Multivariate genetic analysis of specific cognitive abilities in the Colorado adoption project at age 7

INTELLIGENCE 16, 383-400 (1992)

Multivariate Genetic Analysis of Specific Cognitive Abilities in the Colorado Adoption Project at Age 7 LON R. CARDON DAVID W . FULKER

J.C. DEFRIES University of Colorado, Boulder ROBERT PLOMIN

The Pennsylvania State University

A multivariate hierarchical model of specific cognitive abilities was fitted to data from 7year-old adopted and nonadopted sibling pairs in the Colorado Adoption Project in order to assess differential genetic influence on specific mental abilities. Model fitting results and Schmid-Leiman (Schmid & Leiman, 1957) transformations reveal significant heritable variation for verbal, spatial, and memory factors independent of general cognitive ability for the eight ability tests examined. In contrast, environmental influences are primarily measure-specific. The results suggest genetic effects in middle childhood that differentially influence mental ability scores.

Previous behavioral genetic studies o f cognitive abilities have tended to focus either on general intelligence or o n specific mental abilities. Spearman (1927) provided the initial impetus for the interest in general cognitive ability, noting that ability tests share a large proportion o f variance and, thus, may measure a single unified ability, which he termed the general intelligence factor, " g . " Thurstone (1938) subsequently argued in favor of multiple cognitive ability groups rather than a single general intelligence factor. Both views are to some extent correct: A hierarchical model with both general and group factors is generally accepted (Vernon, 1979). Genetic influence is well documented, both for general intelligence and for specific cognitive abilities (Bouchard & M c G u e , 1988; DeFries, Vandenberg, & McClearn, 1976; Plomin, 1988). Genetic influWe thank an anonymous reviewer for many helpful comments and criticisms on an earlier version of this article. This research was supported in part by Grants HD-10333, HD-18426, and HD-19802 from the National Institute of Child Health and Development (NICHD), and by Grant RR-07013-25 awarded to the University of Colorado by the Biomedical Research Support Program, Division of Research Resources, National Institute of Health. This article was written while the fu'st author was supported by NICHD training Grant HD-07289. Correspondence and requests for reprints should be sent to Lon R. Cardon, Institute for Behavioral Genetics, Campus Box 447, University of Colorado, Boulder, CO 80309-0447. 383

384

CARl)ON, FULKER,DEFRIES,AND PLOMIN

ence on cognitive abilities could be general, specific, or both. The "general" hypothesis suggests that genetic factors that affect any cognitive test also affect other cognitive tests, thus creating a "genetic g." In the strong version of this hypothesis, genetic influence on specific cognitive abilities is epiphenomenal in the sense that such specific factors or tests merely reflect genetic influence on g. The "specific" hypothesis suggests that different sets of genes affect different cognitive abilities. Genetic influence on g in this view can be seen as a concatenation of differential genetic effects on specific abilities. The third hypothesis, which we favor, is a hierarchical model that posits a general genetic factor in addition to etiologically distinct genetic factors, independent of g, that affect specific cognitive abilities. It should be noted that although both g and specific cognitive abilities show genetic influence, this does not address the extent to which genetic effects are general or specific. That is, the same genes could influence both general and specific cognitive abilities, or different sets of genes could result in similar heritabilities for general and specific abilities. To assess the heritable bases of general and specific cognitive abilities, multivariate behavioral genetic analyses are needed that analyze the covariance among measures rather than the variance of each measure considered separately. Results from several previous genetic analyses of specific abilities have suggested that different abilities are differentially influenced by genetic and environmental factors (DeFries et al., 1976; Plomin, 1988). Moreover, previous parent-offspring analyses in the Colorado Adoption Project suggest that differential genetic effects may begin to emerge in early childhood (Bergeman, Plomin, DeFries, & Fulker, 1988; Plomin & DeFries, 1985b; Rice, Carey, Fulker, & DeFries, 1989). Most previous behavioral genetic analyses have not attempted to assess specific abilities independent of general cognitive ability. Specific cognitive abilities are typically measured by composites of scores from different tests designed to measure similar abilities. Such composites do not permit explicit assessment of group versus general etiological effects because the heritability of the group ability composite is potentially confounded with shared heritable influences on general ability. However, Nichols (1965) examined residuals from the National Merit Scholarship Qualifying Test (NMSQT) subtests after partialling out total score, and one recent twin study has estimated the heritability of specific cognitive abilities after partialling out observed variation in general mental ability (Petrill & Detterman, 1991). The results indicate that genetic influence on specific cognitive abilities remains after g is partialled out. However, Nichols (1965) and Petfill and Detterman (1991) did not assess the genetic covariance between general and specific cognitive abilities. The method in which observed and latent relationships are analyzed is important for investigation of specific and general abilities. Humphreys (1985, 1989) and Humphreys and Davey (1988) noted that conclusive evidence for cognitive influences corresponding to a single general process with independent primary

SPECIFIC COGNITIVE ABILITIES AT AGE 7

385

abilities can be obtained only by a hierarchical transformation such as the Schmid-Leiman (Schmid & Leiman, 1957) procedure, which extracts factors in a hierarchical order: in the present context, extracting a general factor and then extracting uncorrelated specific factors. Although this transformation has not been utilized often in behavior genetics, the resulting factor structures are useful for interpreting genetic and environmental influence on cognition. For example, using the Schmid-Leiman procedure in analysis of IQ subtests provides a means of separating genetic contributions to verbal components of general intelligence from genetic effects on those verbal abilities unrelated to general intelligence. Thus, transformation of ability measures in this manner allows for assessment of the extent to which correlations among the tests arise from genetic and environmental influences shared by all measures, independent of etiological effects that may operate on specific groups of tests. The purpose of this study is to assess the extent to which genetic and environmental factors that influence cognitive ability measurements in childhood involve general and/or specific components. To examine these effects we apply hierarchical models of genetic and environmental determinants of specific cognitive abilities to data obtained from genetically unrelated and natural siblings in the Colorado Adoption Project at age 7. Hierarchical specification allows the component factor structures to be transformed by the Schmid-Leiman (Schmid & Leiman, 1957) procedure, thus facilitating interpretation of the etiological processes that determine variation in mental ability measurements.

METHOD Subjects The Colorado Adoption Project (CAP) is a longitudinal prospective study of genetic and environmental determinants of behavioral development. Measures are administered to adoptive and biological parents of the adopted children and to matched nanadoptive control families. Siblings of adopted probands are either other adopted children or biological offspring of the adoptive paroats. Detailed descriptions of the CAP sample have been published previously in this journal (DeFries, Plomin, Vandenberg, & Kuse, 1981) and elsewhere (Plomin & DeFries, 1985a; Plomin, DeFries, & Fulker, 1988). The present analyses are based upon data collected after first grade (average age 7.4 years) from 196 adopted and 213 nonadopted children, 52 unrelated siblings of the adopted probands and 68 natural siblings of the control children. Measures Children in the CAP are administered a shortened version of the revised Wechsler Intelligence Scale for Children (WISC-R; Wechsler, 1974) and a battery of six tests of specific cognitive abilities constructed by the CAP staff. These measures are described in a previous publication in this journal (Cyphers, Fulker, Plomin,

386

CARDON, FULKER, DEFRIES, AND PLOMIN

& DeFiles, 1989). Scores from all of the tests are age- and sex-corrected by a multiple regression procedure. Cyphers et al. (1989) presented results from exploratory factor analysis of the CAP data identifying four pairs of tests that load highly on the ability domains of Verbal Reasoning, Spatial Visualization, Perceptual Speed, and Visual Memory. For the study here, these tests again were subjected to a principal components analysis, but with oblique rotation to allow for correlated ability factors, rather than the (orthogonal) varimax method used previously. A listing of the eight measures and the corresponding factor patterns is presented in Table 1. The factor patterns indicate that the eight measures adequately characterize the four domains of cognitive abilities. Correlations among the tests for adopted and nonadopted siblings are presented in the Appendix. Rather than creating factor scales from the cognitive measures as often performed in genetic analyses of specific cognitive abilities, we analyze standardized scores on each ability measure. We have chosen not to analyze factor scales because such scales confound measure-specific influences with cognitive domain effects. Because factor scales are designed to reflect groups, or domains, of cognitive abilities, the scales do not allow assessment of the genetic and environmental influences on particular measures of cognition independent of similar influences on primary ability groups. Analysis of the specific cognitive measures thus allows us to examine etiological differences between measure-specific, primary group, and general cognitive abilities.

TABLE 1 Factor Patterns and Correlations for Measures of Specific Cognitive Abilities Measure

Factor Loadlngs WISC-R Vocabulary CAP Verbal Fluency WISC-R Blocks PMA Spatial Relations Colorado Perceptual Speed CAP Identical Pictures CAP Immediate Memory CAP Delayed Memory

Verbal

Spatial

Perceptual Speed

Memory

.85 .79

.14 -. 13

- . 14 .18

.04 -.02

.05

.81 .87

.11 -.04 .81 .86

- .06 .06

.06 -.03

.85 .88

1.00 .17

1.00

-.04

.00 .01 -.03 .04

.06 .01 .03 -.04

1.00 .16 .26 .12

1.00 .32 .24

.01 .03

Factor Correlations

Verbal Spatial Perceptual Speed Memory

Note. Salient loadings are italicized. PMA = Primary Mental Abilities; ETS = Educational Testing Service; WISC-R = Wechsler Intelligence Scale for Children-Revised; CAP = test constructed by Colorado Adoption Project staff.

SPECIFIC COGNITIVE ABILITIES AT AGE 7

387

Analyses For analysis of the sibling measurements in the CAP, a hierarchical path model was applied to the data. The model was formulatod such that the eight mental ability measures define the Verbal, Spatial, Perceptual Speed, and Memory domains, which are related by a second-order general factor• Figure 1 (p. 388) shows a path diagram corresponding to this hierarchical specification, where the factor loadings for the general factor (IQ), primary factors [Verbal (V), Spatial (S), Perceptual Speed (P), and Memory (M)], and specific measurements are represented by c, p, and s, respectively. Residual influences on the primary factors are symbolized by the path coefficients, r. All of the effects in Figure 1 may be encompassed by a single parameter matrix, constructed as the product and sum of three submatrices in the following form: Pl 0 0 0 0 0 0

0 0 0 0 ~ 0 P4 0 0 Ps 0 P(s 0 0 0 0 A(sx4)

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Figure I. Hierarchical model of Verbal (V), Spatial (S), Perceptual Speed (P), and Memory (M) abilities. IQ represents the general intelligencc factor, VR, SR. PR, and MR correspond to residual effects on each of the ability groups, and Rv~, Rv2, Rst, Rs2, Rj, t, Rp2, RMI, and RM2 represent measurement residuals.

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SPECIFIC COGNITIVE ABILITIES AT AGE 7

389

For unique estimation of the parameters, the hierarchical model requires that the variances of the primary factors be scaled a priori. In order to set the variance scales, we fix at 1.0 one of the path coefficients for each primary factor. Paths p ~, P3, Ps, and P7 have been arbitrarily chosen to accomplish this task. Hierarchical matrix specification in this manner easily accommodates the Schmid-Leiman (Schmid & Leiman, 1957) transformation. For this transformation, the factor structures shown in Figure 1 are orthogonalized by producing group factor loadings that are unrelated to those of the general factor. The orthogonal loadings are embedded within the matrix product in Equation 1 and, thus, do not need to be calculated separately. It is important to note that measurespecific Ioadings are unaffected by the Schmid-Leiman procedure. A path diagram of the resulting transformed model is shown in Figure 2 (p. 390). Comparison of adopted and nonadopted sibling pairs provides a means to assess the extent to which genetic and environmental influences on specific ability measures correspond to the general factor or specific ability domains shown in Figures 1 and 2. Variances and covariances among observed (phenotypic) ability measurements may be presented by Cp

, ,t + = AcAc;

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(2)

in which G, C, and E represent the respective contributions of genetic, shared environmental, and unique environmental effects on the eight measures of specific cognitive abilities. Each A* matrix in Equation 2 is constructed as shown in Equation 1. Differences in genetic resemblance between unrelated pairs and natural siblings provide the necessary information to estimate the genetic and environmental components of covariance. Expected covariances between siblings are given by CB

kA*A*' G G +

AcA c ,

(3)

where k is a scalar which takes on values of 0.0 or 0.5 for the correlations among additive genetic values of adopted siblings and nonadopted siblings, respectively. For significance tests of genetic and environmental primary group and general factors, selected parameters in Figure 2 and in Equation 2 may be set to 0.0 and tested against more saturated specifications. Models with c parameters fixed at 0.0 provide tests of the existence of general genetic or environmental factor structures, whereas elimination of the r parameters allows assessment of primary factor significance. Tests of genetic and environmental measure-specific influences may be performed by dropping the s parameters from models.

Pedigree Analysis The hierarchical model of specific cognitive abilities in Figure 1 was applied to observed scores on the eight ability measures from siblings in the CAP. Because

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SPECIFIC COGNITIVE ABILITIES AT AGE 7

391

of substantial variability in patterns of missing and nonmissing data in the ongoing CAP, we have employed a maximum likelihood pedigree technique to analyze observed measurement scores (Lange, Westlake, & Spence, 1976). The pedigree technique presently employed is similar to other methods of covariance component estimation (Fulker, Baker, & Bock, 1983), yet has the advantage of utilizing every available data point. The model was fitted to the data using the optimization subroutine E04JAF from the Numerical Algorithms Group (NAG, 1988). The following log-likelihood function was minimized: L i = -I/2 lnlX~l-

V2 (x i -

~)'Ei -~ (x~- ~)

(4)

where E~ represents the matrix of expected covariances among family scores corresponding to the ith pattern of missing and nonmissing data (pedigree), x is a vector of observed family data, and ~ is a vector of expected means. This function is calculated for each sibling pair and summed over all pedigree types. For model comparison purposes, twice the difference between two log-likelihoods is distributed asymptotically as chi-square with degrees of freedom equal to the difference in the number of free parameters estimated in fitting the two models. The hierarchical model was initially fitted to the observed sibling measurements and then reduced models were explored in order to test the significance of the genetic and environmental factor structures. At the conclusion of our model comparison series on the sibling data, the factor structures were transformed using the Schmid-Leiman (Schmid & Leiman, 1957) procedure to simplify interpretation of the etiological processes determining individual differences in the test battery. RESULTS A model including all genetic, shared environmental, and unique environmental factor structures was fit to the specific ability data from the adopteff and nonadopted siblings. The model yielded a log-likelihood of -1737.58 with 60 estimated parameters. Parameter estimates from fit of the full model are presented in Table 2 (p. 393). These estimates have been standardized using the procedures outlined for similar structural equation models in the LISREL software package (J6reskog & S/Srbom, 1989, pp. 38-39). In Table 2, the "genetic factor" column indicates genetic overlap between g and latent group factors for the top portion of the table; in the bottom portion of the table, this column indicates genetic overlap between latent group factors and observed measures. The "genetic residual" column refers to genetic influence independent of g (in the top portion of the table) or independent of latent group factors (in the bottom portion). The other columns in the table indicate overlapping ('~factor") and independent ("residual") unique environment and shared environment influences.

392

CARDON, FULKER, DEFRIES, AND PLOMIN

The results vary across factors and measures with one exception: The genetic factor column shows moderate to strong Ioadings for all factors and all measures. This finding indicates that genetic influence on all primary latent factors is to some extent shared with genetic influence on g. Similarly, genetic influence on all observed measures overlaps with genetic influence on the pertinent primary latent factor. The factors and measures differ, however, in the extent to which additional genetic influence (the genetic residual column in Table 2) is present that affects the factor independent of g or affects the measure independent of the latent group factor. For example, for the verbal factor, the residual genetic loading is .83, suggesting substantial genetic influence independent of g. In contrast, for perceptual speed, the residual genetic loading is .00, implying that there is no genetic influence independent of g. The relative influence of unique and shared environmental factor and residual Ioadings also vary considerably across the factors and measures. For example, environmental factors unique to individuals are an important source of overlap between the spatial factor and g (unique environmental factor loading = .77). In contrast, for the verbal factor, neither unique nor shared environmental influences contribute to overlap between the factor and g. The last three columns in Table 2 summarize environmental and genetic components of variance for the latent factors and for the measures. They are the sum of the relevant factor loadings squared. For example, the heritability (h 2) of .90 for the verbal factor is the sum of the squared loadings for the genetic factor (.462 = .21) and the genetic residual (.832 = .69). It is important to recognize that the variance components of the primary ability factors shown in Table 2 are not necessarily comparable with those typically reported in previous studies of specific cognitive abilities. In contrast to the observed factor scales usually examined, the factors here are measures of latent ability dimensions; thus, the proportions of variance refer to latent factor variance. Because unreliability contributes only to the variance of individual tests, estimates of heritability for the latent ability factors are larger than those typically reported (e.g., Cyphers et al., 1989). For example, the Verbal ability factor has an estimated heritability (h 2) of .90. However, h 2 estimates for the individual tests of specific cognitive abilities are fully consistent with previous findings (average h 2 estimates of .40). The similarity of the h 2 estimates for the individual tests with those previously reported is unsurprising because individual tests are affected by measurement unreliability, as are the factor scores or scales typically subjected to behavior genetic analyses. The full hierarchical model of specific cognitive abilities served as a null model for a series of comparisons that were employed to test the significance of the general, primary, and measure-specific factor loadings for the genetic and environmental covariance components of the ability measures. Our first series of model comparisons examined the factor structure of indi-

393

SPECIFIC COGNITIVE ABILITIES AT AGE 7 TABLE 2 Phenotypically Standardized Factor Loadlngs and Variance Components for Specific Cognitive Ability Measures Unique Environment Measure

Shared Environment

Genetic

Factor

Residual

Factor

Residual

Factor

Residual

e2

c~

h2

Primary Factors Verbal Spatial Perceptual Speed Memory

.00 .77 .00 .19

.00 .16 .48 .55

.00 .29 .07 .22

.32 .00 .00 .00

.46 .39 .87 .31

.83 .38 .00 .72

.00 .62 .23 .34

.10 .08 .00 .05

.90 .30 .76 .61

Measures Vocabulary Verbal Fluency Block Design Spatial Relations Perceptual Speed Identical Pictures Immediate Memory Delayed Memory

.00 .00 .72 .26 .33 .33 .45 .46

.68 .68 .00 .77 .55 .67 .64 .61

.23 .09 .26 .27 .05 .07 .16 .00

.11 .45 .40 .00 .00 .25 .00 .00

.69 .54 .50 .51 .60 .61 .61 .52

.00 .20 .00 .00 .48 .00 .00 .39

.46 .46 .52 .66 .41 .56 .61 .58

.07 .21 .23 .07 .00 .07 .02 .00

.47 .33 .25 .26 .59 .37 .37 .42

Note. Residual values represent factor residuals in the context of primary factors and measurement residuals in relation to specific measures. Factor loadings refer to loadings of primary factors on the common factor for the top portion of the table and to observed measures on the primary factors in the bottom section of the table. All estimates have been rounded to the second decimal place, and residual Ioadings for the primary factors are estimated with the constraint of positive sign in accordance with the quadratic form of Equation 2.

vidually unique environmental influences on the eight measures of specific cognitive abilities. The results of these tests are presented in Table 3 (p. 394). An omnibus test of the general factor indicated that nonshared environmental effects are significantly correlated for the eight measures: Model 2, X~ = 19.56, p < .001. Specific tests of the Verbal, Spatial, Perceptual Speed, and Memory general factor loadings suggested that Spatial and Memory abilities are ,primarily responsible for the correlations, for only the Spatial and Memory general factor 2 ioadings were significantly different from zero: Model 4, ×l = 7.74, p < .01; Model 6, ×2 = 7.74, p < .01. The Spatial and Memory effects appeared to account for all of the correlations among unique environmental influences on the test battery, as there are no additional significant sources of covariance for unique environmental effects within the primary factors: Model 8, X2 = 2.22, p > .60. We did not test the statistical significance of measure-specific unique environmental effects because these residual effects are expected to contain test measurement error. Thus, the final model of unique environmental influences on the eight measures of specific cognitive abilities included only the Spatial and Memory general factor Ioadings and residual effects for each measure. This model is listed as Model 9 in Table 3.

394

CARDON, FULKER, DEFRIES, AND PLOMIN TABLE 3

Model Comparisons for Unique Environmental Effects on Specific Cognitive Abilities at Age 7 Model Description

Log-likelihood

NPAR a

Full Model No General Factor Loadings No General Verbal Factor Loading No General Spatial Factor Loading No General Perceptual Speed Factor Loading No General Memory Factor Loading No General Verbal and Perceptual Speed Factor Loadings 8. No Primary Factors 9. No General Verbal and Perceptual Speed Factor Loadings and No Primary Factors b

-1737.58 -1747.36 -1737.58 -1741.45 -1737.58 -1741.45 -1737.58

60 56 59 59 59 59 58

-1738.69 -1738.69

56 52

1. 2. 3. 4. 5. 6. 7.

Xz

df

p

19.56 0.00 7.74 0.00 7.74 0.00

4

1 2

<.001 .99 <.01 .99 <.01 .99

2.22 2.22

4 8

.60 .95

vs.

I I

1 1

I

=NPAR = Number of parameters estimated ~This model also requires omission of the first-order measurement loadings on Verbal and Perceptual Speed abilities.

Model comparisons for tests of the significance of environmental effects shared by siblings were performed in a manner similar to the unique environment test series. The results from these comparisons are presented in Table 4. The omnibus general factor test for shared environmental effects suggested that the shared environment factor does not significantly influence the intercorrelations among the measures: Model 2, ×2 = 2.46, p > .60. Furthermore, shared environmental influences do not differentiate into primary abilities independent of 2 the general factor: Model 3, Xn = 1.76, p > .80. There are also no significant measure-specific environmental effects on the measures: Model 4, ×2 = 4.02, p > .80. In fact, the entire set of shared environment parameters could be dropped from the model without significant loss of model fit: Model 5, ×20 = 6.05, p > TABLE 4 Model Comparison for Shared Environmental Effects on Specific Cognitive Abilities at Age 7 Model Description 1. 2. 3. 4. 5.

Model 9, Table 3 No General Factor Loadings No Primary Factors No Residual Factors No Shared Environment Effects

Log-likelihood -

1738.69 1739.92 1739.57 1740.70 1744.74

aNPAR = Number of parameters estimated.

NPAR = 52 48 48 44 32

vs.

X"

df

p

1 I I 1 2 3 4

2.46 1.76 4.02 6.05 9.64 10.34 8.08

4 4 8 20 16 16 12

.60 .80 .80 .99 .80 .80 .70

SPECIFIC COGNITIVE ABILITIES AT AGE 7

395

.99. Therefore, shared environmental influences were omitted from the model for further tests of the hierarchical structure of specific cognitive abilities. The final series of model comparisons, shown in Table 5, examined genetic influences on specific cognitive abilities. At the common factor level, all measures are significantly correlated through the higher-order genetic factor (Models 2-6). Moreover, genetic model comparisons indicated additional sources of covariation attributable to primary abilities (Model 7). Specific model comparisons revealed significant genetic influences on the Verbal, Spatial, and Memory ability groups: Model 8, ×2 = 35.70, p < .001; Model 9, ×2 = 4.22, p < .05; and Model 11, ×l2 = 71.88, p < .001, respectively. Parameter estimates relating to the Perceptual Speed factor and the measure-specific genetic effects did not significantly differ from zero (Models 10 and 12). Our findings of a general genetic factor with additional genetic influences on Verbal, Spatial, and Memory abilities (Model 13) are consistent with a hypothesis of differential genetic effects on specific and general cognitive abilities. Parameter estimates from the final genetic model are presented in Figure 3 (p. 396). These estimates have been transformed using the Schmid-Leiman (Schmid & Leiman, 1957) technique to facilitate interpretation. As seen in the upper portion of Figure 3, genetic influence for all measures is shared in what can be considered a "genetic g." In addition, however, genetic factors independent of genetic g but shared as group factors (Vg, S s, and Ms¢ in the lower portion of Figure 3) can be seen for all but Perceptual Speed. These orthogonal genetic TABLE 5 Model Comparisons for Genetic Effects on Specific Cognitive Abilities at Age 7

Model Description I. 2. 3. 4. 5. 6. 7. 8. 9. 10. I 1. 12. 13.

Log-likelihood

NPAR"

-1744.74 -1797.02 -1764.09 -1773.71 -1788.12

32 28 31 31 31

-1754.86 -1807.21 -1762.59 -1746.85 -1745.40 -1780.68 -1748.75 -1748.75

31 28 31 31 31 31 24 23

Model 5, Table 4 No General Factor Loadings No General Verbal Factor Loading No General Spatial Factor Loading No General Perceptual Speed Factor Loading No General Memory Factor Loading No Primary Factors No Primary Verbal Factor No Primary Spatial Factor No Primary Perceptual Speed Factor No Primary Memory Factor No Residual Factors No Primary Perceptual Speed or Residual Factors

aNPAR = Number of parameters estimated.

×2

df

p

1 1 1 1

104.56 38.70 57.94 86.76

4 I 1 1

<.001 <.001 <.001 <.001

I0 12

20.24 124.94 35.70 4.22 1.32 71.88 8.02 8.02 6.70 0.00

I 4 1 1 I 1 8 9 8 I

<.001 <.001 <.001 <.05 .20 <.001 .40 .50 .50 .99

vs.

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Figure 3. Parameter estimates from final model after Schmid-Leiman transformation. Estimates shown on the top portion refer to genetic: (G) and unique environmental (E) effects; orthogonal genetic influences on the Verbal (Vg), Spatial (S~), and Memory (M~) abilities are presented in the bottom portion. Residual influences on each measure represent unique environment effects.

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SPECIFIC COGNITIVEABILITIESAT AGE 7

397

factors highlight the notion of differential genetic influences on specific cognitive abilities, particularly with respect to Verbal, Spatial, and Memory abilities. Unique environmental influences overlap for spatial and memory tests. The residual effects are relatively large, ranging from .58 to .84, and include both measure-specific environmental effects and measurement error. DISCUSSION Results of this study suggest that the genetic factor structure of cognitive abilities fits a hierarchical model that posits a general genetic factor, group factors, and variance unique to specific tests. That is, a genetic g exists that represents genetic overlap of all tests and factors. Independent of genetic g, genetic group factors are identified that are similar to the phenotypic factors, at least for Verbal, Spatial, and Memory factors. However, the magnitude of the trait-specific and general genetic effects varies for different abilities. Verbal and Memory abilities are influenced primarily by specific genetic factors, with smaller additional effects from the general genetic factor, Spatial abilities are determined by general and specific genetic effects in roughly equal proportions, and Perceptual Speed abilities do not show any genetic influences independent of those relating to general ability. Environmental contributions to individual differences in ability seem largely measure-specific with additional environmental impact on associations between Spatial and Memory abilities. All environmental effects appear within families; shared environmental influences do not appreciably contribute to variation or covariation of ability scores at age 7. These separations of genetic and environmental effects into orthogonal general and specific components were made possible by Schmid-Leiman (Schmid & Leiman, 1957) transformations of hierarchically modelled mental ability scores. Our findings of genetic influences for specific cognitive abilities, independent of g, provide support for Thurstone's (1938) concept of multiple group factors. However, the results also indicate a common genetic source of covariation for all the ability tests examined. These combined results suggest that individual differences in measures of specific cognitive abilities are determined in part by the genetic factors that also determine general cognitive ability scores, and in part by genetic effects relating to specific ability groups. Although genetic influences on the ability measures are substantial, they do not account for all of the true-score variance. The measure-specific, withinfamily environment effects contain test-measurement error in the present model, but the environmental parameter estimates (see Figure 3) are larger than would be expected if these effects reflected only measurement error (DeFries et al., 1979). Thus, these findings reflect some real environmental influences on the ability measures. Also, our results of no significant effects of shared sibling environments on the tests are consistent with previous genetic analyses of parent-offspring data (Cyphers et al., 1989).

398

CARDON, FULKER, DEFRIES, AND PLOMIN

It is possible that the present findings are influenced somewhat by the confounding effects of assortative mating. Assortative mating, or parental selection for similarities in cognitive abilities, induces covariances among genetic factors (Fisher, 1918), thus complicating distinctions of general and group factors. Although such effects are not estimated in the analyses here, preliminary investigations of the CAP parent-offspring data have indicated that the confounding influences are not substantial (Cardon & Fulker, 1990). Further assessments of these effects are presently underway and will form the basis of a later report. It also is possible that the present results are due, in part, to the relatively small size of the CAP sibling sample, to the tests employed to assess specific abilities, and/or to the characteristics of the model used to describe the data. Although the hierarchical genetic model is intuitively appealing given the popular view of specific cognitive abilities, other models may fit the data equally well (see Loehlin, 1987, pp. 214-218, for a discussion of causal model confirmation and/or disconfirmation). Additional empirical work is needed to replicate the findings here using other samples, measures, and models. The most striking finding from these analyses is that of differential genetic effects on ability groups. These effects, coupled with those of an independent general genetic factor, which accounts for a substantial portion of the covariation among cognitive abilities, indicate that the genetic influences on specific abilities operate at least to some extent independently of the genetic factors contributing to general IQ. That these effects are apparent at age 7 suggests that genetic factors may play an important role in the differentiation of specific and general mental abilities in the early school years. The domain-specific nature of some of these genetic effects further highlights the possibility of developmental differences in genetic expression for different abilities. Data from the ongoing, longitudinal CAP should facilitate behavioral genetic analyses of both continuity and change in specific cognitive abilities throughout childhood and adolescence. REFERENCES Bergeman, C.S., Plomin, R., DeFries, J.C., & Fulker, D.W. (1988). Path analysis of general and specific cognitive abilities in the Colorado Adoption Project: Early childhood. Personality and Individual Differences, 9, 391-395. Bouchard, T.J., & McGue, M. (1988). Familial studies of intelligence: A review. Science, 212, 1055-1059. Cardon, L.R., & Fulker, D.W. (1990). Specific cognitive abilities in the Colorado Adoption Project at age 7: A multivariate genetic analysis [Abstract]. Behavior Genetics, 20, 708-709. Cyphers, L., Fulker, D.W., Plomin, R., & DeFries, J.C. (1989). Cognitive abilities in the early school years: No effects of shared environment between parents and offspring. Intelligence, 13, 369-384. DeFiles, J.C., Johnson, R.C., Kuse, A.R., McClearn, G.E., Polovina, J., Vandenberg, S.G., & Wilson, J.R. (1979). Familial resemblance for specific cognitive abilities. Behavior Genetics, 9, 23-43.

SPECIFIC COGNITIVE ABILITIES AT AGE 7

399

DeFiles, J.C., Plomin, R., Vandcnberg, S.G., & Kusc, A.R. (1981). Parent-offspring resemblance for cognitive abilities in the Colorado Adoption Project: Biological, adoptive, and control parents and one-year-old children. Intelligence, 5, 245-277. DeFrics, LC., Vandenberg, S.G., & McClearn, G.E. (1976). Genetics of specific cognitive abilitics. Annual Review of Genetics, I0, 179-207. Fisher, R.A. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Translations of the Royal Society, Edinburgh. 52, 399-433. Fulker, D.W., Baker, L.A., &Bock, R.D. (1983). Estimating components of covariance using LISREL. Data Analyst, 1, 5-8. Humphreys, L.G. (1985). General intelligence: An integration of factor, test, and simplex theory. In B.B. Wolman (Ed.), Handbook of intelligence: Theories, measurement, and applications. New York: Wiley. Humphreys, L.G. (1989). The first factor extracted is an unreliable estimate of g: The case of discrimination reaction time. Intelligence, 13, 183-197. Humphreys, L.G., & Davey, T.C. (1988). Continuity in intellectual growth from 1 to 9 years. Intelligence, 12. 183-197. J6reskog, K.G., & S6rbom, D. (1989). LISREL 7: A guide to the program and applications (2nd ed.). Chicago: SPSS. Lange, K., Westlake, J., 8/. Spence, M.A. (1976). Extensions to pedigree analysis: !11. Variance components by the scoring method. Annals of Human Genetics, 39, 485-491. Loehlin, J.C. (1987). Latent variable models: An introduction to factor, path, and structural analysis. Hillsdale, NJ: Erlbaum. Nichols, R.C. (1965). The National Merit twin study. In S.G. Vandenberg (Ed.), Methods and goals in human behavior genetics. New York: Academic. Numerical Algorithms Group (NAG). (1988). NAG Fortran library manual--Mark 13. Oxford: Author. Petrill, S.A., & Detterman, D.K. (1991). The effect of g upon the pattern of heritabilities among specific cognitive abilities [Abstract]. Behavior Genetics, 21, 587. Plomin, R. (1988). The nature and nurture of cognitive abilities. In R. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 4). Hillsdale, NJ: Erlbaum. Plomin, R., & DeFries, J.C. (1985a). Origins of individual differences in infancy: The Colorado Adoption Project. Orlando, FL: Academic. Plomin, R., & DeFries, J.C. (1985b). A parent-offspring adoption study of cognitive abilities in early childhood. Intelligence, 9, 341-356. Plomin, R., DeFiles, J.C., & Fulker, D.W. (1988). Nature and nurture during infancy and early childhood. New York: Cambridge University Press. Rice, T., Carey, G., Fulker, D.W., & DeFries, J.C. (1989). Multivariate path aaalysis of specific cognitive abilities in the Colorado Adoption Project: Conditional path model of assortative mating. Behavior Genetics, 19, 195-207. Schmid, J., & Leiman, J. (1957). The development of hiera~hical factor solutions. Psychometrika, 22, 53-61. Spearman, C. (1927). The abilities of man. London: Macmillan. Thurstone, L.L. (1938). Primary mental abilities. Chicago: University of Chicago. Vernon, P.E. (1979). Intelligence: Heredity and environment. San Francisco: Freeman. Wechsler, D. (1974). Manual for the Wechsler Intelligence Scale for Children-Revised. New York: Psychological Corporation.

.27 -.06 .10 .05 .19 .03 .11 .03 -.01 .05 -.09 .09 .07 -.01 .19

.14 .11 .14 .06 .14 .18 -.06 .23 .16 .05 .20 .07 .02 .03

.36

Flu

.41 .08 .13 .16 .09 -.13 .10 .28 -.03 .21 .10 .00 -.07

.04 .13

BIk

.24 .36 .14 .06 -.17 .07 -.02 -.02 -.07 -.17 .13 .04

.03 .17 .49

SpR

.51 .10 .10 -.14 .09 -.08 -.19 -.12 .00 -.11 .32

.20 .17 .25 .27

PS

.16 .11 -.08 -.04 .00 -.05 -.02 .09 -.18 .02

.33 .15 .26 .30 .49

IP

.48 .05 .14 -.10 .05 .02 .05 -.07 -.01

.05 .06 .24 .19 .12 .15

IM

-.t2 -.03 -.29 -.24 -.13 -.05 -.28 -.13

.05 .14 .24 .23 .23 .20 .57

DM

.61 .19 .37 .44 .32 .20 .17

.28 .24 .27 .14 .08 .20 .13 .03

Voc

.20 .27 .42 .13 .21 .10

.18 .36 -.17 -.09 .11 .10 .24 .14 .44

l,l u

.42 .34 .31 .36 .18

.07 -.12 .28 .25 -.02 .21 .05 .05 .07 -.07

BIk

.37 .24 .23 .04

-.04 -.05 .24 .22 .09 .08 .20 .28 .23 .09 .61

SpR

.52 .04 -.22

-.03 .01 .14 .14 .20 .18 .19 .09 .04 -.02 .21 .23

PS

Sibling

.24 .03

.19 .08 .02 .12 .02 .20 .16 .08 .25 .19 .03 .11 .28

IP

.60

.13 .18 .11 .15 -.04 .09 .19 .17 .03 -.13 .14 .06 .36 .24

IM

-.10 .04 -.21 .02 .05 -.04 .03 .12 -.17 -.20 .12 .00 .07 -.07 .39

DM

N o t e . V o c = W1SR-R Vocabulary; Flu = CAP Verbal Fluency; BIk = Wisc-R Blocks; SpR = PMA Spatial Relations; PS = Colorado Perceptual Speed; IP = CAP Identical Pictures; IM = CAP Immediate Memory; DM = CAP Delayed Memory. Sample sizes for correlations: adopted proband-proband (194); adopted proband-sibling (52); nonadopted proband-proband (209); nonadopted proband-sibling (65).

Voc Flu Blk SpR PS IP IM DM Voc Flu Blk SpR PS IP IM DM

Voc

Proband

APPENDIX Observed Correlations for Adopted (Below Diagonal) and Nonadopted (Above Diagonal) Siblings at Age 7