Psychology attd Aging
2000, Vol. 15, No. 1, 44-55
Copyright 2000 by the American Psychological Association, Inc.
0882-7974/00/$5.00 DOI: 10.1037/10882-7974.15.1.44
Structural Constraints on Process Explanations in Cognitive Aging
Timothy A. Salthouse
Sara J. Czaja
Georgia Institute of Technology
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.
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 effects. Similarly, if two variables are suspected to involve qualitatively 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
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 cognitive deficits, because the answer to this question will be relevant
to the number, breadth, and type of interventions that will eventually 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 Technology, Atlanta, Georgia 30332-0170. Electronic mail may be sent to tim.
salthouse @psych.gatech.edu.
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 secondorder factors. In this respect, their analyses are more consistent with the
hierarchical model than the single common factor model.
44
STRUCTURAL CONSTRAINTS
(1) Complete Independence
(3) Independent Factors
45
(2) Single Common Factor
(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 determinants of processing efficiency such as working memory or processing 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 agerelated 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, variables 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 Figure 1 corresponds to the assumption that independent age-related
effects operate at the level of sets of variables. One could distinguish 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 possible 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 mediational model, resembles Models 2 and 4, with two important
differences: (a) the structural diagram is typically rotated 90 degrees 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 postulate 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 common 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 researchers 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 discriminate 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 requirements, 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 independent 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 interested 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 provide different types of information, we will consider a combination
of the two types of fit statistics when evaluating the models.
Analyses o f Variables F r o m 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 reduced 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., Salthouse, 1996), different percentiles of reaction time distributions
(e.g., Salthouse, 1993, 1998b), and items with different solution
47
STRUCTURAL CONSTRAINTS
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
population with respect to level of education. One can assess the representativeness 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 ageadjusted 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 75th percentile 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 reporting 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 significant 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 indicators, 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.
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
Results
Similar-task independence analyses. As previously mentioned, 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
Age decade
Variable
n
20s
30s
40s
50s
60s
70s+
Age
correlation
41
40
30
58
43
47
24.6
2.6
93
59
34.5
2.9
90
65
43.7
2.7
93
60
54.3
2.7
93
66
64.4
3.0
79
58
78.4
5.7
79
70
13.2
2.5
11.3
2.5
11.7
2.3
12.5
2.5
12.1
2.3
12.8
2.5
.01
12.2
2.3
10.8
2.9
11.6
2.5
12.1
2.4
12.5
3.1
11.9
2.7
.05
10.6
2.5
12.0
.67
74.9
10.0
3.0
10.7
.23
59.1
10.3
2.6
11.2
.40
65.5
11.7
2.6
12.1
.70
75.8
11.5
2.5
12.0
.67
74.9
10.3
2.7
11.7
.57
71.6
.05
2.0
0
0
0
2.0
0
8
0
2.2
3
13
1
2.1
7
14
3
2.2
14
33
2
2.5
21
40
4
.19
.29
.36
.02
Age
M
SD
% with some college
% women
Age-adjusted scaled scores
Digit Symbol
M
SD
Block Design
M
SD
Object Assembly
M
SD
Mean scale score
Mean z score
Percentile
Health rating
Cardiovascular surgery (%)
Hypertension medication (%)
Head injury (%)
Note. N --- 259.
-.15
.05
.05
48
SALTHOUSE AND CZAJA
sion analyses, with the controlled variable entered before considering 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 learning (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 a b o v e ' a n d 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 significantly 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 influences 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 A V L T Trial 1
variable, it is possible that the Trail Making B and Rey A V L T
Trial 5 variables shared considerable proportions of their agerelated variance with one another. The next set of analyses examined 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 contains analyses of linear and nonlinear age relations on the variables, 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 W A I S - 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 W A I S - R Block
Design and Object Assembly tests to assess a spatial factor. Although 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 deviations, 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 variables 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
Table 2
Reproduction of Age Correlations, Data Set 1
~/ariable
Digit Symbol
Letter Comparison
Pattern Comparison
Paired Associates 1
Paired Associates 2
Rey AVLT Trial 2
Rey AVLT Trial 6
Shipley Abstraction
WCST Number
Categorization
Object Assembly
Block Design
Root mean squared
deviation
Observed/
Model 1
Model 2
Model 3
Model 4
-.66
-.49
-.66
-.51
-.35
-.47
-.45
-.45
-.41
-.63
-.55
-.60
-.46
-.39
-.40
-.45
-.53
-.38
-.66
-.57
-.60
-.43
-.37
-.47
-.48
-.45
-.41
-.61
-.53
-.56
-.40
-.35
-.41
-.43
-.55
-.39
-.41
- .47
-.45
- .51
-.41
- .47
-.45
-.53
.05
.03
.05
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 average deviations. It is not surprising that the predictions are more
accurate with a greater number o f independent age relations (i.e.,
M o d e l 3 vs. M o d e l s 2 and 4), but it is interesting thai the age
relations on a wide range o f cognitive variables can be reproduced
fairly accurately with a single age-related influence, as in Models 2
and 4.
Statistics for the overall goodness o f fit o f the four models
appear in Table 3. The X2 value provides a test o f the significance
o f deviations o f the data from the model, but it is considered too
sensitive w h e n 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 w h i c h supplementary fit statistics
are most informative, but the other fit statistics that w e report here
reflect the relative degree to w h i c h all o f the covariances are
accurately reproduced by the m o d e l (i.e., the n o n - n o r m e d fit index
[NNFI] and the comparative fit index [CFI]) and the amount o f
residual covariance that is not accounted for by the model (i.e., the
Standardized Root M e a n Residual [Std. RMR]). Better fit o f a
model is therefore reflected in values o f N N F I and CFI closer
to l.0 and values o f Std. R M R closer to zero.
Comparison o f the entries in Table 3 reveals that the hierarchical
m o d e l (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 proportion o f the age-related effects on
the variables operate at a high level in that structure and, consequently, are shared a m o n g all variables at lower levels. The contrast b e t w e e n Models 1 (Complete Independence) and 2 (Single
C o m m o n Factor) indicates that the addition o f a higher order factor
substantially improves the fit o f the model (i.e., a nested comparison o f the two models yields a difference )(2(1, N = 259) = 509).
The contrast b e t w e e n Models 3 (Independent Factors) and 4 (Hierarchical) was also significant (i.e., a nested comparison o f the
two models yields a difference X2(1, N = 259) = 169). This latter
comparison indicates that it is more plausible to conceptualize the
49
groups o f variables or abilities as related to one another than to see
them as independent, and as the age effects operating on what is
c o m m o n 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 c o m p a r e d directly, but inspection o f
the fit statistics suggests that these two models have similar fits to
the data.
Data Set 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 ageadjusted 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 - . 6 6 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
(1)
(2)
(3)
(4)
Complete Independence
Single Common Factor
Four Separate Factors
Hierarchical
x2/df
NNFI
CFI
Std. RMR
882/55
373/54
326/51
157/50
.39
.76
.78
.91
.49
.80
.83
.93
.19
.08
.14
.05
Note. N = 259. NNFI = non-normed fit index; CFI = comparative fit
index; Std. RMR = standardized root mean residual.
50
SALTHOUSE AND CZAJA
Table 4
Descriptive Characteristics of Sample in Data Set 2
Age decade
Variable
20s
n
Age
M
SD
% with some college
% women
Age-adjusted scaled scores
Vocabulary
M
SD
Digit Span
M
SD
Digit Symbol
M
SD
Mean scale score
Mean z score
Percentile
Major operations (%)
Stroke (%)
Head injury (%)
30s
40s
50s
60s
107
70s
Age
correlation
88
83
92
76
77
24.3
2.7
65.1
51.8
34.4
2.9
54.3
52.2
45.0
2.6
65.8
59.2
54.4
2.8
71.4
67.5
65.1
2.5
72.0
59.8
72.6
2.1
69.3
56.8
9.5
3.1
9.3
2.9
11.3
3.4
12.4
3.0
12.7
2.6
12.8
2.3
.44
10.2
2.7
9.7
2.7
10.2
3.1
11.1
3.4
11.1
3.0
12.2
2.8
.26
11.0
3.2
10.3
.10
54.0
10.6
2.6
9.9
-.03
48.8
10.7
2.7
10.7
.23
59.1
11.9
2.7
11.8
.60
72.6
12.3
2.7
12.0
.67
74.9
13.9
2.5
13.0
1.00
84.1
.33
14
3
4
13
5
8
27
9
31
10
.23
.21
.05
7
0
4
9
0
1
• 5
"
3
.08
.05
.45
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
Vocabulary
Digit Span
Digit Symbol
COWA
Trails A and B
FigScan
Source
WAIS-R (Wechsler, 1981)
WAIS-R (Wechsler, 1981)
W A I S - R (Wechsler, 1981)
Controlled Oral Word Associauon
(Benton & Hamsher, 1989)
Trail Making (Reitan, 1958)
PegDH, PegNDH
Figural Scanning and Visual
Discrimination (Ekstrom, French,
Harman, & Derman, 1976)
Purdue Pegboard Test (Tiffin, 1968.)
VisRepC, VisRepI,
VisRepD
CVLTSum, CVLTDel,
CVLTCon
Visual Reproduction
(Wechsler, 1987)
California Verbal Learning Test (Delis,
Kramer, Kaplan, & Ober, 1987)
Note. W A I S - R = Wechsler Adult Intelligence Scale--Revised.
Description
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.
STRUCTURAL CONSTRAINTS
Table 6
significantly greater with increased age, and there was no significant
relation between age and digit span. All other variables had scores indicaring lower performance with increased age.
Proportions of Variance Associated With Linear, Quadratic, and
Cubic Age Relations, Data Set 2
Variable
Linear
Quadratic
Cubic
Vocabulary
Digit Span
COWA
Digit Symbol
Trails A
Trails B
FigScan
PegDH
PegNDH
VisRepl
VisRepD
VisRepC
CVLTSum
CVLTDel
CVLTCon
.156"
.003
.038*
.153"
.123"
.052*
.171 *
.239*
.232*
.151"
.184*
.051 *
.080*
.089*
.016"
.006
.000
.000
.000
.000
.000
.005
.023*
.015"
.001
.001
.000
.009
.001
.008
.009
.001
.000
.008
.000
.003
.003
.002
.000
.008"
.008
.012
.016"
.004
.007
Factor
Factor
Factor
Factor
.263*
.196"
.073*
.111"
.006
.000
.009
.000
.001
.012"
.011
.002
1
2
3
4
51
Resul~
Similar-task independence analyses. A s in D a t a Set 1, we
c o h d u c t e d i n d e p e n d e n c e a n a l y s e s o n the t w o variables f r o m the
Trail M a k i n g tests. T h e R 2 associated with age in the Trail M a k i n g
B score w a s only .052, a n d this w a s r e d u c e d to a n o n s i g n i f i c a n t
.002 (a 9 6 % reduction) after control o f the Trail M a k i n g A score.
U n l i k e the results in D a t a Set 1, therefore, in t h e s e data there w a s
n o e v i d e n c e o f an i n d e p e n d e n t age-related i n f l u e n c e on the Trail
M a k i n g B variable. T h i s m a y be at least partially attributable to the
relatively s m a l l age-related effects o n the Trail M a k i n g B variable
c o m p a r e d to that in the p r e v i o u s data set (i.e., R 2 with a g e o f .052
in t h e s e data v s . . 3 4 8 in Data Set 1).
M o s t o f the age-related variance in the p e g b o a r d t i m e score with
the n o n d o m i n a n t h a n d (i.e., R 2 = .232) w a s shared with the
variance in the t i m e score f r o m t h e d o m i n a n t hand, b u t the residual
age-related variance w a s s i g n i f i c a n d y greater t h a n zero (i.e., .013,
a 9 4 % reduction). It c a n therefore be inferred that there w a s a s m a l l
age-related effect on p e r f o r m a n c e with the n o n d o m i n a n t h a n d that
w a s i n d e p e n d e n t o f the effects o n the d o m i n a n t h a n d .
T h r e e variables were available in the V i s u a l R e p r o d u c t i o n test:
accuracy o f c o p y i n g with the s t i m u l u s pattern present, a c c u r a c y o f
i m m e d i a t e reproduction f r o m m e m o r y , a n d a c c u r a c y o f reproduction f r o m m e m o r y after a 3 0 - m i n delay. T h e r e w a s substantial
residual variance in the i m m e d i a t e m e m o r y variable after control
o f the variance in the copy variable (i.e., f r o m R 2 = .151 to .071,
a 5 3 % reduction). T h i s indicates the e x i s t e n c e o f i n d e p e n d e n t
age-related effects on m e m o r y a b o v e a n d b e y o n d a n y effects
apparent in copying. T h e r e w a s also significant residual age-
Note. 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; Factor
1 = Speed; Factor 2 = Spatial Reproduction and Memory; Factor 3 =
Verbal Memory; Factor 4 = Miscellaneous/Knowledge.
* p < .01.
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.
M
SD
Age
Vocabulary
Digit Span
COWA
Digit Symbol
Trails A
Trails B
FigScan
PegDH
PegNDH
VisRepI
VisRepD
VisRepC
CVLTSum
CVLTDel
CVLTCon
1
2
3
4
5
6
7
8
9
10
11
12
13
14
.40
.05
.19
.34
.35
.23
.41
.49
.48
-.39
-.43
-.22
-.28
-.30
-.13
-.40
.48
-.05
.00
-.21
.04
.09
.10
-.00
-.05
.06
.16
.11
.16
-.45
-.22
-.19
-.31
-.09
-.07
-.05
.16
.12
.17
.20
.16
.15
--.17
-.11
-.27
-.08
.05
.08
.04
-.02
-.03
.15
.11
.18
-.48
.52
.60
.42
.35
-.24
-.30
-.15
-.34
-.34
-.18
-.52
.51
.36
.32
-.26
-.27
-.14
-.24
-.23
-.16
.46
.35
.29
-.30
-.31
-.22
-.37
-.30
-.26
-.44
.41
-.23
-.29
-.13
-.22
-.17
-.17
-.78
-.44
-.44
-.29
-.34
-.37
-.13
--.41
-.43
-.30
-.28
-.27
-.12
-.83
.57
.30
.31
.15
.54
.36
.36
.21
-.22
.20
.15
-.79
.64
50.0
17.1
50.5
13.6
15.7
4.9
39.9
11.7
1.77
0.53
31.3
13.0
77.6
36.5
74.1
22.6
15
16
m
• 82.5
23.2
89.4
25.6
6.9
3.2
5.7
3.5
10.2
2.3
49.0
10.3
m
.44
10.5
3.1
m
80.0
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 time with verbal
material.
Factor analyses. We conducted an exploratory factor analysis
on the data summarized in Table 7 with the eigenvalue-greaterthan-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
he
.65
.57
.61
.68
.65
.60
.82
.79
.64
.89
.75
.64
.61
.60
.64
Factor loadings
Digit Symbol
Trails A
Trails B
FigScan
PegDH
PegNDH
VisRepI
VisRepD
VisRepC
CVLTSum
CVLTDel
CVLTCon
Vocabulary
Digit Span
COWA
.79
.75
,70
.81
,69
,64
-.36
-.41
-.19
-.38
- .35
-.20
.03
-.21
- . 13
-.25
-.25
-.31
-.24
-.59
-.58
.911
.88
.78
.35
.36
.16
- .03
.19
-.06
-.34
-.23
-.37
-.21
-.35
-.28
.29
.37
.21
.94
.86
.79
.18
.17
.17
-.16
-.13
-.38
-.01
.21
.24
.03
-.03
.07
.17
.10
.21
.77
.74
.79
Eigenvalue
Proportion of
variance
4.93
.33
2.17
.15
1.62
.11
1.41
.09
Correlations
Age
F1
F2
F3
F4
.51
-.44
-.27
.33
--.41
-.37
-.06
-.34
-.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, 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; 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).
Discussion
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
Factor2
0.8
0.4
o
o
O9
I..L
o.o
-0.4
-0.8
-1.2
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 Miscellaneous/Knowledge (Factor 4).
variable are not independent of the age-related influences on other
variables.
The similar-task independence analyses are based on two variables that can be hypothesized to be similar except that the criterion 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
Variable
Digit Symbol
Trails A
Trails B
Figural Scanning
VisRepI
VisRepD
VisRepC
CVLTSum
CVLTDel
CVLTCon
Root mean squared
deviation
Observed/
Model 1
Model 2
Model 3
Model 4
.34
.35
.23
.41
-.39
- .43
- .22
- .28
- ,30
- . 13
.31
.28
.32
.28
-.37
-.39
- .27
- .34
- .32
- .23
.36
.32
.31
.36
-.41
-.40
-.27
- .28
- .22
- . 18
.35
.31
.31
.34
-.38
- .39
-.26
- .34
- .27
- .22
.06
.04
.05
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 = California Verbal Learning Test, sum of recalled words; CVLTDel = California 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 agerelated 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 consistent 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
(1)
(2)
(3)
(4)
Complete Independence
Single Common Factor
Three Separate Factors
Hierarchical
x2/df
NNFI
CFI
Std. RMR
2,180/45
1,366/44
240/42
158/41
.04
.39
.90
.94
.21
.51
.93
.96
1.24
.13
.12
.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 characteristic, 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 expected, 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 variables, 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 variation 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 accurately 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 WoodcockJohnson 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 cognitive 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 postulate some general or nonspecific explanatory mechanisms. Furthermore, 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 inadequate 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 processing 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 considered 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 important 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
(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 •