Maddox (2001) Separating perceptual processes from decisional …wexler.free.fr/library/files/maddox...

Perception amp Psychophysics2001 63 (7) 1183-1200

An important goal of psychological inquiry is to under-stand how behavior is influenced by the environmentalstimulation and the task at hand Information about the en-vironment is obtained through the sensory systems andthe task at hand determines which information is relevantfor making a decision A detailed understanding of thiscomplex system requires knowledge of the interplay be-tween perceptual and decisional processes and thus requiresa theory that acknowledges their separate and unique in-fluences The importance of separating perceptual fromdecisional processes in simple tasks such as detection hasbeen well known since the early days of signal detectiontheory (Green amp Swets 1967) Unfortunately the impor-tance of this distinction has been less well understood inpredicting performance in more complex tasks such asidentification and categorization (however see Ashby ampLee 1991 see also Geisler amp Chou 1995 for an applica-tion to visual search) The most common approach is todownplay the importance of perceptual processes by es-sentially ignoring them or by making overly simplified as-sumptions such as assuming that each stimulus is repre-sented by a point in some multidimensional psychologicalspace (eg Nosofsky 1986) This provides an inadequatemodel of perceptual processing for real-world stimuli that

are characterized by noisy perceptual effects (Ashby ampLee 1993 Green amp Swets 1967) generally exaggeratingthe importance of decision processes while assuming(often implicitly) that perceptual processes remain un-changed Even when models that assume noisy perceptualeffects are utilized often the perceptual noise assumptionsare overly simplistic (eg equal uncorrelated perceptualnoise across dimensions and stimuli)

In certain situations perceptual processes and the re-sulting perceptual representation likely remain unchangedacross different types of tasks In these cases different tasksshould require different decision strategies while leavingthe perceptual representation unchanged In other casesthough the task at hand might alter the nature of the per-ceptual representation For example when only some as-pects of the environment (or stimulus) are relevant to solv-ing a particular problem it may be the case that perceptualprocessing is altered to fine-tune or sharpen the perceptualrepresentation along the relevant dimension Given thelarge amount of stimulation from the environment at anyone time and the limited capacity of our attention systemthis type of selective attention is likely commonplace

The overriding goal of the present study was to examinethe separate effects of perceptual and decisional processeson performance in two complex tasks identification andcategorization Identification and categorization were cho-sen because they are primary components of many behav-iors of all organisms and thus are of fundamental impor-tance Two specific hypotheses were of interest First arigorous test of the (often implicit) assumption that changesin task demand affect decisional processes while leavingthe perceptual representation unchanged was undertakenSecond the hypothesis that decisional selective attentiontasks (ie tasks that require the observer to place all weightin their decision on one aspect of the stimulus while ig-

1183 Copyright 2001 Psychonomic Society Inc

This research was supported in part by National Science FoundationGrant SBR-9796206 and NIH Grant R01 MH59196 The author thanksGreg Ashby Sergei Bogdanov Corey Bohil Leslie Cohen Randy DiehlJeffrey Dodd Wilson Geisler and Arthur Markman for discussions thatinfluenced this work and Greg Ashby Anne-Marie Bonnel RobertNosofsky and two anonymous reviewers for comments on an earlier ver-sion of this manuscript The author is especially grateful to Sergei Bog-danov for developing the computer programs used to test the observersCorrespondence should be addressed to W T Maddox Department ofPsychology Mezes Hall 330 Mail Code B3800 University of TexasAustin TX 78712 (e-mail maddoxpsyutexasedu)

Separating perceptual processes from decisionalprocesses in identification and categorization

W TODD MADDOXUniversity of Texas Austin Texas

Four observers completed perceptual matching identification and categorization tasks using separable-dimension stimuli A unified quantitative approach relating perceptual matching identifica-tion and categorization was proposed and tested The approach derives from general recognition the-ory (Ashby amp Townsend 1986) and provides a powerful method for quantifying the separate influencesof perceptual processes and decisional processes within and across tasks Good accounts of the iden-tification data were obtained from an initial perceptual representation derived from perceptual match-ing The same perceptual representation provided a good account of the categorization data exceptwhen selective attention to one stimulus dimension was required Selective attention altered the per-ceptual representation by decreasing the perceptual variance along the attended dimension Thesefindings suggest that a complete understanding of identification and categorization performance re-quires an understanding of perceptual and decisional processes Implications for other psychologicaltasks are discussed

1184 MADDOX

noring all other aspects of the stimulus Maddox amp Ashby1998) affect both decisional and perceptual processes wasexamined Selective attention problems of this sort areubiquitous in everyday life and thus demand a better un-derstanding To achieve these goals requires a theory thatmakes reasonable assumptions about the nature of the per-ceptual representation and that contains parameters asso-ciated with perceptual and decisional processes that areseparately identifiable General recognition theory (Ashbyamp Townsend 1986) a multidimensional generalization ofsignal detection theory provides such a theory

The next two (second and third) sections introducebriefly general recognition theory and review the relevantliterature The details of the theory can be found in numer-ous other articles (Ashby amp Lee 1991 Ashby amp Perrin1988 Ashby amp Townsend 1986) The fourth section intro-duces the experiment and details the method The fifthsection reports the results and theoretical analyses Thesixth section provides a summary and discussion

GENERAL RECOGNITION THEORY

Perceptual Representation AssumptionsGeneral recognition theory acknowledges that a funda-

mental characteristic of all perceptual systems is that re-peated presentations of the same stimulus yield differentperceptual effectsmdashthat is that perceptual noise exists (egAshby amp Lee 1993 Ashby amp Townsend 1986 Geisler1989 Green amp Swets 1967) General recognition theoryassumes that a single multidimensional stimulus can berepresented perceptually by a multivariate probability dis-tribution (Ashby amp Lee 1993) For a two-dimensionalstimulus a bivariate normal distribution is assumed to de-scribe the set of percepts A bivariate normal distributionis described by a mean and variance along each dimensionas well as a covariance term mx my s2

x s2y covxy where the

subscripts x and y denote dimensions x and y Figure 1adepicts hypothetical equal likelihood contours for fourstimuli constructed from the factorial combination of twolevels along two dimensions x and y With bivariate nor-mal distributions the equal likelihood contours are alwayscircular or elliptical In general recognition theory per-ceptual independence holds for a single stimulus if andonly if the perceptual effects for dimensions x and y arestatistically independent (see Ashby 1988 Ashby amp Mad-dox 1991 Ashby amp Townsend 1986 Perrin amp Ashby1991) With bivariate normal distributions perceptual in-dependence holds when the major and minor axes of thecontour are parallel to the coordinate axes (ie when thecovariance is zero) Perceptual independence holds for allfour distributions in Figure 1a A positive slope for themajor axis implies a positive perceptual dependence anda negative slope implies a negative perceptual depen-dence Perceptual separabilityholds when the distributionof percepts associated with one component is unaffectedby the level of the other component (Ashby amp Townsend1986 Maddox 1992) In Figure 1a dimension y is per-ceptually separable from dimension x but dimension x isnot perceptually separable from dimension y

Decision Process AssumptionsIn general recognition theory the experienced observer

learns to divide the perceptual space into response regionsand assigns a response to each region The partitions be-tween response regions are called decision bounds Oneach trial the observer determines the location of the per-ceptual effect and gives the response associated with thatregion of the perceptual space Decision bounds and the

Figure 1 (a) Hypothetical contours of equal likelihood for fourstimuli constructed from the factorial combination of two levelsalong two stimulus components (b) Hypothetical response re-gions and decisional separability bounds for the same four stim-uli (c) Hypothetical response regions and striatal units for thesame four stimuli

IDENTIFICATIONndashCATEGORIZATION 1185

resulting response regions can come in many forms (AshbyWaldron Lee amp Berkman 2001) Decision bounds thatare parallel to the coordinate axes are of particular interestbecause they result when the observer sets a criterion alongone stimulus dimension and ignores the other dimensionThis decision strategy is referred to as decisional separa-bility in general recognition theory and is generally the op-timal strategy in decisional selective attention tasks (Ashbyamp Townsend 1986 Maddox 1992) Hypothetical responseregions and decisional separability bounds for the fourstimuli in Figure 1a are displayed in Figure 1b Details ofthe response regions examined in this article will be reservedfor the Results and Theoretical Analyses section

REVIEW OF THE RELEVANT LITERATURE

Only a few studies in the literature have tested rigor-ously the hypothesis that changing task demands affectdecision processes while leaving perceptual processes un-changed Ashby and Lee (1991 see also Maddox amp Ashby1996) tested this hypothesis with data from an identifica-tion task and several categorization tasks They applied amodel derived from general recognition theory to theidentification confusions to estimate the perceptual repre-sentation Holding this perceptual representation fixedand allowing changes in the decision process across cate-gorization conditions provided a good quantitative accountof the categorization data Interestingly though they foundthat a perceptual representation that satisfied perceptualseparability provided a better account of the categorizationdata than did the perceptual representation estimated fromthe identification data Unfortunately Ashby and Lee(1991) did not examine the possibility that the perceptualrepresentation might be altered differently by differentcategorization decision rules They assumed that the per-ceptual representation was the same across all categoriza-tion conditions

Maddox and Bogdanov (2000) followed up on this workby investigating the possibility that decisional selective at-tention categorization problems alter both perceptual anddecisional processes whereas categorization problemsthat require attention to all stimulus dimensions (ie de-cisional integration tasks) alter only decisional processesThe possibility that decisional selective attention tasksmight have a unique influence on perceptual and deci-sional processes is suggested by the work of ShepardHovland and Jenkins (1961 Shepard amp Chang 1963) andNosofsky (1986) who found that the similarity relationsamong exemplars in a multidimensional scaling (MDS)psychological space were altered in a specific way in thedecisional selective attention conditions but not in the de-cisional integration conditions Unfortunately within theirtheoretical framework it is not possible to determine whetherthis selective attention effect is perceptual decisional orboth

To achieve their objective Maddox and Bogdanov (2000)had observers complete two tasks using the same set ofsimple line stimuli Instead of using an identification task

they used a matching task (described in detail in the Methodsection Alfonso-Reese 1996 1997) to derive an initial per-ceptual representation They then had observers completedecisional integration categorization conditions and a de-cisional selective attention categorization condition Mad-dox and Bogdanov used the perceptual representation derived from matching to predict performance across con-ditions They found support for a model that assumed thatthe decisional selective attention categorization conditionaltered both perceptual and decisional processes whereasthe decisional integration categorization conditions alteredonly decisional processes The model parameters indicatedthat decisional selective attention led to a decrease in per-ceptual variability along the decisionally attended dimen-sion The notion that selective attention can reduce percep-tual variability has a long history in signal detection theory(eg Braida amp Durlach 1972 Luce amp Green 1978Macmillan Goldberg amp Braida 1988 see also Bonnel ampHafter 1998)

The present research builds on the previous body of re-search in a number of ways Prior to Maddox and Bog-danov (2000) all studies that examined the identificationndashcategorization relationship used the identification data toderive an initial MDS psychological space (eg Nosof-sky 1986 1987 1989) or an initial perceptual representa-tion (eg Ashby amp Lee 1991 Maddox amp Ashby 1996)This initial psychological space or perceptual representa-tion was then used to predict categorization performanceTo my knowledge no attempt has been made previouslyto predict identification performance from an initial psy-chological space or perceptual representation estimatedfrom another task The present study used general recog-nition theory to predict both identification and catego-rization performance from a perceptual representation de-rived from the matching task Specifically the hypothesisthat the perceptual representation is identical in both iden-tification and categorization was tested In addition gen-eral recognition theory was used to predict categorizationperformance from a perceptual representation derived fromthe identification data Of particular interest was a com-parison of the matching task perceptual representationwith the identification task perceptual representation in theirability to account for categorization performance The hy-pothesis that decisional selective attention tasks alter thedecision strategy and reduce the perceptual variabilityalong the attended dimension was tested Finally a prelim-inary investigation of possible perceptual representationand decision process changes that might occur with cate-gorization training was undertaken by partitioning the cat-egorization data into two phases early and later training

PERCEPTUAL MATCHING IDENTIFICATION AND

CATEGORIZATION EXPERIMENT

In the present experiment 4 observers completed a largenumber of sessions in each of three tasks perceptual match-ing identification and categorization The same stimulus

1186 MADDOX

ensemble was used in each task The stimuli were 18 lines(see Figure 2a) that varied in length and orientation The4 observers first completed ten 360-trial sessions of per-ceptual matching followed by twelve 480-trial sessions ofidentification The categorization task followed and con-sisted of four separate conditions The 4 observers com-pleted fifteen 800-trial sessions in each of four catego-rization conditions Thus each observer completed a totalof 72 sessions and 57360 trials in the complete experi-ment Two decisional selective attention categorization

conditions were included one with line length relevant(DSAL Figure 2b) and the other with line orientation rel-evant (DSAO Figure 2c) Two decisional integration con-ditions were included One required a linear integrationstrategy (LI Figure 2d) and the other required a nonlin-ear integration strategy (NLI Figure 2e)

The approach was to use the perceptual matching datato estimate an initial perceptual representation The result-ing perceptual representation was then held fixed in an at-tempt to model identification and categorization Specifi-

Figure 2 (a) Stimulus ensemble and numbering scheme for the 18 stimuli used in all tasksStimulus structure and stimulus-to-category assignments for the (b) decisional selective atten-tion to length (DSAL) (c) decisional selective attention to orientation (DSAO) (d) linear inte-gration (LI) and (e) nonlinear integration (NLI) categorization conditions


cally both the identification response frequencies (ieconfusion matrix entries) and the categorization responsefrequencies for each stimulus were predicted quantita-tively from the matching task perceptual representationIn categorization a test of the hypothesis that decisionalselective attention reduced the perceptual variability alongthe attended dimension relative to the perceptual vari-ability along the unattended dimension was undertakenSeveral hypotheses regarding the nature of the responseregions were also examined All analyses were performedat the level of the individual observer Data were not col-lapsed across observers Maddox (1999 see also Maddoxamp Ashby 1998) showed that averaging often alters thestructure of the data in such a way that the correct modelof individual observer performance might provide a pooraccount of the aggregate data (see also Ashby Maddox ampLee 1994 Estes 1956 Smith amp Minda 1998)

MethodObservers

Four observers were solicited from the University of Texas com-munity and were paid for their participation All observers had priorexperience with similar experiments and stimuli All observers had2020 vision or vision corrected to 2020 The same 4 observers par-ticipated in all three tasks

StimuliThe stimulus set consisted of 18 lines These stimuli represent a

subset taken from a larger group of 36 stimuli that were constructedfrom six levels of line length and six levels of line orientation Thesix line lengths were 140 144 148 152 156 and 160 pixels Thesix line orientations were 377 427 477 527 577 and 627 radi-ans The 18 stimuli and a numbering scheme are depicted in Fig-ure 2a Previous research suggests that length and orientation areseparable (eg Garner 1974 Garner amp Felfoldy 1970 Shepard1964 however see Ashby amp Lee 1991 Ashby amp Maddox 1990and Maddox 1992) The observers were seated approximately 40 infrom the computer screen and each stimulus subtended a visualangle of approximately 1deg The stimuli were computer-generated andwere displayed on a 21-in monitor with 1360 3 1024 resolution ina dimly lit room Each line was presented in white on a black back-ground To minimize line jaggedness Alfonso-Reesersquos (1997) anti-aliasing routine developed for use with Brainardrsquos (1997) Psycho-physics Toolbox was applied

ProcedureMatching task The first session was considered as practice and

was excluded from further analyses On each trial one of the 18stimuli was selected at random with equal probability This servedas the standard stimulus on that trial The center of the standard stim-ulus was presented 150 pixels to the left of the horizontal center ofthe computer screen The vertical position of the center of the stan-dard stimulus was normally distributed with a mean of zero and astandard deviation of 55 pixels The center of the comparison stim-ulus was presented 150 pixels to the right of the horizontal center ofthe computer screen and the vertical center was normally distrib-uted with a mean of zero and a standard deviation of 55 pixels Thestimuli were offset vertically to minimize the possibility that the ob-server would use a matching strategy based solely on the endpointsof the stimuli At the start of each trial the comparison stimulus wasa dot The observerrsquos task was to adjust the length and orientation ofthe comparison stimulus until it was perceived (judged) to ldquomatchrdquothe standard stimulus The mouse controlled the adjustments Once

the observer perceived the comparison and standard stimuli tomatch he or she pressed the mouse button The observer then presseda button to ldquoacceptrdquo the match or to ldquorejectrdquo the match and beginagain The observers were instructed ldquoto be as accurate as possiblerdquoEach session consisted of four blocks of 90 trials with breaks be-tween each block

Identification task The first session was considered as practiceand was excluded from further analyses On each trial one of the 18stimuli was selected at random with equal probability The stimuluswas presented centered on the computer monitor for 100 msec fol-lowed by a pattern mask and then a 6 3 6 checkerboard responsegrid The response grid was constructed to mimic the stimulus spacewith 18 valid locations one for each stimulus and 18 invalid loca-tions that were blacked out To respond the observer moved themouse to one of the 18 valid locations and clicked on the mouse but-ton The selected location was then filled with a gray square and thelocation associated with the correct response was brightened to pro-vide the observer with corrective feedback Corrective feedback waspresented for 500 msec followed by a 1000-msec blank screen andinitiation of the next trial

Categorization task Each observer completed four separate cat-egorization conditions The first session of each categorization con-dition was considered as practice and was excluded from further analy-ses The stimulus-to-category response mappings for the DSALDSAO LI and NLI conditions are depicted in Figures 2b 2c 2d and2e respectively The condition orders were as follows for Ob-server 1 NLI LI DSAO DSAL for Observer 2 LI NLI DSAODSAL for Observer 3 NLI LI DSAL DSAO and for Observer 4LI NLI DSAL DSAO The trial-by-trial procedure was identical tothat for the identification experiment except that the checkerboardresponse display was removed and the observers responded bypressing one of two keys on the keyboard In addition the checker-board feedback display was removed and the correct category ldquoArdquoor ldquoBrdquo was displayed on the screen

Results and Theoretical Analyses

Presentation of the results and theoretical analyses is or-ganized as follows First the matching data are summa-rized and are used to derive an initial perceptual represen-tation Second the matching task perceptual representationis used along with general recognition theory to predictquantitatively identification performance Third the match-ing task perceptual representation is used along with gen-eral recognition theory to predict quantitatively early andlater training categorization performance The aim was todetermine whether the matching task perceptual repre-sentation provides a good account of both identificationand categorization performance A second aim was to testthe hypothesis that decisional selective attention tasks leadto changes in both the perceptual representation and theresponse regions whereas decisional integration taskslead to changes only in the response regions Finally iden-tification and categorization are compared directly by de-riving an initial perceptual representation from identifica-tion and then using the resulting representation to predictcategorization performance

Matching ExperimentA perceptual representation was derived separately for

each observer by computing the sample orientation andlength means (mean vector entries) and the sample orienta-

1188 MADDOX

tion and length variances and the sample lengthndashorientationcovariance (covariance matrix entries) Because two stim-uli were presented simultaneously in the matching taskthese variance and covariance estimates represent the sumof the standard and comparison stimulus variances and co-variances (Alfonso-Reese 1997 Maddox amp Bogdanov2000) Assuming statistical independence between thepercepts of the standard and comparison stimuli eachentry in the covariance matrix was divided by two1 Eachmean vector and covariance matrix provided an estimateof the population parameters for each bivariate normaldistribution of perceptual effects Because length and ori-entation are measured in different units a method wasneeded to equate these two measures To facilitate thisgoal all orientation values (measured in radians) weretransformed via a linear transformation with slope = 80and intercept = 10984

Figures 3andash3d display the 18 equal likelihood contours(for likelihood = 003) for Observers 1ndash4 respectivelySeveral aspects of these plots are of interest First the rep-resentations are nearly perceptually separable althoughsome violations exist Second the contours are generallyperpendicular to the coordinate axis this result suggestsperceptual independence Third variability in perceivedlength showed a general (although not always monotonic)

increase as physical length increased Fourth the orienta-tion dimension appears more discriminable than the lengthdimension As we will see shortly this resulted in betterperformance in the DSAO condition than in the DSALcondition Finally notice that the resulting perceptual rep-resentations are similar across observers The similaritiesamong the equal likelihood contours and to those from pre-vious research (eg Ashby amp Lee 1991 Maddox amp Bog-danov 2000) suggest that the matching task provided a rea-sonable approximation of the true perceptual distributions

It is important to note that these analyses provide onlya rough estimate of perceptual noise These analyses ig-nored the possibility that there was noise in the decisionprocess (termed criterial noise) Criterial noise was min-imized by (1) using highly trained observers (2) present-ing the stimuli simultaneously (3) using high-contrast dis-plays and (4) allowing the observer unlimited time toperform each trial However there was probably some cri-terial noise that is not being accounted for Even so oneadvantage of estimating the perceptual representationfrom one task (such as the matching task) and then usingthat representation to predict performance in another task(such as identification or categorization) is that any changesin perceptual and criterial noise across tasks can be esti-mated While it would be best if ldquotruerdquo perceptual noise

Figure 3 Equal likelihood contours that describe the perceptual representation de-rived from the matching task for (a) Observer 1 (b) Observer 2 (c) Observer 3 and(d) Observer 4


estimates could be garnered from the matching task thismultiple-task approach should allow one to adequatelytease apart these two sources of noise Of course thestrongest test of the claim that the matching task yields rea-sonable estimates of the perceptual representation will comefrom actually applying this representation to the identifi-cation and categorization data

Predicting Identification From Perceptual Matching

Overall identification accuracies were 373 233222 and 349 for Observers 1 2 3 and 4 respec-tively The models were fit to the data using an iterativesearch routine that minimized the sum of the squared er-rors between the predicted and observed frequencies foreach of the 324 (18 3 18) cells in the confusion matrix2Several of the models have a nested structure and so it ispossible to test whether the extra parameters of a moregeneral models lead to a significant improvement in fitover the more restricted model Let SSEr and SSEg denotethe sum of squared errors for the restricted and more gen-eral models respectively In addition let dfr and dfg de-note the degrees of freedom for these models Then underthe null hypothesis that the restricted model is the correctmodel the statistic

has an approximately F distribution with dfr dfg degreesof freedom in the numerator and dfg degrees of freedom inthe denominator (eg Khuri amp Cornell 1987)3

Perceptual representation assumption The percep-tual representation derived from the matching task was as-sumed to be the correct perceptual representation for iden-tification with one caveat Recall that during the perceptualmatching task the stimulus exposure duration was unlim-ited whereas during identification the stimulus exposureduration was 100 msec Thus the observer could obtainmore perceptual information on each trial during the match-ing task resulting in less perceptual variability (Green ampSwets 1967 Luce 1986 Nosofsky 1983) In addition thedecision problem is different in the two tasks which willlikely lead to differences in criterial noise Although per-ceptual and criterial noise are nonidentifiable in matchingand identification it was important to accommodatechanges across these two tasks Following Maddox andBogdanov (2000 see also Maddox amp Ashby 1996) theperceptual noise estimates from the matching tasks werescaled by adding a fixed constant to each of the 18 lengthvariances and by adding a fixed constant to each of the 18orientation variances These constants were assumed to pro-vide an estimate of the increase in perceptual noise andthe change in the magnitude of criterial noise in identifi-cation The value of the two constants was estimated fromthe identification data requiring two free parameters No-tice that although the perceptual noise was allowed to bedifferent across matching and identification the ldquoglobalrdquo

structure of the perceptual representation derived frommatching was held fixed in identification Specificallythe perceptual means and perceptual correlations were un-changed and the overall relations among perceptual noisevalues remained constant This is referred to as the match-ing perceptual representation

Response region assumptions Response regions canbe constructed in a number of ways (Ashby et al 2001)For example the decision bounds could satisfy decisionalseparability or be linear or quadratic in form To imple-ment the model some assumptions need to be made aboutthe nature of the response regions Ashby et al offered aneuropsychological theory of this process as applied toidentification The anatomical details and empirical sup-port for the theory are provided in other articles (AshbyAlfonso-Reese Turken amp Waldron 1998 Ashby amp Wal-dron 1999 Ashby et al 2001) In short visual stimuli arerepresented perceptually in higher level visual areas suchas inferotemporal cortex (IT) Since as many as 10000cells in visual cortex project to the same cell in the stria-tum (Wilson 1995) it is assumed that a low-resolution mapof the perceptual space is represented among the striatalunits As the observer gains experience with the task eachunit becomes associated with a particular response Oneach trial the observer determines which unit is closest tothe perceptual effect and gives the associated responseNotice that this is equivalent to minimum distance classi-fication (Ashby amp Maddox 1993) This is referred to asthe striatal pattern classifier (SPC) Hypothetical responseregions and units for the four stimuli in Figure 1a are dis-played in Figure 1c Regardless of whether one accepts theneuropsychological underpinnings of the SPC it has beenfound to provide a good computational model of the ob-serverrsquos response regions in identification

Two versions of the SPC were applied to the data Bothassumed that a single striatal unit was associated witheach stimulus The first SPC(fixed) assumed that theunits corresponded to the perceptual means and requiredno free parameters The second SPC(free) assumed thatthe units were free parameters and required that the loca-tion of each be estimated from the data (36 parameterstotal)

The number of free parameters SSE and percent ofvariance accounted for by each model for each observerare presented in Table 1 For now ignore the rightmostcolumns headed ldquoID Perceptual Representationrdquo Recallthat the models allowed for differences in perceptual andcriterial noise across matching and identification by esti-mating two additive scalars An F test was conducted todetermine whether the addition of these two parameters pro-vided a significant improvement in fit In all cases allow-ing for differences in perceptual and criterial noise acrossmatching and identification provided a significant im-provement in fit [Fs(2304) = 119073 42171 61269 and69869 for Observers 1 2 3 and 4 respectively ps lt0001] As predicted the parameter estimates suggestedthat there was an increase in perceptual and criterial noise

FSSE SSE df df

SSE dfobs

r g r g

g g

=- -( ) ( )

1190 MADDOX

from the matching to the identification task An F test wasalso conducted to determine whether the additional freeparameters of the SPC(free) model provided a significantimprovement in fit over the SPC(fixed) model For all 4observers the SPC(free) model provided a significant im-provement in fit [Fs(36268) = 2365 4628 1874 and3192 for Observers 1 2 3 and 4 respectively ps lt0001] This finding mirrors that of Ashby et al (2001)Notice that the SSE improvement was quite large rangingfrom threefold to sevenfold In addition the improvementin percent of variance accounted for was large ranging from5 to 45

The units and associated response regions from theSPC(free) model for each observer are displayed in Figure 4Scatterplots of the observed confusion matrix frequenciesagainst the predicted confusion matrix frequencies for thesame model for each observer are shown in Figure 5

Brief summary The analyses presented in this sectionrepresent an attempt to predict quantitatively identifica-tion confusions from an initial perceptual representationestimated from the perceptual matching task along withreasonable assumptions regarding the response regions Agood description of the data was provided by a model thatassumed that (1) the ldquoglobalrdquo structure of the perceptual

Figure 4 Response regions and units from the SPC(free) model of the decisionprocess derived from a fit of the matching task perceptual representation to theidentification data for (a) Observer 1 (b) Observer 2 (c) Observer 3 and (d) Ob-server 4

Table 1 Goodness of Fit (SSE) and Percent of Variance ( Var) Accounted for by Several General

Recognition Theory Models as Applied to the Identification Confusion Matrices

Perceptual Representation and Response Region Assumptions

Matching ID

SPC(fixed) SPC(free) SPC(fixed) SPC(free)

Observer SSE Var SSE Var SSE Var SSE Var

1 38853 8705 9302 9674 17566 9387 4413 98522 110334 4721 15289 9166 41780 7863 8881 95173 42077 7514 11961 9150 13943 9032 4691 96664 56776 8037 10738 9613 22416 9231 4952 9832

NotemdashSPC striatal pattern classifier For matching task perceptual representation the numbers of parameters were 2 and 38for SPC(fixed) and SPC(free) respectively For ID perceptual representation the numbers of parameters were 88 and 120 forSPC(fixed) and SPC(free) respectively


representation remained unchanged across tasks exceptfor a global increase in perceptual noise and (2) the re-sponse regions were characterized by the SPC This fairlysimple model accounted (on average) for 94 of the vari-ance in the data

Predicting Categorization From Perceptual Matching

Accuracy rates The accuracy rates for the DSALDSAO LI and NLI conditions for each observer are pre-sented in Table 2 In an attempt to provide a preliminaryexamination of categorization learning the categorizationdata were divided into two phases early learning (Ses-sions 2ndash8) and late learning (Sessions 9ndash15) The resultscan be summarized as follows First performance gener-

ally improved with learning Second performance waspoorest in the NLI condition Finally DSAO performancewas consistently better than DSAL performance Thisfinding is interesting because it is predicted from thematching task perceptual representation (see Figure 3)Recall that the levels of orientation were more discrim-inable than the levels of length for all 4 observers

Model-based analyses The data to be modeled werethe observed response frequencies (for Categories A andB) for each of the 18 stimuli in each of four categorizationconditions resulting in 72 degrees of freedom in the dataThe technical difficulties that precluded the use of maxi-mum likelihood parameter estimation in identification arenot present in the present categorization conditions Thusthe model parameters were estimated using maximum

Figure 5 Scatterplot of the observed and predicted identification frequencies from the identification model that assumed thematching task perceptual representation and the SPC(free) response regions for (a) Observer 1 (b) Observer 2 (c) Observer 3and (d) Observer 4

1192 MADDOX

likelihood procedures (Ashby 1992b Wickens 1982)and the goodness-of-fit statistic was

AIC = 2r ndash 2lnL

where r is the number of free parameters and L is the like-lihood of the model given the data from the four catego-rization conditions (Akaike 1974 Takane amp Shibayama1992) The AIC statistic penalizes a model for extra freeparameters in such a way that the smaller the AIC thecloser a model is to the ldquotrue modelrdquo regardless of the num-ber of free parameters Thus to find the best model amonga given set of competitors one simply computes an AIC

value for each model and chooses the model associatedwith the smallest AIC value

Perceptual representation assumptions Two per-ceptual representation assumptions were tested The firstassumed that the initial perceptual representation esti-mated from the matching task is the correct perceptualrepresentation for categorization and that this perceptualrepresentation is unaffected by different categorizationdecision rulesmdashthat is that there is no effect of differentcategorization decision rules on the perceptual represen-tation The model does allow for the possibility of greaterperceptual noise in categorization by estimating the lengthand orientation scalars that were described earlier This isreferred to as the categorization condition invariance hy-pothesis because the perceptual representation is assumedto be invariant across categorization conditions (Maddoxamp Bogdanov 2000)

The second tested the hypothesis that (1) decisional se-lective attention conditions alter the perceptual represen-tation by reducing the perceptual variance along the rele-vant dimension relative to the perceptual variance alongthe irrelevant dimension and (2) decisional integration con-ditions do not alter the perceptual representation To in-stantiate this hypothesis two additive scalars were appliedto the perceptual noise estimates only from the data fromthe two decisional selective attention conditions Specifi-cally one scalar was applied to the relevant dimension (iethe length perceptual variance in the DSAL condition andthe orientation perceptual variance in the DSAO condi-tion) and the other was applied to the irrelevant dimen-sion (ie the orientation perceptual variance in the DSALcondition and the length perceptual variance in the DSAOcondition) This is referred to as the decisional integrationdecisional selective attention hypothesis (Maddox amp Bog-danov 2000) If this hypothesis is correct then the scalaralong the relevant dimension should be smaller in magni-

Table 3 Goodness of Fit (AIC) and Percent of Variance ( Var) Accounted for by Several General Recognition

Theory Models as Applied to the Early and Late Training Phases of Categorization Performance

Matching ID

CI DIDSA CI DIDSA

Training Phase AIC Var AIC Var AIC Var AIC Var

Observer 1Early 1024 9457 876 9574 1050 9461 924 9563Late 1432 9156 1026 9474 1354 9261 1006 9490

Observer 2

Early 676 9682 636 9753 694 9637 648 9719Late 648 9748 612 9784 740 9559 724 9590

Observer 3

Early 760 9870 638 9900 1074 9724 1008 9752Late 594 9934 548 9952 1072 9766 1060 9773

Observer 4

Early 740 9825 690 9852 926 9706 854 9741Late 712 9843 686 9852 954 9682 886 9720

NotemdashCI categorization condition invariance DIDSA decisional integrationdecisional selective attention The numbers of parameters were 19 and 21 for CI and DIDSA respectively

Table 2 Accuracy Rates for Each Categorization Condition

Categorization Condition

Training Phase DSAL DSAO LI NLI

Observer 1Early 719 769 754 689Late 747 810 766 696




AverageEarly 765 816 787 670Late 782 827 784 684

NotemdashDSAL decisional selective attention to length DSAO deci-sional selective attention to orientation LI linear integration NLI non-linear integration


tude than the scalar along the irrelevant dimension Be-cause these scalars are assumed to measure perceptualprocesses it is imperative that one obtain a separate andunique estimate of criterial noise A series of decision boundmodels derived from general recognition theory has beendeveloped that allows one to estimate separately the effectsof perceptual and criterial noise (for details see Ashby1992a and Maddox amp Ashby 1993)

Response region assumptions Decision bound mod-els assume that there will be trial-by-trial fluctuations inthe memory for the location of the decision bounds andin many cases this criterial noise is identifiable Althoughthe decision bound could take any mathematical formmost applications of the model have assumed either linearor quadratic decision bounds In many cases the responseregions predicted by decision bound models are identicalor are very similar to the response regions predicted by theSPC For example the SPC with one unit assigned to eachcategory is mathematically equivalent to a linear decisionbound model (Ashby amp Waldron 1999 Ashby et al 2001)In addition with only a few units assigned to each cate-gory the SPC can approximate a wide range of quadraticdecision bounds

Two sets of response region assumptions were exam-ined The first assumed that linear decision bounds wereused in the two decisional selective attention conditions(DSAL and DSAO) and that quadratic decision boundswere used in the two dimensional integration conditions(LI and NLI) Each linear bound required that a slope andintercept be estimated and each quadratic decision boundrequired that five quadratic equation coefficients be esti-mated for a total of 14 decision bound parameters In ad-dition three criterial noise parameters were estimated onefor the NLI condition one for the LI condition and a sin-gle criterial noise parameter was estimated simultaneouslyfor both DSAL and DSAO conditions The criterial noiseparameter had to be ldquoyokedrdquo across the two DSA condi-

tions to make it identifiable from perceptual noise Thesecond assumed that quadratic decision bounds were usedin all four conditions This did not lead to a significant im-provement in fit and will not be discussed further

The number of free parameters AIC and percent of vari-ance accounted for by the categorization condition invari-ance and decisional integrationdecisional selective atten-tion models are presented in the two leftmost columns ofTable 3 The decisional integrationdecisional selective at-tention model was superior to the categorization conditioninvariance model for all 4 observers during early and latelearning This replicates the finding of Maddox and Bog-danov (2000) but extends it in two ways First Maddoxand Bogdanov examined a decisional selective attentionto length condition whereas the present study examined a decisional selective attention to length and decisional se-lective attention to orientation conditions Second the present study provided a preliminary investigation of thedecisional selective attention effect on the perceptual rep-resentation across early and late training which will bediscussed shortly Importantly the fit of the model was quitegood with the percent of variance accounted for rangingfrom 95 to 99 during both early and late learning Thusit appears that the matching task perceptual representationprovides a good method for deriving an initial perceptualrepresentation for both identification and categorization

Figures 6 and 7 display scatterplots of the observed andpredicted categorization probabilities from the decisionalintegrationdecisional selective attention model for eachstimulus by condition and observer for early and late train-ing respectively

The decisional integrationdecisional selective atten-tion model assumed that decisional selective attention re-duces the perceptual variance along the decisionally relevantdimension relative to the decisionally irrelevant dimen-sion Table 4 displays the perceptual noise scalar valuesfor the relevant and irrelevant dimensions by training phase(early vs late) for each observer In support of the hypothe-sis the scalar along the relevant dimension was alwayssmaller than the scalar along the irrelevant dimension ex-cept for Observer 3 during early learning One might rea-sonably postulate that the magnitude of this effect wouldincrease with trainingmdashthat is the difference between therelevant and irrelevant scalar values might increase withtraining This pattern held for Observers 1 2 and 3 but itdid not hold for Observer 4

The model assumed also that decisional selective at-tention categorization problems are solved by applyinglinear decision bounds Given the need for decisional se-lective attention the linear decision bounds should benearly orthogonal to the relevant dimension axis Table 5displays the slope of the linear bound for the DSAL andDSAO conditions separately for each training phase byobserver In the DSAL condition a zero slope implies per-fect decisional selective attention As the absolute value ofthe slope approaches zero decisional selective attentionimproves In the DSAO condition an infinite slope im-plies perfect decisional selective attention As the absolute

Table 4 Perceptual Noise Scalar Values Along the Relevant and

Irrelevant Dimension for the Decisional IntegrationDecisionalSelective Attention Model Assuming the Matching Task

Perceptual Representation

Dimension

Training Phase Relevant IrrelevantObserver 1

Early 1291 1801Late 550 3348

Observer 2Early 1546 1869Late 777 5217



1194 MADDOX

value of the slope approaches infinity decisional selectiveattention improves A slope of 1 implies equal decisionalattention to both dimensions Two results stand out Firstin every case more decisional selective attention is beingpaid to the relevant dimension In other words the ab-solute value of the DSAL slopes are all less than 1 and theabsolute value of the DSAO slopes are all greater than 1

Second there was general support for the hypothesis thatthe magnitude of decisional selective attention improvedwith training Observers 1 2 and 3 showed better deci-sional selective attention late in training for both DSALand DSAO categorization conditions Observer 4 showedthe same pattern but only for the DSAO condition Thelearning effects are clearly preliminary and need to be fol-

Figure 6 Scatterplot of the observed and predicted early training categorization probabilities from the decisional integra-tiondecisional selective attention model assuming the matching task perceptual representation for (a) Observer 1 (b) Observer 2(c) Observer 3 and (d) Observer 4


lowed up with future studies Even so they are interestingand suggest that experience has consistent and quantifi-able effects on perceptual and decisional processes

Brief summary The analyses presented in this sectionrepresent an attempt to predict quantitatively the data froma number of categorization conditions from an initial per-ceptual representation derived from perceptual matching

data The analyses suggested that decisional selective at-tention categorization problems reduce the perceptualvariance along the relevant dimension relative to the per-ceptual variance along the irrelevant dimension This modelprovided a good account of the data accounting for 97of the variance in the data on average In addition themodel suggested that experience had some interesting ef-

Figure 7 Scatterplot of the observed and predicted late training categorization probabilities from the decisional integrationdecisional selective attention model assuming the matching task perceptual representation for (a) Observer 1 (b) Observer 2(c) Observer 3 and (d) Observer 4

1196 MADDOX

fects on perceptual and decisional processes In particularas the observer gained experience with the task the mag-nitude of the perceptual variance reduction and decisionalselective attention generally increased

Predicting Categorization From IdentificationThe previous two sections outlined attempts to predict

identification and categorization from an initial percep-tual representation estimated from the matching task Asan additional test of the validity of the matching task as amethod for estimating the perceptual representation andto more fully examine the identificationndashcategorizationrelationship in this section an attempt is made to predictquantitatively categorization performance from a percep-tual representation estimated from identification

Modeling identification We begin by deriving an ini-tial perceptual representation from identification Becausethe goal was to derive the best perceptual representationwe fit a version of general recognition theory that allowedall of the perceptual distribution parameters to be freelyestimated This required 36 perceptual distribution meanparameters 36 perceptual variance parameters and 18 per-ceptual covariance parameters This is referred to as theidentification perceptual representation The SPC(fixed)and SPC(free) decision process models were examinedThe number of parameters SSE and percent of varianceaccounted for are displayed in the two rightmost columnsof Table 1 For all 4 observers the SPC(free) provided a sig-nificant improvement in fit over the SPC(fixed) [F(32186)=1732 2153 1146 and 2050 for Observers 1 2 3 and4 respectively ps lt 00001] Notice that the SSE im-provement was quite large ranging from threefold to five-fold In addition the improvement in percent of varianceaccounted for was large ranging from 5 to 17 Thesevalues are in line with those for the SPC(free) and

SPC(fixed) comparison when the matching perceptualrepresentation was assumed

Because the SPC(free) that assumed the matching taskperceptual representation is nested under the SPC(free)that assumed the identification perceptual representationF tests can be performed For all 4 observers estimatingthe perceptual representation from the identification dataprovided a significant improvement in fit over the case inwhich the matching task perceptual representation wasused to predict identification performance [Fs(82186) =251 164 352 and 265 for Observers 1 2 3 and 4 re-spectively ps lt 01] Although statistically significant itis worth noting that the improvement in fit was relativelysmall (approximately a twofold SSE improvement and a 3improvement in percent of variance accounted for) Per-haps more importantly this small improvement in fit wasobtained by adding 86 parameters whereas the muchlarger improvement in fit for the SPC(free) over theSPC(fixed) required only 36 additional response region pa-rameters In addition the absolute deviations between theperceptual representation parameters from the ID modeland those for the matching model were small Specifi-cally averaged across the 4 observers the absolute devia-tions between the orientation means and standard devia-tions measured in radians were 036 and 031 respectivelyThe average absolute deviations between the length meansand standard deviations measured in pixels were 1963and 1604 respectively Finally the average absolute devi-ations between the correlations were 044 Taken togetherthese analyses suggest that the matching task does providea good initial perceptual representation for identificationnearly as good as the perceptual representation freely es-timated from identification confusions4

Predicting categorization from the identificationperceptual representation In this section we attempt topredict early and late categorization performance in eachof the four categorization conditions from the identifica-tion perceptual representation Both the categorization con-dition invariance hypothesis and the decisional integrationdecisional selective attention hypothesis were examinedIn addition both hypotheses regarding the response re-gions were examined (recall that one assumed linear de-cision bounds in the DSA conditions whereas the otherassumed quadratic decision bounds) In line with the analy-ses presented earlier quadratic decision bounds in theDSA conditions did not provide a significant improvementin fit

The number of free parameters AIC and percent ofvariance accounted for by the categorization condition in-variance and decisional integrationdecisional selectiveattention models for each observer are presented in thetwo rightmost columns of Table 3 Several results stand outFirst the decisional integrationdecisional selective atten-tion models provided a better account of the data than thecategorization condition invariance model for all 4 ob-servers during early and late learning This replicates thefinding of Maddox and Bogdanov (2000) and the previous

Table 5 Slope of the Linear Decision Bound From the Decisional

IntegrationDecisional Selective Attention Model Assuming the Matching Task Perceptual Representation for the DSAL

and DSAO Conditions

Condition

Training Phase DSAL DSAO





NotemdashDSAL decisional selective attention to length DSAO decisionalselective attention to orientation


analyses and extends this finding to the identificationndashcategorization relationship The perceptual noise scalarestimates and linear decision bound slopes from thismodel were very similar and showed a similar patternacross learning to those outlined in Tables 4 and 5 thatwere estimated assuming the matching task perceptualrepresentation Second the matching task perceptual rep-resentation generally provided a better account of catego-rization performance than did the identification task per-ceptual representation Specifically for the decisionalintegrationdecisional selective attention model the match-ing task perceptual representation yielded a better accountof the data for all 4 observers during early and late train-ing with one exception (Observer 1 late training) Evenso both perceptual representations provided good ac-counts of the data accounting (on average) for 9768 and9669 of the variance in the categorization data for thematching and identification perceptual representations re-spectively Thus both tasks provide good methods for de-riving an initial perceptual representation although thereappears to be a slight advantage for the matching task

DISCUSSION

The present study applied general recognition theory toaccount simultaneously for perceptual matching identifi-cation and categorization performance General recogni-tion theory assumes that perceptual processing is noisyand probabilistic and is defined by parameters that areseparately identifiable from those associated with deci-sion processes Two specific hypotheses were tested Firstthe (often implicit) assumption that changing task de-mands affect decision processes while leaving the percep-tual representation unchanged was examined Second thehypothesis that decisional selective attention tasks alterboth decision processes and perceptual processes by re-ducing the perceptual variance along the attended dimen-sion whereas decisional integration tasks alter only deci-sion processes was tested

A perceptual representation for 18 line stimuli was de-rived from the perceptual matching data This representa-tion was then held fixed in an attempt to model data fromthe identification and categorization tasks The matchingperceptual representation was compared with a perceptualrepresentation that was freely estimated from the identifi-cation data in their ability to account for the identificationand categorization data Not surprisingly the identificationperceptual representation was superior to the matchingperceptual representation in accounting for the identifica-tion confusions On average the identification perceptualrepresentation accounted for approximately 97 of vari-ance in the data as compared with the matching task per-ceptual representation that accounted for approximately94 of the variance in the data However this relativelysmall improvement in fit for the identification perceptualrepresentation came about at the expense of 86 additionalfree parameters In addition the parameters of the result-

ing perceptual representations were quite similar Clearlythe matching task perceptual representation is providing agood account of the data More remarkable though is theexcellent fit of the matching task perceptual representa-tion to the categorization data In fact in seven of eightcases (4 observers 3 2 training phases) the matching taskperceptual representation provided a better account of thecategorization data than did the identification perceptualrepresentation This is likely the strongest evidence to datethat the perceptual representation remains relatively un-changed across these different but related tasks

The hypothesis that decisional selective attention tasksalter both perceptual and decisional processes whereas de-cisional integration tasks affect only decisional processesfound support Specifically decisional selective attentionproblems led to the use of decision bounds that placedmore weight in the decision on the relevant dimension anddecreased the perceptual variance along the attended di-mension relative to the unattended dimension The mag-nitude of both effects was found to increase as the observergained experience with the tasks This is an importantfinding because it suggests that some decision problemsmdashin particular those that require selective attentionmdashcanalter both the decision strategy applied and the nature ofthe underlying perceptual representation This also adds tothe growing body of empirical support for the notion thatattention can operate at both perceptual and decisionallevels (Johnston McCann amp Remington 1995 Pashler1989 1991 1993 Posner 1993 Posner Sandson Dhawanamp Shulman 1989) and extends these results to catego-rization (see also Maddox Ashby amp Waldron 2000)

These results converge with current thinking in the cog-nitive neurosciences and a recently proposed neuropsy-chological theory of categorization Ashby Alfonso-Reeseet al (1998) proposed a neuropsychological theory of cat-egorization that postulates two separate and competingcategorization systems one dominated by explicit cate-gorization rules and the other dominated by implicit cat-egorization rules The implicit system bases its decisionon a perceptual representation computed in some visualarea (IT or lower) whereas the verbal system presumablyuses a representation from object-based working memory(thought to be in ventrolateral prefrontal cortex Baddeley1995) Current theories of visual selective attention pos-tulate separate attentional effects in visual areas in IT andin ventrolateral prefrontal cortex (eg LaBerge 1995)Thus the perceptual representation used by the explicitsystem receives different (but overlapping) attentionalprocessing than the representation used by the implicitsystem In the present study it is reasonable to supposethat the decisional selective attention conditions are eachdominated by an explicit rule (eg in the DSAL condi-tion the observer should respond ldquoArdquo if the length is smalland respond ldquoBrdquo if the length is long) whereas the linearand nonlinear integration conditions are dominated by theimplicit system (since no explicit rule exists that could ad-equately solve these categorization problems) Because

1198 MADDOX

the perceptual representations for the explicit and implicitsystems receive different (but overlapping) attention pro-cessing it is possible that the representations would be af-fected differently Clearly this reasoning is tentative andrequires more rigorous empirical testing Even so thesedata and the present approach provide an interesting cross-roads between traditional studies of categorization and thegrowing interest in cognitive neuroscience

Future DirectionsDespite the wealth of information gained from the pres-

ent empirical and theoretical investigation this study rep-resents only a first step along a potentially fruitful path ofinquiry An obvious next step would be to replicate thepresent study with highly integral-dimension stimuli suchas color patches that vary in saturation and brightness Alarge body of research suggests that the efficiency of at-tention is different for integral- and separable-dimensionstimuli (eg Garner 1974) In particular it is argued thatselective attention is easy with separable-dimension stim-uli but is difficult with integral-dimension stimuli (Gar-ner 1974 McKinley amp Nosofsky 1996 Nosofsky 1987however see Ashby amp Maddox 1994 and Maddox1992) It is possible that the attention effects observed inthe present study might not obtain (or might operate lessefficiently) with integral-dimension stimuli Another per-haps more intriguing possibility is that decisional pro-cesses will be relatively unchanged across separable- andintegral-dimension stimuli but that the effects of deci-sional selective attention on the nature of the perceptualrepresentation will be absent with integral-dimension stim-uli Another interesting line of future research would be toinvestigate learning effect more fully The results for theearly and late phases of categorization learning are sug-gestive but future research should examine the time courseof learning across more than two learning phases In addi-tion an examination of possible perceptual and decisionallearning effects in identification could also be fruitful Fi-nally applications to other complex tasks are conceivableFor example the formal model of feature binding in ob-ject perception developed by Ashby Prinzmetal Ivry andMaddox (1998 see also Maddox Prinzmetal Ivry ampAshby 1994) could be generalized by relaxing the all-or-none feature perception and feature sampling indepen-dence assumptions (see Ashby Prinzmetal et al 1998for details) In addition perceptual matching andor iden-tification data could be collected to provide an initial es-timate of the perceptual representation Several other ap-plications are possible For example Geisler and Chou (1995)took a similar approach to the study of the visual searchtask

In conclusion the present study applied a unified theo-retical frameworkmdashgeneral recognition theorymdashto the re-lations among perceptual matching identification andcategorization General recognition theory separates percep-tual from decisional processes Excellent accounts of theidentification and decisional integration categorizationdata were obtained by assuming changes in the response

regions across tasks but a fixed perceptual representationderived from perceptual matching Decisional selective at-tention categorization tasks led to the use of a decisionstrategy that placed more weight in the decision on the rel-evant dimension and decreased the perceptual variancealong the attended dimension relative to the unattendeddimension Both of these effects generally increased inmagnitude with learning

REFERENCES

Akaike H (1974) A new look at the statistical model identificationIEEE Transactions on Automatic Control 19 716-723

Alfonso-Reese L A (1996) Dynamics of category learning Doctoraldissertation University of California Santa Barbara

Alfonso-Reese L A (1997) On the dangers of ignoring noise in high-level perception experiments (Technical report) Bloomington Indi-ana University

Ashby F G (1988) Estimating the parameters of multidimensional sig-nal detection theory from simultaneous ratings on separate stimuluscomponents Perception amp Psychophysics 44 195-204

Ashby F G (1992a) Multidimensional models of categorization In F GAshby (Ed) Multidimensional models of perception and cognition(pp 449-484) Hillsdale NJ Erlbaum

Ashby F G (1992b) Multivariate probability distributions In F GAshby (Ed) Multidimensional models of perception and cognition(pp 1-34) Hillsdale NJ Erlbaum

Ashby F G Alfonso-Reese L A Turken A U amp Waldron E M(1998) A neuropsychological theory of multiple systems in categorylearning Psychological Review 105 442-481

Ashby F G amp Lee W W (1991) Predicting similarity and catego-rization from identification Journal of Experimental PsychologyGeneral 120 150-172

Ashby F G amp Lee W W (1992) On the relationship among identifi-cation similarity and categorization Reply to Nosofsky and Smith(1992) Journal of Experimental Psychology General 121 385-393

Ashby F G amp Lee W W (1993) Perceptual variability as a funda-mental axiom of perceptual science In SC Masin (Ed) Foundationsof perceptual theory (pp 369-399) Amsterdam North-Holland

Ashby F G amp Maddox W T (1990) Integrating information fromseparable psychological dimensions Journal of Experimental Psy-chology Human Perception amp Performance 16 598-612

Ashby F G amp Maddox W T (1991) A response time theory of per-ceptual independence In J P Doignon amp J C Falmagne (Eds) Math-ematical psychology Current developments (pp 389-414) New YorkSpringer-Verlag

Ashby F G amp Maddox W T (1993) Relations between prototypeexemplar and decision bound models of categorization Journal ofMathematical Psychology 37 372-400

Ashby F G amp Maddox W T (1994) A response time theory of per-ceptual separability and perceptual integrality in speeded classifica-tion Journal of Mathematical Psychology 33 423-466

Ashby F G Maddox W T amp Lee W W (1994) On the dangers ofaveraging across subjects when using multidimensional scaling or thesimilarity-choice model Psychological Science 5 144-150

Ashby F G amp Perrin N A (1988) Toward a unified theory of sim-ilarity and recognition Psychological Review 95 124-150

Ashby F G Prinzmetal W Ivry R B amp Maddox W T (1998)A formal theory of feature binding in object perception Psychologi-cal Review 103 165-192

Ashby F G amp Townsend J T (1986) Varieties of perceptual inde-pendence Psychological Review 93 154-179

Ashby F G amp Waldron E M (1999) On the nature of implicit cat-egorization Psychonomic Bulletin amp Review 6 363-378

Ashby F G Waldron E M Lee W W amp Berkman A (2001)Suboptimality in categorization and identification Journal of Exper-imental Psychology General 130 77-96

Baddeley A (1995) Working memory In M S Gazzaniga (Ed) Thecognitive neurosciences (pp 755-764) Cambridge MA MIT Press


Bonnel A-M amp Hafter E R (1998) Divided attention between si-multaneous auditory and visual signals Perception amp Psychophysics60 179-190

Braida L D amp Durlach N I (1972) Intensity perception II Res-olution in one-interval paradigms Journal of the Acoustical Society ofAmerica 51 483-502

Brainard D H (1997) Psychophysics software for use with MAT-LAB Spatial Vision 10 433-436

Estes W K (1956) The problem of inference from curves based ongroup data Psychological Bulletin 53 134-140

Garner W R (1974) The processing of information and structureNew York Wiley

Garner W R amp Felfoldy G L (1970) Integrality of stimulus di-mensions in various types of information processing Cognitive Psy-chology 1 225-241

Geisler W S (1989) Sequential ideal-observer analysis of visual dis-criminations Psychological Review 96 267-341

Geisler W S amp Chou K (1995) Separation of low-level and high-level factors in complex tasks Visual search Psychological Review102 356-378

Green D M amp Swets J A (1967) Signal detection theory and psy-chophysics New York Wiley

Johnston J C McCann R S amp Remington R W (1995) Chrono-metric evidence for two types of attention Psychological Science 6365-369

Khuri A I amp Cornell J A (1987) Response surfaces Designs andanalyses New York Marcel Dekker

LaBerge D (1995) Computational and anatomical models of selectiveattention in object identification In M S Gazzaniga (Ed) The cogni-tive neurosciences (pp 649-664) Cambridge MA MIT Press

Luce R D (1963) Detection and recognition In R D Luce R R Bushamp E Galanter (Eds) Handbook of mathematical psychology (pp 103-189) New York Wiley

Luce R D (1986) Response times Their role in inferring elementarymental organization New York Oxford University Press

Luce R D amp Green D M (1978) Two tests of a neural attention hy-pothesis for auditory psychophysics Perception amp Psychophysics 23363-371

Macmillan N A Goldberg R F amp Braida L D (1988) Resolu-tion for speech sounds Basic sensitivity and context memory onvowel and consonant continua Journal of the Acoustical Society ofAmerica 84 1262-1280

Maddox W T (1992) Perceptual and decisional separability In F GAshby (Ed) Multidimensional models of perception and cognition(pp 147-180) Hillsdale NJ Erlbaum

Maddox W T (1999) On the dangers of averaging across observerswhen comparing decision bound models and generalized contextmodels of categorization Perception amp Psychophysics 61 354-374

Maddox W T amp Ashby F G (1993) Comparing decision bound andexemplar models of categorization Perception amp Psychophysics 5349-70

Maddox W T amp Ashby F G (1996) Perceptual separability deci-sional separability and the identificationndashspeeded classification rela-tionship Journal of Experimental Psychology Human Perception ampPerformance 22 795-817

Maddox W T amp Ashby F G (1998) Selective attention and the for-mation of linear decision boundaries Comment on McKinley andNosofsky (1996) Journal of Experimental Psychology Human Per-ception amp Performance 24 301-321

Maddox W T Ashby F G amp Waldron E M (2000) Multiple at-tention systems in perceptual categorization Manuscript submittedfor publication

Maddox W T amp Bogdanov S V (2000) On the relation between de-cision rules and perceptual representation in multidimensional per-ceptual categorization Perception amp Psychophysics 62 984-997

Maddox W T Prinzmetal W Ivry R B amp Ashby F G (1994)A probabilistic multidimensional model of location discriminationPsychological Research 56 66-77

McKinley S C amp Nosofsky R M (1996) Selective attention and theformation of linear decision boundaries Journal of Experimental Psy-chology Human Perception amp Performance 22 294-317

Myung I J amp Pitt M A (1997) Applying Occamrsquos razor in model-ing cognition A Bayesian approach Psychonomic Bulletin amp Review4 79-95

Nosofsky R M (1983) Information integration and the identificationof stimulus noise and criterial noise in absolute judgment Journal ofExperimental Psychology Human Perception amp Performance 9 299-309

Nosofsky R M (1986) Attention similarity and the identificationndashcategorization relationship Journal of Experimental PsychologyGeneral 115 39-57

Nosofsky R M (1987) Attention and learning processes in the identi-fication and categorization of integral stimuli Journal of Experimen-tal Psychology Learning Memory amp Cognition 13 87-109

Nosofsky R M (1989) Further tests of an exemplar-similarity ap-proach to relating identification and categorization Perception amp Psy-chophysics 45 279-290

Pashler H (1989) Dissociations and dependencies between speed andaccuracy Evidence for a two-component theory of divided attentionin simple tasks Cognitive Psychology 21 469-514

Pashler H (1991) Shifting visual attention and selecting motor re-sponses Distinct attentional mechanisms Journal of ExperimentalPsychology Human Perception amp Performance 17 1023-1040

Pashler H (1993) Dual-task interference and elementary mentalmechanisms In D E Meyer amp S Kornblum (Eds) Attention and per-formance XIV (pp 245-263) Cambridge MA MIT Press

Perrin N A amp Ashby F G (1991) A test of perceptual indepen-dence with dissimilarity data Applied Psychological Measurement15 79-93

Posner M I (1993) Attention before and during the decade of thebrain In D E Meyer amp S Kornblum (Eds) Attention and perfor-mance XIV (pp 342-350) Cambridge MA MIT Press

Posner M I Sandson J Dhawan M amp Shulman G L (1989)Is word recognition automatic A cognitive-anatomical approachJournal of Cognitive Neuroscience 1 50-60

Shepard R N (1957) Stimulus and response generalization A sto-chastic model relating generalization to distance in psychologicalspace Psychometrika 22 325-345

Shepard R N (1964) Attention and the metric structure of the stimu-lus space Journal of Mathematical Psychology 1 54-87

Shepard R N amp Chang J J (1963) Stimulus generalization in thelearning of classification Journal of Experimental Psychology 6594-102

Shepard R N Hovland C I amp Jenkins J M (1961) Learning andmemorization of classif ications Psychological Monographs 75(13Whole No 517)

Smith J D amp Minda J P (1998) Prototypes in the mist The earlyepochs of category learning Journal of Experimental PsychologyLearning Memory amp Cognition 24 1411-1436

Takane Y amp Shibayama T (1992) Structures in stimulus identifica-tion data In F G Ashby (Ed) Multidimensional models of perceptionand cognition (pp 335-362) Hillsdale NJ Erlbaum

Wickens T D (1982) Models for behavior Stochastic processes inpsychology San Francisco Freeman

Wilson C J (1995) The contribution of cortical neurons to the firingpattern of striatal spiny neurons In J C Houk (Ed) Models of infor-mation processing in the basal ganglia (pp 29-50) Cambridge MAMIT Press

NOTES

1 The independence assumption is likely incorrect but in the pres-ent situation it should lead to a constant error across stimuli Since themodel-based analyses of the identification and categorization data willallow for an additive constant to be applied to the perceptual variancesthis ldquoerrorrdquo should not adversely affect our ability to interpret the data

2 The preferred method of parameter estimation is maximum likeli-hood Unfortunately for technical reasons this was not possible in thepresent study (or in other applications of general recognition theory toidentification confusions Ashby amp Lee 1991 Ashby et al 2001 Mad-dox amp Ashby 1996) To estimate the probability of responding j whenstimulus i is presented one must integrate the stimulus i perceptual dis-

1200 MADDOX

tribution over the response region assigned to j Theoretically this prob-ability can never be zero with normal distributions but when fitting themodels numerical integration is required When the response j region isfar from the stimulus i perceptual distribution these numerical integra-tion procedures will yield a predicted response probability equal to zeroPredicted probabilities equal to zero yield infinite fit values from themethod of maximum likelihood This problem could be alleviated by re-placing predicted response probabilities of zero with some small valuesuch as 001 or 0001 but the specific value selected would change dras-tically the fit value Instead of selecting some arbitrary value the leastsquares approach taken by previous researchers was utilized (Ashby ampLee 1991 Ashby et al 2001 Maddox amp Ashby 1996) In addition amajor problem in model fitting is to avoid ldquolocal minimardquo Local min-ima result when the parameter estimation algorithm identifies a set of pa-rameters that are ldquolocallyrdquo superior (ie provide the best fit) but are notldquogloballyrdquo superior Although one can never be certain that the globalminima have been obtained procedures should be followed to minimizethis possibility Along these lines multiple starting parameter valueswere utilized In addition since many of the models were nested the pa-rameters from a more restricted model were used as starting values for a

more general model These procedures likely improve onersquos chances ofidentifying the global minima

3 The results of this test must be interpreted with caution since it as-sumed that the confusion matrix frequencies are independent which islikely not the case Even so Ashby and Lee (1991 1992) showed thatthese F tests generally agree with tests based on a maximum likelihoodapproach that does not assume independence

4 One might argue that it is no surprise that models of this complex-ity with so many free parameters provide good accounts of the identifi-cation data Unfortunately model complexity is a difficult issue that hasnot been adequately defined (however see Myung amp Pitt 1997) How-ever two points are worth mentioning First these models are all falsifi-ablemdashthat is they have fewer free parameters than degrees of freedomin the data which is not a property of many popular models (egANOVA) Second these models have fewer parameters than the bench-mark model of identificationmdashnamely the LucendashShepard similarity (bi-ased) choice model (Luce 1963 Shepard 1957)

(Manuscript received April 10 2000 revision accepted for publication January 24 2001)

1184 MADDOX

noring all other aspects of the stimulus Maddox amp Ashby1998) affect both decisional and perceptual processes wasexamined Selective attention problems of this sort areubiquitous in everyday life and thus demand a better un-derstanding To achieve these goals requires a theory thatmakes reasonable assumptions about the nature of the per-ceptual representation and that contains parameters asso-ciated with perceptual and decisional processes that areseparately identifiable General recognition theory (Ashbyamp Townsend 1986) a multidimensional generalization ofsignal detection theory provides such a theory

The next two (second and third) sections introducebriefly general recognition theory and review the relevantliterature The details of the theory can be found in numer-ous other articles (Ashby amp Lee 1991 Ashby amp Perrin1988 Ashby amp Townsend 1986) The fourth section intro-duces the experiment and details the method The fifthsection reports the results and theoretical analyses Thesixth section provides a summary and discussion

GENERAL RECOGNITION THEORY

Perceptual Representation AssumptionsGeneral recognition theory acknowledges that a funda-

mental characteristic of all perceptual systems is that re-peated presentations of the same stimulus yield differentperceptual effectsmdashthat is that perceptual noise exists (egAshby amp Lee 1993 Ashby amp Townsend 1986 Geisler1989 Green amp Swets 1967) General recognition theoryassumes that a single multidimensional stimulus can berepresented perceptually by a multivariate probability dis-tribution (Ashby amp Lee 1993) For a two-dimensionalstimulus a bivariate normal distribution is assumed to de-scribe the set of percepts A bivariate normal distributionis described by a mean and variance along each dimensionas well as a covariance term mx my s2

x s2y covxy where the

subscripts x and y denote dimensions x and y Figure 1adepicts hypothetical equal likelihood contours for fourstimuli constructed from the factorial combination of twolevels along two dimensions x and y With bivariate nor-mal distributions the equal likelihood contours are alwayscircular or elliptical In general recognition theory per-ceptual independence holds for a single stimulus if andonly if the perceptual effects for dimensions x and y arestatistically independent (see Ashby 1988 Ashby amp Mad-dox 1991 Ashby amp Townsend 1986 Perrin amp Ashby1991) With bivariate normal distributions perceptual in-dependence holds when the major and minor axes of thecontour are parallel to the coordinate axes (ie when thecovariance is zero) Perceptual independence holds for allfour distributions in Figure 1a A positive slope for themajor axis implies a positive perceptual dependence anda negative slope implies a negative perceptual depen-dence Perceptual separabilityholds when the distributionof percepts associated with one component is unaffectedby the level of the other component (Ashby amp Townsend1986 Maddox 1992) In Figure 1a dimension y is per-ceptually separable from dimension x but dimension x isnot perceptually separable from dimension y

Decision Process AssumptionsIn general recognition theory the experienced observer

learns to divide the perceptual space into response regionsand assigns a response to each region The partitions be-tween response regions are called decision bounds Oneach trial the observer determines the location of the per-ceptual effect and gives the response associated with thatregion of the perceptual space Decision bounds and the

Figure 1 (a) Hypothetical contours of equal likelihood for fourstimuli constructed from the factorial combination of two levelsalong two stimulus components (b) Hypothetical response re-gions and decisional separability bounds for the same four stim-uli (c) Hypothetical response regions and striatal units for thesame four stimuli












1186 MADDOX







MethodObservers













1188 MADDOX
















FSSE SSE df df

SSE dfobs

r g r g

g g

=- -( ) ( )

1190 MADDOX








Matching ID



1 38853 8705 9302 9674 17566 9387 4413 98522 110334 4721 15289 9166 41780 7863 8881 95173 42077 7514 11961 9150 13943 9032 4691 96664 56776 8037 10738 9613 22416 9231 4952 9832









1192 MADDOX


AIC = 2r ndash 2lnL







Matching ID

CI DIDSA CI DIDSA



Observer 2

Early 676 9682 636 9753 694 9637 648 9719Late 648 9748 612 9784 740 9559 724 9590

Observer 3

Early 760 9870 638 9900 1074 9724 1008 9752Late 594 9934 548 9952 1072 9766 1060 9773

Observer 4

Early 740 9825 690 9852 926 9706 854 9741Late 712 9843 686 9852 954 9682 886 9720























Dimension


Early 1291 1801Late 550 3348




1194 MADDOX









1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX

















1186 MADDOX







MethodObservers













1188 MADDOX
















FSSE SSE df df

SSE dfobs

r g r g

g g

=- -( ) ( )

1190 MADDOX








Matching ID



1 38853 8705 9302 9674 17566 9387 4413 98522 110334 4721 15289 9166 41780 7863 8881 95173 42077 7514 11961 9150 13943 9032 4691 96664 56776 8037 10738 9613 22416 9231 4952 9832









1192 MADDOX


AIC = 2r ndash 2lnL







Matching ID

CI DIDSA CI DIDSA



Observer 2

Early 676 9682 636 9753 694 9637 648 9719Late 648 9748 612 9784 740 9559 724 9590

Observer 3

Early 760 9870 638 9900 1074 9724 1008 9752Late 594 9934 548 9952 1072 9766 1060 9773

Observer 4

Early 740 9825 690 9852 926 9706 854 9741Late 712 9843 686 9852 954 9682 886 9720























Dimension


Early 1291 1801Late 550 3348




1194 MADDOX









1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX








MethodObservers













1188 MADDOX
















FSSE SSE df df

SSE dfobs

r g r g

g g

=- -( ) ( )

1190 MADDOX








Matching ID



1 38853 8705 9302 9674 17566 9387 4413 98522 110334 4721 15289 9166 41780 7863 8881 95173 42077 7514 11961 9150 13943 9032 4691 96664 56776 8037 10738 9613 22416 9231 4952 9832









1192 MADDOX


AIC = 2r ndash 2lnL







Matching ID

CI DIDSA CI DIDSA



Observer 2

Early 676 9682 636 9753 694 9637 648 9719Late 648 9748 612 9784 740 9559 724 9590

Observer 3

Early 760 9870 638 9900 1074 9724 1008 9752Late 594 9934 548 9952 1072 9766 1060 9773

Observer 4

Early 740 9825 690 9852 926 9706 854 9741Late 712 9843 686 9852 954 9682 886 9720























Dimension


Early 1291 1801Late 550 3348




1194 MADDOX









1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX






1188 MADDOX
















FSSE SSE df df

SSE dfobs

r g r g

g g

=- -( ) ( )

1190 MADDOX








Matching ID



1 38853 8705 9302 9674 17566 9387 4413 98522 110334 4721 15289 9166 41780 7863 8881 95173 42077 7514 11961 9150 13943 9032 4691 96664 56776 8037 10738 9613 22416 9231 4952 9832









1192 MADDOX


AIC = 2r ndash 2lnL







Matching ID

CI DIDSA CI DIDSA



Observer 2

Early 676 9682 636 9753 694 9637 648 9719Late 648 9748 612 9784 740 9559 724 9590

Observer 3

Early 760 9870 638 9900 1074 9724 1008 9752Late 594 9934 548 9952 1072 9766 1060 9773

Observer 4

Early 740 9825 690 9852 926 9706 854 9741Late 712 9843 686 9852 954 9682 886 9720























Dimension


Early 1291 1801Late 550 3348




1194 MADDOX









1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX
















FSSE SSE df df

SSE dfobs

r g r g

g g

=- -( ) ( )

1190 MADDOX








Matching ID



1 38853 8705 9302 9674 17566 9387 4413 98522 110334 4721 15289 9166 41780 7863 8881 95173 42077 7514 11961 9150 13943 9032 4691 96664 56776 8037 10738 9613 22416 9231 4952 9832









1192 MADDOX


AIC = 2r ndash 2lnL







Matching ID

CI DIDSA CI DIDSA



Observer 2

Early 676 9682 636 9753 694 9637 648 9719Late 648 9748 612 9784 740 9559 724 9590

Observer 3

Early 760 9870 638 9900 1074 9724 1008 9752Late 594 9934 548 9952 1072 9766 1060 9773

Observer 4

Early 740 9825 690 9852 926 9706 854 9741Late 712 9843 686 9852 954 9682 886 9720























Dimension


Early 1291 1801Late 550 3348




1194 MADDOX









1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX






1190 MADDOX








Matching ID



1 38853 8705 9302 9674 17566 9387 4413 98522 110334 4721 15289 9166 41780 7863 8881 95173 42077 7514 11961 9150 13943 9032 4691 96664 56776 8037 10738 9613 22416 9231 4952 9832









1192 MADDOX


AIC = 2r ndash 2lnL







Matching ID

CI DIDSA CI DIDSA



Observer 2

Early 676 9682 636 9753 694 9637 648 9719Late 648 9748 612 9784 740 9559 724 9590

Observer 3

Early 760 9870 638 9900 1074 9724 1008 9752Late 594 9934 548 9952 1072 9766 1060 9773

Observer 4

Early 740 9825 690 9852 926 9706 854 9741Late 712 9843 686 9852 954 9682 886 9720























Dimension


Early 1291 1801Late 550 3348




1194 MADDOX









1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX













1192 MADDOX


AIC = 2r ndash 2lnL







Matching ID

CI DIDSA CI DIDSA



Observer 2

Early 676 9682 636 9753 694 9637 648 9719Late 648 9748 612 9784 740 9559 724 9590

Observer 3

Early 760 9870 638 9900 1074 9724 1008 9752Late 594 9934 548 9952 1072 9766 1060 9773

Observer 4

Early 740 9825 690 9852 926 9706 854 9741Late 712 9843 686 9852 954 9682 886 9720























Dimension


Early 1291 1801Late 550 3348




1194 MADDOX









1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX


















Dimension


Early 1291 1801Late 550 3348




1194 MADDOX









1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX






1194 MADDOX









1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX











1196 MADDOX











and DSAO Conditions

Condition









DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX








DISCUSSION






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX






1198 MADDOX






REFERENCES



































































NOTES



1200 MADDOX



















































NOTES



1200 MADDOX






1200 MADDOX






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