given cue depends on such a compari-son of the probability of the effect in the presenceversus absence of the target cause, but on occasionswhen any alternative cause is kept constant.According to this reasoning, the diminishedcausal judgement to X when AX+ occasions arein the context of additional A+ occasionsthatis, blockingis because there is diminished differ-

ence between the probability of the effect when X ispresent (i.e., in the AX trials) than when X isabsent, but A is also present, (i.e., A+ trials). Bythe same reasoning, the increased causal judgementto X when AX+ occasions are in the context ofadditional A occasionsthat is, unovershadow-ingis because there is increased differencebetween the probability of the effect on the AX+trials when X is present than on the comparisonA trials when X is absent.

Such a rule-based model, based upon the aggre-

gate information at the time of judgement, allowsfor retroactive as well as proactive cue competitioneffects, as frequently observed, and conrmed inthe present studies. However, the basic approach,as contained in the probabilistic contrast model,as described, anticipates that the training of Aalone, either before or after the training of AX+,will haveequalinuence on the tested response to

X. The approach well captures the fact of retroac-tive as well as proactive cue competition, but doesnot anticipate the pattern of differences betweenthe two. It is interesting to note that the sameevaluation may be made of the comparator theoryof Stout and Miller (2007), which explains cue

competition effects as a result of a comparison ofthe relative strength of the target stimulus withthe strength of the manipulated cue with which itis in compound. It predicts both proactive and ret-roactive performance effects, but no differencebetween the two.

Rule-based models, of course, need not berestricted to such simple calculation as emphasizedby the probabilistic contrast model (Cheng &Novick, 1990) that was designed to address thefact of cue competition, but have been widely ident-

ied with broader formulations of inferentialreasoning (e.g., Cheng, 1997; Waldmann &Holyoak, 1992) that embody a variety of causalmodels that people may have, including thenotion of hidden as well as observable variables(Luhmann & Ahn, 2011). Any such model isable to offer an account for the fact observed inExperiments 1 and 2, that unovershadowing wasmore demonstrable than blocking. Assume thatthe compound AX is followed by an effect (andthat potential causes do not interact). If one

additionally learns that A alone is also followedby an effect, it remains uncertain whether X alonewould also be followed by an effect; in contrast, ifone learns that A is not followed by an effect, itmay be better concluded that X would be followedby an effect.

Propositional theories of human causal learning(e.g., Mitchell, De Houwer, & Lovibond, 2009)are sufciently welcoming of additional supposi-tions about human learning and decision makingthat they can easily accommodate certain of the

results of Experiments 2, 3a, and 3c that mightappear less congenial to associative interpretation.It is common to assume that propositional reason-ing requires the availability of cognitive resourcesthat are under limited-capacity restraints. Reports(e.g., De Houwer & Beckers, 2003; Sternberg &McClelland, 2009; Waldmann & Walker, 2005)that cue competition effects can be interfered



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with by added task demands, have been taken asconsistent with this notion and the suppositionthat cue competition is, in fact, dependent uponpropositional reasoning. To follow this reasoning,in regard to the ndings of Experiment 2 (andrelated observations of Aiken et al., 2001) one

might still wish for rationalization of why retroac-tive cue competition, as seen in retroactive unover-shadowing, is more uniquely dependent on suchpropositional reasoning than is proactive cue com-petition, as seen in proactive blocking and proactiveunovershadowing.

There is a similarity in the invited propositionalinterpretations of Experiments 3a, 3b, and 3c.Scheduling A alone experience either followingAX+ training (Experiments 3a and 3c) or beforeAX+ training (Experiments 3b and 3c) produced

an unovershadowing effect, but only the formerwas accompanied by an inated judgement of thefrequency of the AX trials, in relationship to thefrequency of occurrence of other compounds. It ispossible that inferential reasoning contributed toboth proactive and retroactive unovershadowing,but the inated memory of AX that accompaniedthe retroactive unovershadowing is suggestive of afunctional importance of the retrieval of the AXmemory in the retroactive case but not in the proac-tive case.

If one is not a committed adherent to eitherassociative or propositional theory, one mightthink that the most obvious theoretical interpret-ation of the pattern of cue competition effectsobserved in the present experiments and relatedstudies would involve both processes. It is possiblethat both associative and propositional inuencesare at work, associative inuences being only effec-tive in producing proactive cue competition, andinferential reasoning effective in producing bothproactive and retroactive cue competition, but

more singularly so in the retroactive case. Thiswould lead to the expectation that cue competitionwould be (a) more robust in proactive than in retro-active instantiations, and (b) more evident in retro-active unovershadowing than in retroactiveblocking. It would further lead to the expectationthat retroactive unovershadowing would be (c)more interfered with by a secondary task than

would proactive unovershadowing, and (d) moreevidently associated with memorial retrieval of thecompound training.

If one takes a broader view of the determinantsof causal judgements, it is reasonable to assumethat some judgements may be based upon simple

associations, as might be described by such formu-lations as the RescorlaWagner model or SOP,while other causal judgements are based upon evi-dentiary searches and sophisticated inferentialreasoning quite beyond this. This is not a newthought, but was articulated well by Hume (1748/1910) who pointed out that whereas philosophers,when acting like philosophers, might followcareful rules of reasoning in making causal judge-ments, othersand philosophers much of thetimemake causal attributions based on the

simpler association of sense data. Nor is it anancient view. In more modern overview, associativeinuences are part of what Kahneman (2011)assumes to be included in a fast-respondingSystem 1, whereas inferential reasoning is a majordeterminant of a slower responding System 2.

A theoretical gambit proposed by Chapman(1991), and advanced by Melchers et al. (2004),and more recently explored by Ludvig, Mirian,Sutton, and Kehoe (2010), has been conceived asan extension of the RescorlaWagner model, but

should be recognized as a two-process formulationthat uses the error-correction rule to operate upontwo different sets of information. It assumes twopotential products of training experience. There isassociative learning, which is assumed to proceedin the trial-by-trial manner of the RescorlaWagner model. In addition, experienced trials areassumed to be stored as episodic memories thatcan be subsequently replayed to computational con-sequences. The robust proactive cue competition,as commonly seen, can be taken to be dominated

by the trial-by-trial associative learning. The morefragile retroactive cue competition can be assumedto reveal the added memorial computation. Forexample, according to this view, when A+or Ais experienced after AX+, there would not onlybe the trial-initiated associative learning, but alsothe potential for replay or rehearsal of somenumber of remembered trials of A+ or A in the



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context of remembered trials of AX+. The compu-tational consequence of any rehearsal of A priorto AX+ would presumably lead to a reduction inthe associative value of A upon the rehearsal ofAX+ and thus to an increase in the associativevalue of Xthat is, to retroactive unovershadowing

in relationship to a control compound without suchelement nonreinforcement. It is notable that by thismanner of account, retroactive blocking should beless anticipated than retroactive unovershadowing,since a decrease in the value ofXshould dependon the rehearsal of A+ driving the associativevalue of AX above what is supported byreinforcement.

This particular two-process approach wouldhave to be more fullyeshed out than it has been,to include the rules for what of an episode is

stored and retrieved from memoryfor example,whether it includes not only the stimulus eventsbut the V and behavioural responses at thetime. Likewise, decision must be made aboutwhat initiates retrieval and replay. For instance, itcould be assumed that the replay may simplyoccur because there is a periodic sampling of epi-sodes from memory (Ludvig et al., 2010; Ratcliff,1990), or because episodes are retrieved by anassociated cue (Chapman, 1991; Melchers et al.,2004). The fact that in Experiments 3a and 3c

there was an inated memory of the target com-pound (AB) but not of the equally experiencedcontrol compound (CD), favours the idea thatrehearsal of the AB compound was cued by thesubsequent presentations of A.

This replay reasoning is as accommodating asother invokings of a presumed vulnerability tocompeting task demands (e.g., De Houwer &Beckers, 2003; Le Pelley, Oakeshott, &McLaren, 2005). The results of Experiment 2,showing that a secondary memory task had more

of an interfering effect upon retroactive unoversha-dowing than upon proactive unovershadowing,could be taken as support for a two-processaccount in which relatively automatic associativeprocesses are held largely responsible for proactiveblocking and unovershadowing, whereas episodicmemory processing is required for retroactiveunovershadowing. Perhaps most in need of

specication is how the computations based uponthe trial-by-trial experienced episodes combinewith the computations based upon the replayedepisodes, to yield a summary causal judgement.But this would be equally true of any two-process account.

In presenting the SOP model, Wagner (1981)offered the characterization that it was a model ofautomatic memory processing that might be rela-tively sufcient to address phenomena ofPavlovian conditioning and habituation in inarticu-late animals, but avoided any assumptions aboutcontrolled processing, such as that presumed (e.g.,Shiffrin & Schneider, 1977) to be important inapproaching more complex issues of human learn-ing and performance. Studies of human causallearning have since provided a challenging testing

ground for the degree to which the containedassociative principles are more generalizable, orcan be made so with thoughtful changes, orrequire more fundamental supplementation.

Supplemental Material

Supplemental content (the full instructions thatwere given to the participants in each of the exper-iments) is available via the Supplemental tabon the articles online page (http://dx.doi.org/10.1080/17470218.2015.1014378).

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http://dx.doi.org/10.1080/17470218.2015.1014378http://dx.doi.org/10.1080/17470218.2015.1014378http://dx.doi.org/10.1080/17470218.2015.1014378http://dx.doi.org/10.1080/17470218.2015.1014378

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