Developmental Psychology
1998, Vol. 34, No. 5, 851-864
Copyright 1998 by the American Psychological Association, Inc.
0012-1649/98/$3.00
Independence of Age-Related Influences on Cognitive Abilities
Across the Life Span
Timothy A. Salthouse
Georgia Institute of Technology
Age-related increases in childhood and age-related decreases in adulthood have been reported for a
wide variety of cognitive variables, but relatively little research has addressed the question of the
independence of these influences. In this project, cross-sectional life span data (age 5 to 94 years)
from the nationally representative sample used to establish the norms for the Woodcock-Johnson
Psycho-Educational Battery (R. W. Woodcock & M. B. Johnson, 1989, 1990) were subjected to
several types of analyses. The results indicated that the majority of age-related differences appear
to be shared across different cognitive variables and are well predicted by individual differences in
higher order factors. These findings suggest that the role of task-specific interpretations of developmental differences in cognition needs to be reevaluated to take into consideration the lack of independence of age-related influences on a variety of cognitive variables.
researchers interested in reasoning have speculated that factors
such as integration and abstraction might be involved in the
developmental differences observed in measures of inductive
reasoning. Interpretations based on factors or processes restricted to particular types of tasks are clearly valuable, but they
may be misleading if the possibility of broader and potentially
more fundamental developmental influences is neglected.
Of course, it is quite conceivable that there are no broad
developmental influences and that the age-related effects on different types of tasks are largely independent of one another. To
the extent that this is the case, and there is little predictability
of the direction and magnitude of the age-related differences on
one type of task from knowledge of the direction and magnitude
of the age-related differences on another type of task, then researchers would be justified in focusing exclusively on taskspecific interpretations of developmental differences.
However, if it were discovered that a substantial proportion
of the age-related influences on a particular task was shared
with individual differences on other tasks, then a task-specific
research strategy might no longer be optimal. That is, if large
proportions of the age-related variance were found to be shared
with individual differences in other cognitive variables, then
many of the task-specific mechanisms that have been inferred
to exhibit age-related differences might simply be consequences
of a broader developmental phenomenon. At the very least, the
magnitude of the age-related effects that could be uniquely explained by specific processes would be substantially reduced if
much of the age-related variance in different variables was found
to be shared with both individual differences in other cognitive
variables and more general dimensions of individual differences
in cognitive functioning.
The question of the independence of age-related influences is
obviously relevant across the entire life span, but because the
patterns could differ in childhood and in adulthood, it is probably most meaningful to consider the two periods separately.
Nevertheless, if the same variables are available across all ages,
it would be informative to compare the composition of any
common influences that might be discovered. For example, are
Many cognitive variables have been found to be significantly
related to age both across the childhood years and across the
adult years. However, very little is currently known about the
interrelations of the age relations on different variables. That is,
to what extent are the age-related influences on different cognitive variables shared and in common as opposed to distinct and
independent? This deceptively simple question has important
implications for understanding the nature, and perhaps ultimately the causes, of age-related differences in cognitive functioning. For example, if most of the age-related variance in
many different cognitive variables was found to be distinct and
independent of the age-related variance in other cognitive variables, then a large number of specific age-related influences
would presumably have to be postulated to account for the agerelated differences observed in these variables. In contrast, if a
substantial proportion of the age-related variance in many cognitive variables was found to be shared and in common with the
age-related variance in other cognitive variables, then a relatively
small number of broad or general age-related influences might
be responsible for many of the age-related differences in cognitive functioning.
Most contemporary interpretations of cognitive development
in both childhood and adulthood have focused on mechanisms
designed to account for the age-related differences observed in
single variables or in a small set of closely related variables.
For example, researchers interested in memory have speculated
that factors such as effectiveness of encoding or retrieval contribute to developmental differences in memory functioning, and
Preparation of this article was supported by a research grant (R37
AG 6826) from the National Institute on Aging.
I am very grateful to Richard W. Woodcock for generously providing
access to the normative data from the Woodcock-Johnson battery and
to Ulman Lindenberger for many valuable suggestions.
Correspondence concerning this article should be addressed to Timothy A. Salthouse, School of Psychology, Georgia Institute of Technology,
274 Fifth Street, Atlanta, Georgia 30332-0170. Electronic mail may be
sent to tim.salthouse@psych.gatech.edu.
851
852
SALTHOUSE
there a few core cognitive abilities that are central to cognitive
development across both the period of childhood and the period
of adulthood, or is there a shift in the composition of the core
abilities after the period of maturity?
The analyses to be described are based on cross-sectional
data from the normative samples in the Woodcock-Johnson
Psycho-Educational Battery--Revised (Woodcock & Johnson,
1989, 1990), which consists of 35 tests of cognitive ability
and achievement. Five characteristics of this test battery are
important for the current purposes: (a) the cognitive ability
tests were designed to reflect distinct psychometric factors or
abilities; (b) all but two of the tests are administered in an
untimed manner, with a modified adaptive testing procedure;
(c) all variables have good levels of reliability, with internal
consistency values between .8 and .9, and test-retest values
only slightly lower; (d) a similar Rasch scaling was used for
all variables in an attempt to create an equal interval scale
throughout the entire measurement range; and (e) the normative
sample was large (over 6,300 individuals) and involved quota
sampling in an attempt to represent the U.S. population across
the range from approximately 5 to 94 years of age.
The primary analyses designed to investigate the independence of age-related influences essentially involve examining
the relations between age and individual variables (or first-order
ability factors), after considering the relation between age and
what all the variables have in common. The analytical procedures are based on the assumption that the age-related variance
in a variable is a function of error, unique influences, and common influences (i.e., influences shared with individual differences in other cognitive variables). More determinants could
clearly be specified, but this is a useful level of abstraction
because it provides a heuristic framework for investigating the
nature of the age-related influences on a given variable. That is,
within this framework, it is possible to decompose age-related
variance into unique and shared components (cf. Kliegl & Mayr,
1992; Lindenberger, Mayr, & Kliegl, 1993; McArdle & Prescott,
1992; Salthouse, 1992, 1994). Unique effects represent agerelated differences that cannot be predicted on the basis of individual differences in other variables. In contrast, shared effects
refer to age-related differences that are correlationally linked to
individual differences in other cognitive variables. For the current purposes, the magnitudes of unique and shared effects are
used as empirical indicators of the relative importance of distinct
(i.e., variable-specific) or more general (i.e., common) agerelated influences on cognitive functioning in childhood and
aging.
All of the data to be analyzed are cross-sectional. Although
results from cross-sectional comparisons are sometimes dismissed as uninteresting or nonmeaningful, strong relations have
consistently been reported between many cognitive variables
and the individual's age in cross-sectional samples, and eventually those relations need to be explained. It is true that crosssectional differences are sometimes assumed to directly reflect
intrinsically determined age changes. This assumption is questionable because cross-sectional differences could be due to
endogenous influences (i.e., factors originating within the organism, such as maturation), exogenous influences (i.e., factors
originating outside the organism and related to changes in the
context in which the individual lives while he or she is maturing), or a combination of both endogenous and exogenous in-
fluences. The uncertainty associated with cross-sectional results
is often acknowledged by referring to them as age-related differences to emphasize that the differences are related to age but
are not necessarily caused by age (i.e., in the sense of intrinsic
or endogenous processes).
The current project is not designed to distinguish between
endogenous and exogenous influences but, instead, to examine
the pattern of developmental differences across a diverse set of
variables. Nevertheless, information about the manner in which
age-related effects are manifested should be relevant in eventually determining the nature and source of those influences. In
particular, the focus of future explanatory research would presumably shift somewhat if it were discovered that age-related
effects were associated with a relatively small number of shared
influences rather than a large number of independent influences.
Two different approaches are used to examine the structure
of age-related variation within a set of variables. In the first
approach, no structure among the variables is assumed; instead,
it is postulated that all age-related effects are mediated through
whatever is common to all variables in addition to independent
age-related effects on certain variables. This analytical method
is conceptually analogous to hierarchical regression analysis in
which the first component from a principal-components analysis, representing the variance shared by all variables, is controlled before examining the relation of age to individual variables. Because these models only attempt to account for the
relations of age to the variables, and not for all of the covariances
among variables, the fit of the models to the entire data is of
only secondary interest. The information of greatest importance
from these analyses are the relative strengths of shared agerelated influences (through the common factor) and unique agerelated influences (direct from age to the variable).
The second analytical strategy resembles the traditional psychometric approach in that structure is imposed on the variables
before examining age-related influences. However, rather than
specifying the entire structure a priori, on the basis of theories
or previous empirical results, in the current analyses, the structure is partly determined from the pattern of age-related effects
among the variables. This hybrid strategy was considered desirable because although the tests in this data set were designed
to reflect distinct abilities according to a particular psychometric
model of intellectual abilities, the major purpose of the analyses
was to determine the level at which age-related influences are
manifested.
Overview
The primary goal of the analyses to be reported was to investigate the extent to which the age-related influences on different
cognitive variables were independent of individual differences
in other cognitive variables across the periods of childhood (age
5 - 1 7 years) and adulthood (age 18-over 90 years). Two different sets of analyses were conducted for this purpose. In the first
analyses, a single common factor was postulated with relations
from each variable and from age, and then the independent
relations from age to the individual variables were determined.
The second set of analyses examined a variety of more complex
structural relations among the variables and investigated the
level at which independent age-related influences were evident.
853
INDEPENDENCE OF AGE-RELATED EFFECTS
was positively skewed in the adult data. To illustrate, in the children
data, 31% of the individuals were under the age of 9 years, 41% were
between 9 and 13 years, and 29% were between 14 and 17 years of age.
In the adult data, 50% of the individuals were under the age of 40 years,
26% were between 40 and 59 years of age, and 24% were over the age
of 60 years.
Sixteen of the 35 variables from the two Woodcock-Johnson scales
were selected on the basis of the availability of complete results from
the largest number of individuals (total of 5,470) and a pattern of seven
clearly distinct factors in the college student reference group. The 16
variables are briefly described in Table 1.
All of the structural equation analyses were based on covariance
matrices derived from the Rasch scores. Because chi-square statistics
may be misleading with large samples, as was the case here, three
additional fit indices that are less dependent on sample size were also
examined. The Benfler-Bonett non-normed fit index (NNFI) and the
Bentler comparative fit index (CFI) both range from 0 to 1.0, with
values closer to 1.0 representing better fit of the model to the data. The
standardized root mean residual (SRMR) reflects the deviation of the
estimated covariance matrix from the observed covariance matrix, and
Method
Three different data sets were formed, consisting of children (age 5 17, n = 3,155), college students (age 18-22, n = 735), and noncollege
student adults (age 18-94, n = 1,580). There were three reasons for
separating the college students from the other groups. First, the empirical
results (illustrated in Figure 1) suggest that this group may not be
precisely comparable to the other groups because of discontinuities in
the age trends for some variables. Second, college students represent a
transition between the other two groups; hence, their classification either
as children or as adults would be arbitrary. And third, for certain comparisons it is desirable to have a reference sample with a restricted age
range.
In the children data there were between 169 and 324 individuals at
each year from age 6 to 17 years and 115 individuals who were 5 years
of age. Individuals in the adult sample were categorized into one of
seven decade groups ranging from under 30 to over 80 years of age.
There were only 59 adults in the over-80 age group, but the range of
individuals in the remaining groups was 158 to 444. In very broad terms,
the age distribution was close to rectangular in the children data and
56O
Reasoning
Knowledge
56O
,
Quantitative
Social Studies
54O
540
540 ~
52O
52O
52o i
~,.~...k.¢~-_~. Applied Problems
¢D
O500
O
¢/)
~48o
O
44O
440
44o
420
400
1020304050607080
Chronological
42o
.
Age
....... Short-Term Memory
O
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1020304050607080
Chronological A g e
Closure
56O
54O
52O
6
¢3
1020304050607080
Chronological Age
52O
¢D
o500
O
co
,-.480
4oo
i
Visual Matching
54O
Memory for Sentences
.
Perceptual Speed
56O
54O
52O
O
46o
420
560
48o
o
~oo
rr"
400
oo 50o
¢o
¢- 480
Visual Closure
5OO
O
48O
(.)
o
Sound Blending "'...o
46O
Jr"
44O
44O
44O
420
420
42O
4OO
4OO
1020304050607080
Chronological Age
1020304050607080
Chronological A g e
AssociativeMemory
56O
540
¢}
520
oo~oo
¢/)
4::480
~,~o
rr"
--~
Visual-Auditory Learning "~
44O
42O
4O0
1020304050607080
Chronological
Age
Figure 1. Means for variables as a function of age.
400
'
"
'
.
.
.
.
.
.
.
.
.
lO 2 0 3 0 4 0 5 0 6 0 7 0 8 0
!
Chronological Age
~
i
J
i
854
SALTHOUSE
Table 1
Description of Variables Included in the Analyses
Variable
Description
Analysis - synthesis
Concept formation
Calculation
Applied problems
Science
Social studies
Humanities
Incomplete words
Visual closure
Sound blending
Memory for names
Visual-auditory learning
Memory for sentences
Memory for words
Visual matching
Cross out
Logical reasoning involving combinations of abstract figural stimuli
Identification of the concept relating sets of stimuli
Numerical abilities ranging from arithmetic to geometry and calculus
Word problems requiring arithmetic and mathematical concepts
Test of knowledge about biological and physical science
Test of knowledge about history, geography, government, and economics
Test of knowledge about art, music, and literature
Identification of words from auditory fragments
Identification of pictures that are distorted or incomplete
Integration of sound fragments to make words
Associations between unfamiliar names and pictures of novel creatures
Associations between unfamiliar visual symbols and familiar words
Immediate reproduction of auditorily presented words, phrases, and sentences
Immediate reproduction of unrelated words in the correct sequence
Targets to be found and marked among a set of alternatives
Identical drawings to be marked among a set of alternatives
thus values closer to 0 represent better fit. Decisions about model fit
were based on a combination of information from these different indices.
However, because few of the models had nested relations to one another,
direct statistical comparisons among models were not always possible.
Results
Interrelations of Variables
Whenever examining relations among sets of variables, it is
possible that some of the relation between two or more variables
is a consequence of the relation of each variable with a third
variable. That is, some of the relation between variables X and
Y could be attributable to the relation that both X and Y have
to variable Z. In the current situation, at least some of the
interrelations among a set of variables i n age-heterogeneous
samples could be due to the relations that all variables have
with age. There are two ways to estimate the extent to which
the results of the analyses might be affected by this type of
influence. These consist of comparing the patterns of factor
loadings and the interrelations of factors in the original ageheterogeneous samples with those: (a) from a sample with a
narrow age range (i.e., college students) and (b) from the original samples after partialing the influence of age from all variables. If the interrelations of the variables corresponding to the
single common factor and the grouping of variables into firstorder ability factors and higher order factors are solely attributable to the relations that all variables have with age, then the
patterns of loadings and factor correlations should be close to
zero in the data without age variation.
The results summarized in Tables 2 and 3 indicate that this
is not the case. Table 2 summarizes the results of a confirmatory
factor analysis model in which all variables are postulated to
be related to a single higher order factor. The numbers in each
column correspond to the loadings on the common factor in
each data set when no age relations are postulated. The data in
the second column are derived from the 735 college students
between 18 and 22 years of age, the data in the third column
are derived from the 3,155 children between 5 and 17 years of
age, and the data in the fifth column are derived from the 1,580
adults between 18 and 94 years of age. The fourth and sixth
columns represent the results after the relations of age were
partialed from all variables in the children data (fourth column)
and in the adult data (sixth column). Although the loadings of
the variables were weaker when there is no age variation (i.e.,
in the student and age-partialed data sets), they are still moderately large for most variables. These similar patterns indicate
that the variables share considerable variance with one another
regardless of the relations they each have with age.
An initial exploratory factor analysis on the data from the
college student sample revealed seven factors that were very
similar to those reported in the Woodcock-Johnson manuals
(McGrew, Werder, & Woodcock, 1991; Woodcock & Johnson,
1989, 1990; see also Bickley, Keith, & Wolfle, 1995), with the
exception that the Visual Processing and Auditory Processing
factors were collapsed into a single factor. This discrepancy in
the factor pattern is probably attributable to the fact that the
picture recognition variable, which was a marker for Visual
Processing, was not included in the current analyses because of a
relatively large number of missing observations. A confirmatory
factor analysis model with seven correlated factors was applied
to the same five data sets described above. The results of these
analyses are presented in Table 3 where it can be seen that the
model provided a good fit in each data set. The fact that a
similar structure among the variables was evident even when all
age-related influences on the variables were removed provides
some assurance that the structure in the age-heterogeneous samples is not merely an artifact of the large age relations in these
data sets.
Age Relations
Figure 1 illustrates the age relations for all variables, with
the variables grouped according to the factors identified in the
confirmatory factor analyses just described. Nonlinear age relations were examined by generating three orthogonal age variables: a linear age variable, a quadratic age variable created by
partialing the linear component from the age-squared term, and a
cubic age variable created by partialing the linear and quadratic
INDEPENDENCE OF AGE-RELATED EFFECTS
855
Table 2
Factor Loadings in Different Data Sets of a Model With a Single
Common Factor But No Age Relations
Variable
Analysis-synthesis
Concept formation
Calculation
Applied problems
Science
Social studies
Humanities
Incomplete words
Visual closure
Sound blending
Memory for names
Visual-auditory learning
Memory for sentences
Memory for words
Visual matching
Cross out
Mdn
X2 (df = 104)
NNFI
CFI
SRMR
Students
(N = 735)
Children
(N = 3,155)
Children
partial age
(N = 3,155)
Adults
(N = 1,580)
Adults
partial age
(N = 1,580)
.638
.666
.660
.784
.765
.785
.713
.468
.411
.479
.472
.549
.542
.367
.378
.460
.828
.810
.936
.951
.925
.937
.903
.695
.753
.735
.618
.731
.764
.648
.894
.892
.514
.530
.350
.473
.515
.452
.533
.462
.343
.516
.487
.548
.535
.431
.320
.343
.798
.814
.803
.791
.815
.772
.823
.710
.699
.735
.695
.797
.672
.602
.768
.771
.643
.659
.737
.806
.764
.832
.784
.546
.448
.528
.494
.614
.611
.468
.540
.502
.546
.819
.480
.772
.613
1375.42
.70
.74
.08
6291.44
.88
.89
.04
4996.96
.90
.92
.03
4007.43
.78
.81
.07
3074.85
.82
.87
.05
Note. NNFI = Bentler-Bonett non-normed fit index; CFI = comparative fit index; SRMR = standardized
root mean residual.
components from the age-cubed term. The proportions of variance associated with linear, quadratic, and cubic age relations
for each variable in the children and adult groups are reported
in Table 4.
It is apparent that there were very strong linear and moderate
quadratic age relations for all variables across the period of
childhood. The quadratic trend for most variables reflects a
somewhat slower rate of increase in the older (teenage) years.
Moderately strong linear and quadratic age relations were evident across adulthood for all variables. The quadratic trend in
most of these variables reflects an acceleration of the decline
in older ages. The cubic trends in both data sets reflect fluctuations in the overall patterns and are not easily described.
Single C o m m o n Factor A n a l y s e s
Single common factor analyses were next conducted on the
data from the children and adult samples to determine the degree
of shared age-related effects in each data set. That is, because
it is apparent in Figure 1 and Table 4 that most of the variables
had significant age-related influences, the goal of these analyses
was to determine the extent to which those influences were
independent of one another.
The same analytical procedure was used with both the children data and the adult data. Initially, for purposes of comparison, a model (Model 0) was examined in which there were no
interrelations among variables but independent relations of age
to every variable. As can be seen in Table 5, this model provided
a very poor fit to the data for both children and adults. It can
therefore be inferred that the data are not consistent with the
existence of completely independent age-related influences on
the individual variables.
The next model (Model 1 ) involved a single factor that was
related to all variables; hence, it represented what the variables
had in common with one another, and a relation between the
linear component of age and that factor, but no direct relations
from age to the individual variables. In a sense, Model 1 can
be viewed as the opposite extreme from Model 0 in that it
postulates that there is only a single shared age-related influence
on all variables. This model had a considerably better fit than
the model with completely independent age relations, but it still
did not provide a very good fit to the data.
Because the goal of this set of analyses was to examine
influences associated with age on individual variables after controlling the age-related effects on what the variables have in
common, in the next model, the parameters of the relations
between the common factor and individual variables, and between age and the common factor, were fixed to the values
estimated from Model 1. This procedure is somewhat analogous
to hierarchical regression in that because the interest is in determining the age-variable relations after taking into consideration the age-related effects shared among all variables, the best
estimate of the shared effects is partialed out before examining
independent age-related effects on individual variables. (If these
parameters are not fixed, then with the computer program used
in these analyses, the age-related effects on the variables are
redistributed between the common and unique influences in such
a manner that the common factor no longer resembles that obtained in the analyses with no age relations [cf. Table 2] or in
856
SALTHOUSE
Table 3
Factor Loadings in Different Data Sets o f a Model With
Seven Ability Factors But No Age Relations
Factor variable or
correlation
t. Reasoning
Analysis-synthesis
Concept formation
2. Quantitative
Calculation
Applied problems
3. Knowledge
Science
Social studies
Humanities
4. Closure
Incomplete words
Visual closure
Sound blending
5. Associative memory
Memory for names
Visual-auditory learning
6. Short-term memory
Memory for sentences
Memory for words
7. Perceptual speed
Visual matching
Cross out
Mdn
1- 2
1-3
1-4
1-5
1-6
1-7
2-3
2-4
2- 5
2-6
2-7
3-4
3-5
3-6
3-7
4-5
4-6
4-7
5-6
5-76-7
Mdn
x~(df --- 83)
NNFI
CFI
SRMR
Students
(N = 735)
Children
(N = 3,155)
Children
partial age
(N = 3,155)
Adults
(N = 1,580)
Adults
partial age
(N = 1,580)
.738
.762
.881
.863
.582
.594
.863
.875
.735
.743
.788
.953
.958
.959
.386
.508
,883
,900
.801
.882
.825
.847
.767
.949
.959
.925
.554
.493
.569
,885
.887
.877
.807
.893
.814
.671
.517
.629
.745
.773
.782
.547
.373
.596
,781
.758
.806
.665
.497
.628
.671
.833
.744
.890
.605
.710
.796
,913
.623
.780
.902
.583
.932
.770
.746
.572
.818
,730
.797
.613
.634
.851
.962
.947
.454
.460
.910
.922
.725
.671
.765
.908
.562
.876
.739
.733
.738
.620
.691
.468
.493
.743
.425
.514
.487
.465
.700
.522
.566
.415
.585
.505
.535
.338
.421
.282
.925
.896
.916
.852
.795
.854
.949
.912
.779
.774
.949
.919
.796
.826
.878
.843
.804
.885
.731
.726
.717
.855
.752
.779
.764
.626
.638
.823
.749
.673
.599
.750
.765
,680
.698
.567
.728
,637
.661
.565
.533
.442
.813
.788
.841
.861
.735
.787
.911
.694
.704
.717
.695
.757
.716
.755
,658
,855
.789
.851
,701
.749
.639
,791
.765
.761
.799
,661
.685
.896
.655
.656
.663
.662
.742
.671
.709
.621
.758
.737
.725
,610
,604
.528
.514
.852
.680
.755
.685
302.74
.94
.96
.04
1329.17
.97
.98
.02
897.04
.98
.99
,01
690,24
.96
,97
.03
458.31
.97
.98
.02
Note. NNFI = Bentler-Bonett non-normed fit index; C F / = comparative fit index; SRMR = standardized
root mean residual.
the analyses with age related only to the common factor [i,e.,
Model 1].)Model 1A therefore differed from Model t by adding
direct relations from age to the individual variables in cases in
which the coefficients differed from zero by more than 2 SEs,
while preserving the same shared age-related influences deter-
mined from Model 1. Table 5 reveals that this model resulted
in an appreciable improvement o f fit, indicating that at least
some variables had age-related influences that were independent
o f the influences shared by all other variables.
Models 2 and 2A were similar to Models 1 and IA except
INDEPENDENCE OF AGE-RELATED EFFECTS
857
Table 4
Proportions of Variance Associated With Linear, Quadratic, and Cubic Age Trends
From Age 5 to 17 and From Age 18 to 94
Children (age 5-17; n = 3,155)
Adults (age 18-94; n = 1,580)
Variable
Age
Age2
Age3
Age
Age2
Age3
Analysis-synthesis
Concept formation
Calculation
Applied problems
Science
Social studies
Humanities
Incomplete words
Visual closure
Sound blending
Memory for names
Visual-auditory learning
Memory for sentences
Memory for words
Visual matching
Cross out
.433*
.397*
.774*
.674*
.596*
.676*
.541'
.289*
.450*
.306*
.191"
.283*
.334*
.255*
.715"
.689*
.064*
.044*
.070*
.049*
.035*
.023*
.022"
.058*
.050*
.058*
.014"
.037*
.023*
.015"
.051"
.041"
.009*
.005*
.002*
.005*
.002*
.000
.000
.011'
.003*
.015"
.003*
.017"
.002*
.001
.000
.000
.205*
.214"
.132"
.058*
.124*
.032*
.105"
.191"
.336*
.269*
.240*
.241"
.083*
.142"
.316"
.396*
.024*
.033*
.017"
.033*
.045*
.060*
.045"
.042*
.036*
.032*
.005*
.030*
.018'
.020*
.040*
.038*
.004*
.001
.005*
.009*
.011"
.006*
.005"
.002
.001
.003*
.001
.000
.003
.001
.002
.001
.442
.475
.043
.041
.003
.005
.198
.193
.033
.032
.003
.003
Mdn
M
Note. All quadratic coefficients were negative, and all cubic coefficients were positive.
* p < .01.
that in the initial model, quadratic and cubic components of age
to the common factor (Model 2) and to individual variables
(Model 2A) were considered in addition to the linear age component. Comparison of Models 2 with l, and 2A with 1A,
reveals that although many variables had significant quadratic
and cubic age trends (cf. Table 4), the addition of the nonlinear
age relations did not result in an improvement of fit, particularly
as indexed by the chi-square statistic. Values of the standardized
regression coefficients were - . 2 3 for both children and adults
for the quadratic term and .05 for children and .07 for adults
for the cubic term.
Figures 2 and 3 illustrate the best-fitting single common factor
model (Model 1A) in the children and adult data, respectively.
The illustrated models represent the shared (through the common factor) and unique (direct) age-related influences in each of
the variables. The figures contain the relations from the common
factor to the right of the variables, the independent relations of
age on the variables to the far left of the variables, and the
correlation of the variable with age to the immediate left of the
variable. The age correlations are not part of the structural model
but are included in the figures to facilitate comparisons of total
and unique age-related influences on the variables.
The best-fitting model of the childhood data is illustrated in
Figure 2. It is apparent that there was a very strong positive
relation between age and the common factor (.86) and that all
variables had moderate to large relations from the common
factor. Independent age-related effects were evident in some
variables, with most of them negative in direction, indicating
that there was a smaller age-associated increase in the variable
than what would be expected if all of the age-related influences
were channeled through the common factor.
For purposes of comparison, the median of the absolute standardized path coefficients between age and the variable (includ-
ing those that were not significant and consequently are not
represented in Figure 2) was computed to provide an estimate
of the median age relation after considering the influence of age
on what the variables have in common. This value was .06. In
contrast, the median of the zero-order age correlations, which
are equivalent to standardized path coefficients when age is
the only predictor in the equation, was .67. These dramatically
different values indicate that on average, most of the age-related
variance on the individual variables was shared with other variables and therefore predictable by individual differences in what
the variables have in common (i.e., the common factor). Comparison of the independent age relations, on the far left of the
figure, with the age correlations, to the immediate left of the
variables, reveals that a similar overall pattern was evident on
each variable.
The best-fitting model for the adult data is illustrated in Figure
3. It can be seen that there was a large negative relation ( - . 5 5 )
between age and the common factor, and all variables had strong
relations with the common factor. There was a mixed pattern
of independent age-related effects. Five variables had no independent age-related effects; six had positive effects, indicating
that the negative age-related influences would have been overestimated if only the age-related effects through the common factor were considered; five had negative effects, indicating that
the negative age-related influences on the variables would have
been underestimated by considering only the age-related effects
on the common factor.
Once again, medians of the absolute age relations can be
computed before and after control of what all the variables have
in common. The values of these total and unique age relations
for the variables were .45 and .10, respectively. As was the case
with the data from the children, then, it appears that much of
the age-related variance in the individual variables was shared
858
SALTHOUSE
Table 5
Model Fit Statistics
Model
Description
df
X~
CFI
NNFI
SRMR
120
119
27,684.38
7,580.29
.57
.88
.51
.87
.20
.05
122
7,010.81
.89
.88
.09
152
8,505.35
.87
.86
.05
157
7,961.92
.88
.87
.08
113
112
12,659.30
3,527.50
.80
.95
.76
.94
.18
.04
106
2,169.23
.97
.96
.02
109
2,680.98
.96
.95
.04
109
3,298.86
.95
.94
.04
109
3,375.48
.95
.94
.05
111
3,605.29
.95
.93
.05
145
4,325.05
.94
.93
.04
139
3,063.76
.96
.95
.03
142
3,644.61
.95
.94
.04
142
4,092.88
.94
.93
.04
Children
0
1
1A
2
2A
3
4
4A
4B
4C
4D
4E
5
5A
5B
5C
Only direct linear age-variable relations
Single common factor with linear age-common,
no residual age relations
Single common factor with linear age-common,
fix parameters from Model 1, estimate
residual linear age relations to variables
Single common factor with linear and nonlinear
age-common, no residual age relations
Single common factor with linear and nonlinear
age-common, fix parameters from Model
2, estimate residual linear age relations to
variables
Only direct linear age-ability factor relations
Hierarchical with linear age-higher order
relations, no residual age relations
Hierarchical with linear age-higher order
relations, residual linear age relations to
lst-order factors
Hierarchical with linear age-higher order
relations, two 2nd-order factors (C2, C3)
plus 3rd-order factor (C1)
CI: Reasoning, C2, C3
C2: Speed, Quantitative, Knowledge, Closure
C3: Associative Memory, Short-Term
Memory
Hierarchical with linear age-higher order
relations, two 2nd-order factors (C2, C3)
plus 3rd-order factor (C1)
CI: Reasoning, C2, C3
C2: Knowledge, Quantitative, Short-Term
Memory
C3: Speed, Closure, Associative Memory
Hierarchical with linear age-higher order
relations, two 2nd-order factors (C2, C3)
plus 3rd-order factor (C1)
CI: Reasoning, C2, C3
C2: Knowledge, Quantitative
C3: Associative Memory, Short-Term
Memory
Hierarchical with linear age-higher order
relations, one 2nd-order factor (C2) and
3rd-order factor (C1)
CI: Reasoning, Speed, Associative Memory,
Short-Term Memory, C2
C2: Knowledge, Quantitative
Hierarchical with linear and nonlinear age
relations to higher order factors, no
residual age relations
Hierarchical with linear and nonlinear age
relations to higher order factors, residual
linear age relations to lst-order factors
Hierarchical with linear and nonlinear age
relations to higher order factors, two 2ridorder factors (C2, C3) plus 3rd-order
factor (C1)
CI: Reasoning, C2, C3
C2: Speed, Quantitative, Knowledge, Closure
C3: Associative Memory, Short-Term
Memory
Hierarchical with linear and nonlinear age
relations to higher order factors, two 2ndorder factors (C2, C3) plus 3rd-order
factor (C1)
C 1: Reasoning, C2, C3
C2: Knowledge, Quantitative, Short-Term
Memory
C3: Speed, Closure, Associative Memory
859
INDEPENDENCE OF AGE-RELATED EFFECTS
Table 5 (continued)
Model
5D
5E
df
Description
X2
CFI
NNFI
SRMR
4,211.24
.94
.93
.05
4,423.44
.94
.92
.05
120
119
16,539.08
4,680.04
.25
.79
.16
.76
.36
.07
124
3,692.12
.84
.82
.09
152
4,797.78
.79
.77
.07
159
3,811.52
.84
.82
. .08
113
112
7,351.59
2,029.33
.67
.91
.60
.89
.33
.06
106
1,323.80
.95
.93
.04
109
1,216.75
.95
.94
.06
145
2,148.87
.91
.89
.06
139
1,445.73
.94
.93
.04
142
1,338.20
.95
.94
.05
Children (continued)
Hierarchical with linear and nonlinear age
142
relations to higher order factors, two 2ndorder factors (C2, C3) plus 3rd-order
factor (C1)
CI: Reasoning, Speed, Closure, C2, C3
C2: Knowledge, Quantitative
C3: Associative Memory, Short-Term
Memory
Hierarchical with linear and nonlinear age
144
relations to higher order factors, one 2ndorder factor (C2) and one 3rd-order factor
(C1)
CI: Reasoning, Speed, Associative Memory,
Short-Term Memory, C2
C2: Knowledge, Quantitative
Adults
0
1
IA
2
2A
4A
4B
5A
5B
Only direct linear age-variable relations
Single common factor with linear age-common
no residual age relations
Single common factor with linear age-common,
fix parameters from Model 1, estimate
residual linear age relations to variables
Single common factor with linear and nonlinear
age-common, no residual age relations
Single common factor with linear and nonlinear
age-common, fix parameters from Model
2, estimate residual linear age relations to
variables
Only direct linear age-ability factor relations
Hierarchical with linear age-higher order
relations, no residual age relations
Hierarchical with linear age-higher order
relations, residual linear age relations to
lst-order factors
Hierarchical with linear age-higher order
relations, two 2nd-order factors (C2, C3)
plus 3rd-order factor (C1)
CI: Reasoning, C2, C3
C2: Knowledge, Quantitative, Short-Term
Memory
C3: Speed, Closure, Associative Memory
Hierarchical with linear and nonlinear age
relations to higher order factors, no
residual age relations
Hierarchical with linear and nonlinear age
relations to higher order factors, residual
linear age relations to I st-order factors
Hierarchical with linear and nonlinear age
relations to higher order factors, two 2ndorder factors (C2, C3) plus 3rd-order
factor (C1)
C 1: Reasoning, C2, C3
C2: Speed, Quantitative, Short-Term
Memory
C3: Speed, Closure, Associative Memory
Note. CFI = comparative fit index; NNFI = Bentler-Bonett non-normed fit index; SRMR = standardized
root mean residual.
860
SALTHOUSE
.86
AGE
-.o6
-.07
.o6
COMMON
.66
.63
-.06
.86
Concept Formation
~
.85
Calculetlon
~
.90
Applied Problems
~
.95
Science
~
.94
Social Studies
~
.94
Humanities
~
.93
Incomplete Words
~
.72
Visual Closure
~
.75
Sound Blending
~
.77
Memory for Names
~
.64
.77
.82
-.o5
~
.88
.82
-.o3
Analysis-Synthesis
,74
.54
completely independent age-related influences on first-order
cognitive abilities.
The next model (Model 4) was hierarchical, with the seven
ability factors at the first order, a single second-order common
factor ( C 1 ) , and linear age relations only to the second-order
common factor. In both the children and the adult data, this
model provided a much better fit than the model with independent age-ability relations (Model 3). However, the fit was substantially improved by also allowing direct age-ability relations
in addition to the a g e - c o m m o n relation, as was the case in the
next model, Model 4A. Only the Associative Memory Ability
factor did not have an independent age relation in the children
data, and the Reasoning Ability factor was the only one without
an independent age relation in the adult data. The relatively good
fit of Model 4A suggests that there are both shared age-related
influences (through the common factor) and unique age-related
.67
-.o9
-.lO
-.lO
-.o9
-.06
.06
.o5
.55
A4
.53
.58
.51
.85
,83
Visual-Auditory Learning
~
,77
Memory for Sentences
~
.80
-,91----
-.46
.66
.24 ~
Visual Metchlng
~
.86
.12 ~
Cross Out
~
.87
.30 ~
Age Correlation
.16 ~
-.36
-.24
-,35
-.18
",33
-.44
Figure 2. Structural coefficients for the single common factor analysis
of the variables in the children. Numbers above or to the left or right
of the arrows are standardized path coefficients, and the numbers to the
immediate left of the variables are correlation coefficients representing
the total age-related influences on the variable. Fit statistics for this
model are in Table 5 (Model 1A for children).
-.16 ~
-.08 ~
-.08 ~
-.58
-.52
-.49
-.49
with individual differences in the factor representing what the
variables have in common.
Hierarchical Analyses
The next set of analyses examined the effects of imposing
structure in the pattern of relations among the variables before
investigating relations between age and the variables. A summary of the model testing sequence and the associated fit statistics is contained in Table 5.
The initial model (Model 3) was a model in which the only
relations among variables were those used to specify the seven
ability factors, with independent relations of age to each firstorder factor. It is apparent in Table 5 that this model provided
a rather poor fit to both the children and adult data. These results
imply that the data are not consistent with the existence of
~-~
COMMON
-.45
.11 ~
Memory for W o r d s
-.55
AGE
.11 ~
",29
".38
-.11 ~
-,16 ~
-.56
-.63
Analysis-Synthesis
~
.80
Concept Formation
~
.82
Calculation
~
.84
Applied Problems
~
.86
Science
~
.85
Social Studies
~
.86
Humanities
~
.88
Incomplete Words
~
.72
Visual Closure
~
,67
Sound Blending
~
.72
M e m o r yfor N a m e s
~
.68
Visual-Auditory Learning
~
.80
Memory for Sentences
~
.69
Memory for Words
~
.61
Visual Metchlng
~
,75
Cross Out
~
.74
Age Correlation
Figure 3. Structural coefficients for the single common factor analysis
of the variables in the adults. Numbers above or to the left or the right
of the arrows are standardized path coefficients, and the numbers to the
immediate left of the variables are correlation coefficients representing
the total age-related influences on the variable. Fit statistics for this
model are in Table 5 (Model 1A for adults).
INDEPENDENCE OF AGE-RELATED EFFECTS
influences (direct from age) on many of the factors representing
distinct cognitive abilities.
Additional analyses were conducted to examine different possibilities for the level at which the age-related influences were
operating. Somewhat different procedures were followed in
specifying subsequent models for the children and adult data.
For the adults, the next model (4B) consisted of combining the
first-order factors with positive residual age relations into one
second-order factor (C2), and combining the first-order factors
with negative residual age relations into another second-order
factor (C3). Both of these factors were related to age and to
the third-order factor (C 1 ), which was indicated by the Reasoning first-order factor. Examination of the fit statistics in Table 5
reveals that this model resulted in a good fit to the adult data.
The initial second-order model for the children (Model 4B)
grouped the first-order ability factors with the strongest independent age relations into one second-order factor (C2), and the
first-order ability factors with weaker independent age relations
into another second-order factor (C3). These factors were both
related to age and to the third factor (C1), which was scaled
by the Reasoning first-order factor. The fit statistics in Table 5
reveal that this model did not fit the data as well as Model 4A.
Several additional models with higher order factors were also
examined in the data from children because the fit of Model 4B
was poorer than that with the less-differentiated model. For
example, Model 4C involved the same groupings of first-order
ability factors to second-order factors as in the adult data, ignoring the strength of the residual age relations. Model 4D examined second-order factors roughly corresponding to Knowledge
and to Memory, and Model 4E specified only one second-order
factor corresponding to Knowledge and Quantitative abilities.
However none of these models fit the data as well as the model
with a single second-order common factor (i.e., Model 4A).
Models 5 through 5E for the children (and 5 through 5B for
the adults)are identical to Models 4 through 4E (4 through 4B
for the adults) with the exception that quadratic and cubic age
terms as well as the linear age term were allowed to influence
the highest order factor. Inspection of Table 5 reveals that as
was the case with the previous single common factor models,
the addition of the nonlinear age relations did not improve the
overall fit of the models relative to when only linear age relations
were specified. The nonlinear relations were significantly different from zero (i.e., the standardized coefficient for the quadratic
term was -.31 in the children data and - . 2 4 in the adult data,
and the standardized coefficient for the cubic term was .08 in
the children data and .07 in the adult data), but the fits for
the series of models with only linear age relations were nearly
identical to those containing the additional age relations and
had smaller values of chi-square.
It is also apparent in Table 5 that the addition of the nonlinear
age relations did not alter the relative fit of the models. That is,
the model with one second-order factor and direct age-ability
relations (Model 5A) provided the best fit to the children data,
and the model with two second-order factors and a third-order
factor (Model 5B) provided the best fit to the adult data.
The best-fitting model for the children (Model 4A, illustrated
in Figure 4) was a hierarchical model in which there was a single
second-order common factor with residual linear age relations to
all but one of the first-order ability factors. Although other models were examined, there was no evidence of a further grouping
861
of the age relations in the abilities beyond that represented in
the common factor. Four points should be noted about the model
portrayed in Figure 4. First, this model (Model 4A in Table 5)
provided a substantially better fit than models that ignored the
grouping of the variables into abilities (i.e., Models 0 to 2A in
Table 5) and than the model assuming independent relations
between age and each ability (i.e., Model 3). Second, as in the
models based on individual variables, each of the first-order
abilities had moderately high relations from the (second-order)
common factor. Therefore, although distinct cognitive abilities
can be identified, they are not independent of one another but
instead share moderately large proportions of variance and apparently also have common age-related influences. Third, in the
model represented in Figure 4, six of the seven ability variables
also had moderate to large independent age-related influences.
However, the fact that none of the models with more complicated
relations among the ability variables led to improvements in fit
suggests that there are both shared and ability-specific influences
on cognitive development during the period of childhood. The
final point regarding Figure 4 is that the unique age-related
influences are much smaller than the total age-related influences
on the first-order ability factors. To illustrate, the median of the
six significant age-ability coefficients was .30, whereas the
median of the age correlations for those abilities, displayed in
the bottom of Figure 4, was .80.
The best-fitting model for the adults (Model 4B, Figure 5)
involved two second-order factors and a third-order factor. There
was a large negative linear age relation on the third-order factor
(C1), and although both second-order factors (C2 and C3)
were strongly related to C1, they had independent and opposite
relations to age. The direct age relation was positive for C2,
indicating that although there was a decrease with age in the
relevant abilities because of relations through C 1, the magnitude
of this decrease was less for these abilities than for other abilities. The residual age relation was negative for C3, indicating
that the age-related declines in those abilities were larger than
that mediated through the highest order common factor (C1).
The two second-order factors may correspond to crystallized
and fluid abilities, respectively (cf. Horn & Hofer, 1992), but it
is important to emphasize that a large proportion of the age
relations of both second-order factors were explained by individual differences in the third-order factor. Furthermore, rather than
the two sets of abilities balancing one another out with respect
to the overall age trend, there were substantial negative relations
of age to the third-order factor, and the correlations of age to
the abilities were all negative.
Discussion
The results portrayed in Figure 1 and summarized in Table
4 indicate that there were large developmental differences on a
wide variety of cognitive variables across the periods of childhood and adulthood. The age relations on the variables were
not all equivalent in magnitude but varied with respect to both
the strength of the linear age relation and the presence of significant quadratic and cubic age relations.
Despite the differential pattern of age relations, however, the
results from both analytical procedures indicate that the agerelated influences on the variables were not independent of one
another. First, the single common factor analyses revealed that
862
SALTHOUSE
Age
Correlation
.83
.89
.64
.74
.88
.77
.59
Figure 4.
The best-fitting structural model, with standardized coefficients, for the children data. Fit statistics
for this model are in Table 5 (Model 4 A for children). C1 = higher order factor; know = knowledge; quant
= quantitative; STM = short-term memory; reas = reasoning; speed = perceptual speed; clos = closure; assoc
= associative memory.
I Ae I
r"53
~1
Age
Correlation
Figure 5.
-.32
-.36
-.43
-.53
-.25
-.65
-.64
-.58
The best-fitting structural model, with standardized coefficients, for the adult data. Fit statistics for
this model are in Table 5 (Model 4B for adults). C1, C2, and C3 = higher order factors; know = knowledge;
quant = quantitative; STM = short-term memory; reas = reasoning; speed = perceptual speed; clos = closure;
assoc = associative memory.
INDEPENDENCE OF AGE-RELATED EFFECTS
all variables had moderate to large loadings on the common
factor and that the independent age-related effects, after considering the relations of age to what all variables had in common,
were small relative to the total age-related effects. And second,
although the hierarchical models indicated that the variables
could be grouped in terms of distinct first-order abilities, these
first-order abilities shared moderate to large amounts of variance
with each other, and the higher order factors representing these
common portions of variance accounted for substantial proportions of the age-related variance in the first-order abilities. Furthermore, models assuming that the age relations on either the
individual variables (Model 0) or the first-order cognitive ability
factors (Model 3) were completely independent of one another
were found to provide very poor fits to the data in both children
and adults.
Most of the analyses were somewhat abstract, and therefore
it is useful to make the discussion more concrete by referring to
a particular cognitive variable. Consider the measure of visualauditory learning that reflects the individual's success at learning to associate unfamiliar visual symbols with familiar words.
The study of association processes has had a long history in
cognitive psychology, and the formation of associations is often
considered to be an important elementary cognitive operation.
Moderately large developmental differences in this measure of
association efficiency were evident in these samples, as the correlation of the visual-auditory learning variable with age was
.53 in the range from 5 to 17 years and - . 4 9 in the range from
18 to 94 years.
A cognitive researcher interested in analytical interpretations
might therefore attempt to explain the developmental differences
in the visual-auditory learning variable in terms of individual
differences in a specific process, such as elaboration or integration. That is, the increase in the variable across the period of
childhood, and the decrease in the variable across the period of
adulthood, might be attributed to a rise and fall of the effectiveness of one or more task-specific processes.
However, now consider the implications of the analyses reported above for the researcher interested in explaining agerelated differences in the visual-auditory learning variable with
task-specific processes or mechanisms. The results summarized
in Figures 2 and 3 indicate that after taking into account the
relation of age to what the variables have in common, the relation of age to the visual-anditory learning variable is eliminated
in the sample of adults and actually changes direction from an
age-related increase to an age-related decrease in the sample of
children. A very similar pattern is evident in the hierarchical
models in which the visual-auditory learning variable is combined with the memory-for-names variable to form a latent construct representing associative memory. When the relations of
age to this construct were examined in the context of the age
relations to other constructs, there was no independent age relation in either the children or the adult data.
In light of these results, the question can be raised as to what
a researcher should be attempting to explain with task-specific
processes and mechanisms. Although it is true that moderately
large proportions of variance in the visual-auditory learning
variable were associated with age (i.e., 28.3% in children and
24.1% in adults), little or no age-related variance remained after
the age-related variation in other variables was controlled. The
age-related variance in a variable that is "mediated" through
863
the common factor can be assumed to represent influences associated with age that operate at a relatively broad, rather than taskspecific, level. Therefore, only the residual age-related effects
on that variable can be attributed with confidence to direct or
independent age-related influences on task-specific processes.
However, these residual effects were very small, and, in many
cases not significantly different from zero, and thus for many
variables there may not be a distinct phenomenon in need of
explanation by task-specific processes or mechanisms.
An alternative approach to the role of task-specific interpretations of age-related differences might focus on the linkage between the variable and the factor representing what all the variables have in common. That is, instead of attempting to account
for the generally small or nonexistent direct relations from age
to the variable, the emphasis could shift to attempting to account
for the strong relations evident between the common factor and
the variable. In other words, specific mechanisms could be used
to explain how age-related variations in a broad or general factor
become manifested in particular individual variables, such as
visual-auditory learning. Regardless of whether researchers ultimately adopt this analytical strategy, the current perspective
implies that major goals for future research should consist of
determining the reasons for the relations between age and the
common factor and how particular variables are related to, and
distinct from, what is common to other variables.
The analyses that have been reported reflect somewhat different perspectives and assumptions. For example, the hierarchical
approach resembles efforts concerned with specifying the psychometric structure of abilities, and the single common factor
approach considers all variables to be alternative indicators of
a single factor. However, results from both analytical procedures
converge on the conclusion that rather than being independent,
a very large proportion of the age-related differences in each of
the variables is shared with individual differences in the other
variables.
Nevertheless, it should be noted that the discovery that a large
proportion of the age-related influences on different cognitive
variables appears to be shared does not imply that the age relations on those variables are necessarily uniform in magnitude.
Even if there were no independent age-related effects, the age
relations would vary because of variations in the strength of the
relation between the common factor and the variable. In fact, if
there were no independent age-related influences, the magnitude
of the age relation (i.e., age-variable correlation) would be
expected to be highly related to the magnitude of the relation
of the common factor to the variable (i.e., the common variable
coefficient). This expectation was confirmed in the data from
children (cf. Figure 2), as the relevant correlation was .86. The
correspondence between the variable coefficients and the age
relations was much weaker in the adult data. Because stronger
age relations for these variables in the adult years would be
represented by correlations that were more negative, large positive coefficients on the common factor would be expected to be
associated with large negative relations between age and the
variable. However, instead of a large negative correlation, the
correlation between the variable coefficients and the age relations in the adult data (cf. Figure 3) was moderately positive
(i.e., .47). The greater relative magnitudes of the independent
age relations in the sample of adults are probably responsible
for the failure to find the expected correspondence in the adult
864
SALTHOUSE
data because these independent age relations serve to modulate
the total age-related effects on the variables.
The high degree of shared age-related variance observed in
these cross-sectional data sets is consistent with the hypothesis
that age-related influences primarily operate at a higher order
level than that represented by individual variables. That is, a
large portion of the age-related effects on behavior does not
seem to operate at the level of specific tests or primary abilities
but rather at the level of broader or more general clusters of
abilities. However, a number of questions still remain regarding
the estimates of shared age-related variance. For example,
whether and to what extent process-specific age-related effects
may contribute to the covariance among the variables has not
been fully clarified, nor has the relation between age-independent and age-related variance in the computation of shared effects. Moreover, although the analyses described in this article
suggest that many of the age-related influences on different
cognitive variables are shared, the elementary mechanisms or
fundamental processes responsible for the hypothesized common factor are not yet obvious.
Relevant information on this latter issue may be available
from an examination of the pattern of relations between the
variables and the common factor. Because all variables in these
data sets had similar reliabilities and nearly the same number
of variables were available for each ability, the patterns of relations do not merely reflect the amount of systematic variance
in the variable available for association or the dominance of a
particular type of variable in the data set. The variables with
the highest relations with the common factor may therefore
provide a clue as to the nature of that factor.
A similar pattern of variable coefficients was apparent in both
children and adults (cf. Figures 2 and 3), as the correlations
between the coefficients in the two groups was .87. The highest
coefficients in both age groups were with variables representing
knowledge, reasoning, and perceptual speed abilities, and the
lowest coefficients were with variables representing associative
memory, short-term memory, and closure abilities. If the former
variables are really the most central to cognition, then a challenge for future research is to discover why this is the case.
Finally, it is important to mention several qualifications on
the interpretation of the results of these analyses. First, the inclusion of a variable labeled age in the models and figures should
not be construed as representing only endogenous or maturational aspects of development. As noted in the introduction, it
is difficult, if not impossible, to distinguish between endogenous
and exogenous determinants of development with cross-sectional designs. The current results should therefore be assumed
to reflect an unknown mixture of intrinsic and extrinsic influences on development. And second, the discovery that much of
the age-related influences on many different cognitive variables
are shared does not necessarily imply that there is a single
cause of the shared effects. That is, several distinct sets of
developmental mechanisms could be contributing to the agerelated effects on the common factor. The results of these analyses suggest that important developmental influences are operating at a fairly broad or general level, but they should not be
interpreted as implying that only a single developmental mechanism is responsible for the observed effects.
In summary, two different analytical procedures were carried
out on a large data set derived from a nationally representative
sample. The results of both procedures converged on the conclusion that a relatively large proportion of the age-related variance
in a wide range of cognitive variables appears to be shared and
can be predicted by individual differences in higher order factors
of cognitive functioning. Because a very similar pattern was
obtained for the periods of both childhood and adulthood, theories of cognitive development across the life span will need to
consider this lack of independence when formulating explanations of developmental differences in cognitive functioning.
References
Bickley, P. G., Keith T. Z., & Wolfle, L. M. (1995). The three-stratum
theory of cognitive abilities: Test of the structure of intelligence across
the life span. Intelligence, 20, 309-328.
Horn, J. L., & Hofer, S. M. (1992). Major abilities and development in
the adult period. In R. J. Sternberg & C. A. Berg (Eds.), Intellectual
development (pp. 44-99). New York: Cambridge University Press.
Kliegl, R., & Mayr, U. (1992). Commentary. Human Development, 35,
343 -349.
Lindenberger, U., Mayr, U., & Kliegl, R. ( 1993 ). Speed and intelligence
in old age. Psychology and Aging, 8, 207-220.
McArdle, J. J., & Prescott, C. A. (1992). Age-based construct validation
using structural equation modeling. ExperimentalAging Research, 18,
87-115.
McGrew, K. S., Werder, J. K., & Woodcock, R. W. (1991). WoodcockJohnson--Revised technical manual. Allen, TX: DLM.
Salthouse, T. A. (1992). Shifting levels of analysis in the investigation
of cognitive aging. Human Development, 35, 321-342.
Salthouse, T.A. (1994). How many causes are there of age-related
decrements in cognitive functioning?Developmental Review, 14, 413437.
Woodcock, R. W., & Johnson, M. B. (1989, 1990). Woodcock-Johnson
Psycho-Educational Battery--Revised. Allen, TX: DLM.
Received December 19, 1996
Revision received October 20, 1997
Accepted October 20, 1997 •