Genetic factor analyses of specific cognitive abilities in 5-year-old Dutch children.
ABSTRACT The genetic and environmental factor structures of intellectual abilities in 5-year-old Dutch twins were examined. Six subtests of the RAKIT, a Dutch intelligence test, were administered to 209 twin pairs. The subtests were categorized as either verbal or nonverbal. The genetic covariance structure displayed a two-common factor structure including specific factors to account for subtest residual variance. The correlation between the genetic Verbal and genetic Nonverbal factors did not differ significantly from zero. The shared environmental influence displayed a single-common factor structure. Unique environmental influences did not contribute to the covariance between subtests and were specific in origin. Estimates of heritability of the subtests ranged from 15% to 56%. Shared environmental influences were significantly present, but were modest in magnitude. The phenotypic data was best described by an oblique two-factor model. This model was not mirrored in the factor structures found for either the genetic or environmental covariances.
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ABSTRACT: Cross-sectional reports suggest heritability of cognitive ability increases throughout adulthood. To investigate this hypothesis, quantitative genetic analyses were conducted on four measures of cognitive ability (verbal, spatial, perceptual speed, memory). Data from Minnesota and Swedish twin studies of aging were compared. Heritability estimates and the factor structure of cognitive abilities could be equated across younger twins (age, 27-50) and middle-aged twins (age, 50-65) from both studies, suggesting stability of heritability during adulthood. The heritability of 81% for a general cognitive factor confirmed earlier findings of high heritability in younger and middle-aged samples. Older Swedish twins (age, 65-85) demonstrated significantly lower heritability estimates for cognitive abilities (54%) and a significantly different factor structure of cognitive ability.Behavior Genetics 10/1995; 25(5):421-31. · 2.61 Impact Factor
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ABSTRACT: This study examined the hypothesis that psychometric tests retain equivalent factor structures across samples widely differing in age. We estimated a best-fitting measurement model for 17 psychometric tests covering the 5 primary abilities of Inductive Reasoning, Spatial Orientation, Verbal Ability, Numerical Ability, and Perceptual Speed, using a sample of 1,621 participants (ages 22 to 95) from the 5th wave of the Seattle Longitudinal Study. We disaggregated the participants into 9 subsets ( M ages = 29, 39, 46, 53, 60, 67, 74, 81, and 90) and tesed the fit of the accepted model for each subset. We confirmed configural invariance for all subsets, but could not establish either complete or incomplete metric invariance for any set. These results confirm the stability of factor patterns across age but indicate serious limitations for valid cross-age comparisons of individual markers of psychometric abilities in age-comparative studies. (PsycINFO Database Record (c) 2012 APA, all rights reserved)Developmental Psychology 06/1989; 25(4):652-662. · 3.21 Impact Factor
- Psychological Science - PSYCHOL SCI. 01/1998; 9(3):183-189.
in age (Reinert, 1970; Schaie et al., 1989; Werdelin
and Stjernberg, 1995). The association between age
and differentiation of abilities relates to the differen-
tiation hypothesis (Garret, 1946) which suggests that
abilities tend to cohere strongly in infancy and child-
hood, insofar as it is testable. When maturation pro-
ceeds, the factorial pattern of intelligence changes and
intellectual abilities become more independent from
A useful approach to study the structure of intel-
ligence is factor analysis. A factor model includes a set
of common factors to explain the variance shared by
various measurements and test-specific factors to ex-
plain any residual variance. In a second-order factor
model the intercorrelation among the first-order com-
mon factors is explained by positing one or more
second-order common factors. The intercorrelation
among the variables is then decomposed into a part that
is attributable to the first-order common factors and into
a part that is attributable to the second-order common
factors. The hierarchical factor model is a popular mul-
tivariate factor technique to examine the structure of
The factor structure of genetic and environmental in-
fluences on specific cognitive abilities measured at
one point of time in childhood is investigated in the
present study. Six subtests of a Dutch intelligence test
were administered to 5-year-old twins. The examina-
tion of cognitive abilities is particularly interesting
during childhood when rapid accumulation of learn-
ing and experience takes place. In school, children are
exposed to many novel environmental effects which
act specifically on the development of their intellec-
tual abilities. The accumulating effects of these envi-
ronmental influences may result in a different pattern
of cognitive abilities in groups of individuals varying
Genetic Factor Analyses of Specific Cognitive Abilities
in 5-Year-Old Dutch Children
M. J. H. Rietveld,1,3G. C. M. van Baal,1C. V. Dolan,2and D. I. Boomsma1
Received 13 Jan. 1999—Final 3 Sept. 1999
The genetic and environmental factor structures of intellectual abilities in 5-year-old Dutch twins
were examined. Six subtests of the RAKIT, a Dutch intelligence test, were administered to
209 twin pairs. The subtests were categorized as either verbal or nonverbal. The genetic co-
variance structure displayed a two-common factor structure including specific factors to account
for subtest residual variance. The correlation between the genetic Verbal and genetic Nonver-
bal factors did not differ significantly from zero. The shared environmental influence displayed
a single-common factor structure. Unique environmental influences did not contribute to the co-
variance between subtests and were specific in origin. Estimates of heritability of the subtests
ranged from 15% to 56%. Shared environmental influences were significantly present, but were
modest in magnitude. The phenotypic data was best described by an oblique two-factor model.
This model was not mirrored in the factor structures found for either the genetic or environ-
KEY WORDS: Specific cognitive abilities; factor models; heritability; children.
Behavior Genetics, Vol. 30, No. 1, 2000
0001-8244/00/0100-0029$18.00/0 © 2000 Plenum Publishing Corporation
1Department of Biological Psychology, Vrije Universiteit, Amster-
dam, The Netherlands.
2Department of Psychology, Universiteit van Amsterdam, Amster-
dam, The Netherlands.
3To whom correspondence should be addressed at Vrije Univer-
siteit, Department of Biological Psychology, De Boelelaan 1111,
1081 HV Amsterdam, Fax: +31.20.444.8832. e-mail: mjh.rietveld@
intellectual abilities (Carroll, 1993; Gustafsson, 1984).
A hierarchical model presents a general intelligence fac-
tor, usually referred to as g, as a second-order general
factor common to first-order factors. These first-order
factors represent various dimensions of intelligence, e.g.,
verbal and spatial intelligence. As pointed out by Ver-
non (1965) this model integrates both Spearman’s con-
cept of a general cognitive ability (Spearman, 1927) and
the Primary Mental Abilities theory of Thurstone (1938).
Studies on the differentiation of cognitive abili-
ties have been summarized by Carroll (Carroll, 1993,
p. 677). In his extensive survey of factor-analytic stud-
ies, he concluded that the same cognitive ability fac-
tors are present at various ages, from the early school
years to adulthood and beyond, and that there is no ev-
idence to support the differentiation hypothesis. Two
possible explanations that can account for the early
differentiation of abilities were proposed. One is that
young children already experience a variety of envi-
ronmental influences which promotes the development
of different abilities. Alternatively, the observed dis-
tinction between cognitive ability factors at young age
may be the result of genetic specificity. Genetic speci-
ficity implies that intellectual abilities have no genetic
source in common and that genetic effects result from
independent sets of genes. The identification of a par-
ticular factor model at the observed, phenotypic level
is not necessary reflected in the same factor model at
the underlying genetic and environmental level. The
structure of these genetic and environmental influences
can be studied through use of multivariate genetic fac-
tor models and requires genetically informative sub-
jects such as twins or adoptees. Application of factor
models to such designs can reveal whether an observed
association between measures results from a shared ge-
netic source or a shared environmental source, or both.
So far, a handful of genetic studies on intellectual abil-
ities and elementary cognitive abilities in children and
adults have been carried out using hierarchical or first-
order factor models (Cardon et al., 1992; Cardon,
1994; Casto et al., 1995; Finkel et al., 1995; LaBuda
et al., 1987; Luo et al., 1994; Pedersen et al., 1994;
Petrill et al., 1996; Petrill et al., 1998; Rijsdijk et al.,
under revision). Results suggest that one general fac-
tor, group factors, and test-specific factors are all re-
quired to account for the genetic covariance structure.
Shared environmental influences display either a single-
common factor structure or a multiple factor structure.
Unique environmental influences to variation in cog-
nitive abilities are largely subtest-specific effects. The
magnitude of the genetic and environmental influences
30Rietveld, van Baal, Dolan, and Boomsma
appears to be a function of both the tests used and of
the sample investigated.
The field of analyzing individual differences in
specific cognitive abilities in young children with ge-
netic factor models is relatively unexplored. To our
knowledge, the only recent reports on genetic factor
models applied to data collected in childhood are re-
ports from the Colorado Adoption Project (CAP). The
CAP is a prospective longitudinal adoption study on
behavior development starting in infancy (e.g., Plomin
and DeFries, 1985). Cardon (1994) reported results of
analyses of longitudinal cognitive data collected in
adoptees and nonadopted sibling pairs at various ages.
A hierarchical model with one second-order factor and
four first-order factors was fitted to the data. At age 4,
a substantial genetic effect common to the first-order
ability factors was found. Heritable variation on the
specific subtests was dominated by the effects of these
first-order factors and little test-specific genetic effects
were found. The unique environmental influences
showed considerable ability-specific effects on the
first-order common factors. Also, in contrast to the ge-
netic influences, large unique environmental effects
specific to each subtest were found. Notably, shared
environmental factors contributed little to the observed
phenotypic variation at this young age. At the age of
7, the magnitude of genetic and environmental influ-
ences changed slightly. Again, the influence of shared
environmental factors was nearly absent. The genetic
covariance matrix was dominated by a general second-
order common factor and the first-order group factors.
Compared to age 4, ability-specific genetic effects
were found to be greater. Unique environmental in-
fluences were primarily subtest-specific in origin.
In an ongoing longitudinal study of brain func-
tion (Van Baal, 1997) and cognition in young Dutch
twins data on six intelligence subtests were collected
in 5-year-old boys and girls. This paper explores the
genetic and environmental structure of specific cog-
nitive abilities by evaluating a number of alternative
factor models to the six measures of verbal and non-
The participants were 209 twin pairs recruited from
the Netherlands Twin Register. The register contains
around 50% of all Dutch twins born after 1986
(Boomsma et al., 1992). All 209 pairs participated in a
study of the development of brain-activity and cogni-
tive development at ages 5 and 7 (Van Baal et al., 1996;
Boomsma & Van Baal, 1998). Families were selected
on the basis of the age and zygosity of the twins, and
of their city of residence. Mean age of the children in
the present study was 5 years and 3 months (80% within
range 5 years and 1 month to 5 years and 6 months).
School attendance was 100%; all children were in their
first year of formal education.
Zygosity of the same-sex twins was determined by
analysis of bloodgroup (142 pairs) or DNA polymor-
phisms (20 pairs), and in a few cases by physical re-
semblance (8 pairs). Because one twin did not complete
all subtests, the pair was excluded from the genetic analy-
ses. The complete sample comprised 47 monozygotic
female (MZF), 37 dizygotic female (DZF), 42 mono-
zygotic male (MZM), 44 dizygotic male (DZM), and
39 dizygotic pairs of opposite sex (DOS). Approxi-
mately two years prior to the experiment, information
on parental occupation and education was obtained
from 186 families by questionnaire. Socioeconomic sta-
tus (SES) was assessed on a 5-step scale relating to
current occupation of the fathers (NCBS, 1993a). Of
186 families, information on occupation was obtained in
178 fathers. The majority of these families (48%) was
of middle SES, 24% was of lower SES, and 28% was
of higher SES. Parental education was rated on a 7-points
scale (NCBS, 1993b). Midparent score for education
was positively correlated with the average offspring IQ
score (r = .29). A correlation of .47 was found for level
of education between the spouses.
The brain-activity study required participants to
come to the university. After arrival at the laboratory
the protocol was explained to the twins and their par-
ents. While one of the twins participated in the electro-
physiological experiment, the other twin received the
intelligence test which took approximately one hour to
administer. IQ of each child was assessed individually
by an experienced test-administrator. The whole ses-
sion, including a break, lasted between three and four
hours. All children received a present afterwards.
The RAKIT, a Dutch intelligence test, was used
in the present study to assess cognitive abilities (Ble-
ichrodt et al., 1984). The RAKIT manual defines intel-
ligence as a multidimensional construct composed of
Specific Cognitive Abilities31
different factors (Bleichrodt et al., 1987). This defini-
tion is closely related to Thurstone’s theory of intel-
lectual functioning (Thurstone, 1938). The full-scale test
comprises 12 subtests. The concurrent validity with the
WISC-R is .86 for total IQ. Raw subtest-scores are stan-
dardized to facilitate comparison among performances
on subtests. In this study, six subtests of the RAKIT
were employed to assess cognitive functioning. The Ex-
clusion subtest measures reasoning by assessing the
child’s ability to induce a relationship between four fig-
ures, and the ability to determine that one of the figures
is deviant; the Discs subtest measures spatial orienta-
tion and speed of spatial visualization; the Hidden Fig-
ures subtest relates to transformation of a visual field,
convergence/flexibility of closure; the Verbal Meaning
subtest is a vocabulary index and a measure of passive
verbal learning; the Learning Names subtest measures
active learning and remembering meaningful pictures;
the Idea Production measures verbal fluency. The com-
bination of these six subtests has been shown to corre-
late .93 with the full-scale test score within this age
group and is generally accepted as a shortened version
of the full-scale test (Bleichrodt et al., 1987). Regard-
ing the nature of the subtests and the way in which the
child has to respond it was hypothesized that three sub-
tests load on a Nonverbal factor (Exclusion, Discs, Hid-
den Figures) and three subtests load on a Verbal factor
(Learning Names, Verbal Meaning, Idea Production).
The response of the child when performing the non-
verbal subtests is to point at the right picture or to move
blocks to the proper place. The mode of response to the
verbal subtests relates more strongly to language skills.
Means, standard deviations, variance-covariance
matrices, and correlations among IQ subtests were cal-
culated separately for the first and second born twins
(twin a and twin b respectively) using SPSS/Windows
7.5. Twin a refers to the boy in opposite-sex twin pairs.
We fitted four factor models to the phenotypic data,
namely, an oblique two-factor model, an orthogonal
two-factor model, a one-factor model, and a model with
specifics only. These analyses were conducted in Mx
(Neale, 1997), using maximum likelihood estimation
PRELIS 2 (Jöreskog and Sörbom, 1993) was used
to compute the variance-covariance matrices of the ob-
servations, separately for each sex-by-zygosity group.
These covariance matrices as well as the cross-twin
cross-trait correlations are to be found at the website
of the Netherlands Twin Register, http://www.psy.
To obtain an estimate of additive genetic (A),
shared environmental (C), and unique environmental
(E) contributions to the observed variances and co-
variances between measures, structural equation mod-
eling was employed (Neale and Cardon, 1992). Let Σp
represent the expected phenotypic covariance matrix
between traits. The expected covariance matrix can be
partitioned into additive genetic covariance (Σa), into
common environmental covariance (Σc) and into
unique environmental covariance (Σe) as follows:
Σp = Σa + Σc + Σe
First, these three covariance matrices were estimated
by means of Cholesky decompositions. Next, a series
of oblique first-order factor models was fitted to the
data. The oblique factor model is equivalent to a hier-
archical factor model with one second-order factor and
two first-order factors, where factor loadings of these
first-order factors on the second-order factor are con-
strained to be equal.
The path diagram in Figure 1 represents the most
general phenotypic factor model. In view of the nature
of the subtests, we considered three different factor
models derived from this general model. We started
with fitting correlated genetic two-factor models. The
path diagram in Figure 2 shows the decomposition of
the covariance between subtests into two group factors.
This model also includes test-specific effects.
Next, we viewed the subtests as indicators of gen-
eral intelligence (Jensen, 1998), that is, we fitted a com-
mon single-factor model to the covariance matrices.
The importance of one general genetic and one general
shared and one general unique environmental factor is
represented in the path diagram in Figure 3. In this
model it is suggested that the observed covariation be-
tween the subtests results from one shared, underlying
factor at each of the genetic and shared and unique en-
vironmental levels. Factors specific to each subtest
were added to test for any residual variance.
Finally, the third model that was considered is one
in which there are no sources of variation common to
The structure of the shared environment was ex-
amined first. The various factor structures were evalu-
ated for C, while genetic and unique environmental in-
fluences were modeled by Cholesky decompositions.
32 Rietveld, van Baal, Dolan, and Boomsma
The model that best accounted for the shared environ-
mental component was retained in subsequent analyses
of the unique environment. Having established the best
fitting model for E, this again was retained in examin-
ing the structure of the genetic part of the model.
The genetic analyses were performed with the pro-
gram Mx (Neale, 1997). Mx provides estimates of the
parameters in the model and an overall chi-square (χ2)
goodness-of-fit index. If the χ2has a probability smaller
than a predetermined value (in this study, for α=.05),
then the model is rejected and requires modification. The
best fitting model in a sequence of models is determined
by means of the hierarchical χ2tests. When a more re-
stricted model does not describe the data significantly
Fig. 1. Phenotypic first-order factor model with a Nonverbal factor
(NV), a Verbal factor (V) and Specific factors (Seto Sip) unique to
each subtest. NV and V are oblique factors, represented by r (NV, V).
Exclusion, E; Discs, D; Hidden Figures, HF; Verbal Meaning, VM;
Learning Names, LN; Idea Production, IP.
Fig. 2. This two-factor model (subscripts nv and v) with test-specifics
(subscripts s) suggests that two factors are needed to explain variance
among subtests. Proportion of total variance due to genetic, shared
and nonshared environmental influences upon factors are represented
by A, C, and E, respectively. The double-headed arrow between the
Nonverbal and Verbal factor represents a correlation.
worse than the more general model, the most parsimo-
nious model is chosen.
Inspection of the scores on 5 RAKIT subscales
showed that the variables were approximately normally
distributed (z-tests for skewness and kurtosis were non-
significant). The distribution of scores on Hidden Fig-
ures differed slightly but significantly from a normal
distribution (z-tests for skewness and kurtosis exceeded
1.96 and −1.96). The data were scanned for outliers by
visual inspection, but none was found. Mean scores and
standard deviations for total IQ and subtests are pre-
sented in Table I. No differences in means were found
between sexes, between zygosities, or between twin a
and twin b. The normative mean score for IQ is 100
(SD = 15) and the normative score on each subtest is
15 (SD = 5). The majority of the observed means were
slightly higher than the population means. However,
these differences were not significant for either males
Phenotypic correlations among the subtests are
presented in Table II. As mentioned earlier, based on
the nature of the subtests and mode of response we hy-
pothesized that Exclusion, Discs, and Hidden Figures
load on a Nonverbal factor and Verbal Meaning, Learn-
ing Names, and Idea Production load on a Verbal fac-
tor. The intercorrelations among subtests loading on the
Nonverbal factor (r ranging from .26 to .40), and among
Specific Cognitive Abilities33
subtests loading on the Verbal factor (r ranging from
.16 to .55) were generally higher than the intercorrela-
tions among subtests from different factors (r ranging
from .07 to .36). The Nonverbal subtest Exclusion,
however, showed a relatively large degree of overlap
with Verbal subtests.
Various factor models were specified to investi-
gate the structure of the phenotypic data. These mod-
els were fitted to the variance-covariance matrix of twin
a and twin b separately. We first applied an oblique
two-factor model to the data. The results of this analy-
sis indicated that the fit of the model was acceptable
(twin a, χ2= 8.23, df = 8, p = .41; twin b, χ2= 16.64,
df = 8, p = .03). Inspection of the data of twin b re-
vealed no systematic source for the deviation from the
expected model. The mean intercorrelation among Ver-
bal and Nonverbal subtests was .58 for twin a, and .57
for twin b. This two-factor model is represented by the
path diagram in Figure 1. Subsequent reduced models,
like an orthogonal two-factor model (twin a, χ2= 42.75,
df = 9, p = .00; twin b, χ2= 38.87, df = 9, p = .00), an
one-factor model (twin a, χ2= 34.04, df = 9, p = .00;
twin b, χ2= 37.51, df = 9, p = .00), and a model with
residuals only (twin a, χ2= 206.21, df = 15, p = .00;
twin b, χ2= 151.97, df = 15, p = .00) did not lead to
an improvement in fit.
Correlations between twin a and twin b for each
subtest for each zygosity group are shown in Table III.
Inspecting the correlations of the twins we found higher
values for monozygotic twins for all subtests compared
to dizygotic twins. Except for Discs, the correlations
of monozygotic twins were less than twice the corre-
lations of dizygotic twins suggesting the presence of
shared environmental influences.
Results of the Cholesky decomposition and sub-
sequent multivariate factor models are presented in
Table IV. No significant difference was found between
a Cholesky model with sex differences and a Cholesky
model in which estimates for A, C and E were con-
strained to be equal across sexes (χ2difference = 53.42,
df = 63, p = .80). The genetic and environmental fac-
tor loadings derived from the Cholesky decomposition
are reported in Table V. No clear pattern emerged from
the genetic factor loadings. Formal testing of various
factor models is necessary to resolve which factor
model best describes the genetic structure. Clearly, a
genetic one-factor structure is unlikely because a num-
ber of large factor loadings of the second through sixth
Fig. 3. This one-factor model (subscripts g) with test-specifics (sub-
scripts s) suggests that one general factor explains all covariance
among subtests. Proportion of total variance due to genetic, shared
and nonshared environmental influences upon factors are represented
by A, C, and E, respectively.
factor are found. In addition, a model with only genetic
specifics is not expected either since the off-diagonal
factor loadings are substantial. The interpretation of the
pattern of shared environmental factor loadings seems
more straightforward. Since large factor loadings are
found on the first factor, a one-factor structure is plau-
sible. Regarding the unique environmental effects, spe-
cific factors appear important since the largest factor
loadings are on the diagonal.
As indicated by the genetic factor loadings derived
from the Cholesky decomposition, the genetic correla-
tions varied substantially, ranging from −.56 to .91. The
correlations among subtests which load on either the
Nonverbal or Verbal factor did not exhibit consistently
higher estimates compared to the intercorrelations
among subtests from different factors. As expected, the
34 Rietveld, van Baal, Dolan, and Boomsma
correlations calculated for shared environmental effects
showed more coherence (range from .27 to .94). Cor-
relations between subtests for unique environmental ef-
fects were very low (range from −.12 to .20).
The Cholesky decomposition without sex differ-
ences was taken as a reference for evaluating changes
in χ2and associated degrees of freedom of more par-
simonious factor models. The structure of the common
environmental contribution was investigated first while
additive genetic and unique environmental influences
were modeled by means of the Cholesky decomposi-
tion. Since the shared environmental correlations esti-
mated from the full Cholesky decomposition suggested
a one-factor structure, first a model including a General
factor and Specifics was applied to the data (Model 3).
The fit of this model did not lead to a significant increase
Table I. Means and Standard Deviations for Subtests and Total IQ-Score for Females and Males.
Descriptives are Calculated Separately for Twin a (First Row) and Twin b (Second Row)
Females (N = 207)a
Males (N = 211)
Mean SDMean SD
aN = number of participants
bN − 1. SD = standard deviation.
Table II. Phenotypic Pearson Correlations for Subtests for Twin a (Below Diagonal) and Twin b (Above Diagonal)a
ExclusionDiscsHidden figures Verbal meaningLearning names Idea production
aN = 209.
bN − 1. ns= nonsignificant correlation, p > .05.
in χ2. The test-specific effects explaining residual
variance could be omitted from this model without de-
terioration in fit. This resulted in Model 4 including
only one General factor explaining the common envi-
ronmental variance and covariance (χ2= 300.04, df =
342, p = .95). Next, taking Model 4 as a point of de-
parture, unique environmental effects were examined
in a similar way. Model 5 and Model 6 postulated a
two-factor structure with Specifics and a one-factor
structure with Specifics, respectively. Although both
models gave a good description of the data, the most
parsimonious model, Model 7, included only Specifics
(χ2= 318.52, df = 357, p = .93). This indicated that
unique environmental effects did not contribute to the
observed covariance between subtests, but only to sub-
test-specific variance. The concluding analyses inves-
tigated the structure of A, additive genetic effects.
Model 7 was taken as the new reference model. In
Model 7 the shared environmental structure was de-
fined by one General factor, unique environmental in-
Specific Cognitive Abilities35
fluences were defined by Specifics only, and genetic
effects were still specified as a Cholesky decomposi-
tion. Application of Model 8, the reduced model in-
cluding a Nonverbal genetic factor and a Verbal ge-
netic factor with Specifics resulted in a good fit. The
correlation between the genetic Nonverbal and Verbal
factor was estimated at .10 with the 95% confidence
interval ranging from −.26 to .10. This outcome pro-
vided strong evidence for a genetic factor structure with
two independent factors. The independency was ex-
plicitly tested in Model 9 and this resulted in an ade-
quate description of the data (χ2= 324.33, df = 366, p
= .94). More parsimonious models did not fit the data.
The importance of each source of variance was tested
in various sequences of model fitting. The outcome of
each order was identical in the sense that A, C, and E
were all found to be indispensible.
Thus, specifying a General factor for the shared
environmental effects, Specific factors for the unique
environmental effects, and a Nonverbal factor, a Ver-
Table III. Twin Correlations for IQ Subtests for All Zygosity Groups
(N = 47)
(N = 37)
(N = 42)
(N = 44)
(N = 39)
aN = number of twin pairs.
bN − 1.
Table IV. Model Fit Indices for Cholesky Decomposition and Nested Sequence of Factor Modelsa
1. Cholesky decomposition ACE, + sex differences
2. Cholesky decomposition ACE, no sex differences
3. A one-factor structure imposed on C, + Specifics
4. Only one factor
5. A two-factor structure imposed on E, + Specifics
6. A one-factor structure imposed on E, + Specifics
7. Only Specifics
8. A two-factor structure imposed on A, + Specifics
9. Correlation between genetic factors constrained to zero
10. A one-factor structure imposed on A, + Specifics
11. Only Specifics
aχ2= chi-square, ∆χ2= change in chi-square, df = degrees of freedom, ∆df = change in number of degrees of freedom.
* p < .03. p-value for all other ∆χ2tests > .25.
bal factor and Specific factors for the additive genetic
effects best accounted for the variances and the co-
variances among subtests. The model is illustrated in
Figure 4, with parameter estimates.
The genetic correlations between subtests can eas-
ily be calculated from the parameter estimates depicted
in Figure 4. Correlations among Nonverbal subtests
ranged from .22 to .69, and correlations among Verbal
subtests ranged from .32 to .66. The variation in
strength of the correlation reflected the influence of
test-specific genetic effects. These effects only con-
tributed to the observed variance and not to the ob-
served covariance. Since no significant correlation was
found between the genetic Verbal and Nonverbal fac-
tor, the intercorrelations among subtests loading on
these two factors were zero.
Table VI contains the estimates for the influence
of the genetic factors and estimates for shared and
unique environmental influences based on Model 9.
The parameter estimates for the genetic factors showed
no clear pattern. Contribution to the total variance of
36 Rietveld, van Baal, Dolan, and Boomsma
Table V. Genetic (First Panel), Shared Environmental (Second Panel), and Unique Environmental (Third Panel)
Factor Loadings Estimated for the Full Cholesky Decompositiona
aA-Chol1to A-Chol6= genetic Cholesky factors, C-Chol1to C-Chol6= shared environmental Cholesky factors,
E-Chol1to E-Chol6= unique environmental Cholesky factors.
Fig. 4. Parameter estimates for best fitting model: two genetic factors
(Anvand Av), one shared environmental factor (Cg), genetic specifics
(single headed arrows placed above squares) and unique environmen-
tal specifics (single headed arrows placed below squares).
Specific Cognitive Abilities37
Verbal tests loaded on the other genetic factor. These
two factors were independent. Genetic subtest-specific
effects were needed to explain residual variance. The
C covariance matrix was dominated by a single factor,
accounting for the observed covariance among all sub-
tests. Unique environmental influences were subtest-
specific in origin, contributing to the variance specific
to the subtests. The estimates for the genetic influences
calculated separately for the Nonverbal, Verbal and
Specific factors did not exhibit a clear pattern. The Non-
verbal genetic factor explained only 5% of the total vari-
ance of the Hidden Figures subtest. In contrast, this fac-
tor explained all genetic variation in Discs. The genetic
two-factor model included a correlation between the ge-
netic Nonverbal and genetic Verbal factor. This corre-
lation was found not to differ significantly from zero.
This indicates that the genes influencing Verbal tests
are independent from the genes influencing Nonverbal
tests. This independency among the two genetic factors
implies that the observed covariance between Non-
verbal and Verbal tests is solely due to shared envi-
ronmental influences. The standardized estimates for
genetic influences and unique environmental influences
were on average of the same magnitude. Genetic es-
timates ranged from 15% to 56% and unique envi-
ronmental estimates ranged from 29% to 57%. A large
influence of shared environment was found for Verbal
Meaning (42%). For the other five subtests this influ-
ence was only modest (ranging from 3% to 25%).
The number of reports of genetic analyses on spe-
cific cognitive abilities in early childhood and in early
school years is limited (Boomsma, 1993; Cardon et al.,
1992; Cardon, 1994). The method used in older stud-
ies conducted in childhood involved comparison of MZ
the Nonverbal factor ranged from 5% to 40% and the
contribution to the total variance of the Verbal factor
ranged from 9% to 30%. Hidden Figures shared little
variance with other Nonverbal subtests, just as a rela-
tively small loading on the Verbal factor was found for
Idea Production. Discs seemed to be a typical Nonver-
bal subtest; all genetic variance was shared with the
other Nonverbal subtests. Looking at the pattern of her-
itability estimates, no clear distinction could be made
between Verbal and Nonverbal tests. On average, the
influences of genetic factors and unique environmen-
tal factors were of similar magnitude. The influence of
shared environmental factors was much more modest.
Verbal Meaning was the exception: a large estimate for
shared environmental influences was found (42%).
We examined the factorial structure of genetic and
environmental influences on specific cognitive abilities
by fitting a number of oblique first-order factor models
to data on specific cognitive abilities in 5-year-old
Dutch twins. Bearing in mind that our sample size is not
very large, we first summarize the results and subse-
quently compare these with findings reported in other
studies. An oblique two-factor model gave a good de-
scription of the phenotypic covariance matrices. This
does not necessarily imply, however, that a two-factor
model will adequately describe the genetic and non-ge-
netic covariance structure. It was found that the data
were best described by a model with different factor
structures for A, C and E. The genetic component of co-
variance displayed a two-factor structure. The Nonver-
bal tests loaded on one common genetic factor and the
Table VI. Percentages of Total Variance Explained by Nonverbal Genetic Factor, Verbal Genetic
Factor, Specific Genetic Factors, and Environmental Factorsa
Variance accounted for by genetic and environmental effects (%)
aAnv= Nonverbal genetic factor, Av= Verbal genetic factor, Asp= Specific genetic factors. h2=
proportion of total variance explained by genetic factors, c2= proportion of total variance explained
by shared environmental factors, e2= proportion of total variance explained by unique environ-
correlations with DZ correlations for subtest scores or
factor scores (Foch and Plomin, 1980; Garfinkle, 1982;
Segal, 1985; Wilson, 1975). While the results in these
studies were indicative of genetic variation for some of
the measures, not all separate subtest scores displayed
heritability. In addition to the report of analyses of sep-
arate subtests, Segal (1985) and Wilson (1975) both re-
ported on greater concordance in the pattern of subtest
scores in MZ twins compared to DZ twins. The appli-
cation of various factor models to examine the genetic
and environmental covariance structure of specific cog-
nitive abilities using a model fitting approach has just
recently gained more attention. A small number of re-
cent studies examining cognitive abilities involved the
application of a hierarchical model to data collected in
children and adults (Cardon et al., 1992; Cardon, 1994;
Luo et al., 1994; Petrill et al., 1996).
Results obtained from twin studies on intelligence
in childhood suggest differential heritability for verbal,
spatial, memory and perceptual speed tests (reviewed
by Plomin, 1986). We did not observe this distinction
in estimates of genetic influences between different
subtests. Not all subtests in the administered Dutch in-
telligence test can be classified as purely verbal or
purely nonverbal. Although the mode of response is
distinctively verbal or nonverbal, the execution of the
tasks may partly involve, for example, memory (Learn-
ing Names) and, for example, verbal fluency (Idea Pro-
duction). Therefore, a difference in heritability esti-
mates may arise compared to studies in which more
pure subtests or factors are used.
Our results resemble those obtained by Plomin
and Vandenberg (1980) in a reanalysis of Koch’s
(1966) Primary Mental Abilities data obtained in 5-
to 7-year-old twins. Plomin and Vandenberg (1980)
reported that verbal and spatial abilities, both show-
ing a large genetic influence, are genetically inde-
pendent at this stage in development. Cardon (1994)
applied a hierarchical model to cognitive ability data
collected in CAP participants at various ages. Both at
ages 4 and 7 years, a genetic general factor was ap-
parent and genetic subtest-specific effects were small.
These results are in clear contrast to our findings. Our
analyses revealed the presence of two independent ge-
netic factors and genetic subtest-specific effects con-
tributed significantly to the genetic variance. The hi-
erarchical model (Cardon, 1994) also included genetic
effects on the group factors independent of g with in-
creasing influence from 4 to 7 years. This last find-
ing is more in line with our observation of two sepa-
rate genetic factors at age 5. In our study, shared
38 Rietveld, van Baal, Dolan, and Boomsma
environmental influences were modest but signifi-
cantly present while Cardon (1994) reported a mini-
mal contribution of C. This is quite remarkable since
several reviews on developmental intelligence agree
upon a large influence of shared environmental fac-
tors in early life (e.g., Boomsma, 1993; McCartney
et al, 1990; Thompson, 1993).
Most genetic factor analyses have been performed
on cognitive ability data collected in participants of
older age. Our findings here are to some extent con-
sistent with those reported in studies on specific intel-
lectual abilities in which older samples were examined,
even in the elderly (Petrill et al., 1998). Genetic influ-
ences are significantly present and environmental in-
fluences are largely not shared by members of the same
family. Regarding the structure of the latent factors
more differences between studies are observed. Some
studies reported on substantial ability-specific genetic
effects (Casto et al., 1995; LaBuda et al., 1987) while
others reported a dominant role of g (Pedersen et al.,
1994; Petrill, et al., 1998). The significant effects of
both a general genetic factor and genetic group factors
were reported in studies in which the data were analyzed
through application of hierarchical models (Cardon et
al., 1992; Luo et al., 1994; Petrill et al., 1996). As in
the majority of these studies, we found that a one-factor
structure best explained the shared environmental co-
variance matrix. Among these reports of multivariate
analyses most agreement was on unique environmental
influences. Those influences are predominantly subtest-
Boomsma and Van Baal (1998) performed a lon-
gitudinal analysis of total IQ data collected in the same
sample at ages 5 and 7. Shared environmental factors
contributed to half of the observed variance at age
5 while we found a modest contribution of shared en-
vironmental factors on specific subtests. This apparent
inconsistency arises because the impact of genetic and
environmental influences shared by subtests is aug-
mented, and the genetic and environmental influences
specific to subtests are decreased when analyzing a
composite IQ score (Eaves et al., 1989; p. 201–202).
Since our analysis revealed the importance of C in ex-
plaining the covariance between verbal and nonverbal
subtests, a higher estimate of shared environmental fac-
tors was detected when analyzing total IQ.
We also collected information on occupation and
education in the parents. Parental education showed a
positive but moderate correlation with total IQ in their
children. The correlation between education of the
mother and education of the father was strong (.46).
Although education level is not equivalent to IQ, a
strong positive relationship exists (Ceci, 1991). The re-
lationship between education and IQ in parents may
have an impact on the estimate of genetic and envi-
ronmental influences on intelligence in their children.
Since IQ is a heritable phenotype in adults, the esti-
mates of shared environmental contributions may be
inflated if the resemblance in IQ of spouses is based on
Results from recent studies which focused on the
differentiation hypothesis indicated that the same fac-
torial pattern of cognitive abilities is maintained
across time (Schaie et al., 1989; Werdelin and Stjern-
berg, 1995). Behavior genetic factor models provide
the means to examine whether this structural invari-
ance at the phenotypic level also applies to the un-
derlying genetic and environmental level. Our results
show that at age 5, the phenotypic factor structure dif-
fers from the factor structure found for the genetic,
shared environmental, and unique environmental
sources of variance.
A related issue to the exploration of the factor
structure of intellectual abilities is the relationship be-
tween cognitive functioning and behavior disorders.
This negative association is found in clinical (e.g.,
Frick et al., 1991) and in healthy populations (e.g.,
Dietz et al., 1997). The covariance between intelli-
gence and problem behaviors is indicative of a shared
source, either environmental or genetic in origin, or
both. Considering the findings in this study, an asso-
ciation of behavior problems with both verbal and non-
verbal aspects of intelligence would suggest that en-
vironmental factors which are shared by children in
the same family play a role in explaining the associa-
tion. A stronger association of either verbal or non-
verbal IQ with behavior problems would suggest a
common genetic source.
This study is part of an ongoing longitudinal proj-
ect in which intelligence and behavior problems in
childhood are investigated (Van den Oord et al., 1996;
Van der Valk et al., 1998). Therefore, we aim to fur-
ther explore the stability of the genetic and environ-
mental factor structure of cognitive abilities in a lon-
gitudinal design, and to examine the relationship
between intelligence and problem behaviors.
This work was financially supported by the USF
(grant number 96/22). The authors gratefully acknowl-
edge the assistance of Sophia Kramer with the admin-
Specific Cognitive Abilities39
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funding the work of Caroline van Baal (575-65-052).
The research of Conor Dolan was made possible by a
fellowship of the Royal Netherlands Academy of Arts
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