Psychonomic Bulletin & Review 1996,3 (3),287-299
Constraintson theories of cognitive aging TIMOTHYA. SAI]THOUSE Georgia Insti,tute of Technology,Atlanta, Georgia There is currently little consensusregardingwhat must be explained by theories of cognitive aging. In the present article, four empirical generalizationsthat seem to imply certain constraints in theorizing are identified. These generalizations,and their possible implications or constraints, are that (l) age-relateddifferences are found in a wide range of cognitive variables, implying that either a large number of specific factors or a small number of generalfactors must be coniributing to the agerelated differences; (2) the age-relatedinfluences on different cognitive variables are not independent, and unique age-relatedinfluences appear to be few in number and small in magnitude, implying that some fairly general factors need to be postulated to account for the shared age-related influences; (3) only a small proportion of distinct age-relatedvariance occurs late in practice and at long presentationdurations, implying that adequateexplanationsmust include faciors operating when the individuals are just beginning to perform the task and when the stimuli can first be registered; and (4) measuresof how quickly very simple cognitive tasks can be performed share conJiderable age-relatedvariance with many cognitive variables, implying that factors related to simple processingefficiencyneedto be incorporatedinto the explanations.
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Researchconcernedwith the relations betweenadult age and cognitive performancehas been increasingdramaticallyoverthe lastseveraldecades.Despitethe rapid expansionof research,however,there is still little consensusregardingthe reasonsfor the negativerelations that aretypically reportedbetweenchronologicalageand the measuresof memory,reasoning,and spatialability sometimesreferredto as comprisingTypeA (Hebb, 1942) or fluid (Horn & Cattell, 1963)cognition.The primary purposeof this articleis to describeseveralsetsof empirical resultsthat appearto placeimportantconstraintson theoreticalexplanationsof age-relatedcognitivedecline phenomena. It is helpful to beginby describingthe broadphenomenonin needofexplanationby theoriesofcognitiveaging. Considerthe distributionof scoreson a cognitivetest, suchas immediatefree recallof a list of unrelatedwords. In a recentexperiment(Salthouse,1993b),a total of 305 adultsbetweenl9 and 84 yearsof age attemptedto remembertwo l2-word lists (presentedauditorilyat a rate of I word every 2 sec), and their averagescoresacross the two lists rangedfrom near zero to perfect (top panel of Figure I ). Becausethe sampleincludedpeopleof different ages,the distribution can be disaggregatedby age. That is, the individualscan be orderedby their ages,and then the scoresplottedby age(as in the bottom panelof Figure I ). This type of disaggregation typicallyresulrsin considerable variabrlityat eachage,but with an average
This researchwas supportedby National Institute on Aging Grant R37 AG6826 to T.A.S. I would like to thank three reviewersfor their c o n s t r u c t l v ec o m m e n t so n a n e a r l i e rv e r s i o no f t h i s m a n u s c r i o t T . he a u t h o r ' sm a i l i n g a d d r e s si s S c h o o l o f P s y c h o l o g yG , e o r g i aI n s t i t u t e o f T e c h n o l o g y ,A t l a n t a , G A 3 0 3 3 2 - 0 1 7 0( e - m a i l : t i m . s a l t h o u s e ( d psych.gatech e .d u) .
trend that is clearly negative, indicating that increased age is associatedwith lower performance.For example, in this particulardata set, the R2 value for age in a regressionequationwas .162,and thusa moderateproportion of the total variance in the free-recallmeasurewas associated with chronologicalage. Similar patternsof sharedvariancewith agehavebeen found for many cognitive variables.To illustrate, problems in the Raven'sAdvanced ProgressiveMatrices Test consistof a 3 X 3 matrix of symbolsor geometricelementsin all but one of the cells of a matrix. The task for the examineeis to use abstractreasoningto identify the patternthat providesthe bestcompletionof the missing cell. A recentstudyinvolving221 adultsbetween20 and 80 yearsof age (Salthouse,1993a)found that 32.2ohof the variancein the Raven'sscore was associatedwith chronological age,and in a similarstudy(Babcock,1994) 2l 2% of the variancein the Raven'sscorewas found to be relatedto age. There is clearly substantialscatterin the data of Figure l, and the proportionsof varianceassociatedwith agearealwayssubstantiallylessthan 1.0.Becausemany researchersmay not be comfortablethinking in terms of proportions of variance,it is reasonableto question the magnitude of the age-relatedeffects in Type A or fluid measuresof cognitivefunctioning. Fortunately,thesevaluescanbe placedin contextby referenceto Cohen( I 988), who, in his influential book on power analysis,has suggestedthat in the behavioralsciencesproportionsofvarianceof .01 are small,thoseof .09 aremedium,and those of .25 are large. The effectsjust describedare therefore in the medium-to-largerange with respectto behavioral scienceresearch. The phenomenonof age-relatedcognitivedecline in Type A or fluid aspectsof cognition is not only moder-
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BASED CONSTRAINTS
A l t h o u g h m a n y r e s e a r c h e r sa, n d e s p e c i a l l yt h o s e trainedin experimentalratherthanmultivariatetraditions, tend to focus on single dependentvariables,the agerelatedcognitivedeclinephenomenonis actuallyquite broad,becausea greatmany cognitivevariableshavebeen found to exhibit age-relateddifferences.The breadthof by inspectingthe conthe phenomenoncan be assessed tentsof majorjournalsin the field (e.g.,Psvchologt'und Aging and Journal of Gerontologv: Psvchologicul Sciences\and notingthe rangeof variablesin which signit-icantagedifferenceshavebeenreported.To illustrate.in the last5 yearsyoungadultshavebeenreported.in thc-sc' journals,to performsignificantlybetterthanolderadults in the following cognitivetasks:memory for *ords. prosc. pictures.faces.source.activities.locapairedassociates, tions,phonenumbers,routes,grocerylists.and golfshot information;reasoningwith seriescompletion.matrl\. analogy,letter sets,and categorizationproblems:block rotation.and intcdesign,paperfolding,objectassembly. gration spatialtasks;divided, selectivc.and.focusedatcomprehcntention;and miscellaneoustasksassessin-s sion, following instructions.and seriallearning.
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Age Chronological Figure l. Distribution of scores in a I 2-word free-recall task in a sample of305 adults. Data from Salthouse (1993b).
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0.4 ately large but also robust, becauseit has been docuE with replicated 1920 and has been at least mentedsince 8 o'2 many differenttypes of tests,with both cross-sectional C" and longitudinaldata-collectionprocedures,in several E (u 0 differentcultures,and in a varietyofspecies(e.g.,for reviews, see Birren & Schaie,1996,Craik & Salthouse, E i.2 (U 1992,andSalthouse,l99l). One of the major questions -0.4 6 in the field at the currenttime is: how canthesenegative age relationsbe explained?That is, what is responsible -0.6 for the lower levels of cognitive performanceoften associatedwith increasedage? .0.8 The goal in this article is not to describea specific the-1' 2 0 3 0 4 0 5 0 6 0 7 0 8 0 ory or explanation,but insteadto identify severalbroad constraintsthat presumablymust be satisfied by any cognitivedeclinepheplausibletheoryofthe age-related Age Chronological nomenon.The rationalefor this approachis the assumpFigure 2. Mean standard scores by age decade for six cognitive tion that it may be easierto reach a consensuson theoData for the free-recall and paired associatestasks are m€asures. retical explanationsif, first, there is agreementon the from Salthouse (1993b), data for the Wisconsin Card Sorting and must satisfy. broad constraintsthat plausibletheories Shipley Abstraction tasks are from Salthouse. Fristoe, and Rhee To qualifo astrue constraints,the relevantresultsshould (in press), and data for the Surface Development and Paper Foldbe robust, with numerousreplicationsacrossdifferent ing tasks are from Salthouse and Mitchell (1990).
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The scopeofthe phenomenoncan also be appreciated by examining the age trends for different variables in moderatelylarge samplesof adults from a wide rangeof ages.For example,Figure 2 illustratesthe agerelations for six different variables(i.e., number correct in free recall of two lists of 12 words each, number correct in paired associatesmemory of 6 word pairs, percent perseverative errors in the WisconsinCard Sorting Test,and number ofcorrect responsesin the Shipley Abstraction Test, in the SurfaceDevelopmentTest,and in the PaperFolding Test)from three separatestudies.The original scores on eachofthe various testswere first convertedto z scores to produce units on a comparablescale,and then the meanswere plotted by decade.Note that the age trends are very similar for measuresof memory ability (paired associate and freerecall),reasoningability (ShipleyAbstractionand Wisconsin Card Sorting), and spatial ability (paperfolding and surfacedevelopment).For eachof theseabilities thereis a differenceof approximatelyI SD betweenpeoplein their 20sandpeoplein their 70s.Similar age trendsin an age-heterogeneous sampleof 1,628 adults across l7 different cognitive measureshave also recentlybeenreportedby Schaieand Willis ( 1993). The existenceof statisticallysignificant, and often roughly comparable,age-relateddifferencesacrosssuch a wide varietyof cognitivemeasuresleadsto the first constrainton theorizingabout cognitiveaging phenomena. Constraint I Either a small number of ./airly broad and general mechanismsor a large number of specific mechanisms are needed to account for the age-related diJ.ferences found across a wide range oJ'cognitive variables-
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that is, becausethe phenomenonofage-relatedcognitive decline encompasses such a large number of cognitive variables,explanationsof the phenomenonmust either incorporatea largenumberof factorswith highly specific effectsor a relativelysmall numberof factorswith broadreachingconsequences. Theoriespostulatingdeficits in a few processes specificto a limited numberof cognitive taskswill thereforenot sufficeto providea completeaccount of the age-relatedcognitivedeclinephenomenon. In light of the wide rangeof variablesexhibitingsignificant age relations,and of the apparentsimilarity of the age patternsacrossdifferent variablesin moderately largesamples,the questionarisesasto the extentto which age-relatedeffects on different variablesare independent. The issueof independence is also relevantto the numberof distinctmechanismsnecessary to accountfor cognitive aging phenomena,becausemany separate mechanismswould presumablybe neededif most of the age-relatedeffectswere found to be independent.In contrast,a common or generalage-relatedfactor would probably be implicatedif largeproportionsof the age-related effectswere found to be shared. In the past there has been a tendencyamong many cognitive researchersto assumethat all age-relatedeffects were attributableto specific deficits, with these
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deficits possibly even localizablein discreteprocessing stagesor components.Becausethe focus was often on single dependentvariables,such as an index of performance on a particular type of memory task, the issueof sharedage-relatedinfluenceswas never seriouslyevaluated sincetherewas no meansof separatingcommon (or shared)and specific (or unique) age-relatedeffects. Broader interpretationshave sometimesbeen considered, but they were often dismissedbecauseof results (e.g.,the existenceof age X conditioninteractions)interpretedas suggestingthat a generalfactor was not sufficient to account for all of the observedeffects. For a variety ofreasons(e.g.,failure to considerthe role ofdifferentialreliability of factorswith a multiplicative influence, of processesthat might vary in their reliance on a generalfactor,and ofthe possibility that both generaland specific influencesmight operatesimultaneously),these analysesmay not have been optimal (Salthouse,1991, p p . 2 9 l - 3 0 0 ; S a l t h o u s e& C o o n , 1 9 9 4 ) .I n a n y c a s e , however,it seemsmore productiveto evaluatethe relative contribution of different types of influencesrather than to attemptto distinguishbetweenextremeall-or-noneinterpretations(such as only specific or only general). Contemporary researchconcernedwith aging and cognitioncan be characterized as consistingofa surplus of sensitivityevidencebut a shortageof specificityevidence.Claims of sensitivityare basedon evidencethat the variableor theoreticalprocessis significantly related to age.As noted above,there are many reportsof significant age relationsacrossa wide rangeof cognitive variables,and thus age sensitivity has been convincingly demonstratedfor many variables.The term specificity in this contextcan be usedto refer to evidencethat the agerelated influenceson one variable are distinct from, and independentof, the age-relatedinfluenceson other variables.Becauseof the dominanceof researchbasedon small-sample, extreme-groupdesignsfocusingon a single dependentvariable,very little researchrelevantto the issueofspecificity is currentlyavailablein the field ofcognitive aging. This is unfortunatebecauseconvtncing evidenceof specificity is neededbefore interpretations basedon separateand distinctage-relatedinfluences can be consideredplausible.That is, ifa largeproportion ofthe age-relatedeffectson different cognitive variables is found to be shared, or in common, then attempts to identify mechanismsspecific to one of the variablesmay merely be describingsymptoms of a much broaderphenomenon.Moreover,evenif only someofthe age-related influencesare shared,the magnitudeof the uniqueagerelated effects that remain to be explained by taskspecific mechanismswill dependon how much of the total effectsare attributableto more generalfactors. lndependenceis often assessed with correlationalprocedures,becausethe squareofthe correlationindicates the proportion of variancein two variablesthat is shared. However,becausethe current interest is in sharedagerelated influences,the relevant variance is not the total amount of variance; instead, it correspondsonly to the amount of age-relatedvariancethat is shared.For exam-
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ple, ifthe proportionofage-relatedvarianceis .162,then the question of interest in the presentcontext is how much of this varianceis sharedwith other variables.The relevant proportions of variance can be estimatedwith correlation/regressionproceduresbecauseprediction of the criterion variablewhen age is the only predictorvariable in the regressionequation indicates the total agerelated variance,and the increment in variance associated with age after partialling out the effects of another control variable indicatesthe unique age-relatedvaria n c e . S u b t r a c t i o no f t h e u n i q u e a g e - r e l a t e dv a n a n c e from the total age-relatedvariance and division by the total age-relatedvariancethereforeyields the proportion of age-relatedvariancein the criterion variablethat is shared,or in common,with the othervariable.(SeeSalthouse,1992,1994b,in press-a,for furtherdiscussionof theseprocedures.) If only a small proportionof the age-relatedvanance in a given variableis sharedwith anothervariable,then most of the age-relatedinfluenceson that variablecan be inferredto be independent,distinct,and potentially specific. However,if the ratio of shared(or common) age-related varianceto total age-related varianceis high, then one can infer that most of the age-relatedeffectson the two variablesare shared. To ensuremaximum generalizability,it is important to examinetheseproportionsacrossmany combinations of variables.Among the criteriadesirablein datasetsto be usedfor this purposcare:( I ) multiplevariablesshould be availablefrom the sameindividualsor else no independenceanalysesare possible;(2) the variablesshould haveat leastmoderatereliability to ensurethat there is sufTicientsystematicvarianceto be sharedwith other variables;(3) the sampleshouldhavea wide age range, and preferablyconsist of a continuousdistribution of ages,to ensureaccurateassessments of the age-related influences;and (4) the samplesshouldbe largeenough to ensurereasonablypreciseestimatesof the relevant proportionsofvariance.Severalstudiesfrom my laboratory havethe requisitecharacteristics, and thus datafrom thosestudiescanbe examinedto estimateproportionsof age-relatedvariancesharedacrossdifferent cognitive variables. It is useful to illustratetheseprocedureswith an example of the relevantcomputations.In a recent study ( S a l t h o u s eF, r i s t o e ,& R h e e ,i n p r e s s ) ,2 5 9 a d u l t sb e tween I 8 and 94 years of age performed tasksof inductive reasoning(i.e.,ShipleyAbstraction)and verbalmemory (i.e., paired associates) that are usuallyassumedto representdistinct cognitiveabilities.An initial regressi^onanalysison the abstractionmeasurerevealedthat the R' associatedwith age was .199, indicatingthat l9.9Vo of the variancein this measurewas relatedto age.A hierarchicalregressionequationin which the paired associatesmemory measurewas controlledbeforethe effects of age on the abstractionmeasurewere examinedrevealedthat the incrementin R2 associated with age was .062.An estimateof the sharedage-relatedvariancecan be derivedby subtractionofthis value,which represents
v the uniqueage-relatedvariance,from the total age-related varianceof . I 99 to yield a valueof .137. In this particular case,then, 68.8% (i.e., . I 371.199)of the age-related variance in the abstractionmeasurecan be inferred to have been sharedwith the age-relatedvariancein the pairedassociatememory measure.Becausethe amount ofage-relatedvarianceis not necessarilyidenticalfor the two variables,the estimatesof uniqueand sharedproportions need not be equivalent.In fact, the percentageof age-relatedvariancefor the paired associatesmemory measureestimatedto havebeen sharedwith that in the abstractionmeasurewas 58.9% (i.e., .1421 .241). A recentarticleby Salthouse( 1994b)reportedresults of analysessimilar to these,conductedon 855 pairs of variablesobtainedfrom l3 separatestudies.The variables were derived from a wide variety of tasks,ranging from reactiontime to numberof items correcton the Raven's Progressive MatricesTest,and rangingfrom accuracyin paired associatesmemory tasks to accuracy in paper folding spatialtasks.The meanof these855 valueswas . 5 0 0 ( m e d i a n o f . 5 2 0 ) , i n d i c a t i n gt h a t a n a v e r a g eo f about50% ofthe age-related variancein many cognitive variablesis shared,or in common.Becausean averageof only l9o/oof the total variancefor these same variables was shared,it can be concludedthat the simplecorrelation betweentwo variablesis not sufficientto determine t h e e x t e n tt o w h i c h t h o s ev a r i a b l e ss h a r ea g e - r e l a t e d vanance. T h e f r e q u e n c yd i s t r i b u t i o n f o r t h e p r o p o r t i o n so f s h a r e dv a r i a n c ea m o n g l 6 v a r i a b l e s( 1 2 0 p a i r s )i n t h e Salthouse, Fristoe,and Rhec(in press)studyis portrayed in Figure3. Notice that the patternwas nearlyidentical to that found in the Salthouse( I 994b)analysesin that an averageofover 50% ofthe age-relatedvariancein pairs of variableswas shared.The similarity in outcomesis particularlynoteworthybecausethe variablesin the Salthouse,Fristoe,and Rhee (in press)study were derived from neuropsychological testsoften postulatedto be sensitiveto functioningin diff'erentregionsof the brain. For
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example,the Wisconsin Card Sorting Test and the FAS fluency test have been hypothesizedto be sensitive to frontal lobe damage,visual spatial tests such as the WAIS-R Block Design and Object Assembly tests have been hypothesizedto be sensitiveto right parietal lobe damage,and damageto the medial temporal lobe hasbeen postulatedto affect performanceon verbal learning and memory tests such as paired associatesand free recall. The resultsjust describedindicatethat the age-related effectson what appearto be quite different variablesare not independent.That is, an averageof approximately halfofthe age-relatedinfluenceson a givencognitivevariable appearto be sharedwith other cognitive variables, even when those variableshave little or no resemblance to one anotherand when they are usually interpretedas representingdistinctcognitiveabilitiesor reflectingfunctioning in differentbrain regions. Another analyticalprocedurethat can be usedto generateestimatesof common and unique age-relatedinfluencesis one proposedby Kliegl and Mayr ( l992) based on a structuralequationmodel with a single common factor. Within this model, both general(i.e., mediated throughthe common factor)and specific(i.e., unmediated,or direct) age-relatedeffectsare postulatedto exist. Furthermore,the relativecontributionsof each type of influcncecan be estimatedfrom standardized pathcoeff i c i e n t s d e r i v e d f r o m t h e s t r u c t u r a lm o d e l . T h a t i s , within this framework,the generalinfluenceis estimated by the productofthe path coefficientsbetweenage and the common factor and betweenthe common factor and the individualvariable,and the estimateof the specific influencecorrespondsto the coefficient betweenageand the individualvariable. Becausethe common factor in this type of model is definedby the variableswith significantloadings,it can be interpretedas representingwhat all of the variables havein common.The interestingquestionin the present contextconcernsthe magnitudeof the relationsbetween age and the individual variablesafter the relation betweenageand an estimateofwhat all of the variableshave in commonhasbeentakeninto consideration.Ifthose distinct agerelationsare largerelativeto the total age-related effectson the variable,then substantialuniqueor specific age-relatedinfluencescan be inferred to exist. However, if the distinct (or direct) relation betweenage and the variableis very small, then therewould be little evidence for specific age-relatedinfluencesaboveand beyondthe age-relatedinfluencessharedamong all of the variables. A variety ofstructural equationmodeling procedures (e.g.,EQS, LISREL) can be usedto deriverhe estimares for the relevantpath coefficients.Becausethe prerequisitesfor thesetypesof analysesaresimilarto thosementioned earlier(i.e.,moderatelylargesamplesfrom a wide age rangewith severalvariablesavailablefrom eachparticipant),the procedureswill againbe illustratedwith data from my laboratory.(But see Lindenberger& Baltes, 1994,and Lindenberger,Mayq & Kliegl, 1993,for particularly elegantexamplesof this type of analysis.)Re-
sults from four independentdata sets are illustrated in Figures4 and5. Figure 44, containsdata from Salthouse (1993a),with measuresof perceptualspeed,working memory, and inductive reasoning from 221 adults between 20 and 80 yearsofage. The seconddata set, portrayed in Figure 48, consistsof measuresof perceptual speedand three setsof verbal and spatial memory measuresfrom 173 adultsbetween l8 and 88 yearsofage (Salthouse,I 995a).The datasetrepresentedin Figure54, consistsofmeasuresfrom neuropsychologicaltestsfrom a sample of 259 adults between l8 and 94 years of age (Salthouse,Fristoe,& Rhee,in press).Finally,the dataset in Figure 5B consistsof measuresof conceptidentification, associativelearning, working memory, perceptual comparisonspeed,and visual acuity from 197 adultsbetween l8 and92 yearsof age(Salthouse,Hancock,Meinz, & Hambrick,in press). The models summarizedin Figures 4 and 5 were all generatedin the same manner. First the data from the study were convertedinto a covariancematrix, and then a single common factor rnodel was specified with relations from age to the common factor. Relationsbetween variablessharingsimilar methodswere next examined and includedin the model if the coefficientsdifferedfrom zero by more than 2 standarderrors. Successivemodels were then examinedin which direct relationswere specified betweenage and each individual variable,and relations with coefficients differing from zero by more than 2 standarderrors were retained in the model. The final models,representedin Figures4 and 5, thereforeportray all of the significant relations betweenage and the observedvariables.Becausethere was little attemptto representpossiblerelationsamongsubsetsof the variables, the modelscan be consideredrelativelycrude summaries of the structureof thedata.lHowever.the imoortantissue from the currentperspectiveconcernsthe relativemagnitudesof the mediated,or common,and the direct,or specific,age-relatedinfluences.Notice that a similar pattern is apparentin each data set in that there is a large common or generalinfluenceon all variables,along with small specific age-relatedinfluenceson a few of the variables.zTheseresultssuggestthat thereare relatively few uniquerelationsbetweenageand the individual variables beyondthose sharedamong all variables. The two analytical methodsdescribedaboveare both quiterecent,and consequently their potentiallimitations have not yet been fully explored. Furthermore,because relatively few studieshavebeen conductedwith the requisite data,the resultsillustratedwere all derived from a single investigator'slaboratory.Despite thesequalifications, the outcomes of both types of analysesare quite consistentin suggestingthat the age-relatedinfluences on many differentcognitivevariablesarenot independent. That is, the moderate-to-largeproportionsof sharedagerelated variance and the small-to-nonexistentdirect relations between age and individual cognitive variables after taking into account the relation of age to a single common factor both suggestthat the age-relatedeffects
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Figure 4. Single common factor structural models for data (A) from Salthouse (1993b) and (B) from Salthouse (1995a). Variables in Panel A are: DigSym = WAIS-R Digit Symbol Substitution score; Letcom = Letter Comparison; Patcom = Pattern Comparison; Shipley = Shipley Abstraction Score; Raven = Raven's Progressive Matrices score; CSpan = computation span working memory score; and LSpan = listening span working memory score. Variables in Panel B are: PatCom = Pattern Comparison; LetCom = Letter Comparison; KT:V = keeping track of verbal information; KT-S = keeping track of spatial information; EM-V = element memory for verbal information; EM-S = elem€nt memory for spatial information; MM-V = matrix memory for verbal information; and MM-S = matrix memory for spatial information.
on different^cognitivevariables are not independentof one another.rTheseresultslead to the secondimoortant constrainton theoriesofcognitive aging. Constraint 2 Somefairly general or broad mechanismsare apparently needed to account.for the lack of independencein the age-related influences on cognitive variables
in other words, becausea large proportion of the agerelatedeffectson different cognitivevariablesappearsto be shared,theoriesbasedexclusivelyon specificmechanismswill not be sufficient to accountfor cognitiveaging phenomena.Although somespecific age-relatedmechanisms appearto exist, they must be supplementedby broaderor more generalmechanismsin order to account for the commonality apparentin the age-relatedeffects on different cognitive variables.
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Figure 5. Single common factor structural models for data (A) from Salthouse, Fristoe, and Rhee (in press) and (B) from salthouse, Hancock, et al. (in press). variables in panel A are: DigSym = wAlS-R Digit symbol substitution score; Letcom = Letter comparison; patCom = Pattern comparison; PAI = Trial I in Paired Associates Memory; pA2 = Trial 2 in Paired Associates Memory; RVLT2 = Trial 2 in the Rey Auditory verbal Learning Test; RVLT6 = Trial 6 in the Rey Auditory verbal Learning Test; wcSTpE = percent perseverative errors in the Wisconsin Card Sorting Test; WCSTCL = perc€nt conceptual level responses in the wisconsin Card Sorting Test; objAssm = wAIS-R object Assembly score; BlkDes = wAIS-R Block Design score; F60 = number of words beginning with F produced in 60 sec; and 560 = number of words beginning with S produced in 60 sec. Variables in panel B are: = number of category responsesin the wisconsin card Sorting Test; Assocpc = wcsr:-Nc percentage correct in associative learning; NB2 = percentage correct in reporting items twoback in a sequence; NBI = percentage correct in reporting items one-back in a sequencel wM-N = numeric (computation span) working memory score; wM-v = verbal (reading span) working memory score; DSRT = digit symbol reaction time; DDRT = digit digit reaction time; Patcom = pattern comparison; LetCom = letter comparisonl vision-R = visual acuity in the right eye; and Vision-L = visual acuity in the left eye.
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An obviousnext question,in light of the evidencesuggestingthat a common or generalage-relatedfactor exists, concernsthe nature ofthat factor. One approachto investigatingthe natureofthe generalfactor involvesex-
amining where, in an ordered sequence,independent age-relatedeffects occur (Salthouse,in press-b). The issue of primary interest in these sequentialanalysesis how much of the age-relatedvariance in later variables
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in the sequenceis sharedwith, and presumablymediated through,age-relatedeffectson variablesearlier in the sequence.Consider the possible interpretationsif the sequenceofvariables correspondsto successivelevels of practice on the task, or to progressivelylonger stimulus durations.If only a small proportion of the age-related variancein variableslate in practice,or in variablescorrespondingto long stimulus presentationdurations,is sharedwith variablesearly in practice or with variables correspondingto short stimulus presentationdurations, then one could infer that distinctage-relatedinfluences emergeas a function of increasedpracticeor longer presentationdurations. For example, some types of higher order processingor strategiesmight develop with practice on the task,or may be effectiveonly after the presentation durationof the stimuli exceedsa minimum value. However,if a substantialproportion of the age-related variancein latervariablesin an orderedsequenceis shared with variablesearlier in the sequence,then one could infer that the factorsresponsiblefor many of the agerelated effects are presentvery early in practice and as soonas the relevantstimuli can be registered. Perhapsthe simplestmethodof determiningthe amount ofindependentage-related varianceon a particularvariable in a sequenceis to use hierarchicalregressionproceduresin which the variancein the prior variablein the sequenceis controlledbeforethe amountofage-related variancein the targetvariableis assessed. The residual age-relatedvariancein this situationindicatesthe agerelatedinfluencethat is independent of the prior variable in the sequence,and it can be expressedas a proportion by dividing the independentage-relatedvarianceby the total age-relatedvariancefor that variable. Analysesofthis type requireaccessto the raw data,or at leastto a completecorrelationmatrix, from studiesin which eitheramountof practiceor the time of stimulus presentationhavebeenmanipulatedin samplesof adults ofdifferent ages.Resultsfrom severalsuch studies,includingthoseby Charnessand Campbell( 1988),Cooper (1994),and Rogers,Fisk, and Hertzog(1994),were recently describedby Salthouse(in press-b).Figures6 and 7 illustratetheseand relatedresultsin the form ofthe percentage(i.e.,the proportioncomputedas describedabove multiplied by 100) of the age-relatedvariancefor each variablein the sequencethat was independentofthe agerelatedvariancein the previousvariablein the sequence. The data in the upper left panel ofFigure 6 represent performancein fairly complex multiple-task(i.e., synthetic work) or mental squaringstudiesacrosssuccessive 25-min (syntheticwork) or 38-trial (mental squaring) sessions.The upperright panel containsdatafrom visual and memory searchreactiontime taskscollapsedacross setsof 240 or 600 trials. Data in the bottom two panels of Figure 6 correspondto singletrials in free recall,maze learning, or associativelearning tasks.Although the results basedon single trials are clearly much noisier than thosein which eachdatapoint is basedon a greaternumber of observations,a similar pattern of greatly reduced
unique age-relatedvarianceacrosssuccessivepoints in practiceis evidentin every panel.It can thereforebe concluded that most of the independentage-relatedinfluencesin severaldifferent types ofcognitive tasksare apparentin the earliestphasesoftask performance. Resultsfrom studiesmanipulatingthe amountof time relevantstimuli in the task were presentedare illustrated in Figure 7 . Each point in thesefigures reflectsthe average level of performanceacrossa moderatenumber of trials at a given stimulus duration in studiesin which stimulusdurationvariedas a within-subjectsmanipulation. Despitethe variationin tasksand stimuli, a clear patternofmost ofthe unique age-relatedvarianceoccurring at the shortestpresentationdurationsis apparentin each function. The resultssummarizedin the last two figures indicate that very little distinct age-relatedeffects appearto occur on measuresofperformancerepresentinglater sessionsof practiceor longerstimulusdurations.This leads to the third constraintfor theoriesof cognitiveaging. Constraint 3 Factorsoperatingwhile stimuli are initially being registered,or in the early sessionsof practice on the task, need to be postulated to acc'ount.fbrmuch o/ the agerelated efkcts in at least severalcognitive tasks--that is, becausea very largeproportionofthe age-related influenceslatein practiceandwith long stimuluspresentation durationsare apparentlymediatedthrough inlluencesoperatingearlyin practiceand with shortpresentation durations,plausibletheoriesofcognitiveagingneed to incorporatemechanismswith earlyandrapid influences. An alternativeapproachto investigatingthe natureof the hypothesizedcommon factor consistsof examining the extentto which the age-relatedvariancein the cognitive variablesof interestis reducedafler controlling for the variancein variablesthat might be postulatedto function as mediatorsof the age-cognitionrelations.Selection of potentialmediatorscould bejustified on theoretical grounds,or couldbe basedon empiricalcriteriasuch as the variablesthat either appearto be the simplestor havethe highestloadingson the commonfactor.Hierarchical regressionanalysescannext be conductedin which the variance in the presumablyfundamentalmeasureis controlledbeforethe relationof ageto the othermeasures is examined.The plausibilityof a variable'sacting as a mediator of the relationsof age to other variablescan be inferred to increasein proportion to the degreeto which the age-relatedvariancein the criterionvariableis reduced after the variance in the potential mediating variable is controlled. A relativelylarge number of recentstudieshave reported results of statisticalcontrol analyseswhen measuresof working memory or processingspeedhaveserved as the controlledvariables.Becausetasksdesignedto assessprocessingspeedcan be arguedto be simpler than thoseassessingworking memory, and becauseresultsof
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statisticalcontrol analysesindicate that there is greater reduction of the age-relatedvariance in measuresof working memory after control of measuresof speedthan vice versa(e.g.,Salthouse, in press a), the followingdiscussionwill focuson researchin which measurespostulatedto reflect processingspeedservedas the controlled variable.a A wide variety of speedvariableshave been used in thesetypes of analyses,ranging from measuresof simple reactiontime to measuresof decisiontime in moderately complexcognitivetasks(e.g.,Bieman-Copland& Charness,1994;Bors & Forrin, 1995;Bryan &Luszcz, in press;Graf & Uttl, 1995;Hartley, 1986, 1993;Hertzog, 1989; Hultsch,Hertzog,& Dixon, 1990; Hultsch, Hertzog, Small, McDonald-Miszczak,& Dixon, 1992: K w o n g - S e e& R y a n , 1 9 9 5 ;L i n d e n b e r g eer t a l . , 1 9 9 3 ;
N e t t e l b e c k& R a b b i t t ,1 9 9 2 ;S c h a i e ,1 9 8 9 ,1 9 9 0 ) .A l though nearly all ofthe relevantstudieshavereportedat leastmoderateattenuationof the age-relatedvariancein the criterion cognitive variableafter control ofthe speed measure,the degreeof attenuationappearsto be greatestwith speedmeasuresfrom taskswith elementarycognitive requirements(Salthouse,1993b,1994c).This could be becausetasks such as simple reaction time, marking lines,or copying digits tend to emphasizeperipheralsensory and motor factors,and performancein complextasks may be heavily influencedby amount of relevantknowledgeand varioushigherordercognitiveabilities.In contrast,tasksinvolving simplesearch,comparison,and substitution operationsclearly have a cognitive component, but are likely to be only minimally influencedby quantity of knowledgeor levelof spatial,reasoning,or memory
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abilities.In thepsychometricabilitiesliterature,thesetasks are consideredto assessperceptualspeed(includedare suchtestsas FindingAs, IdenticalPictures,NumberComparison,Visual Matching, and varioussubstitutiontests). Two tasksthat have been used in many recent studies to assessperceptualspeedinvolve the presentationof pairs of lettersor line patternswith the researchparticipant instructedto classify them as same or dilJbrentas rapidly as possible.Becausethe measuresofperformance on these tasks typically have moderateto high correlations with one another(e.g.,in the rangeof .70),a more reliable compositespeedindex can be formed by averaging the z scoresfrom the two tasks. Resultsfrom severalstudiesin which the age-related variancein different cognitive measureshas been compared before and after control of the compositeletter comparison/pattern comparisonspeedindex arereported in TableI ofSalthouse( I 993b)and in Table5 ofSalthouse (in press-a).The analysesin the Salthouse(1993b)article indicatedthat almost 80% of the age-relatedvanance in variousmeasuresof reasoningand spatialabilitieswas eliminatedafter control of measuresof perceptualspeed. Similar reductionsof the age-relateddifferencesin measures of memory performance were reported by Salthouse (in press-a). To illustrate, the percentagereduction in age-relatedvarianceranged from 87 to 96 for measuresof free recall, from 58 to 84 for measuresof associativelearning, from 83 to 100 for measuresof asso-
ciative memory,and from 78 to 97 for measuresof workphenomenonis also ing memory.This speed-attenuation evident with criterion variablesoften consideredto reflect higher order cognitivefunctioning.For example,the age-relatedvariancein performanceon the Raven'sProgressiveMatrices Testwas reducedby 82.0% after control of the letter comparison/patterncomparison speed index in a studyby Salthouse(1993b)and by 60.8%in a studyby Babcock(1994).The reductionin the age-related variancein the numberof categoriesmeasurein the WisconsinCard Sorting Testafter control of this samespeed index was 75.4"/oin a study involving 259 adults,reported by Salthouse, Fristoe,and Rhee(in press),and 85.5%in a studyinvolving 197adults,reportedby Salthouse,Hancock,et al. (in press).Finally,the age-related variancein the WAIS-R Block Design and Object AssemblyTests was reducedby 86.3% and87.60/o, respectively,after control of the letter comparison/patterncomparison speed index in the Salthouse,Fristoe,and Rhee(in press)study. The results summarizedabove indicate that there is considerableoverlap of the age-relatedinfluenceson very simple speededtasks and on complex cognitive tasks,even when the latter are administeredunder selfp a c e dc o n d i t i o n s( e . g . ,S a l t h o u s e1, 9 9 3 a , 1 9 9 4 c S ; althouse,Fristoe,& Rhee,in press).There are at least two possible interpretationsof these well-documentedrelations. One is that measuresof performancein simple tasksprimarily reflect how quickly basic operatronscan
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CONSTRAINTSON THEORIESOF COGNITIVEAGING be executed,and that processingspeedis a critical mediating factor contributingto the age differencesin many differentcognitivevariables(e.g.,Salthouse,in press-a). An alternativeinterpretationis that speedis not necessarilythe critical causalfactor responsiblefor the agecognition relations,but rather that there are one or more other factors that influence basic processingefficiency, and that the only way effects on processingefficiency can be manifestedin thesetypesof very elementarytasks is in terms of a reduction in the speedof performanceof the operations.That is, most of the tasks used to assess perceptualspeedare so simple that errors are relatively infrequent,and nearly everyonewould perform without m i s t a k e si f t h e r e w a s n o t i m e p r e s s u r e .A s a c o n s e quence,virtually all ofthe individual differencesin these tasksare evidentin the speedwith which the requisite operationscan be completedratherthan in the quality or accuracyof performance,but this does not necessarily meanthat the primarycauseof thesedifferencesis an alteration in one or more processing-speed factors. Both interpretationsagreethat simple processingefficiencyis compromisedwith increasedage,but they differ in that in the first interpretationa slower processing speedis postulatedto be the critical mediating factor, whereasin the latter interpretationspeedof performance is viewed merely as the mannerin which differencesin processingefficiencyare exhibited.Additionalresearch is neededto distinguishbetweenthesepossibilities,but it is importantnot to lose sight of the fact that whatever their cause,thesevery simplemeasures of processingefficiency have been found to share large proportions of age-related variancewith complexmeasures of cognitive performance.This leadsto the fourth and lastconstraint fiortheoriesof cognitiveaging. Constraint 4 Factors related to simple processing fficiency need to be incorporated in explanations oJ'age-relatedcognitive ddferencesthat is, becausestatisticalcontrol ofvariablesreflecting an individual's efficiency at carrying out elementary cognitive operationshas been found to reduce the agerelated variancein a wide variety of cognitive variables by between50ohand 100%,factorscontributing to basic processingefficiency must play a prominentrole in comprehensivetheoriesof cognitiveaging. IMPLICATIONS
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FOR FUTURE R.ESEARCH
Ifthe constraintsdescribedaboveare acceptedas reasonable,then they presumablymust be incorporatedin any plausible theory attempting to account for agerelatedcognitivedeclinephenomena.Theoriesfocusing exclusivelyon processes specificto a particulartype of c o g n i t i v ef u n c t i o n i n g( e . g . ,d e l i b e r a t er e c o l l e c t i o ni n memory, or mental rotation in spatialtasks)or on higher order processes(e.g.,metacognitiveevaluations,or overt
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compensatorystrategies)will thereforeneed to be supplementedbefore they can be consideredcompletetheories of cognitive aging. Furthermore,to the extent that the constraintsare valid, they suggesttwo important directions for future research.One line ofresearch should be directed at investigatingthe sourcesof the age relations on measuresof simple processingefficiency and of the mechanismsby which they affect cognitivefunctioning. The secondfocus for future researchshould be investigation of the mechanismsresponsiblefor specific age-relatedinfluences.That is, in addition to learning more about the nature of the hypothesized general or common factor and how it exertsits influence, research should also be directed toward examining the operation of mechanismsthat are independentof the generalfactor. There are at leasttwo major reasonswhy it can be arguedthat the highestpriority for futureresearchand theorizing should be understandingthe natureofage-related differencesin simpleprocessingefficiency.First,specific influencesare, by definition, more limited in scopethan generalinfluences,and thus havea more restrictedrange of explanatorypower.And second,limitations at a basic levelmay influencethe type or effectiveness of any higher levelprocessingthat canbe carriedout. Analysesofspecific age-relatedinfluenceswould thereforelikely be meaningful only to the extent that procedureshave first been employedto control or adjust for any generalagerelatedinfluencesthat might exist. In view of the large amount of evidence indicating that general age-related factorscontributeto the observedage-relateddifferences in many cognitivevariables,researchersinterestedin investigatingspecific age-relatedinfluenceswould be well advisedto considerthe impactofbroaderinfluencesbefore placingmuch confidencein their interpretations of specificinfluences.For example,to ensurethat the effects ofinterestare truly specificand independentofbroader or more general factors, these researchersmight focus on explaining the residual age-relatedvariance that remainsafterthe influenceof measuresof simpleprocessing efficiencyhavebeenstatisticallycontrolled. An initial step in researchaimed at investigatinggeneral age-relatedinfluencesmight consistof specifying possiblesourcesof age-relateddifferencesin simple processingefficiency. Among the categoriesof explanation that could be consideredare nonspecific factors such as level of motivation (e.g., amount of interestin, or effort expendedon, the task) or cautiousness (e.g.,relativeemphasison accuracyor quality comparedwith speed),input and outputfactorssuchas sensoryabilities(e.g.,sensitivity to environmentalstimulation)and motor abilities(e.g., quicknessof emitting or controllingovertresponses), and cognitivesystemcharacteristicssuchas working memory (e.g.,the ability to maintaininformationaboutthe task requirementswhile alsofluently performingthe relevantoperations),attention(e.g.,the ability to allocate,inhibit, sustain,or redirectattentionto relevantaspectsof the task), and processingspeed(e.g.,the rate at which many differentprocessingoperationscan be executed).
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The next step in this type of researchmight involve a detailed examination of one or more of the candidate sourcesofage-relateddifferences.There area numberof ways in which this investigationcould proceed,but several broad principles or guidelines can be identified. Much of the previous researchexamining the variables listed abovehas been limited in its informativenessbecauseone or more of theseprinciples havebeenneglected. One guideline is that two or more measuresof the relevant constructshould be assessedto minimize the influence of method-specificvariance,maximize the contribution of the theoreticallyinterestingconstructvariance, and increasethe reliability of the assessment. When only a single variable is used to assessthe construct,it is impossibleto distinguishthe influencesassociatedwith the materials,procedures,and forms of assessmentfrom thoseattributableto the theoreticalconstructof primary interest.Reliability can also be improvedby aggregation acrossdifferentvariablesas well as by aggregationacross additional observationsinvolving the same variable. A secondguideline is that both correlational and experimental proceduresshould be employedwheneverpossible. Correlational proceduresare useful to evaluatethe explanatorypower of the hypothesizedmediator by determining the relative magnitudesof the mediated and unmediatedrelationsbetweenage and various measures of cognitiveperformance.For example,a constructwould probablynot be consideredplausibleas a mediatorif the age-relatedvariancein the criterion variablewas not substantially reducedafter measuresof that constructwere held constantby statisticalmeans.Furthermore,questions of independenceand specificity are most directly addressedwith correlationalmethods.However,experimental proceduresare desirablefor the investigationof the mechanismsresponsiblefor relationsbetweenage and the hypothesizedconstructand betweenthe construct and the cognitive measures.Finally, the researchshould be replicatedacrossindependentsamplesand variations in methodologyin order to establishthe robustnessand generalizabilityof the major results. SUMMARY The primary focus of this article has been on summarizing the empirical evidencerelevant to what are proposedas four important constraintsthat must be consideredin explanationsof cognitiveaging phenomena.First, becauseofthe great variety ofvariables exhibiting significant age differences,plausible theories need to incorporateeither a large number of highly specific agerelatedinfluencesor a small number of more general influences.Second,becausea largeproportionofthe agerelatedvarianceon different cognitivevariableshasbeen found to be sharedand not independent,plausibletheories needto postulatea generalfactor to accountfor this lack ofindependence. Third, becausemost ofthe independent age-relatedvariancein an orderedsequenceofvariablesoccursearly,major age-relateddeterminantsmust
be postulatedto be operatingas soon as the stimuli can be registeredand at the earliest stagesofpractice. And fourth, becausemeasuresof simpleprocessingefficiency share considerableproportions of age-relatedvariance with many complex cognitive measures,adequatetheoretical accountsmust include factors related to simple processingefficiency. Finally, it was suggestedthat a high priority for future researchshould be to investigatethe natureof age-relateddifferencesin simpleprocessingefficiency and to discoverthe mechanismsby which cognitive performanceis affectedwhen the efficiency of elementaryaspectsof processingis compromised. REFERENCES B A B c o c K ,R . L . ( 1 9 9 4 ) . A n a l y s i s o f a d u l t a g e d i f f e r e n c e s i n t h e Raven'sAdvanced ProgressiveMatrices Test.Psychology& Aging, 9 , 3 0 3 - 31 4 . BIEue.u-Copr-aNn S,. , & C s e n N E S sN , . (1994).Memory knowledge a n d m e m o r y m o n i t o r i n g i n a d u l t h o o d . P s y c h o l o g y& A g i n g , 9 , 287-302. BInnnN,J. 8., & ScHnrs, K. F. ( I 995b). Handbook of the psychology of aging (4th ed.). San Diego: Academic Press. Bons, D. A., & FonnrN,B. ( I 995). Age, speedof information processing, recall, and fluid intelligence. Intelligence, 20, 229-248. B n y n n , J . , & L u s z c z , M . A . ( i n p r e s s ) .S p e e do f i n f o r m a t i o np r o c e s s ing as a mediator between age and free recall performance. Pslchology & Aging. CrnEr-1a,,J. ( I 990). Aging and information processingrates in the elderly. fn J. E. Birren & K. W. Schaie(Eds.), Handbooko/'the psvc h o l o g y o f a g i n g( 3 r d e d . ,p p . 2 0 l - 2 2 1 ) .N e w Y o r k :A c a d e m i cP r e s s . C s a . n x e s sN , . , & C a n , t p s E r -Jr.-I,. D . ( 1 9 8 8 ) .A c q u i r i n g s k i l l a t m e n t a l calculation in adulthood: A task decomposition.Journal o/'Experimental Psychology: Ceneral, I17, I I5-I29 CoueN, J. (1988). .t/d/n/ical pou'er analysis for the hehavioral scie n c e . rH . i l l s d a l e .N J : E r l b a u m . Coopnn, B. P ( I 994). Age-related dil/brences in search/decision perJbrmance and trans.fbr:An evuluation of learning and skill acquisil i o n . U n p u b l i s h e dm a s t e r ' st h e s i s ,G e o r g i aI n s t i t u t eo f T e c h n o l o g y , Atlanta. Curx, F. L M., & Sa,rrsousr, T. A. ( 1992). Handbook of aging and c o g n i t i o n .H i l l s d a l e ,N J : E r l b a u m . Gner, P, & Urrl, B. ( I 995). Componentprocesses ofmemory: Changes acrossthe adult lifespan. SwissJournal of Psychology,54, I I 3- I 38. Hanrr-Ev, J. T. (1986). Readerand text variablesas determinantsof discoursememory in adulthood.Psychology& Aging, l, I 50- I 58. Hanrley, J. T. ( I 993). Aging and prosememory: Testsofthe resourced e f i c i t h y p o t h e s i sP. s y c h o l o g y& A g i n g , 8 , 5 3 8 - 5 5 1 . Heen, D. O. (1942). The effect ofearly and late brain injury upon test scoresand the nature ofnormal adult intelligence. Proceedingsof the American Philosophical Society, 85, 27 5-292. H E n r z o c , C . ( 1 9 8 9 ) . I n f l u e n c e so f c o g n i t i v e s l o w i n g o n a g e d i f f e r encesin intelligence.DevelopmentalPsychology,25, 636-651. H o n N , J . L . , & C e r r s L L , R . B . ( 1 9 6 3 ) . A g e d i f f e r e n c e si n f l u i d a n d crystallized intelligence.Acta Psychologica,26. 107-129. H u r r s c H , D . F . , H r n r z o c , C . , & D r x o N , R . A . ( 1 9 9 0 ) .A b i l i t y c o r r e latesof memory performancein adulthood.Psychology& Aging,S, 356-368. HulrscH, D. F.,HEnrzoc, C., Sunr-r-,B. J., McDoNnlo-Mrszcznx, L., & DrxoN, R. A. ( I 992). Short-term longitudinal changein cognitive performance in later life. Psychology& Aging,7,5'71-584. K l t r c r , R . , & M a y n , U . ( 1 9 9 2 ) . C o m m e n t a r yo n S a l t h o u s e( 1 9 9 2 ) "Shifting levels ofanalysis in the investigationofcognitive aging." Human Development, 35, 343-349. KwoNc SEs,S. T., & RveN, E. B. ( I 995). Cognitive mediation of adult age differencesin languageperformance.Psychology& Aging,l0, 458-468. LrNosNsnncrn, U., & BllrEs, P. B. (1994). Sensory functioning and
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CONSTRAINTSON THEORIESOF COGNITIVEAGING intelligence in old age: A strong connection.Psychology& Aging, 9.339-355. [ - r \ D E N B E R c EU R.,, M a y n , U . , & K l r e c l , R . ( 1 9 9 3 ) .S p e e da n d i n t e l l r g e n c ei n o l d , a g e P . s y c h o l o g y& A g i n g , 8 , 2 0 7 - 2 2 0 . \lr ensoN,J., Ha.Le,S., Wacsupr', D., Pool, L. W, & Slrrrs, G. A. t 1990).The information loss model: A mathematicaltheory of agerelatedcognitive slowing. PsychologicalReview, 97, 47 5-48'7. N r r r t L s E r - x , T . , & R n s s r r r , P M . A . ( 1 9 9 2 ) . A g i n g , c o g n i t i v ep e r lbrmance, and mental speed.Intelligence, 16, lB9-205. R o c r - n s ,W . A . . F r s K ,A . D . , & H E R r z o c , C . ( 1 9 9 4 ) . D o a b i l i t y performancerelationshipsdifferentiate age and practice effects in rrsuaf search'l Journal o.f Experimental Psychology; Learning, .ll emory. & C ognit ion. 20, 7 | 0-738. Srr.rsouss, T. A. ( l99l ). Theoreticalperspectiveson cognitive aging. H i l l s d a l e .N J : E r l b a u m . S r r . r s o u s s , T . A . ( 1 9 9 2 ) .S h i f t i n g l e v e l so f a n a l y s i s i n t h e i n v e s t i g a tion of cognitive aging. Human Development,35, 321-342. S , r rr. u o u s n ,T . A . ( 1 9 9 3 a ) I. n f l u e n c eo f w o r k i n g m e m o r yo n a d u l ta g e differencesin matrix reasoning.British Journal o.fPsvchotogy,S4, l7t-199. S.rr ruousE, T. A. ( I 993b). Speedmediation of adult age differences in cognition. DevelopmentulPsychology,29, 722-735. S r r .r n o u s e . T . A . ( I 9 9 4 a ) .A g i n g a s s o c i a t i o n sI:n f l u e n c eo f s p e e do n a d u f t a g c d i f f e r e n c e si n a s s o c i a t i v el e a r n i n g .J o u r n a l o l E t p e r i ntental Ps.vchoktgv: Learning,Memory.& Cognition.20, 1486-1503. S . r r r H o u s e , T . A ( I 9 9 4 b ) . H o w m a n y c a u s e sa r e t h e r e o f a g i n g r e l a t e dd e c r e m e n t si n c o g n i t i v e f u n c t i o n i n g ' ?D e v e l o p m e n t a !R e lrex', 14, 413-437. S r r . r ' x o u s r -T . ,. A . ( 1 9 9 4 c ) . T h e n a t u r e o f t h e i n f l u e n c eo f s p e e do n aduft age differencesin cognition. DevelopmentalPsychoktgv,30. 240-259. S . r r . ur o u s t , T . A . ( I 9 9 5 a ) . D i f f e r e n t i a la g e - r e l a t e di n f l u e n c e so n m e m o r y f o r v e r b a l - s y m b o l i ci n f o r m a t i o na n d v i s u a l - s p a t i ailn f o r mation. Journal of Gentntology: Pst,t.hological Scjence.r,50B. Pr93-P20t. S n r - r ' H o u s rT- ., A . ( I 9 9 5 b ) -I n f l u e n c eo f p r o c e s s i n gs p e e do n a d u l t a g e d i f f e r e n c e si n l e a r n i n g .S w , i sJso u r n u l o f P s y t h o l o g r - , 5 4 , 1 0 2 - l 1 2 . S , r . r H o u s n ,T . A . ( i n p r e s s - a ) .T h e p r o c e s s i n gs p e e dt h e o r y o f a d u l t age differencesin cognition. Psythologicul Revieu'. S r r - r H o u s t -T, . A . ( i n p r e s s b ) . W h e r e i n a n o r d e r e ds e q u e n c eo f v a r i abfcs do independentage-relatedeffects occur'l Journal of Ceront o I og.r': Ps.vt'ho I ogic a I St ie nces. S , r t . t u o u s nT , . A . , & C t x t N ,V E . ( I 9 9 4 ) . I n t e r p r e t a t i o n of differential deficits: The caseofaging and mental arithmetic.Journal o/ Experimental Ps.vchologl,: Learning.Memory.& Cognition,20, | 172-l lB2. S n t . r n o u s e ,T . A . , F n r s r o E ,N . , & R H E e ,S . ( i n p r e s s ) .H o w l o c a l i z e d a r e a g e - r e l a t e de f f e c t s o n n e u r o p s y c h o l o g i c am l e a s u r e s ?N e a r o p.s.vt'hologr'. S n l r u o u s r - , T . A . , H A n r s R r c ' rD, . 2 . , L u K A s , K . 8 . , & D a r r _ .T . C . ( i n press)D . e t e r m i n a n t os f a d u l t a g ed i f f e r e n c e o s n s y n t h e t i cw o r Kp e r formance. Journal ol Experimental Psyt.holog.v; Apptied. Snt-'rHouse,T. A., & HnNcocK, H. J. (1995\. E/lbctsof'age and speed on memor.r'as a .function of stimulus presentation time. Unpobl i s h e dm a n u s c r i p t . S n r r s o u s E , T . A . , H r N r r r x , H . J . , M E r N z ,E . J . , & H l l r n n r c K , D . Z . ( l n p r e s s ) .I n t e r r e l a t i o n so f a g e , v i s u a l a c u i t y ,a n d c o g n i t i v ef u n c tioning. JournuI o| GerontoIogv: Ps),chologicaI Scient.es.
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SelrHousn, T. A., & MrrcHrr-r, D. R. D. (1990). Effects of age and naturallyoccurring experienceon spatialvisualizationperformance. Develop mental Psychology,26, 845-854. Scnare, K. W. ( 1989). Perceptualspeedin adulthood:Cross-sectional and longitudinal analyses.Psychology& Aging, 4, 443-453. S c H a r e ,K . W . ( 1 9 9 0 ) . C o r r e c t i o n t o S c h a i e( 1 9 8 9 ) . P s y c h o l o g y& Aging, 5, l7 | . ScHetp,K. W., & WIrr-rs,S. L. ( 1993).Age differencepatternsof psyc h o m e t r i c i n t e l l i g e n c ei n a d u l t h o o d :G e n e r a l i z a b i t i t yw i t h i n a n d a c r o s sa b i l i t y d o m a i n s .P s y c h o l o g y& A g i n g , 8 , 3 7 1 - 3 8 3 . V E R H A E G H EPN,, & M l n c o p N , A . ( 1 9 9 3 ) . M o r e o r l e s st h e s a m e ?A m e m o r a b i l i t y a n a l y s i so n e p i s o d i c m e m o r y t a s k s i n y o u n g a n d older adults. Journal of Gerontology: Psychological Sciences, 48, Pt72-P178. NOTES l . I n d i c e s o f t h e g o o d n e s so f f i t o f t h e m o d e l s w e r e a s f o l l o w s : M o d e l i n F i g u r e 4 A , ,X 2 ( t t ) : 8 3 . 9 9 , S t d . R M R - . 0 5 0 , C F t : . 9 4 : M o d e l i n F i g u r e4 8 , X 2 Q D - 6 5 . 2 7 .S t d . R M R : . 0 5 1 ,C F I : . 9 4 . M o d e l i n F i g u r e5 4 , X 2 ( O g ): 1 3 5 . 8 0 ,S t d . R M R - . 0 5 6 . C F t : . 9 i : M o d e l i n F i g u r e5 8 , X 2 ( J 9 ): 1 3 5 . 0 6 ,S t d . R M R : . 0 6 9 . C F I : . 9 4 . 2. The patternofresults for all data setswas also quite similar when the following procedure,based on a principal-componentsanalysis, was performed. First, a principal-componentsanalysiswas performed on all variables;second,the first (unrotated)principal componentwas extractedto serve as an index of the general factor in the set of variables;and third, a seriesofhierarchical regressionanalyseswere perf o r m e d i n w h i c h e a c h i n d i v i d u a lv a r i a b l es u c c e s s i v e l fyu n c t i o n e da s the criterion variable,and the first principal componentwas usedas a control variable before examining the variance associatedwith age. The residual age-relatedvariancein theselatter analysesindicatesthe age effects that are independentofthe generalor common factor, and t h u s t h e y c a n b e c o n s i d e r e dt o b e s p e c i f i co r u n i q u e . 3 . I t s h o u l da l s ob e n o t e dt h a tt h c c o n c l u s i o nt h a t t h e a s e - r e l a t e d influences on different variablesare not independentis coirsistentwith l n t e r p r e t a t i o nosf a n a l y s e sb a s e do n t h e e x i s t e n c eo f s t r o n g s y s t e m a t i c r e l a t i o n sb e t w e e nt h e m e a nl e v e l so f p e r f o r m a n c ea c r o s sc o n d i t i o n si n s a m p l e so f y o u n g a n d o l d a d u l t s f o r b o t h s p e e dv a r i a b l e s( e . g . , C e r e l l a , 1 9 9 0 ; M y e r s o n , H a l e , W a g s t a f f ,P o o n ,& S m i t h , 1 9 9 0 )a n d a c c u r a c yv a r i a b l e s( e . g . ,V e r h a e g h e n & M a r c o e n .1 9 9 3 ) . 4 . I t i s i m p o r t a n tt o n o t et h a t t h e f o c u so n p r o c e s s i n gs p e e da s a p o tential mediator of age-cognition relations differs in at least two respectsfrom the approachofother theoristswho have been concerned w i t h a g e d i f f e r e n c e si n m e a s u r e so f s p e e d( e . g . ,C e r e l l a ,1 9 9 0 ;M y e r s o n e t a l . , I 9 9 0 ) . F i r s t ,t h e t a r g e tv a r i a b l e st o b e e x p l a i n e di n t h e p r e s e n t a n a l y s e sc o n s i s to f a l m o s t a l l c o g n i t i v ev a r i a b l e sf o u n d t o b e r e l a t e dt o a g e i n a d u l t h o o d ,a n d n o t m e r e l yv a r i a b l e sm e a s u r e di n u n i t s o f t i m e . A n d s e c o n d ,t h e r e s u l t so f p r i m a r y i n t e r e s th e r ea r e c o m p a r i s o n so f t h e a m o u n to f a g e - r e l a t e dv a r i a n c ei n t h e t a r g e tv a r i a b l eb e fore and after control ofan index ofspeed, ratherthan the number and n a t u r eo f t h e f u n c t i o n sr e l a t i n gt h e m e a n s p e e d so f o n e a g e g r o u p t o t h e m e a n s p e e d so f a n o t h e r a g e g r o u p .
( M a n u s c r i p tr e c e i v e dA u g u s t 3 , 1 9 9 5 ; r c v r s i o na c c e p t e df o r p u b l i c a t i o nJ a n u a r y2 5 , I 9 9 6 . )
