Global and Domain-Specific Changes in Cognition throughout Adulthood

Abstract

Normative adult age-related decrements are well documented for many diverse forms of effortful cognitive processing. However, it is currently unclear whether each of these decrements reflects a distinct and independent developmental phenomenon, or, in part, a more global phenomenon. A number of studies have recently been published indicating moderate to large magnitudes of positive relations among individual differences in rates of changes in different cognitive variables. This suggests that a small number of common dimensions, or even a single common dimension, may underlie substantial proportions of individual differences in aging-related cognitive declines. This possibility was directly examined using data from 1,281 adults 18-95 years of age who were followed longitudinally over up to 7 years on 12 different measures of effortful processing. Multivariate growth curve models were applied to examine the dimensionality of individual differences in longitudinal changes. Results supported a hierarchical structure of aging-related changes, with an average of 39% of individual differences in change in a given variable attributable to global developmental processes, 33% attributable to domain (abstract reasoning, spatial visualization, episodic memory, and processing speed)-specific developmental processes, and 28% attributable to test-specific developmental processes. Although it is often assumed that systematic and pervasive sources of cognitive decline only emerge in later adulthood, domain-general influences on change were apparent for younger (18-49 years), middle aged (50-69 years), and older (70-95 years) adults.

Average levels of performance on many different forms of effortful cognitive processing decline continuously with adult age. Beginning as early as the third decade of life, average levels of performance on measures of reasoning, spatial visualization, episodic memory, and processing speed begin to decline (Salthouse, 2009). Two major, as-of-yet unanswered, questions within the field of cognitive aging concern the extent to which the mechanisms that underlie these declines occur at global versus specific levels, and the extent to which this pattern differs at different ages. In other words it is currently unclear (1) whether deficits that are observed on specific cognitive tasks each represent an independent developmental phenomenon in need of a new unique mechanistic account, or whether they are all symptomatic of a more general developmental phenomenon, and (2) if general influences on cognitive aging do exist, whether these influences are present in early adulthood, when the deficits first occur, or emerge in later adulthood when the deficits become more severe. These issues were directly addressed for the current project by analyzing the dimensionality of individual differences in aging-related cognitive changes in adults ranging in age from 18 to 95 years of age.

Background

One reason to expect that changes in many different cognitive variables may fall along a small number of dimensions is that parsimonious few-factor representations of the cross-sectional interrelations among cognitive variables are well established (Carroll, 1993; Salthouse, 2004; cf. Tucker-Drob, 2009, Tucker-Drob & Salthouse, 2008). Approximately 40 percent of the between-person variation in performance on diverse batteries of cognitive tests can be accounted for by a single dimension, often termed “g,” along which people can be ordered relative to one another (see, e.g., Deary, 2001, for a general overview). Upwards of an additional 25 percent of this variation can be accounted for by secondary dimensions, sometimes termed broad abilities, cognitive abilities, or cognitive domains. Many different sources of evidence support this balanced domain general and domain specific account. The most basic evidence comes from the general pattern of correlations that has been replicated across many different cognitive test batteries and samples of participants. The pattern is one in which tests hypothesized to rely on the same cognitive domain are highly related, and tests hypothesized to measure different cognitive domains are more moderately related (see, e.g., Deary, 2001, for a general overview). A related line of evidence is that, using a factor analytic model, the tests' relations with one another can be very closely approximated by way of their mutual relations to a combination of domains specific factors and a domain general factor (Carroll, 1993). Evidence for the discriminant validity of the cognitive domains is further derived from their relations to exogenous variables. For example, measures associated with different domains exhibit different lifespan age gradients (Li et al, 2004; McArdle, Ferrer-Caja, Hamagami, & Woodcock, 2002; Salthouse, 2004), exhibit different patterns of relations to demographic variables such as education (Salthouse, 2004), gender (Salthouse & Ferrer-Caja, 2003), and job performance (Gottfredson, 2003), are associated with independent genetic influences (Petrill, 1997), and are associated with different neuroanatomical substrates (Colom et al., 2009).

Past Cross-Sectional and Longitudinal Approaches

Age-heterogeneous cross-sectional data have often been examined with the hope of gaining insight into the dimensionality underlying aging-related deficits. Using multivariate cross-sectional data, Salthouse and colleagues (Salthouse, 2004; Salthouse, 2009; Salthouse & Ferrer-Caja, 2003) have demonstrated that aging-related influences on many different cognitive variables can be well accounted for by way of aging-related influences on a small number of dimensions: typically a high in magnitude negative influence of age on the general factor, and moderate in magnitude influences of age on an episodic memory dimension and a processing speed dimension.

Cross-sectional examinations of individual and age-related differences, however, provide only indirect evidence for the factor structure of individual difference in longitudinal cognitive changes. For example, it is possible that common age-related influences on multiple variables are produced by similar age-related differences in mean performance even when variables do not change in unison for specific individuals (Hofer & Sliwinski, 2001). In fact, that multivariate longitudinal data are needed in order to draw conclusions about the dimensionality of individual differences in changes is nearly a truism. Multivariate longitudinal cognitive test data, along with improved analytical (Bryk & Raudenbush, 1987; McArdle & Epstein, 1987) and computational methods for analyzing them, are becoming increasingly available. A number of recent studies (Anstey et al., 2003; Ferrer et al., 2005; Lemke & Zimprich, 2005; Reynolds et al., 2002; Sliwinski & Buschke, 2004; Hall, 2003; Tucker-Drob et al., 2009; Zelinski & Stewart, 1998; Zimprich & Martin, 2002) have reported correlations among longitudinal changes in multiple cognitive variables. Consistent with hypotheses that common sources of aging-related cognitive changes operate across multiple domains of functioning, the majority of these studies have found the correlations to be positive, medium to large in magnitude, and significantly different from zero. Plainly put, a person who declines quickly in one cognitive domain relative to his or her peers is also likely to be declining quickly relative to his or her peers in another cognitive domain.

Four studies (Hertzog, Dixon, Hultsch, & MacDonald, 2003; Lindenberger & Ghisletta, 2009; Reynolds, Gatz, & Pederson, 2002; Wilson et al., 2002) have in fact reported that a single common fact accounts for large proportions (i.e. between approximately 30% and 60%) of individual differences in age related changes in cognitive abilities. However each of these studies has either only included one or two measures reflective of the same cognitive domain, or the changes being correlated reflect changes in composite scores or latent constructs instead of individual variables. This level of analysis reduces the ability to make inferences about whether a more complex factor structure of changes might hold – in other words, whether domain-specific dimensions of change exist in addition to a domain-general dimension. By investigating the organizational structure of changes at the level of multiple individual tests, the current project was able to evaluate this possibility.

Different Patterns at Different Stages of Adulthood?

A second major issue concerns whether the covariational structure of cognitive changes differs at different ages. Early-adulthood declines are often largely dismissed as resulting from diverse sorts of random and haphazard causes (see Salthouse, 2009, for a review and rebuttal). It is perhaps because of this perspective that the majority of cognitive aging researchers focus their attention and resources on middle and late adulthood, when general and systematic sources of decline are presumed to arise (de Frias, Lövdén, & Lindenberger, 2007). The implication of contentions that general and systematic declines only emerge in middle and late adulthood is that in young adulthood changes across multiple cognitive domains should be uncorrelated or modestly correlated, whereas in middle and later adulthood, correlated changes in different cognitive domains should emerge and strengthen.

Objectives

The current project addresses two main questions. First, to what extent do aging-related cognitive declines represent a single global phenomenon, a few domain-specific phenomena, or many variable-specific phenomena? Second, if global patterns of aging-related cognitive declines exist, do they only emerge in later adulthood? The first question is addressed by examining the factor structure of individual differences in aging-related changes in performance on 12 cognitive variables representative of 4 domains of effortful cognitive processing. If any of the causal mechanisms of adult cognitive declines operate across multiple domains (i.e. if cognitive aging is, in part, a global phenomenon), at least one common factor should account for changes in multiple cognitive variables. Here, a number of alternative factor models of changes are considered, including a single common factor model, a spatial/figural and verbal/numeric two factor model, a hierarchical four factor model, and a model derived from exploratory analyses. The second question is addressed by estimating factor structures of cognitive changes for younger, middle-aged, and older adult age groups. For this project, the younger group is composed of adults 49 years of age and younger, an age range much younger than is typically examined in longitudinal studies of cognitive aging. If general sources of aging-related deficits only emerge in middle or late adulthood, as is implied by a number of the perspectives reviewed above, a common change factor should only be supported in these latter two age groups (50 to 69 and 70 to 97, respectively).

This project is innovative in two major respects. First, this project is innovative in comprehensively examining the number of dimensions underlying individual differences cognitive changes in adulthood. While there is some previous research to suggest that changes in different cognitive variables are indeed positively interrelated, no researcher has yet to have conducted a systematic examination of alternative dimensional representations of such patterns. Second, this project is innovative in examining whether global sources of individual differences in cognitive changes occur before middle adulthood. Most previous investigations have only included middle-aged and older adults, and have therefore been limited in their capabilities to examine age differences in patterns of change interrelations.

Method

Participants

The data analyzed here were collected as part of the Virginia Cognitive Aging Project (VCAP), which is an ongoing longitudinal study being conducted at the Cognitive Aging Lab at the University of Virginia. Collection of baseline data as part of independent cross-sectional studies began in 2001, and is ongoing. Participants are recruited from the Charlottesville, Virginia community with newspaper advertisements, flyers, and referrals from other participants. In order to be eligible for participation, individuals must speak English and have completed at least a high school education. Ages span continuously from 18 to 95 years of age. Beginning in 2004, participants returned to the Cognitive Aging Lab for a second round of testing on many of the same cognitive tests that they were originally administered. In order to create variability in the longitudinal retest intervals across persons, only a subset of participants were invited to return for retesting during a given year. This variability in retest intervals helps to attenuate the confounding (in traditional longitudinal studies, complete confounding) between the amount of time that participants have matured, and the amount of previous experience that participants have had with being tested. The growth curve models employed, which are described later, capitalize on this feature to separate total change into components associated with developmental change and components associated with retest-related learning.

A total of 2,853 participants were initially tested between 2001 and 2006, and therefore eligible for retesting. Of the 2,853 participants eligible for retesting, 559 had moved, 970 could not be contacted, 80 were not interested in participating again, 4 had developed dementia and were living in assisted care facilities, and 9 had died. The remaining 1,227 participants (94% of those who could be contacted and had not moved, died, or developed dementia) originally tested between 2001 and 2006 returned for retesting. Attrition/retention information is not available for the 444 participants tested in 2007 because only a fraction of them were contacted for retesting in 2008. Of those participants initially tested in 2007 who were contacted, 54 returned in 2008, resulting in total longitudinal sample of 1,281. The distributions of participants by age group and longitudinal interval are reported in Table 1. It can be seen that the majority of longitudinal participants were tested 2 or 3 years apart, with some participants tested as close as a year apart, and small proportions tested as much as 6 and 7 years apart.

Table 1.

Cross-Sectional and Longitudinal Sample Sizes by Age Group and Time Lag.

Age Range at Baseline	Mean Age at Baseline (SD)	Longitudinal Interval
		1 Year N	2 Year N	3 Year N	4 Year N	5 Year N	6 Year N	7 Year N	All Time Lags N
18-49	35.42 (9.90)	67	190	114	57	19	6	2	455
50-69	58.55 (6.01)	96	231	146	58	22	9	0	562
70-95	77.30 (5.06)	44	123	70	13	11	2	1	264
Total Sample	54.20 (17.30)	207 (16.2%)	544 (42.5%)	330 (25.8%)	128 (10.0%)	52 (4.1%)	17 (1.3%)	3 (0.2%)	1,281

Measures

Participants were administered a battery of up to 12 cognitive tests (3 for each cognitive domain) selected to measure abstract reasoning (Gf), spatial visualization (Gv), episodic memory (Gm), and processing speed (Gs).

Abstract reasoning (Gf), refers to the ability to reason in novel ways, make use of unfamiliar information, identify relations, draw inferences, and form concepts. It was measured using the Matrix Reasoning test (Raven, 1962), the Shipley Abstraction test (Zachary, 1986), and the Letter Sets test (Ekstrom et al., 1976).

Spatial visualization (Gv) refers to the ability to mentally rotate, manipulate, and reason with two and three dimensional patterns. It was measured using the Spatial Relations test (Bennett et al., 1976), the Paper Folding test (Ekstrom et al., 1976), and the Form Boards test (Ekstrom et al., 1976).

Episodic memory (Gm) refers to the ability to retrieve and explicitly state previously encoded information. It was measured using the Logical Memory test (Weschler, 1997b), the Free Recall test (Wechsler, 1997b), and the Paired Associates test (Salthouse et al., 1996).

Processing speed (Gs) refers to the ability to quickly and efficiently carry out mental operations. It was measured using the Digist Symbol Substitution test (Wechsler, 1997), the Letter Comparison test (Salthouse & Babcock, 1991), and the Pattern Comparison test (Salthouse & Babcock, 1991).

The paired associates test and all tests of abstract reasoning (Gf) and spatial visualization (Gv) were scored using a 2 parameter logistic Item Response Theory (IRT). The recall test, logical memory test, and all three tests of processing speed (Gs) could not be scored with IRT because the recall and logical memory tests required sequential responses that are not independent of one another (e.g. multiple trials of recalling the same list of words, or recalling multiple idea units from each story), and the processing speed tests did not contain distinct categorical items. For these tests, scores were therefore standardized to the z metric, based on the test means and standard deviations of all available data from VCAP. Because the distributions were approximately normal for all scores, no other transformations were performed. Means, and standard deviations of baseline performance on the 12 cognitive tests are presented in Table 2. A comparison of returning and non-returning participants is provided in a later section.

Table 2.

Descriptive Statistics by Age Group (Baseline Assessment).

Variable	Age Groups			Full Longitudinal Sample	Age r	rOE
	18-49	50-69	70-95
	M (SD)	M (SD)	M (SD)	M (SD)
N	455	562	264	3,560
Age	35.42 (9.90)	58.55 (6.01)	77.30 (5.06)	54.20 (17.30)
Digit Symbol Scaled Score	11.09 (2.90)	11.71 (2.73)	11.97 (2.71)	11.54 (2.81)	.13
Logical Memory Scaled Score	11.40 (2.76)	12.40 (2.77)	12.61 (2.80)	12.09 (2.82)	.18
Recall Scaled Score	11.95 (3.35)	13.23 (3.06)	12.29 (3.01)	12.58 (3.27)	.08
Education	14.98 (2.35)	16.23 (2.55)	16.0 (3.04)	15.74 (2.65)	.21
Male (0) vs. Female (1)	.68	.67	.58	.65	-.04
MMSE	28.62 (1.70)	28.83 (1.50)	28.09 (1.99)	28.61 (1.71)	-.11
Abstract Reasoning (Gf) Measures
Matrix Reasoning (θ)	.32 (.88)	-.04 (.74)	-.70 (.70)	-.05 (.87)	-.48	.81
Shipley Abstraction (θ)	.26 (.92)	-.01 (.79)	-.55 (.88)	-.02 (.91)	-.34	.87
Letter Sets (θ)	.13 (.83)	.06 (.78)	-.49 (.80)	-.03 (.84)	-.25	.79
Spatial Visualization (Gv) Measures
Spatial Relations (θ)	.17 (1.01)	.02 (.85)	-.50 (.67)	-.03 (.91)	-.29	.89
Paper Folding (θ)	.24 (.87)	.03 (.78)	-.47 (.70)	-.00 (.84)	-.33	.75
Form Boards (θ)	.22 (.92)	-.11 (.80)	-.58 (.72)	-.10 (.88)	-.39	.88
Episodic Memory (Gm) Measures
Recall (z)	.34 (.84)	.17 (.81)	-.64 (.92)	.07 (.92)	-.38	.92
Paired Associates (θ)	.28 (.88)	.08 (.87)	-.48 (.73)	.04 (.89)	-.32	.85
Logical Memory (z)	.15 (.99)	.10 (.88)	-.33 (.99)	.03 (.96)	-.17	.86
Processing Speed (Gs) Measures
Digit Symbol (z)	.47 (.84)	-.02 (.76)	-.87 (.76)	-.02 (.93)	-.54
Pattern Comparison (z)	.50 (.93)	.01 (.81)	-.75 (.77)	.03 (.96)	-.51	.87
Letter Comparison (z)	.46 (.88)	-.01 (.86)	-.71 (.84)	.01 (.96)	-.45	.82

Note: M = mean. SD = Standard Deviation. r = correlation. r_OE = odd-even split half reliability estimate corrected with the Spearman-Brown prophecy formula. (θ) denotes that scores were produced from a 2-parameter logistic item response theory model. (z) denotes that scores were computed by subtracting the mean and dividing by the standard deviation of all available data from VCAP. Reliabilities for the Digit Symbol test could not be computed because it does not contain distinct items.

Descriptive Analyses and Results

Basic characteristics of the participants are presented in Table 2. One way of evaluating the selectivity of a sample involves comparing scores on a number of standardized measures to the scores for the normative sample of the WAIS III (Wechsler, 1997a) and WMS-III (Wechsler, 1997b), which was matched to the US population on a number of demographic variables including gender, ethnicity, years of education, and region of residence in the country. Age-adjusted scaled scores have means of 10 and standard deviations of 3 in the normative sample, but the scaled score means in the current sample were all above 11 (with standard deviations very close to 3). Although this indicates that the individuals in this sample were functioning above the average of the normative sample, this was true to nearly the same extent at all ages, as the correlations between age and the scaled scores were very low. Results from this dataset may therefore be most applicable to people with higher-than-average levels of functioning, but the age comparisons should be meaningful because there is little evidence that participants of different ages were differentially representative of their age groups, and because there were similar amounts of variability as is observed in the normative sample.

Longitudinal Participants, compared to those who did not return, were very similar in proportion female (66.0% for returners compared to 65.9% for nonreturners), self-rated health (mean rating for returners = 2.20 out of 5, 1 being “excellent”, 5 being “very poor”, compared to 2.18 out of 5 for nonreturners), years of education (mean years completed for returners = 15.7 compared to 15.6 for nonreturners), and scaled scores on the WAIS Digit Symbol test (11.5 for returners compared to 11.4 for nonreturners), the WMS Logical Memory test (12.1 for returners, compared to 11.8 for nonreturners), and the WMS recall test (12.6 for returners compared to 12.3 for nonreturners). Returning participants were approximately 6 years older on average than nonreturning participants (mean age for returners = 54.2 compared to 47.3 for nonreturners), which is largely attributable to the fact that a number of younger participants were university students who were very likely to move away after graduating.

Analyses & Results¹

Univariate Growth Curve Models

The analyses for the current project made use of a growth curve modeling approach with provisions for retest effects (McArdle & Woodcock, 1997). This model specifies performance at a given measurement occasion to be determined by three factors: 1) an initial level factor, which represents performance at baseline, 2) a developmental change factor, or growth curve slope, which represents yearly change in performance over the longitudinal study period, and 3) a retest effect factor, which represents the benefits from having been previously tested. Equations formally representing the growth models implemented are provided in Appendix A. Growth curve models were estimated with Full Information Maximum Likelihood (FIML) estimation in Mplus (Muthén, & Muthén, 1998-2010).

In initial growth models, each variable's retest effect was initially allowed to have a mean and a variance, however the retest variance estimates were frequently very close to zero, or even negative. Removing this random effect on the retest component allowed for modeling of the interactions between age and retest, and baseline performance and retest. Such interactions would not have been identifiable simultaneously with the random retest effect using the 2 occasion data that were available. The selected specification therefore included a random effect on baseline performance, a random effect on developmental change, an age by baseline performance interaction, an age by developmental change interaction, a baseline performance-developmental change covariance, a constant retest component, an age by retest interaction, and a baseline performance by retest interaction.

The benefit of previous testing experience differed for the different tests, ranging from approximately 6% to 35% of the magnitude of the level standard deviations, which is similar in magnitude to estimates based on other methods and types of data (e.g. Hausknecht, Halpert, Di Paolo, & Gerrard, 2007; Salthouse & Tucker-Drob, 2008). Retest-corrected estimates of mean yearly development also differed for the different tests, with magnitudes ranging from approximately 2% to 10% the magnitudes of the standard deviations of the levels. The lower estimate suggests that the average performance level is displaced by a full standard deviation after 50 years of aging, whereas the upper estimate suggests that this displacement occurs after only 10 years of aging. The standard deviation of this effect ranged from approximately 6% to 19% of the magnitude of the level standard deviations, which is small relative to standard deviations of the levels, but fairly large compared to the estimated magnitudes of mean yearly longitudinal changes.

Confirmatory Factor Models of Change

The twelve univariate growth curve models, which had previously been specified individually, were combined into all-encompassing multivariate growth curve models, with separate factor models superimposed on the levels and the changes. The factor structure of the levels was prespecified based on a vast literature on the factor structure of cognitive variables in general (Carroll, 1993), and these variables more specifically (e.g. Salthouse, 2004). Standardized parameter estimates for this prespecified factor structure of the levels are presented in Table 5. Note that the standardized loading of abstract reasoning on the general factor is slightly out of bounds (i.e. greater than 1). This is not much of a concern, because the parameter is very close to being in bounds.

Table 5.

Fit Indices for Alternative Multivariate Growth Curve Models.

Model	Log-Likelihood	Free Parameters	RMSEA	CFI	TLI	AIC	BIC
A. Single Common Change Factor	-98513.521	161	.029	.931	.932	197349.043	198179.062
B. Spatial/Visual & Verbal/Numeric Factors	-98478.469	171	.029	.933	.934	197298.938	198180.510
C. Four Correlated Change Factors	-98468.799	172	.028	.934	.935	197281.599	198168.327
D. Four Change Factors with Higher Order Factors	-98483.197	169	.029	.933	.934	197304.393	198175.655
E. EFA-Informed CFA Model	-98456.532	172	.028	.935	.936	197257.063	198143.791
F. Correlated Curves of Four Factors	-99319.930	108	.041	.861	.868	198855.859	199412.642
G. Factors of Curves of Four Factors	-99336.948	105	.041	.860	.868	198883.896	199425.212

Four plausible alternative factor models of the changes (a.k.a. the slopes) were focused on for this project. These were a single common change factor model (Model A), a spatial/figural change and verbal/numeric change two factor model (Model B), and an abstract reasoning change, spatial visualization change, episodic memory change, and processing speed change four factor model both with and without a higher order factor (Models C and D). Standardized parameter estimates for these alternative factor structures of the slopes are presented in Table 4.

Table 4.

Standardized Parameter Estimates for Alternative Factor Structures of Longitudinal Slopes.

Variable	Single Factor (A)	Figural and Verbal/Numeric (B)		Confirmatory Four Factor Solution (C & D)					EFA-Informed CFA of Growth Curve Slopes (E)
	F1 Gs	F1 (Spatial/Figural)	F2 (Verbal/Numeric)	F1 (Gfs)	F2 (Gvs)	F3 (Gms)	F4 (Gss)	Higher Order General Factor (gs)	F1	F2	F3	F4
Matrix Reasoning	.69*	.76*		.77*						.92*
Shipley Abstraction	1.01*		1.03*	.96*					1.01*
Letter Sets	.80*		.79*	.81*					.78*
Spatial Relations	.58*	.56*			.98*					.78*
Paper Folding	.48*	.34			.90*					.64*
Form Boards	.54*	.41*			.49**						.50*
Recall	.99*		.99*			1.16*					1.01*
Paired Associates	.66*		.70*			.80*					.82*
Logical Memory	.76*		.82*			.92*					.88*
Digit Symbol	–a		– a				–a				–a
Pattern Comparison	.40*	.42*					.58*					.38*
Letter Comparison	.67*		.68*				.97*					1.37*
F1		–		–				1.09*	–
F2		.87*	–	.76*	–			.72*	.98*	–
F3				.55*	.41*	–		.54*	.75*	.50*	–
F4				.52*	.24†	.31*	–	.52*	.45*	.26*	.28*	–

Note:

^*p<.01

^**p<.05.

^†p=.05.

^aThe standardized loadings for Digit Symbol could not be computed because, while its unstandardized loading was significantly positive in all models considered, its model-implied slope variance was very close to zero.

The single common change factor model (Model A) provides initial evidence for domain-general sources of variation in adult cognitive changes, as all standardized loadings are positive and statistically significant. While this model is perhaps the simplest representation of change interrelations, multifactor models can potentially provide more nuanced representations of change interrelations.

The two-factor model (Model B) again provides evidence of domain-general sources of variation in cognitive changes, as the loadings are positive and the two factors correlate very highly, at .87. This high factor intercorrelation suggests that a model with spatial/visual and verbal/numeric change factors may not have adequate levels of discriminant validity.

The four factor model (Models C & D) provides clear evidence for both domain general and domain-specific dimensions of individual differences. In other words, the high positive loadings of the changes in the individual variables on the first order factors is strong evidence for the convergent validity of domain-specific changes, and the moderate-sized first order factor interrelations (and, in the hierarchical version of this model, moderately high loadings of the first order factors the higher order general factor) are consistent with a partially global basis of the changes across domains. Interestingly, this solution indicates that change in abstract reasoning loads at unity on global change, which parallels cross-sectional findings that fluid intelligence and general intelligence are statistically isomorphic (Gustafsson, 1988; Tucker-Drob & Salthouse, 2009).

Fit indices for the above-described one, two, and four factor models are presented in top portion of Table 5. It can be seen that the best fitting of the factor models of change was the one containing the four correlated change factors. Even according to the fits statistics that correct for degrees of freedom and penalize for lack of parsimony, the four correlated change factors model fit the data best. The support for this four factor structure suggests that changes may indeed be occurring along the same dimensions as those underlying individual differences in performance on a given occasion. Moreover, that all loadings and correlations are positive in all of the models reported thus far, suggests that changes in performance that occur on many different cognitive tests during adulthood can, in part, be characterized as a global, domain-general, phenomenon.

Exploratory Factor Models of Change

After fitting the above-reported confirmatory models, an exploratory factor analysis was performed. This exploratory analysis was carried out in a multistage process. First a 12 by 12 correlation matrix, corrected for measurement error using split-half reliability estimates, was produced for the simple longitudinal change scores. This correlation matrix, which overwhelmingly consisted of positive values, was then submitted to an exploratory factor analysis with oblique rotation. Based on the Eigen value greater than 1 criterion, four factors were retained, all of which were positively correlated with one another. The exploratory solution approximated simple structure, in that the tendency was for each change score to have a high loading on a single factor and low loadings on the remaining factors. Based on these results, a four factor confirmatory model was then superimposed directly onto the multivariate growth curve models, with each slope only loading on the factor on which the corresponding change score loaded the highest in the exploratory solution. Parameter estimates for this model are presented in the right portion of Table 4, and its fit indices are presented in Table 5. It can be seen that the configural factor structure from this exploratory model was quite similar to that from the purely confirmatory model that had been fashioned based on the well-established cross-sectional structure. While the fit indices indicate that this exploratory model describes the data better than the purely confirmatory model does, the two models are substantively very similar, and both fit quite well in absolute terms. Finally, the factor intercorrelations for both solutions are similar to one another. Because of these similarities, and because it did not capitalize on potentially chance patterns of relations, the four factor confirmatory model was accepted as the optimal representation of the structural pattern of cognitive changes in adulthood.

Moving from Factors of Changes to Changes in Factors

That the factor structure of changes that closely resembles the factor structure of levels fit the data well, suggests that developmental changes might actually occur at the factor level. This hypothesis was explicitly considered by fitting growth models to factors representing abstract reasoning (Gf), spatial visualization (Gv), episodic memory (Gm), and processing speed (Gs), each of which had its own measurement model which was assumed to be measurement invariant over time. Moreover each of the twelve individual tests was specified to include a constant retest component, a baseline factor score by retest interaction, and an age by retest interaction (as in McArdle et al., 2002). After McArdle (1998), this is termed a curves of factors model (see Appendix B for formal specification).

Correlations among the levels and slopes of the resulting curves of factors model are reported in Table 6. In the rightmost columns are the loadings from a model in which the levels and slopes are specified to load on respective common factors. These results are consistent with those from the factors of curves models reported earlier. As in the confirmatory four factor solution presented in Table 4, the correlations among the changes in each domain are moderate to large in magnitude, as are the loadings of these changes on a common factor. Moreover, the higher order factor solutions for levels and slopes are very similar.

Table 6.

Standardized Parameter Estimates for Structural Portion of Curves of Factors Model.

Variable	Standard Deviation of Change	Correlations				Higher-Order Structure
		Abstract Reasoning (Gf0)	Spatial Visualization (Gv0)	Episodic Memory (Gm0)	Processing Speed (Gs0)	General Factor (g0)	Global Change Factor (gs)
Levels
Abstract Reasoning (Gf0)		–				.96*
Spatial Visualization (Gv0)		.72*	–			.76*
Episodic Memory (Gm0)		.56*	.44*	–		.59*
Processing Speed (Gs0)		.45*	.31*	.36*	–	.47*
Slopes		Abstract Reasoning Slope (Gfs)	Spatial Visualization Slope (Gvs)	Episodic Memory Slope (Gms)	Processing Speed Slope (Gss)
Abstract Reasoning Slope (Gfs)	.09*	–					1.00*
Spatial Visualization Slope (Gvs)	.08*	.74*	–				.67*
Episodic Memory Slope (Gms)	.12**	.72*	.58*	–			.70*
Processing Speed Slope (Gss)	.08**	.78*	.39**	.65*	–		.77*

Note:

^*p<.01

^**p<.05.

Each standard deviation of change has been standardized relative to the standard deviation of the respective level (i.e. by taking ratio of the standard deviation of the change to the standard deviation of the level).

The fits of the curves of factors models are reported in the bottom portion of Table 5. The curves of factors and the factors of curves models are not nested within one another, but because they are based on the same data, their absolute fits can be compared. Because fewer change components are estimated by the curves of factors model, it is more parsimonious than factors of curves model, but its fit is poorer as a consequence. Inspection of the AIC and BIC indices suggest that this difference is appreciable. Moreover, while the CFI and TLI statistics are in the acceptable range for the factors of curves model, they are on the low end for the curves of factors model. The RMSEA estimates for all solutions are very good. All in all, the curves of factors model does not fit as well as the factors of curves model, but both models fit the data acceptably, and both produce substantively congruent results in that they both indicate that approximately 50% of the changes occurring in a given cognitive domain are shared across domains. ²

Comparisons of Age Groups

The results to this point have been consistent with the hypothesis that rates of change across different cognitive domains are positively interrelated, and that these positive change interrelations at the first order level can be described by loadings on a common factor at the second order level. The next set of analyses asks whether the positive relations among rates of change in different cognitive domains exist in both early adulthood and late adulthood. Two questions were addressed: 1) can positive change interrelations be detected at all phases of adulthood? If so, 2) is domain-general variation in cognitive changes more pronounced for older adults compared to for younger adults?

Multiple-group models were fit, with group membership assigned according to age at baseline testing occasion. Individuals 18 to 49 years of age were assigned to the youngest age group, individuals 50 to 69 years of age were assigned to the middle age group, and individuals 70 to 95 years of age were assigned to the oldest age group. These groupings were chosen so that the younger group would be composed of an age range younger than is typically examined in longitudinal studies of cognitive aging, and so that the older group would be composed of individuals past the typical age of retirement.³ In order to reduce the complexity associated with fitting multiple-group growth curves to 12 variables simultaneously, multiple-group analyses were based on composite scores representative of abstract reasoning (Gf), spatial visualization (Gv), episodic memory (Gm), and processing speed (Gs). Growth curves were each specified to have a random initial level, a random slope, a level-slope covariance, a constant retest effect, and a level by retest effect interaction.

Parameter estimates from each age group are presented in Table 7. Two features are particularly relevant. First, for all three groups there is evidence for moderate positive intercorrelations among rates of change across domains. This same pattern is demonstrated by the moderately large positive loadings of the slopes on a common factor. Second, there is some indication that there is greater variation in the slopes in the oldest age group. To formally compare age differences in the amount of common variation in changes across the 4 domains, cross-age group equality constraints were imposed on the unstandardized loadings of the slopes on the common change factor. These constraints did not result in a significant reduction in model fit, χ²(8)= 9.50 (p = .31). The hypothesis of higher common variance at older ages therefore cannot be statistically supported by this analysis. These results therefore indicate global sources of aging-related changes of comparable magnitudes at all ages.

Table 7.

Standardized Parameter Estimates from Multiple Group Model of Cognitive Changes in Younger Adults (18-49 years), Middle Aged (50-69), and Older Adults (70-95 years).

	Standard Deviation of Change	Correlations				Standardized Loading
		Abstract Reasoning Slope (Gfs)	Spatial Visualization Slope (Gvs)	Episodic Memory Slope (Gms)	Processing Speed Slope (Gss)	Global Change Factor (gs)
18-49 years
Abstract Reasoning Slope (Gfs)	.08**	-				.72*
Spatial Visualization Slope (Gvs)	.09*	.23	-			.36†
Episodic Memory Slope (Gms)	I I **	.61*	47*	-		.73*
Processing Speed Slope (Gss)	.15*	44**	.10	46**	-	.62*
50-69 years
Abstract Reasoning Slope (Gfs)	.11*	-				.84*
Spatial Visualization Slope (Gvs)	.10*	.69*	-			.78*
Episodic Memory Slope (Gms)	.13*	.53*	.38**	-		.58*
Processing Speed Slope (Gss)	.09	.52**	.58*	.53**	-	.73*
70-95 years
Abstract Reasoning Slope (Gfs)	.11*	-				.85*
Spatial Visualization Slope (Gvs)	.08**	.38	-			.62**
Episodic Memory Slope (Gms)	.27*	40**	.54*	-		.52*
Processing Speed Slope (Gss)	.14**	.83*	.47	32**	-	.86*

Note: Each standard deviation of change has been standardized relative to the standard deviation of the respective level (i.e. by taking ratio of the standard deviation of the change to the standard deviation of the level). In order to keep all groups' standard deviations on comparable metrics, the standard deviation in the denominator is always from the young group.

^*p<.01

^**p<.05.

^†p=.05.

Robustness of Results

While the substantial majority, if not all, of the participants included in the current study were cognitively healthy adults, one may wonder whether failures to exclude “pre-clinical” cases of dementia may have contributed to the positive change interrelations reported here. This does not appear to have been the case, as the same general patterns of statistically significant positive relations among estimated rates of developmental changes persisted across age groups when: 1) participants scoring below 27 on the Mini Mental State Exam (a common dementia screening instrument; Folstein, Folstein, & McHugh, 1975) at any occasion were excluded, 2) participants with age-adjusted scores greater than 2.5 standard deviations from the mean on one or more composite measure of abstract reasoning (Gf), spatial visualization (Gv), episodic memory (Gm), or processing Speed (Gs) at any occasion were excluded, and 3) participants whose change score on any of the four composite measures was more than 2.5 standard deviations from the mean change score for that measure were excluded.

Discussion

Although “shared influence” models of cognitive aging have been popular for some time (Salthouse, 1994, 2004), only recently has it become well-acknowledged that multivariate longitudinal data are needed to begin to rigorously test many of their predictions. Deater-Deckard & Mayr (2005, p.25) recently lamented the dearth of multivariate longitudinal research, and commented that the “ultimate answer to the question of whether cognitive aging is a general factor or a multifaceted phenomenon will come from careful longitudinal data that allow for testing whether changes in one ability explain changes in other abilities.” They further commented that “it will be critical [to uncover] the dimensionality of change across a wide range of cognitive abilities.” The current project took an approach consistent with these recommendations. The major finding is illustrated in Figure 1, which presents the hierarchical factor solution of individual differences in rates of longitudinal changes. Above the solution is a pie diagrams displaying the average proportions of variation associated with global dimensions, the cognitive domains, and the specific cognitive tests. While this solution is clearly supportive of the hypothesis that declines in many different aspects of cognition are highly overlapping, it is also important to observe that an additional third of the variation in both solutions are specific to the cognitive domains. As the title of this paper indicates, these findings suggest that the process of cognitive aging is characterized by both global and domain-specific declines. Theories and accounts of cognitive aging that only focus on global changes, and those that only focus on domain-specific changes, are therefore both likely to be incomplete.

Figure 1.

Graphical representation of the standardized factor solution for longitudinal changes. Gm= Memory; Gv = Spatial Visualization; Gf = Abstract Reasoning; Gs = Processing Speed. The standardized loadings for Digit Symbol Change could not be computed because, while its unstandardized loading was significantly positive in all models considered, its model-implied change variance was very close to zero.

A second major finding reported here is that a common change dimension was apparent in the youngest group of participants (ages 18 to 49). That the magnitude of variation in cognitive changes accounted for by this dimension was not statistically different from those found in the older age groups runs counter to predictions by those such as de Frias et al. (2007; p. 381) who recently predicted that “how individuals change in one cognitive ability is increasingly related to the ways they change in other cognitive abilities with advancing age.” Rather, it appears that the global and pervasive sources of cognitive change that are apparent in later life in fact emerge at similar ages as mean declines emerge, i.e. in early adulthood.

Limitations, Assumptions, and Future Directions

Two Occasion Data

Two occasion data strongly limit the sorts of models that can be fit. Because the retest intervals varied in this project, change was able to be decomposed into development and retest components. However, these complex models stretch the available information to its limit (for discussions, see McArdle & Woodcock, 1997; and McArdle et al., 2002). As the Virginia Cognitive Aging Project continues, added occasions of observation, combined with the variable retest interval design, will provide a great deal of added modeling flexibility. For example, with multiple time points, one can begin to consider models that capture the shapes of individual trajectories in detail, and perhaps even accurately diagnose individual change points.

Limited Time-Lags

A related limitation of the current study was that the longitudinal time lag was limited to a maximum of seven years, and the majority of participants had intervals of less than four years. The most apparent implication of the limited time-lags is reduced power to detect changes that occur very slowly, i.e. over many years. However, formal power analyses (e.g. Hertzog et al., 2006), suggest that the low power of shorter time lags can be compensated for with more reliable measures, more frequent measurements, or larger sample sizes. The brevity of time lags therefore seems to have its most major consequences when researchers are interested in accurately capturing the shape of a slow nonlinear process, tracking event occurrences that are few and far between, diagnosing change points, or comparing different phases of development.

Convergence

The unavailability of long term longitudinal data forces researchers to seek out surrogate sources for developmental information. The most extreme type of surrogate approach is the pure cross-sectional study, in which different people of different ages are compared to make inferences about how individuals change over development. In the current study, longitudinal information was used to make inferences about patterns of change, but age-comparative approaches were still used to make inferences about how these change patterns differ across younger, middle, and older adulthood. The assumption that age-related differences and age-related changes can be combined to examine the same developmental phenomenon has sometimes been termed the convergence assumption (Bell, 1953). To avoid making this assumption, a researcher interested in comparing the patterns of change that occur surrounding 30 years and 80 years of age, for example, would have to obtain at least 50 years of longitudinal data, which is in most cases not feasible.

Causal Inference

This project was concerned with characterizing the behavioral aspects of normative aging. Specifically, estimated changes in performance on multiple cognitive tasks were used to make inferences regarding whether and how cognition changes both qualitatively and quantitatively with adult age. Given that all behaviors must have some neurobiological basis, the current findings are informative about how neurobiological influences associated with aging are manifest. However, on the basis of behavioral data alone, it would be entirely speculative to make inferences about what those neurobiological influences are. A corollary of this rationale is that examining the factor structure of cognitive changes can help us to identify the number of behavioral dimensions (within the set of variables examined) on which the causes of changes operate, but cannot actually tell us about how many distinct causes there are at the biological level. A global dimension of cognitive decline could, for instance, be the outcome of multiple independent biological mechanisms each of which broadly affects cognition.

Dimensionality of Decline or Dimensionality of Maintenance?

It is also likely that individual differences in aging-related behavioral changes reflect both individual differences in the causes of cognitive deficits and individual differences in the resistance to cognitive deficits. The current finding that large proportions of individual differences in cognitive changes operate along a single dimension could suggest that the causes of cognitive decline have global effects on functioning, or more optimistically, that the inhibitors of cognitive decline have globally protective effects. Future research concerned with identification of correlates of cognitive changes would help to enable for separation these two sources.

Why People Differ from One Another in Rates of Change, versus Why People Change?

Finally, it is of note that while these results are quite informative about individual differences in changes, they offer somewhat less new information about mean changes. That is, longitudinal data provide unique and powerful information about the patterns by which some people decline faster than others, but provide very similar information to cross-sectional data about the patterns by which people decline on the whole. While a tenable assumption may be that the reasons that some people decline faster than others, are the same as the reasons that people are declining on average, it is also viable to conceptualize these reasons as independent of one another. An example of one such possibility was offered above– it may be case that the causes of large mean declines are biological, but the causes of individual differences in such rates are protective/lifestyle in nature. Cross-sectional analyses such as those by Salthouse (2004) and Salthouse & Ferrer-Caja (2003) may be best suited for examinations of mean age-related cognitive changes, whereas longitudinal analyses may be best suited for examinations of individual differences in age-related cognitive changes.

Breadth of Outcomes

The current investigation was concerned with characterizing the dimensionality of changes in a selection of cognitive variables that decline continuously with adult age. A diverse battery of tests requiring effortful processing was therefore examined. Tests of previously acquired knowledge were not examined, as performance on such tests tends to increase through most of adulthood, presumably as a result of the accumulation of experience. Also not examined here were measures of health, physiology, or sensation/perception (e.g. vision and hearing). Some researchers (e.g. Baltes & Lindenberger, 1997; Lindenberger & Ghisletta, 2009) have emphasized a perspective that a single dimension of decline underlies knowledge, health, and sensory domains, in addition to multiple cognitive domains, particularly in old age. It will therefore be important for future work to examine how aging-related changes in all of these different domains relate to one another.

Predictors of Change

With the general features of aging-related longitudinal cognitive changes becoming better established, researchers can more systematically examine variables that have been hypothesized to predict such changes, and whether such predictive relations operate at domain-general or domain-specific levels. Variables that are frequently mentioned as being related to late-life cognitive functioning include mental activity, physical exercise, social engagement, and educational attainment (see Hertzog, Kramer, Wilson, & Lindenberger, 2009, for a review). Future research will benefit from systematically examining how measures of these hypothesized protective factors relate to the global and domain-specific facets of aging-related changes.

Conclusion

In summary, multivariate growth curve models were applied to two occasion, 12 variable, data from 1,281 adults ranging in age from 18-95, with up to seven years between assessments. Results were generally supportive of a positive manifold of change interrelations. A series of alternative factor models were fit to these change interrelations. Results were consistent with a hierarchical factor structure very similar to that established for levels of performance. An average of 39% of individual differences in change in a given variable was attributable to global developmental processes, 33% was attributable to domain-specific developmental processes, and 28% was attributable to variable-specific developmental processes. Age comparative analyses produced evidence that a global change factor accounts for comparable magnitudes of change variation in 18-49 year, 50-69 year, and 70 to 95 year age groups. These results together suggest that the process of cognitive aging is in large part a domain-general phenomenon with secondary domain-specific components, and that domain-general sources of change begin early in the aging process. Crucial next steps will be to identify the biological and environmental predictors and correlates of cognitive changes, and determine where on this hierarchical structure their influences operate.

Table 3.

Standardized Parameter Estimates for Factor Structure of Initial Levels of Cognitive Performance.

Variable	Level Structure
	Abstract Reasoning (Gf0)	Spatial Visualization (Gv0)	Episodic Memory (Gm0)	Processing Speed (Gs0)	General Factor (g0)
Matrix Reasoning	.78
Shipley Abstraction	.82
Letter Sets	.85
Spatial Relations		.89
Paper Folding		.88
Form Boards		.70
Recall			.78
Paired Associates			.77
Logical Memory			.82
Digit Symbol				.69
Pattern Comparison				.64
Letter Comparison				.70
Abstract Reasoning (Gf0)	-				1.06
Spatial Visualization (Gv0)	.87	-			.83
Episodic Memory (Gm0)	.67	.53	-		.65
Processing Speed (Gs0)	.61	.43	.48	-	.58

Note: All parameters are significant at p<.01.

Appendix A: Formula for the Factors of Curves Model

The factors of curves model combines lower order growth curve models with higher order factor models. The growth curves are written as

$$\mathrm{Y}{[t]}_{w,x,z,n}={\mathrm{y}}_{\mathit{0},w,x,n}+\mathrm{A}{[t]}_{w,z}\cdot {\mathrm{y}}_{s,w,z,n}+\mathrm{B}{[t]}_w\cdot {\mathrm{y}}_{r,w,n}+e{[t]}_{w,n},$$ (Eq. A1)

where Y[t]_n is score of person n on variable Y at time t, y_0,n is the unobserved baseline performance score (initial level) for person n, y_s,n is the unobserved change score (slope) of person n, y_r,n is a second unobserved change score for person n, and e[t]_n is a unique factor score (disturbance) of person n at time t. By setting A[t] to be a function of time since baseline, y_s,n is interpreted as person-specific developmental change. Similarly, by setting the coefficient B[t] to be equal to the number of prior assessments, y_r,n can is interpreted as the person-specific retest effect. The subscript w denotes the cognitive test, the subscript x denotes the factor (G_0,x) on which the level (y₀) loads, and the subscript z denotes the factor (G_s,z) on which the slope (y_s) loads. These factor models are written as

$$y_{\mathit{0},w,x,n}={\upsilon }_{\mathit{0},w,x}+{\lambda }_{\mathit{0},w,x}\cdot {\mathrm{G}}_{\mathit{0},x,n}+{\mathrm{u}}_{\mathit{0},w,n},$$ (Eq. A2)

$${\mathrm{y}}_{s,w,z,n}={\upsilon }_{s,w,z}+{\lambda }_{s,w,z}\cdot {\mathrm{G}}_{s,z,n}+{\mathrm{u}}_{s,w,n},$$ (Eq. A3)

where the υ's represent regression intercepts, the λ's represent factor loadings, and the u's represent residuals.

Appendix B: Formula for the Curves of Factors Model

The curves of factors model combines lower order factor models with higher order growth curve models. The lower order factor models are written as

$$\mathrm{Y}{[t]}_{w,x,n}={\upsilon }_{w,x}+{\lambda }_{w,x}\cdot \mathrm{G}{[t]}_{x,n}+\mathrm{B}{[t]}_{w,n}\cdot {\mathrm{y}}_{r,w,n}+\mathrm{e}{[t]}_{w,x,n},$$ (Eq. B1)

where Y[t]_n is score of person n on variable Y at time t, υ is a regression intercept, λ is a factor loading, G[t]_x,n is the score of person n on factor x at time t, and y_r is a variable-specific retest effect, and e is a variable-specific unique factor score. The growth curve portions of the models are written as

$$\mathrm{G}{[t]}_{x,n}={\mathrm{y}}_{\mathit{0},x,n}+\mathrm{A}{[t]}_{x,n}\cdot {\mathrm{y}}_{s,x,n}+\mathrm{u}{[t]}_{x,n},$$ (Eq. B2)

where y_0,n is the unobserved baseline performance score (initial level) for person n, and y_s,n is the unobserved change score (slope) of person n.