Structural constraints on process explanations in cognitive aging

Psychology attd Aging Copyright 2000 by the American Psychological Association, Inc. 2000, Vol. 15, No. 1, 44-55 0882-7974/00/$5.00 DOI: 10.1037/10882-7974.15.1.44

Structural Constraints on Process Explanations in Cognitive Aging

Timothy A. Salthouse Georgia Institute of Technology

Sara J. Czaja University of Miami

Much of the current research in the area of cognitive aging has been focused on investigating specific processes presumed to be responsible for the age differences observed in particular cognitive tasks. A central thesis of this article is that age-related effects on cognitive variables seldom occur in isolation, and hence, they are best interpreted in the context of the structural interrelations that exist among variables and the relations of age on that organizational structure. Results from analyses of 2 separate data sets suggest that large proportions of the age-related effects across a wide range of cognitive variables are shared and that independent, or unique, age-related effects often contribute relatively little to the age differences observed in many cognitive variables. These findings imply that it is important to consider the structure within which a variable occurs when attempting to investigate the processes responsible for age-related differences on that variable.

Research has found many cognitive variables to be significantly related to age, but relatively little is currently known about whether, and if so, to what extent, those influences are independent of one another. This question is important because it is relevant to the nature of the eventual explanations of those effects. That is, in accounting for the age-related influences on a variety of different cognitive variables, do researchers need many narrow and specific explanations, a smaller number of broad and general explanations, or some mixture of the two? Moreover, although this is primarily a theoretical issue, it could have practical implications if one was interested in designing interventions to remediate age-related cog- nitive deficits, because the answer to this question will be relevant to the number, breadth, and type of interventions that will even- tually be necessary for successful remediation.

Four interesting possibilities for characterizing the pattern of age-related effects on a set of variables appear in Figure 1. In each case, the observable variables are represented as boxes, and the arrows can be interpreted as correlations. Circles in these diagrams indicate latent constructs that represent variance common to the variables or constructs to which they are connected.

The complete independence model in the upper left panel (Model 1) portrays a situation in which the age-related effects on individual variables are completely independent of one another. This model is consistent with the view that age-related effects on different variables are qualitatively distinct, either with respect to distal origin (e.g., maturational or experiential) or in terms of proximal manifestation (e.g., involvement of different cognitive

Timothy A. Salthouse, School of Psychology, Georgia Institute of Technology; Sara J. Czaja, Department of Psychiatry and Behavioral Sciences, University of Miami.

This research was supported by National Institute of Aging Research Grants AG06826 and AG11748.

Correspondence concerning this article should be addressed to Timothy A. Salthouse, School of Psychology, Georgia Institute of Technol- ogy, Atlanta, Georgia 30332-0170. Electronic mail may be sent to tim. salthouse @psych.gatech.edu.

processes, reliance on particular neuroanatomical regions). One could advance a number of arguments to support the plausibility of this complete independence model. For example, a considerable amount of research on patients with discrete brain damage and on normal adults with neuroimaging indicates that there is at least some localization of function (e.g., Banich, 1997; Martin, 1997), and therefore, independent and specific influences of age might be expected on variables presumed to reflect functioning in different neuroanatomical regions. To illustrate, if one variable is affected by damage to the prefrontal cortex and another is impaired by lesions in the medial temporal lobe complex, one might expect those variables to have distinct and independent age-related ef- fects. Similarly, if two variables are suspected to involve qualita- tively distinct cognitive processes, one might expect them to have little or no overlap 9 f their age-related effects.

Model 2 (Single Common Factor) in the upper right panel of Figure 1 portrays all of the age-related effects on the relevant variables as determined by the operation of a single factor. The key feature of models of this type is that one causal factor is presumed to be responsible for the age-related influences on many different variables. Baltes and Lindenberger (1997; Lindenberger & Baltes, 1994) recently referred to a variant of this single factor model as the common cause model because the age-related effects on a wide variety of variables, including those assessing traditional cognitive abilities such as memory and reasoning as well as those reflecting sensory discrimination and motor strength, may share a common cause. 1 Baltes and Lindenberger are yet to determine the nature of the hypothesized common cause, but it could be related to the involvement of a particular neuroanatomical region, reliance on a

44

i Although the simplest version of the common cause interpretation does not imply the existence of any structure among the variables except that which occurs through the common factor, it should be noted that Baltes and Lindenberger (1997; Lindenberger & Baltes, 1994) have relied on models in which the cognitive variables were grouped into first-order and second- order factors. In this respect, their analyses are more consistent with the hierarchical model than the single common factor model.

STRUCTURAL CONSTRAINTS 45

(1) Complete Independence (2) Single Common Factor

(3) Independent Factors (4) Hierarchical

Figure 1. Four alternative structural models portraying possible patterns of age relations on a set of variables. The boxes represent observable variables, the circles represent latent constructs, and the arrows indicate relations between constructs or variables.

certain type of cognitive process, dependence on broader determi- nants of processing efficiency such as working memory or pro- cessing speed, or the functioning of as-yet-unspecified aspects related to central nervous system integrity. Although a single factor is ultimately assumed to be responsible for the age-related effects on all variables, it is important to recognize that this model does not necessarily imply that every variable should have the same magnitude of age relation. That is, because the total age- related effect on a variable in the single common factor model depends on the product of the relation between age and the critical factor and the relation between the factor and the variable, vari- ables could differ in their age-related effects because of variations in the strength of the factor-variable relation.

Model 3 (Independent Factors) in the lower left panel of Fig- ure 1 corresponds to the assumption that independent age-related effects operate at the level of sets of variables. One could distin- guish sets of variables in many different ways, such as in terms of traditional cognitive domains (e.g., memory, reasoning, decision making), use of the same cognitive processes, involvement of the same neuroanatomical structure, or by any number of other pos- sible bases. Regardless of the nature of the grouping, however, the primary characteristic of this class of model is that each group of variables has a separate and independent age-related influence. This type of model may be more plausible than Model 1 because it is usually possible to identify similar variables that could be grouped together on some basis.

The final model to be considered, Model 4 (Hierarchical), postulates a hierarchical structure of the variables with the age-

related influences operating only at the highest level. This model is similar to Model 2, but it differs by allowing structure among the variables and postulating that age-related effects primarily occur at the highest level in the hierarchy. Because the highest level in the hierarchy includes variables at all lower levels, influences at this level necessarily correspond to very broad effects.

Another type of structural model, sometimes known as a medi- ational model, resembles Models 2 and 4, with two important differences: (a) the structural diagram is typically rotated 90 de- grees counterclockwise such that age is on the far left and the observable (manifest) variables are on the far fight; and (b) the circle closest to age corresponds to a construct that is postulated to be a mediator of age-related effects on other variables instead of a construct representing the variance shared among lower order variables or constructs. In other words, mediational models pos- tulate that many of the age-related effects on some variables or constructs are mediated through effects on other variables or constructs. Many published studies have examined mediational models, often with indices of working memory or processing speed representing the primary mediator construct (e.g., Park et al., 1996; Salthouse, Fristoe, & Rhee, 1996; Verhaeghen & Salthouse, 1997). Although we will not consider mediational models in this article, it is important to note that they are similar to Models 2 and 4 in that they postulate that the age-related influences on a variety of cognitive variables are not independent. The models differ in that the single common factor and hierarchical models postulate that age-related effects operate on a factor representing variance com- mon to many variables, whereas mediational models postulate that

46 SALTHOUSE AND CZAJA

the age-related effects on many variables are at least partially mediated through age-related effects on a small number of other variables or constructs.

As portrayed in Figure 1, each of the models is an extreme case because all of the age-related influences on the variables are postulated to be of the same type. Potentially, researchers could obviously create more plausible hybrid models by allowing direct connections from age to individual variables in Models 2, 3, and 4 or from age to groups of variables in Model 4. However, it is useful to consider the current models first because they are the simplest versions of each category, and hence, one can presume comparisons among them to be informative about the classes of models that are ultimately likely to be most viable.

It should be clear that it is impossible to distinguish among models such as those represented in Figure 1 when researchers restrict their focus to a single variable, as is the case in much of the past research in aging and cognition. However, one way research- ers can examine the plausibility of these models is with structural equation analyses, if multiple Variables are available from the same samples of individuals.

Three important requirements for such analyses are (a) variables that reflect different constructs (to ensure that the independent factors and hierarchical models can be examined), (b) that the samples be moderately large (to ensure adequate power to discrim- inate among alternative models), and (c) that the samples include a wide range of ages (to ensure that there is ample opportunity for age-related effects to be manifested). Although researchers could conduct the analyses on either longitudinal or cross-sectional data, few if any longitudinal data sets exist that satisfy these require- ments, and thus, the analyses that we describe are based on cross-sectional data.

We now consider two types of fit information with structural equation models. One type consists of the fit between model predictions and empirical data for only the relations between age and the target variables. As an example, if the data set contains four variables, researchers could restrict their focus to the fit of the relations between age and those four variables. One can obtain a quantitative index of the accuracy of the predictions by comparing the observed age-related effect, as reflected by the correlation between age and the variable, with the total predicted effect, which corresponds to the sum of all direct and indirect relations in the model. To illustrate, in the Independent Factors Model (Model 3), the predicted correlation between age and a variable is the product of the standardized coefficient for the relation between age and the first-order factor and the standardized coefficient for the relation between the first-order factor and the variable. Predicted age relations for other models can result from a similar multiplication of the coefficients for all the paths leading from age to the variables. However, it is important to recognize that accurate reproduction of the age correlations is only one possible criterion for evaluating models, and it is not always the most informative. For example, the Complete Independence Model (Model i), in which the age relations on each variable are completely indepen- dent of one another, will always result in a perfect reproduction of the age correlations, but it is very unparsimonious with respect to the number of independent age relations that are postulated, and it completely ignores all other relations that might exist among the variables.

One can also compare the models with conventional fit statistics designed to evaluate the degree to which a model accounts for all relations among variables (e.g., Kline, 1998; Loehlin, 1998). To illustrate, if the data set contains four variables in addition to age, then global fit statistics evaluate the degree to which the model can accurately reproduce the relations of age to the four variables (i.e., V1, V2, V3, V4), in addition to the six relations among variables (i.e., V1-V2, V1-V3, V1-V4, V2-V3, V2-V4, V3-V4).

Both types of fit information are useful because they address different questions. That is, global fit statistics evaluate the degree to which the model can account for all relations among variables, those between variables as well as those between age and the variables. In contrast, fit statistics restricted to the age-variable relations focus on what is of primary interest to researchers inter- ested in aging, but they ignore all other relations among variables. Furthermore, this more limited type of fit information introduces the need to consider issues of parsimony because the age relations can always be perfectly reproduced if separate and independent age relations are postulated for each variable. Because they pro- vide different types of information, we will consider a combination of the two types of fit statistics when evaluating the models.

Analyses of Variables F rom Similar Tasks

A related type of independence analysis can be conducted when researchers obtain the variables under consideration from the same or very similar task(s). These comparisons can be particularly informative because variables derived from similar tasks are often assumed to be equivalent, except for the addition of one or more critical processes postulated to contribute to one of the variables. The primary question of interest in these similar-task analyses is the degree to which there are independent age-related influences on the complex variable (i.e., with the additional processes) after statistical control of the variance in the simpler variable (i.e., without the additional processes). This comparison is somewhat analogous to the distinction between Model 1 (i.e., completely independent effects) and Model 2 (i.e., all effects operating through a single common factor), yet there are only two variables that are both obtained from similar tasks (cf. Salthouse & Coon, 1994). The rationale for the analytical procedure is that if the age-related effects on the two variables are independent (as in Model 1), then there should be little or no attenuation of the age-related variance in one variable after statistical control of the other variable. However, if the age-related effects on the variables are not independent (and share age-related influences, as in Model 2), then one can estimate the degree of dependence by the extent to which the age-related variance in the criterion variable is re- duced by this type of statistical control. If the residual age-related variance is close to zero, then the two variables largely overlap with respect to their age-related influences, and it can be inferred that the variables share most if not all of their age-related effects. In contrast, if there is little reduction in the age-related variance in the target variable after control of the other variable, then it can be inferred that the age-related influences on the two variables are largely independent.

Studies have reported analyses of this type with variables from the same task representing different stages of practice (e.g., Salt- house, 1996), different percentiles of reaction time distributions (e.g., Salthouse, 1993, 1998b), and items with different solution

STRUCTURAL CONSTRAINTS 47

probabilities (e.g., Salthouse, 2000). In the present context, we apply the analyses to variables obtained from similar tasks that might be hypothesized to differ in terms of one or more critical processes.

Overview

This article describes the results of structural equation and similar-task independence analyses, such as those just described, conducted on two separate data sets. One set of data was based on a study by Salthouse et al. (1996) that involved a total of 259 adults between 18 and 94 years of age. The other data set was assembled from samples used in several recent studies conducted by Czaja and colleagues (e.g., Czaja & Rubert, 1998; Czaja & Sharit, 1998a, 1998b; Sharit & Czaja, 1999). The total number of participants in the Czaja data set was 523, and the participants ranged between 19 and 77 years of age. The major questions in both data sets asked which of the four models appearing in Figure 1 provides the best characterization of the nature of age-related influences on sets of cognitive variables and for which similar-task contrasts is there evidence of specific age-related influences.

Data Set 1

Method

A summary of characteristics of the sample in Data Set 1 appears in Table 1. (Further details of the sample, tests, and variables are contained in the original Salthouse et al., 1996, article.) It can be seen that a high percentage of the participants had completed at least some college, and thus, the sample is likely to be positively selected relative to the general

population with respect to level of education. One can assess the repre- sentativeness of the total sample, and of the subsamples at each age decade, more precisely by referencing age-adjusted scores from the three Wechsler Adult Intelligence Scale---Revised (WAIS-R) tests administered to all participants. The procedure consists of converting the raw scores to age- adjusted scaled scores (M = 10, SD = 3) according to the norms provided in the WAIS-R manual (Wechsler, 1981), converting the mean scaled scores to z scores, and then determining the percentile in the normal distribution that corresponds to each z score. It is apparent in Table 1 that the sample was positively biased at each age decade relative to the normative sample for the WAIS-R. The average was near the 75 th percen- tile for most age decades, but the averages were somewhat lower in the 30s and 40s than in the other age decades; thus, the various age groups in the current sample were not completely comparable to one another.

Increased age was associated with greater percentages of people report- ing that they had cardiovascular surgery or were taking hypertension medications. Scores on many of the cognitive variables were lower among those reporting surgery or taking hypertension medications, hut only the Trail Making A and Trail Making B (Reitan, 1958) variables had signifi- cant interactions with age, in the direction of greater age-related decline for individuals with these health conditions. However, because most of the Cognitive variables did not have interactions with any of the health indi- cators, we ignored health status in subsequent analyses. None of the variables had significant interactions of age and sex, but women had significantly higher scores than men on the digit symbol variable and significantly lower scores than men on the block design variable.

Results

Similar-task independence analyses. As previously men- tioned, we examined independence of the age-related influences on two variables from similar tasks by means of hierarchical regres-

Table 1 Descriptive Characteristics of Sample in Data Set 1

Variable 20s

Age decade

30s 40s 50s 60s 70s+

n 41 40 Age

M 24.6 34.5 SD 2.6 2.9

% with some college 93 90 % women 59 65

Age-adjusted scaled scores Digit Symbol

M 13.2 11.3 SD 2.5 2.5

Block Design M 12.2 10.8 SD 2.3 2.9

Object Assembly M 10.6 10.0 SD 2.5 3.0

Mean scale score 12.0 10.7 Mean z score .67 .23 Percentile 74.9 59.1

Health rating 2.0 2.0 Cardiovascular surgery (%) 0 0 Hypertension medication (%) 0 8 Head injury (%) 0 0

30 58 43 47

43.7 54.3 64.4 78.4 2.7 2.7 3.0 5.7

93 93 79 79 60 66 58 70

11.7 12.5 12.1 12.8 2.3 2.5 2.3 2.5

11.6 12.1 12.5 11.9 2.5 2.4 3.1 2.7

10.3 11.7 11.5 10.3 2.6 2.6 2.5 2.7

11.2 12.1 12.0 11.7 .40 .70 .67 .57

65.5 75.8 74.9 71.6

2.2 2.1 2.2 2.5 3 7 14 21

13 14 33 40 1 3 2 4

Note. N --- 259.

Age correlation

-.15 .05

.01

.05

.05

.05

.19

.29

.36

.02

48 SALTHOUSE AND CZAJA

sion analyses, with the controlled variable entered before consid- ering the relations of age in the prediction of the criterion variable. The criterion variable in the initial analysis consisted of the time score in the Trail Making B test, in which the task is to connect circles in an alternating sequence of numbers and letters as rapidly as possible. The R 2 associated with age for this variable was .348, but it was reduced to .056 (an 84% reduction) after control of the time score in the Trail Making A test, in which the task is to connect circles in numerical sequence as rapidly as possible. The residual age-related variance was still significantly greater than zero, indicating that there are age-related effects on one or more processes involved in Trail Making B (e.g., switching between sequences, use of letters in addition to numbers, practice or fatigue associated with the second test in the series) that are independent of the age-related effects in Trail Making A.

We conducted the remaining similar-task analyses on variables derived from the Rey Auditory Verbal Learning Test (AVLT) (Schmidt, 1996). This test consists of five successive study-test trials with the same list of 15 unrelated words (Trials 1 through 5), an interference list composed of a different set of words, recall of the original list without another presentation of the words (Trial 6), and then a 20-min delay followed by another recall attempt of the original list (Trial 7). We formed three contrasts between pairs of variables to examine independence of age-related effects on learn- ing (criterion variable = Trial 5, controlled variable = Trial 1), on interference (criterion variable = Trial 6, controlled variable = Trial 5), and on retention (criterion variable = Trial 7, controlled variable = Trial 6).

Age was associated with an R 2 of .164 in the prediction of the Trial 5 variable, and this was reduced to .071 (a 57% reduction) after control of the Trial 1 variable. The residual age-related variance was significantly greater than zero, and thus, it can be inferred that there are some age-related effects on the rate of learning above 'and beyond the effects evident on the first recall trial. The R 2 associated with age in the prediction of recall on Trial 6, after the interference list, was .199, and this was reduced to .021 (an 89% reduction) after control of the recall score on Trial 5. Once again, the residual age-related variance was signif- icantly greater than zero, and thus, it can be inferred that there are age-related effects on processes associated with interference that are independent of the age-related effects on processes associated with prior learning. Finally, age was associated with an R 2 of .177 in prediction of recall on Trial 7, after a 20-rain delay, but this was reduced to .001 (a 99% reduction) after control of the recall score on Trial 6. In this case, the residual age-related variance was not significantly different from zero, and thus, there was no evidence of independent age-related effects on the retention of information over a 20-min delay.

• These similar-task analyses suggest that some independent, or specific, age-related influences do exist, but we restricted all of the analyses to a pair of variables from very similar tasks. It is conceivable that a variable that has independent age-related influ- ences relative to a similar variable may nevertheless share most or all of its age-related variance with other types of variables. For example, even though some of the age-related variance in the Trail Making B variable was not shared with the Trail Making A variable, and some of the age-related variance in the Rey AVLT Trial 5 variable was not shared with the Rey AVLT Trial 1 variable, it is possible that the Trail Making B and Rey AVLT

Trial 5 variables shared considerable proportions of their age- related variance with one another. The next set of analyses exam- ined the issue of independence of age-related effects from the perspective of a wider range of variables.

Structural analyses. The Salthouse et al. (1996) article con- tains analyses of linear and nonlinear age relations on the vari- ables, a complete correlation matrix, the results of an exploratory factor analysis, and a figure of age relations on the factor scores• We based the current analyses on 11 variables, representing four of the cognitive abilities identified in the earlier factor analysis. 2 A speed factor was represented by scores on three tests: the WAIS-R Digit Symbol Substitution test and the Letter Comparison and Pattern Comparison tests (Salthouse et al., 1996), in which the task is to make speeded same-different decisions about the identity of pairs of letter strings or pairs of line patterns. A verbal memory factor was represented by four variables. Two variables were based on the number of word pairs recalled from each of two lists of paired associates. The other two verbal memory variables were based on the number of words recalled from the second and sixth lists in the Rey AVLT multiple-trial free-recall task. We defined a reasoning factor by two variables that consisted of the number of items answered correctly in the Shipley Abstraction Test (Zachary, 1986) and the number of categories successfully completed in the Wisconsin Card Sorting Test (e.g., Heaton, Chelune, Talley, Kay, & Curtiss, 1993). Finally, we used scores on the WAIS-R Block Design and Object Assembly tests to assess a spatial factor. Al- though we included two fluency variables in the original data set, we deleted them from the current analyses because they had a somewhat different pattern of age-related influences than the other variables, both in this data set and in Data Set 2.

We created structural models for the four models portrayed in Figure 1, and we fit the data (raw scores converted to a covariance matrix) with the EQS statistical package (Bentler, 1995). Table 2 contains the predicted age correlations for the I 1 variables in each model. As previously noted, the predicted values are the product of the standardized coefficients for all paths leading from age to the variable in the model. We obtained the index of fit in the bottom row of the table by squaring the deviations between the predicted and observed values, determining the mean of these squared de- viations, and then taking the square root of the mean to convert back to the original units. Inspection of the entries in Table 2 reveals that all models were quite accurate in reproducing the observed correlations. Other than with Model 1, which perfectly reproduces the correlations because each variable has an indepen-

2 Because the structural models assume that the relations between vari- ables are similar across age, we conducted the following analyses to examine the validity of this assumption. For every pair of variables, we created two regression equations. In one equation, the first variable was predicted from age, the second variable, and the interaction of age and the second variable; in the second equation, the second variable was predicted from age, the first variable, and the interaction of age and the first variable. If both of the interaction terms were significant at a relatively liberal criterion (i.e., p < .05 with 55 pairs of variables), then we would conclude that the relation between the variables varied significantly as a function of age. However, none of the 55 variable pairs in this data set, and none of the 45 variable pairs in Data Set 2, met this criterion, and thus, there is no indication of a systematic shift with age in the strength of the relations between variables.

STRUCTURAL CONSTRAINTS 49

Table 2 Reproduction of Age Correlations, Data Set 1

Observed/ ~/ariable Model 1 Model 2 Model 3 Model 4

Digit Symbol - . 66 - .63 - . 66 - .61 Letter Comparison - . 49 - .55 - .57 - .53 Pattern Comparison - . 66 - . 60 - . 6 0 - .56 Paired Associates 1 - .51 - . 46 - .43 - . 40 Paired Associates 2 - .35 - . 39 - .37 - .35 Rey AVLT Trial 2 - .47 - .40 - .47 - .41 Rey AVLT Trial 6 - .45 - .45 - .48 - .43 Shipley Abstraction - .45 - .53 - .45 - .55 WCST Number - .41 - . 3 8 - .41 - .39

Categorization Object Assembly - .41 - .45 - .41 - .45 Block Design - .47 - .51 - .47 - .53

Root mean squared .05 .03 .05 deviation

Note. AVLT = Auditory Verbal Learning Test; WCST = Wisconsin Card Sorting Test.

dent age relation, the smallest deviations were with independent age effects on separate abilities (Model 3), with the single factor

(Model 2) and hierarchical (Model 4) models having similar av- erage deviations. It is not surprising that the predict ions are more accurate with a greater number of independent age relations (i.e., Model 3 vs. Models 2 and 4), but it is interesting thai the age relations on a wide range o f cognit ive variables can be reproduced fairly accurately with a single age-related influence, as in Models 2 and 4.

Statistics for the overall goodness of fit o f the four models appear in Table 3. The X 2 value provides a test o f the significance o f deviat ions of the data f rom the model , but it is considered too sensitive when the sample size is large, and thus, studies typically provide other fit statistics (cf. Kline, 1998; Loehlin, 1998). There is no consensus with respect to which supplementary fit statistics are most informative, but the other fit statistics that we report here reflect the relative degree to which all o f the covariances are accurately reproduced by the model (i.e., the non-normed fit index [NNFI] and the comparat ive fit index [CFI]) and the amount o f residual covariance that is not accounted for by the model (i.e., the Standardized Root Mean Residual [Std. RMR]). Better fit o f a model is therefore ref lected in values o f NNFI and CFI closer to l .0 and values of Std. R M R closer to zero.

Compar ison of the entries in Table 3 reveals that the hierarchical model (Model 4) is clearly superior to the other models, indicating that the variables in this data set are organized into a definite structure, and that a large proport ion o f the age-related effects on the variables operate at a high level in that structure and, conse- quently, are shared among all variables at lower levels. The con-

trast be tween Models 1 (Complete Independence) and 2 (Single C o m m o n Factor) indicates that the addition of a higher order factor substantially improves the fit o f the model (i.e., a nested compar- ison o f the two models yields a difference )(2(1, N = 259) = 509). The contrast be tween Models 3 ( Independent Factors) and 4 (Hi- erarchical) was also significant (i.e., a nes ted compar ison o f the two models yields a difference X2(1, N = 259) = 169). This latter compar ison indicates that it is more plausible to conceptual ize the

groups of variables or abilities as related to one another than to see them as independent , and as the age effects operating on what is common to all abilities than as having separate effects on each ability. Models 2 and 3 do not have a simple nested relation to one another and thus could not be compared directly, but inspect ion of the fit statistics suggests that these two models have similar fits to the data.

D a t a S e t 2

Method

The data in this data set have not previously been published in the current form, and therefore, we are including more details about the variables and initial analyses than we have for Data Set 1. Data were available from a total of 523 participants, and a summary of characteristics of the sample appears in Table 4. Table 5 contains a brief description of the major variables included in the analyses. We based all of the variables on published tests for which details of the test administration and scoring are available.

As was the case in Data Set 1, a majority of the participants in each age decade had completed some college, although the percentages were smaller than in Data Set 1. Because we administered several subtests from the WAIS-R, we carried out conversion to age-adjusted scaled scores and percentiles in the same manner as in Data Set 1. Inspection of the age- adjusted scaled scores and the z scores and percentiles reveals that there was greater selectivity of the subsamples with increased age. That is, adults in their 20s and 30s were close to the 50th percentile of their age norms, but those in their 50s, 60s, and 70s were in the 70th and 80th percentiles. This differential representativeness probably contributes to smaller age trends for many variables in this data set compared to other data sets. As an example, the correlation between age and Digit Symbol test score was - . 3 4 in these data, but it was - . 66 in Data Set 1. Furthermore, correlations for the Trial Making A and B test scores were .35 and .23, respectively, in these data, but they were .51 and .59, respectively, in Data Set 1.

There were more reports of major operations and strokes with increased age, but there were no significant interactions of these health indicators with age on any variables, and thus, we ignored health status in the subsequent analyses. As in the prior data set, none of the Age X Sex interactions were significant. However, women had significantly higher scores than men on the digit symbol variable and on the three verbal learning variables (all derived from the California Verbal Learning Test [CVLT]).

Three individuals had missing values for the vocabulary variable, two individuals had missing data for the pegboard (with nondominant hand) and the Controlled Oral Word Association (COWA) variables, and one individual did not have a score for the Trail Making B variable. We replaced all missing values by the mean of that variable in the age decade of the individual whose data were missing.

We also examined errors in the Trail Making A and B, Figural Scanning, and Pegboard tests. The absolute frequencies of errors were low in each

Table 3 Fit Statistics for Structural Models, Data Set 1

Model x2/df NNFI CFI Std. RMR

(1) Complete Independence 882/55 .39 .49 .19 (2) Single Common Factor 373/54 .76 .80 .08 (3) Four Separate Factors 326/51 .78 .83 .14 (4) Hierarchical 157/50 .91 .93 .05

Note. N = 259. NNFI = non-normed fit index; CFI = comparative fit index; Std. RMR = standardized root mean residual.

5 0 SALTHOUSE AND CZAJA

Table 4

Descriptive Characteristics of Sample in Data Set 2

Variable 20s

Age decade

30s 40s 50s 60s Age

70s correlation

n 83 92 76 Age

M 24.3 34.4 45.0 SD 2.7 2.9 2.6

% with some college 65.1 54.3 65.8 % women 51.8 52.2 59.2

Age-adjusted scaled scores Vocabulary

M 9.5 9.3 11.3 SD 3.1 2.9 3.4

Digit Span M 10.2 9.7 10.2 SD 2.7 2.7 3.1

Digit Symbol M 11.0 10.6 10.7 SD 3.2 2.6 2.7

Mean scale score 10.3 9.9 10.7 Mean z score .10 - . 03 .23 Percentile 54.0 48.8 59.1

Major operations (%) 7 9 14 Stroke (%) 0 0 3 Head injury (%) 4 1 4

77

54.4 2.8

71.4 67.5

12.4 3.0

11.1 3.4

11.9 2.7

11.8 .60

72.6

13 5 8

107 88

65.1 72.6 2.5 2.1

72.0 69.3 .08 59.8 56.8 .05

12.7 12.8 .44 2.6 2.3

11.1 12.2 .26 3.0 2.8

12.3 13.9 .33 2.7 2.5

12.0 13.0 .45 .67 1.00

74.9 84.1

27 31 .23 9 10 .21

• 5 " 3 .05

Note. N = 523.

test, and none of the error rates were significantly correlated with age (all rs > - . 0 7 and < .10). There was a tendency for poor performance to be manifested in both more errors and slower time in the Trail Making B (r = .51) and the pegboard tasks (rs = .20 and .27), but because error frequency was not related to age, we ignored errors in subsequent analyses.

We examined linear and nonlinear age effects on the variables with hierarchical regression analyses in which we first used the linear, then the quadratic, and finally the cubic age terms in predicting each variable. Results from these analyses are contained in Table 6. Notice that most of

the age relations on the variables are linear, as there were significant nonlinear effects on only a few variables, and the proportion of variance associated with the quadratic or cubic terms was always small relative to the variance associated with the linear terms. On the basis of these results, we only considered linear age relations in subsequent analyses.

Table 7 contains the correlation matrix for the major variables in Data Set 2. (In order to place all speed variables in the same scale, the Digit Symbol test score was divided into 90 s to convert it into seconds per item.) It can be seen that the vocabulary and fluency (COWA) variables were

Table 5

Description of Variables in Data Set 2

Variable Source Description

Vocabulary Digit Span Digit Symbol COWA

Trails A and B

FigScan

PegDH, PegNDH

VisRepC, VisRepI, VisRepD

CVLTSum, CVLTDel, CVLTCon

WAIS-R (Wechsler, 1981) WAIS-R (Wechsler, 1981) WAIS-R (Wechsler, 1981) Controlled Oral Word Associauon

(Benton & Hamsher, 1989) Trail Making (Reitan, 1958)

Figural Scanning and Visual Discrimination (Ekstrom, French, Harman, & Derman, 1976)

Purdue Pegboard Test (Tiffin, 1968.)

Visual Reproduction (Wechsler, 1987)

California Verbal Learning Test (Delis, Kramer, Kaplan, & Ober, 1987)

Oral definition of words. Sum of number of digits recalled correctly in forward and backward orders. Speeded substitution of digits for symbols according to a code table. Participants say as many words as possible in a fixed time beginning with

particular letters (P, R, W). Participants rapidly draw lines to connect circles in numerical sequence (A)

or in alternating numeric and alphabetic sequence (B). Speeded identification of a target figure within a set of 5 alternatives.

Rapid placement of pegs into holes, with dominant hand (DH) or with nondominant hand (NDH).

Reproduction of visual designs either while the design is present and can be copied (C), immediately after presentation (I), or after a 30-min delay (D).

Recall of a categorized word list presented 5 times, with scores consisting of the sum of the recalled words (Sum), recall after a 20-min delay (Del), or consistency of recall (Con) across trials.

Note. WAIS-R = Wechsler Adult Intelligence Scale--Revised.

STRUCTURAL CONSTRAINTS 51

Table 6

Proportions of Variance Associated With Linear, Quadratic, and Cubic Age Relations, Data Set 2

significantly greater with increased age, and there was no significant relation between age and digit span. All other variables had scores indi- caring lower performance with increased age.

Variable Linear Quadratic Cubic

Vocabulary .156" .006 .009 Digit Span .003 .000 .001 COWA .038* .000 .000 Digit Symbol .153" .000 .008 Trails A .123" .000 .000 Trails B .052* .000 .003 FigScan .171 * .005 .003 PegDH .239* .023* .002 PegNDH .232* .015" .000 VisRepl .151" .001 .008" VisRepD .184* .001 .008 VisRepC .051 * .000 .012 CVLTSum .080* .009 .016" CVLTDel .089* .001 .004 CVLTCon .016" .008 .007

Factor 1 .263* .006 .001 Factor 2 .196" .000 .012" Factor 3 .073* .009 .011 Factor 4 .111" .000 .002

Note. COWA = Controlled Oral Word Association; FigScan = Fig- ural Scanning and Visual Discrimination; PegDH = Purdue Pegboard Test, dominant hand; PegNDH = Purdue Pegboard Test, nondominant hand; VisRepI = Visual Reproduction, immediately after presentation; VisRepD = Visual Reproduction, after a 30-s delay; VisRepC = Vi- sual Reproduction, design present and can be copied; CVLTSum = Cali- fornia Verbal Learning Test, sum of recalled words; CVLTDel = Califor- nia Verbal Learning Test, recall after a 20-min delay; CVLTCon = California Verbal Learning Test, consistency of recall across trials; Factor 1 = Speed; Factor 2 = Spatial Reproduction and Memory; Factor 3 = Verbal Memory; Factor 4 = Miscellaneous/Knowledge. * p < .01.

Resul~

Similar-task independence analyses. As in Data Set 1, we

cohduc ted independence ana lyses on the two var iables f rom the

Trail M a k i n g tests. The R 2 associa ted wi th age in the Trail M a k i n g

B score was only .052, and this was reduced to a nons ign i f i can t

.002 (a 96% reduct ion) after control o f the Trail M a k i n g A score.

Unl ike the resul ts in Data Set 1, therefore, in these data there was

no ev idence o f an independen t age-rela ted inf luence on the Trail

M a k i n g B variable. This m a y be at least part ial ly at tr ibutable to the

relat ively smal l age-re la ted effects on the Trail M a k i n g B var iable

compared to that in the prev ious data set (i.e., R 2 with age o f .052

in these data v s . . 3 4 8 in Data Set 1).

M o s t o f the age-rela ted var iance in the pegboard t ime score with

the n o n d o m i n a n t hand (i.e., R 2 = .232) was shared wi th the

var iance in the t ime score f rom the d o m i n a n t hand, but the res idual

age-re la ted var iance was s ign i f i candy greater than zero (i.e., .013,

a 94% reduct ion) . It can therefore be inferred that there was a smal l

age-rela ted effect on pe r fo rmance wi th the n o n d o m i n a n t h an d that

was independen t o f the effects on the dominan t hand.

Three var iables were avai lable in the Visua l Reproduc t ion test:

accuracy o f copying wi th the s t imulus pat tern present , accuracy o f

immed ia t e reproduct ion f rom m e m o r y , and accuracy o f reproduc-

t ion f rom m e m o r y after a 30 -min delay. There was substant ia l

res idual var iance in the immed ia t e m e m o r y variable after control

o f the var iance in the copy var iable (i.e., f rom R 2 = .151 to .071,

a 53% reduct ion) . Th i s indicates the ex is tence o f independen t

age-rela ted effects on m e m o r y above and b e y o n d any effects

apparent in copying. There was also s ignif icant res idual age-

Table 7

Correlation Matrix for Variables, Data Set 2

Variable 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1. Age 2. Vocabulary .40 - - 3. Digit Span .05 .40 - - 4. COWA .19 .48 .45 - - 5. Digit Symbol .34 - . 05 - . 2 2 - . 17 - - 6. Trails A .35 .00 - . 19 - .11 .48 - - 7. Trails B .23 - .21 - .31 - . 2 7 .52 .52 8. FigScan .41 .04 - . 0 9 - . 08 .60 .51 9. PegDH .49 .09 - . 0 7 .05 .42 .36

10. PegNDH .48 .10 - . 05 .08 .35 .32 11. VisRepI - . 3 9 - . 0 0 .16 .04 - . 2 4 - . 2 6 12. VisRepD - . 43 - .05 .12 - . 0 2 - . 3 0 - . 27 13. VisRepC - . 22 .06 .17 - . 03 - . 15 - . 1 4 14. CVLTSum - . 28 .16 .20 .15 - . 3 4 - . 2 4 15. CVLTDel - . 3 0 .11 .16 .11 - . 3 4 - .23 16. CVLTCon - . 13 .16 .15 .18 - . 18 - . 1 6

M 50.0 50.5 15.7 39.9 1.77 31.3 SD 17.1 13.6 4.9 11.7 0.53 13.0

m

.46 - -

.35 .44 - -

.29 .41 .78 - - - . 3 0 - . 23 - . 4 4 - .41 - - - .31 - . 29 - . 4 4 - . 43 .83 - . 2 2 - . 13 - . 2 9 - . 3 0 .57 - . 37 - . 2 2 - . 3 4 - . 2 8 .30 - . 3 0 - . 17 - . 37 - . 27 .31 - . 2 6 - . 17 - . 13 - . 1 2 .15

77.6 74.1 • 82.5 89.4 6.9 36.5 22.6 23.2 25.6 3.2

.54 - -

.36 .22 - -

.36 .20 .79

.21 .15 .64

5.7 10.2 49.0 3.5 2.3 10.3

m

. 4 4 m

10.5 80.0 3.1 10.2

Note. Correlations with an absolute value of .11 or greater are significant at p < .01. COWA = Controlled Oral Word Association; FigScan = Figural Scanning and Visual Discrimination; PegDH = Purdue Pegboard Test, dominant hand; PegNDH = Purdue Pegboard Test, nondominant hand; VisRepI = Visual Reproduction, immediately after presentation; VisRepD = Visual Reproduction, after a 30-s delay; VisRepC = Visual Reproduction, design present and can be copied; CVLTSum = California Verbal Learning Test, sum of recalled words; CVLTDel = California Verbal Learning Test, recall after a

• 20-min delay; CVLTCon = California Verbal Learning Test, consistency of recall across trials.

52 SALTHOUSE AND CZAJA

related variance in the delayed memory variable after control of the variance in the immediate memory variable (i.e., from R 2 = .184 to .014, a 92% reduction), suggesting the presence of some age-related impairment in the retention of nonverbal visual information.

Immediate and delayed memory variables were also available in the CVLT. The analysis on the delayed memory variable revealed the existence of small but significant residual age-related variance in the 20-min delayed recall variable after control of the immediate recall variable (i.e., from R 2 = .089 to .006, a 93% reduction). This result again suggests the existence of specific or independent age-related impairments in retention, this t ime with verbal material.

Factor analyses. We conducted an exploratory factor analysis on the data summarized in Table 7 with the eigenvalue-greater- than-one factor extraction criterion and oblique (promax) rotation. We have summarized the results of this analysis in Table 8. Notice that the analysis yielded four separate factors, with the first three corresponding to speed, spatial reproduction and memory, and verbal memory, respectively, and the fourth factor involving the vocabulary, digit span, and fluency variables. Age trends for these factors appear in Figure 2, and the proportions of variance in the factor scores associated with linear, quadratic, and cubic age trends are contained in the bottom of Table 6. As with the individual variables, most of the age-related effects on the factor scores were linear.

We deleted the fourth factor from the subsequent analyses because unlike the other factors, it had positive relations to age, presumably at least in part reflecting greater accumulation of knowledge with increased age. We also dropped the pegboard variables from subsequent analyses because they were factorially complex, as the loadings were split between the speed and the spatial reproduction and memory factors. We therefore based the structural models on a total of 10 variables corresponding to factors of Speed (i.e., Digit Symbol, Trail Making A, Trail Making B, Figural Scanning), Spatial Reproduction and Memory (i.e., copy, immediate, and delayed visual reproduction), and Verbal Memory (i.e., consistency of recall, sum of items recalled across the first five trials, and delayed recall in the CVLT).

Structural analyses. We fit structural models corresponding to the four models represented in Figure 1 to the data of Data Set 2, and the two types of fit statistics appear in Tables 9 and 10. We summarize information about the accuracy of reproducing the age correlations in Table 9. As was the case in Data Set 1, all of the models were fairly accurate in accounting for the age relations, with the smallest deviations (other than Model 1) for Model 3 (i.e., independent age relations on three groups of variables). However, again, it is interesting that it is possible to account for most of the age relations on a wide range of variables with a single age-related influence, as in Models 2 and 4.

Table 10 contains global fit statistics for the four models. The pattern is very similar to that from Data Set 1 in that the best overall fit was with the hierarchical model (Model 4), in which the variables are organized in terms of distinct abilities, but those abilities are related to one another through a higher order factor and the age-related effects are postulated to operate at the highest level in the hierarchy. As in Data Set 1, nested comparisons revealed that a model with a single common factor significantly improved the fit relative to a model with completely independent

Table 8 Factor Loadings for Exploratory (Promax Rotation) Factor Analysis, Data Set 2

Variable Age F1 F2 F3 F4 h e

Factor loadings

Digit Symbol .79 -.25 -.34 -.16 .65 Trails A .75 -.25 -.23 -.13 .57 Trails B ,70 -.31 -.37 -.38 .61 FigScan .81 -.24 -.21 -.01 .68 PegDH ,69 -.59 -.35 .21 .65 PegNDH ,64 -.58 -.28 .24 .60 VisRepI - .36 .911 .29 .03 .82 VisRepD -.41 .88 .37 -.03 .79 VisRepC -.19 .78 .21 .07 .64 CVLTSum -.38 .35 .94 .17 .89 CVLTDel - .35 .36 .86 .10 .75 CVLTCon -.20 .16 .79 .21 .64 Vocabulary .03 - .03 .18 .77 .61 Digit Span -.21 .19 .17 .74 .60 COWA - . 13 -.06 .17 .79 .64

Eigenvalue 4.93 2.17 1.62 1.41 Proportion of .33 .15 .11 .09

variance

Correlations Age F1 .51 - - F2 -.44 -.41 - - F3 -.27 -.37 .34 F4 .33 -.06 -.04 A8

Note. Boldface entries were the highest for the factor and were used to identify the factor. FigScan = Figural Scanning and Visual Discrimination; PegDH = Purdue Pegboard Test, dominant hand; PegNDH = Purdue Pegboard Test, nondominant hand; VisRepI = Visual Reproduction, im- mediately after presentation; VisRepD = Visual Reproduction, after a 30-s delay; VisRepC = Visual Reproduction, design present and can be copied; CVLTSum = California Verbal Learning Test, sum of recalled words; CVLTDel = California Verbal Learning Test, recall after a 20-min delay; CVLTCon = California Verbal Learning Test, consistency of recall across trials; COWA = Controlled Oral Word Association; F1 = Factor 1 (Speed); F2 = Factor 2 (Spatial Reproduction and Memory); F3 = Factor 3 (Verbal Memory); F4 = Factor 4 (Miscellaneous/Knowledge).

age-related effects (i.e., Model 2 vs. Model 1, difference X2(1) = 814), and that a model with a hierarchical structure significantly improved the fit relative to a model with independent age-related effects on each factor (i.e., Model 4 vs. Model 3, difference X2(1) = 82). Direct comparisons between Models 2 and 3 were not possible because they do not have a simple nested relation to one another, but inspection of the fit statistics reveals that the separate factors model (Model 3) provides a much better fit to the data than the single common factor model (Model 4).

Discuss ion

In this article, we report results from two different types of analyses on two separate data sets relevant to the question of the independence of age-related influences on cognitive variables. Both sets of analyses reveal that there is structure among the variables in the sense that most of the variables are interrelated with one another, and that the age-related influences on one

STRUCTURAL CONSTRAINTS 53

1.2

0.8

0.4

o o

O9 o.o

I..L -0.4

-0 .8

-1.2

Factor 2

20 30 40 50 60 70 80

Age in Years

Figure 2. Mean factor scores (and standard errors) as a function of age in Data Set 2. The factors correspond to Speed (Factor 1), Spatial Reproduction and Memory (Factor 2), Verbal Memory (Factor 3), and Miscella- neous/Knowledge (Factor 4).

variable are not independent of the age-related influences on other variables.

The similar-task independence analyses are based on two vari- ables that can be hypothesized to be similar except that the crite- rion variable is presumed to include one or more processes in addition to those included in the controlled variable. In all of the similar-task analyses, the age-related variance in the criterion (predicted) variable was substantially reduced, often by 90% or more, after control of the variance in the controlled variable. Because these variables share large proportions of their age-related

Table 9 Reproduction of Age Correlations, Data Set 2

Observed/ Variable Model 1 Model 2 Model 3 Model 4

Digit Symbol .34 .31 .36 .35 Trails A .35 .28 .32 .31 Trails B .23 .32 .31 .31 Figural Scanning .41 .28 .36 .34 VisRepI - .39 -.37 -.41 -.38 VisRepD - .43 - .39 - .40 - .39 VisRepC - .22 - .27 -.27 - .26 CVLTSum - .28 - .34 - .28 - .34 CVLTDel - ,30 - .32 - .22 - .27 CVLTCon - . 13 - .23 - . 18 - .22

Root mean squared .06 .04 .05 deviation

Note. VisRepl = Visual Reproduction, immediately after presentation; VisRepD = Visual Reproduction, after a 30-s delay; VisRepC = Visual Reproduction, design present and can be copied; CVLTSum = Califor- nia Verbal Learning Test, sum of recalled words; CVLTDel = Cali- fornia Verbal Learning Test, recall after a 20-rain delay; CVLTCon = California Verbal Learning Test, consistency of recall across trials.

variance, it is conceivable that they may also share many of the same age-related influences.

There was evidence of significant residual age-related variance for certain variables in these analyses, indicating that there were specific age-related effects on processes involved in the predicted variable but not in the controlled variable. These are potentially important findings because evidence for the independence of age- related influences is often most convincing when the comparisons consist of variables that are very similar, except with respect to a small number of critical processes. However, it should be noted that all of the estimates of residual or independent age-related effects were small relative to the total age-related effects on the variable, and the pattern of significant effects was not very con- sistent across the two data sets. To illustrate, there was significant residual age-related variance in the Trail Making B variable in Data Set 1 but not in Data Set 2, and there was significant residual age-related variance in the delayed verbal recall variable in Data Set 2 but not in Data Set 1. Furthermore, it is important to recognize that the unique age-related effects in this similar-task procedure are always relative to the other variable in the analysis, which is derived from a very similar task. It is therefore possible

Table 10 Fit Statistics for Structural Models, Data Set 2

Model x2/df NNFI CFI Std. RMR

(1) Complete Independence 2,180/45 .04 .21 1.24 (2) Single Common Factor 1,366/44 .39 .51 .13 (3) Three Separate Factors 240/42 .90 .93 .12 (4) Hierarchical 158/41 .94 .96 .05

Note. N = 523. NNFI = non-normed fit index; CFI = comparative fit index; Std. RMR = standardized root mean residual.

54 SALTHOUSE AND CZAJA

that the independence is local, and relative to another very similar variable, but not necessarily global and relative to a broader mixture of variables.

The second set of analyses considered the issue of independence with a wider variety of variables, in terms of the four models portrayed in Figure 1. A consistent pattern of results was evident across the two data sets.

Model 1, with completely independent age-related effects on each variable, does not appear plausible for two reasons. First, the age relations on the variables can be accounted for almost as well by postulating a much smaller number of age-related influences; second, this model completely ignores the many interrelations that exist among the variables. As a consequence of this latter charac- teristic, the overall fit of the model to the complete data was very poor (cf. Tables 3 and 10).

The other three models were similar in their ability to account for the age relations on the variables, although as might be ex- pected, reproduction of the age correlations was more accurate when we postulated a greater number of independent age-related influences. However, models with a single age-related influence (i.e., Models 2 and 4) were fairly accurate, and thus for most of the variables in these data sets, it is apparently not necessary to postulate specific age-related influences to account for the age relations on the variables. The fit of the models can obviously be improved by adding direct relations from age to individual vari- ables, but even these simple models indicate that a relatively large amount of the age-related influences on each variable is shared with the influences on other variables. An apparent implication of these findings is that broad or general mechanisms are needed to account for the shared age-related effects (cf. Salthouse, 1996). Specific mechanisms may or may not also be needed to account for the age-related effects on certain variables, but even when they are operating, the current results suggest that they are likely to account for only a small proportion of the observed effects on individual variables because such a large proportion seems to be associated with these general or shared effects.

The hierarchical model (Model 4) is clearly superior to the other models in terms of overall fit, which suggests that the variables do have structure and are organized in a coherent manner. This outcome is not surprising because it is consistent with a great deal of prior research on psychometric abilities (e.g., Carroll, 1993). However, an interesting new finding from the current analyses is that most of the age-related effects on a wide range of variables can be accounted for with the assumption that the age-related influences primarily operate at a high level in the hierarchical organization of variables.

A suggestion from Carroll (1993) motivated us to use the strategy of analyzing influences on a hierarchical structure from the top down:

Performance on a series of tasks that are loaded on abilities at three levels of analysis must be explained, first, in terms of individual differences on the factor at the highest level of analysis. These differences must be controlled for or partialled out in studying vari- ation at the second level of analysis--variation that will depend upon the particular aspects of ability represented in tasks at the second level of analysis. A similar process of control or partiaUing occurs in the transition to the explanation of differences at the first level of analysis. (p. 623)

Because the results of these analyses indicate that the pattem of age-related effects on the variables can be explained fairly accu- rately with age-related influences affecting only the highest level in the hierarchy, it can be inferred that most of the age-related effects are quite broad and are not restricted to particular types of variables. A similar pattern of results surfaced in analyses of the normative data from the cognitive variables in the Woodcock- Johnson Psycho-Educational Test Battery reported by Salthouse (1998a). As in the current analyses, the best fit to the data was some form of hierarchical model in which most of the age-related influences operated at the highest level in the hierarchy.

In conclusion, the results from these structural analyses impose clear constraints on the nature of plausible explanations for cog- nitive aging phenomena. That is, because many age-related effects seem to operate at relatively broad levels, which affect a wide variety of cognitive variables, researchers must apparently postu- late some general or nonspecific explanatory mechanisms. Fur- thermore, the results suggest that explanations of age differences that focus exclusively on processes specific to a particular task, or to a small number of related tasks, will probably have limited explanatory power. The current findings also imply that although researchers focusing on effects specific to particular variables may be able to account for some proportion of the age-related effects on those variables, that proportion will probably be small relative to the general or broad effects that are also occurring. Moreover, by definition, any specific mechanisms that might be operating are unlikely to be involved in the age-related effects occurring on other variables and, thus, will be unable to account for the large proportions of the age-related effects that are shared across variables.

The current results also have implications for the design of remediations of age-related cognitive impairments. That is, just as local or highly specific explanations seem unlikely to be sufficient in accounting for the observed age-related influences on different variables, narrow task-specific interventions may also prove inad- equate to completely remediate most age-related cognitive deficits. What remains to be determined, in addition to their precise nature, is how broad interventions must be in order to be effective.

What are these broad or general influences? Two possibilities, which are not mutually exclusive, are worth considering. One possibility is that they are best conceptualized at the level of cognitive processes, and they correspond either to a particular type of process (e.g., encoding, association) or to a property of process- ing common to many variables (e.g., involvement of working memory, speed of processing, use of controlled attention). A second possibility is that they are most meaningful when consid- ered at the level of neurophysiology or neuroanatomy and are related either to the functioning of a discrete neuroanatomical structure (e.g., dorso-lateral prefrontal cortex) or to a specific neural circuit (e.g., dopaminergic). These alternatives cannot be distinguished with the reported analyses, but the current results strongly suggest that broad explanatory mechanisms play an im- portant role in the age-related effects found in many cognitive variables. Furthermore, although it may not be possible to identify the nature of the broad mechanisms at this time, the analytical procedures described, along with the empirical phenomenon of considerable shared age-related influences, may serve a valuable role as tools for investigating the plausibility of explanations that propose independent age-related influences on specific processes

STRUCTURAL CONSTRAINTS 55

(also see Salthouse, McGuthry, & Hambrick, 1999). That is, to the extent that large proportions of the age-related influences on a particular variable are found to be shared with other cognitive variables, it may be difficult to justify the claim that they are unique or specific.

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Received January 26, 1999 Revision received May 13, 1999

Accepted May 16, 1999 •