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Genetic Ancestry and General Cognitive Ability in a Sample of American Youths

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Abstract and Figures

Black and Hispanic children in the United States have lower mean cognitive test scores than White children. The reasons for this are contested. The test score gap may be caused by sociocultural factors, but the high heritability of g suggests that genetic variance might play a role. Differences between self-identified race or ethnicity (SIRE) groups could be the product of ancestral genetic differences. This genetic hypothesis predicts that genetic ancestry will predict g within these admixed groups. To investigate this hypothesis, we performed admixture-regression analyses with data from the Adolescent Brain Cognitive Development Cohort. Consistent with predictions from the genetic hypothesis, African and Amerindian ancestry were both found to be negatively associated with g. The association was robust to controls for multiple cultural, socioeconomic, and phenotypic factors. In the models with all controls the effects were as follows: (a) Blacks, African ancestry: b =-0.89, N = 1690; (b) Hispanics, African ancestry: b =-0.58, Amerindian ancestry: b =-0.86, N = 2021), and (c) a largely African-European mixed Other group, African ancestry: b =-1.08, N = 748). These coefficients indicate how many standard deviations g is predicted to change when an individual's African or Amerindian ancestry proportion changes from 0% to 100%. Genetic ancestry statistically explained the self-identified race and ethnicity (SIRE) differences found in the full sample. Lastly, within all samples, the relation between genetic ancestry and g was partially accounted for by cognitive ability and educational polygenic scores (eduPGS). These eduPGS were found to be significantly predictive of g within all SIRE groups, even when controlling for ancestry. The results are supportive of the genetic model.
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Genetic Ancestry and General Cognitive Ability in a Sample of American
John G.R. Fuerst, Meng Hu, and Gregory Connor
Black and Hispanic children in the United States have lower mean cognitive test scores than
White children. The reasons for this are contested. The test score gap may be caused by
sociocultural factors, but the high heritability of g suggests that genetic variance might play a
role. Differences between self-identified race or ethnicity (SIRE) groups could be the product of
ancestral genetic differences. This genetic hypothesis predicts that genetic ancestry will predict g
within these admixed groups. To investigate this hypothesis, we performed admixture-regression
analyses with data from the Adolescent Brain Cognitive Development Cohort. Consistent with
predictions from the genetic hypothesis, African and Amerindian ancestry were both found to be
negatively associated with g. The association was robust to controls for multiple cultural,
socioeconomic, and phenotypic factors. In the models with all controls the effects were as
follows: (a) Blacks, African ancestry: b = -0.89, N = 1690; (b) Hispanics, African ancestry: b = -
0.58, Amerindian ancestry: b = -0.86, N = 2021), and (c) a largely African-European mixed
Other group, African ancestry: b = -1.08, N = 748). These coefficients indicate how many
standard deviations g is predicted to change when an individual's African or Amerindian ancestry
proportion changes from 0% to 100%. Genetic ancestry statistically explained the self-identified
race and ethnicity (SIRE) differences found in the full sample. Lastly, within all samples, the
relation between genetic ancestry and g was partially accounted for by cognitive ability and
educational polygenic scores (eduPGS). These eduPGS were found to be significantly predictive
of g within all SIRE groups, even when controlling for ancestry. The results are supportive of the
genetic model.
There are substantial differences in mean cognitive test scores between self-identified racial and
ethnic (SIRE) groups such as Whites, Hispanics, Blacks, and Asians in the United States (Roth et
al., 2017; Murray, 2021). These differences are not attributable to psychometric bias, since
cognitive-test batteries typically exhibit measurement invariance across American SIRE groups
(Scheiber, 2016a,b; Warne, 2020a). As such, they represent real differences in latent cognitive
Although cognitive ability researchers disagree as to the causes of these differences
(Rindermann, Becker & Coyle, 2020), a number of explanatory factors have been proposed.
Most of these factors appeal to either cultural differences between groups or differing social and
economic circumstances such as differences in poverty levels. Many researchers studying
cognitive ability attribute some part of the differences to genetics (Rindermann, Becker & Coyle,
Analyses of both nationally representative samples and cognitive battery standardization data
(Magnuson & Duncan, 2006; Weiss & Saklofske, 2020) indicate that socioeconomic status
(SES) can statistically explain a substantial percentage of test score variance across SIRE groups.
However, it is not clear to what extent SES captures predominantly environmental or genetic
causes, since SES is related to both genetic and environmental differences within groups (Belsky
et al., 2018; Krapohl & Plomin, 2016; Rowe, Vesterdal & Rodgers, 1998). Regardless, the data
suggest that even after fully accounting for average SES differences, there remains unexplained
variance in cognitive test scores between groups.
The genetic hypothesis is that differences in genes inherited from ancestors play a significant
role in causing the SIRE related variation in cognitive test scores. Twin studies show non-trivial
heritability for individual differences in cognitive ability within ethnic groups (Pesta et al.,
2020). SIRE groups differ in European ancestry-based polygenic scores, and these scores are
predictive of cognitive ability within ethnic groups (Lasker et al., 2019). Taken together, these
results suggest that variation in cognitive ability among SIRE groups may be due in part to allele
frequency differences at trait-associated gene loci.
Most studies that investigate the source of group differences categorize individuals by SIRE.
However, SIRE reflects both genetic and sociocultural factors. This makes interpretation of
simple SIRE-based results ambiguous. Admixture regression analyses, by including both SIRE
and admixture variables simultaneously, can quantify the association between genetic ancestry
and phenotype in admixed populations (Halder et al., 2015). These analyses test the extent to
which the genetic differences between SIRE groups are responsible for observed trait
If continental populations differ polygenically in trait-related phenotypes, these continental
differences are expected to contribute to individual differences in admixed populations. In
aggregate, alleles that vary between ancestral populations will be associated with phenotype in
admixed populations. Individuals who have a larger proportion of their global ancestry from the
ancestral group with higher average frequencies of trait-enhancing alleles are likely to also have
higher polygenic scores and higher average values in the phenotype. As such, associations
between genetic ancestry and phenotype in admixed populations would suggest that phenotypic
differences between continental populations have a genetic basis (Halder et al., 2015). This
admixture regression methodology can be extended by including polygenic scores (PGS) to see
if PGS mediate the association between g and ancestry.
In this way, admixture-regression analysis allows researchers to separate the genetic element
of SIRE from its cultural, behavioral, and psychosocial aspects, which may alternatively be
responsible for the observed phenotypic differences. As Fang et al. (2019, p. 764) note: SIRE
“acts as a surrogate to an array of social, cultural, behavioral, and environmental variables” and
so “stratifying on SIRE has the potential benefits of reducing heterogeneity of these non-genetic
variables and decoupling the correlation between genetic and non-genetic factors.”
These analyses require a substantial degree of admixture in populations, and are more robust
when that admixture has taken place in the course of the last seven to ten generations (Halder et
al., 2015). In the USA, African and Hispanic Americans meet these requirements. They exhibit a
wide range of European, African, and/or Amerindian ancestry due to admixture over the course
of several generations.
Thus we apply admixture analysis to examine if SIRE differences in general cognitive ability
(g) can be accounted for by genetic variation related to continental ancestry. We hypothesize that
g will be lower in African and Hispanic American samples relative to European American
samples. These differences will be associated with African and Amerindian genetic ancestry
within the SIRE groups. Additionally, we hypothesize that the association between genetic
ancestry and g will be robust to controls for possible socio-environmental confounds and that
genetic ancestry will also statistically account for the SIRE differences found in the full sample.
Finally, we hypothesize that current polygenic scores for cognitive ability and education
(eduPGS) will both predict individual differences within SIRE groups and explain a portion of
the effect of ancestry on g.
1. Dataset
The Adolescent Brain Cognitive Development Study (ABCD) is a collaborative longitudinal
project involving 21 sites across the USA. ABCD is the largest, longitudinal study of brain
development and child health ever conducted in the USA. It was created to research the
psychological and neurobiological bases of human development. At baseline, around 11,000
children aged 9-10 years were sampled, mostly from public and private elementary schools. A
probabilistic sampling strategy was used, with the goal of creating a broadly representative
sample of US children in that age range. Children with severe neurological, psychiatric, or
medical conditions were excluded. Children were also excluded if they were not fluent in
English or if their parents were not fluent in either English or Spanish. Parents provided
informed consent. For this study, we utilized the baseline ABCD 3.01 data. We excluded
individuals missing either cognitive or admixture scores. We also excluded any individual
identified as being either Asian or Pacific Islander in order to focus on groups who were
primarily of African, European, and Amerindian ancestry. This left 10,370 children.
For the admixture-regression analyses, SIRE groups were delineated using the ABCD
race_ethnicity variable. This was a summary variable computed from 18 separate multiple choice
questions asking about the child’s race (“What race do you consider the child to be? Please check
all that apply”) and one question asking if the child is of Hispanic ethnicity (“Do you consider
yourself Hispanic/Latino/Latina?”). Children were classified into one of five mutually exclusive
groups: non-Hispanic White (White), non-Hispanic Black (Black), Hispanic of any race
(Hispanic), non-Hispanic Asian (Asian) or any other (Other). The Other category included any
non-Hispanic children who were reported to be two or more racial groups. Because we dropped
the Asian category, we were left with four mutually exclusive SIRE groups.
2. Variables for admixture regression analyses
The following variables were used for the admixture regression analyses:
1. g scores
ABCD baseline data contain the following cognitive subtests, the first seven of which are from
the NIH Toolbox® cognitive battery: Picture Vocabulary, Flanker, List Sorting, Card Sorting,
Pattern Comparison, Picture Sequence Memory, Oral Reading Recognition, Wechsler
Intelligence Scale for Children’s Matrix Reasoning, The Little Man Test (efficiency score), The
Rey Auditory Verbal Learning Test (RAVLT) immediate recall, and RAVLT delayed recall. For
details about these measures, see Thompson et al. (2019).
We conducted multi-group confirmatory factor analysis (MGCFA) on these subtests, as
detailed in Supplementary File 1. Briefly, we first checked whether outliers and missing data had
any impact, and whether our results remained strong after correction. We then conducted
exploratory factor analysis and multi-group confirmatory factor analysis on the aforementioned
set of subtests as a check for bias. After adjustment for age, we did not find any non-linear
effects on age. Adjustment for sex did not reveal any evidence of meaningful differences in fit
between the competing models, the g-model and the correlated factors model. We find that a
three broad factor model (memory, complex cognition, and executive function) with g at the
apex fits the data well. Moreover, strict measurement invariance holds between SIRE groups.
The best fitting model (M6A, Table S2 of Supplementary File 1; CFI = .954, RMSEA = .044)
was one in which g alone explains SIRE group differences. We output the g-factor scores from
this model for use in the analyses. These score magnitudes are approximately the same as those
derived from exploratory factor analysis.
2. Socioeconomic status (SES)
We identified seven indicators of SES: financial adversity, area deprivation index, neighborhood
safety protocol, parental education, parental income, parental marital status, and parental
employment status. These are detailed in Supplementary File 2. We submitted the seven SES
indicators to Principal Components Analysis (PCA). We used the R package PCAmixdata, which
handles mixed categorical and continuous data (Chavent, Kuentz-Simonet, & Saracco, 2014).
The first unrotated component explained 42% of the variance. The PCA_1 loadings for the seven
SES indicators were as follows: financial adversity (.31), area deprivation index (.49),
neighborhood safety protocol (.31), parental education (.53), parental income (.66), parental
marital status (.42), and parental employment status (0.21). More details and the correlation
matrix for the SES indicators is provided in Supplemental File 2.
3. Child US-born
Parents were asked about the country of the child’s birth. We recoded this variable as 1 for
“United States” and 0 for all other responses.
4. Immigrant family
Parents were asked if anyone in the child’s family, including maternal or paternal grandparents,
was born outside of the United States. This variable was coded as 1 for “Yes” and 0 for all other
5. Nationality (Puerto Rican, Mexican, and Cuban)
If a child was reported to be Hispanic, parents were additionally asked about the specific Latin
American nation of origin (“Please choose the group that best represents the child's Hispanic
origin or ancestry”). Seventy percent of the Hispanic children were reported as being either
Mexican, Mexican American, or Chicano (N = 1028), Puerto Rican (N = 210), or Cuban or Cuban
American (N = 174). Dummy variables were created for these three nationality groups, with “1”
indicating “Yes” and “0” indicating “No”.
6. Frac_SIRE
Four dummy SIRE variables (Black, White, Native American, and Not Otherwise Classified
(NOC) were computed from the 18 questions asking about the child’s specific race. The NOC
SIRE group included those who were marked as: “Other Race,” “Refused to answer,” or “Don’t
Know.” These were then recoded into interval variables in which individuals are assigned a
SIRE fraction ranging from 0 to 1 (Liebler & Halpern-Manners, 2008). These were calculated as
the value selected for each of the four groups (0 or 1) over the total number of responses (0 to 4)
chosen. For example, someone marked as only Black and White would be assigned scores of
(Black: ½; White: ½; Native_American: 0; NOC = 0). This SIRE coding was used as it was
previously found to be the most predictive in models which also included genetic ancestry
(Kirkegaard et al., 2019).
7. Hispanic
For the admixture-regression analysis conducted on the full sample, we additionally included a
dummy variable for Hispanic ethnicity. This was coded as “1” for “Hispanic” and “0” for not
Hispanic. As the subsamples were either Hispanic or non-Hispanic, this variable was not used in
the subsample analyses.
8. Ethnic attachment
Parents were given the Multigroup Ethnic Identity Measure-Revised (MEIM-R) Survey. In this
they were asked six Likert-scaled (1 = strongly agree; 5 = strongly disagree) questions regarding
their ethnic group: “I have spent time trying to find out more about my ethnic group, such as its
history, traditions, and customs”, “I have a strong sense of belonging to my own ethnic group,”
“I understand pretty well what my ethnic group membership means to me,” “I have often done
things that will help me understand my ethnic background better,”, “I have often talked to other
people in order to learn more about my ethnic group,”, “I feel a strong attachment towards my
own ethnic group.” ABCD computed MEIM-R summary scores, which we standardized. We
treat this as a measure of family ethnic-related culture. We only included this variable in the
subsample analyses. In these the members belonged to the same broad ethnic group (e.g., Black
or Hispanic).
9. State racism
ABCD calculated state-level indicators of both racism and immigrant bias. These were based on
both implicit bias measures and state-level structural variables. The two indicators correlated at r
= .41 (N = 9386). We standardized both measures (M = 0, SD = 1) and then averaged them and
standardized the resulting average.
10. Discrimination factor
In Year 1 follow-up, the children were asked 6 questions regarding perceived ethnic, racial,
national, or color based discrimination. The questions were as follows: “In the past 12 months,
have you felt discriminated against: because of your race, ethnicity, or color?”, “In the past 12
months, have you felt discriminated against: because you are (or your family is) from another
country?”, “How often do the following people treat you unfairly or negatively because of your
ethnic background?” (Teachers? Other adults outside school? Other students?), “I feel that others
behave in an unfair or negative way toward my ethnic group.” We imputed missing data using
the mice package (df, m = 5, maxit = 50, method = 'pmm', seed = 500). We used the mirt package
in R to perform factor analysis on the six questions. We then standardized and saved the factor
11. Skin_color, P_Brown_Eye, P_Intermediate_Eye, P_Blue_Eye, P_Black_Hair, P_Brown
Hair, P_Red_or_Blond_Hair).
Conley and Fletcher (2017) have suggested that phenotypic-based discrimination might mediate
the association between cognitive ability and genetic ancestry. This is called the colorism model
(Hu, Lasker, Kirkegaard, & Fuerst, 2019). It can be tested by including indices of race-related
phenotype into the regression models to see if these capture the association between ancestry and
cognitive ability. As such, we include measures of eye, hair, and skin color. Skin, Hair, Eye color
were calculated based on the publicly available, “Hirisplex Eye, Hair and Skin Colour DNA
Phenotyping Webtool.” This tool and score calculations have been detailed by Lasker et al.
(2019). We additionally combined (summed) the red and blond hair probabilities. Skin color was
scaled as detailed in Lasker et al. (2019), with higher scores representing darker color, and then
standardized. The eye and hair color variables represent the percent in the full sample with the
specific color and were left unstandardized to retain interpretability.
12. Admixture estimates
Imputing and genotyping was done by the ABCD Research Consortium using Illumina XX.
516,598 variants survived the quality control. Before global admixture estimation, we applied
quality control using PLINK 1.9. We used only directly genotyped, bi-allelic, autosomal SNP
variants (494,433, 493,196, before and after lifting). We pruned variants for linkage
disequilibrium at the 0.1 R² level using PLINK 1.9 (--indep-pairwise 10000 100 0.1). This
variant filtering was done in the reference population dataset to reduce bias from sample non-
representativeness. 99,642 variants were left after pruning. We merged the target samples from
ABCD with reference population data for the populations of interest. A k=5 solution with
European, Amerindian, African, East Asian and South Asian components provides the most
comprehensive but parsimonious model of the US population, capturing all the predominant
ancestral backgrounds in the US population. We merged our sample with relevant samples from
1000 Genomes and from the HGDP to perform the cluster analysis and identify these k=5
components. The following populations from 1000 Genomes and from the HGDP reference
populations were excluded: Adygei, Balochi, Bedouin, Bougainville, Brahui, Burusho, Druze,
Hazara, Makrani, Mozabite, Palestinian, Papuan, San, Sindhi, Uygur, Yakut. We excluded these
populations because they were overly admixed or because the individuals in the ABCD sample
lacked significant portions of these ancestries (e.g., Melanesians and San). We split the ABCD
target samples into 50 random subsets (222 persons each) and merged them sequentially with the
reference data. Admixture at k = 5 was run on each of the 50 merged subsets. This repeated
subsetting was done to avoid skewing the admixture algorithm to European ancestry which was
predominant in the ABCD sample.
13. First 20 Principal components
For the analysis of PGS predictivity within SIRE groups we controlled for the first 20 ancestry
principal components to take into account population structure related effects. These components
were generated by PLINK v1.90b6.8 when computing polygenic scores.
14. eduPGS
For polygenic scores (PGS), we scored the genomes using PLINK v1.90b6.8. For background, a
polygenic score (PGS) “is an estimate of an individual's genetic liability to a trait or disease,
calculated according to their genotype profile and relevant genome-wide association study
(GWAS) data” (Choi, Mak & O’Reilly, 2020). We used the genome-wide association study
(GWAS) results from Lee et al. (2018). Specifically, we used the multi-trait analysis of genome-
wide association study (MTAG) eduPGS SNPs (N = 8,898 variants in this sample) to compute
eduPGS. The MTAG eduPGS were computed using MTAG, a method for analyzing statistics
from genome-wide association studies (GWAS) on different but genetically correlated traits
(e.g., education and intelligence). These scores were based on cognitive ability (n = 257,841),
hardest math class taken (n = 430,445), and mathematical ability (n = 564,698) (Lee et al., 2018).
We use these PGS because previous research has shown them to have trans-ethnic predictive
validity in European, Hispanic, and African American populations (Lasker et al., 2019; Fuerst,
Kirkegaard, & Piffer, 2021). Moreover, common forms of bias were found not to account for the
ancestry-related eduPGS differences (Fuerst et al., 2021). Thus, we can say that these PGS
plausibly captures genetic effects between ancestry groups.
15. The NIH Toolbox® (NIHTBX) neuropsychological battery
For one validation analysis of the eduPGS which included Asians, we used the NIHTBX
summary scores. This was because we did not run MGCFA on the small Asian samples and so
did not have g scores for these groups. This battery has been shown to be measurement invariant
across American Black, Hispanic, and White SIRE groups (Lasker et al., 2019). The effects of
age and sex were controlled for. We standardized the residuals.
3. Methods (Analyses)
We first present the descriptive statistics for the sample and the subsamples. We then explore the
bivariate relation between European admixture and g-scores. We include both linear regression
lines and loess lines in the regression plots (based on the gg_scatter package in R). These
analyses are descriptive and do not take into account the complex structure of the data.
After, we run a series of within-SIRE (Black, Hispanic, and Other) admixture-regression
analyses to control for potential environmental confounds. For these analyses, we set European
ancestry as a reference value with a value of zero. Following Heeringa and Berglund’s (2021)
recommendations, we used a multi-level mixed effects three-level (site, family, individual)
model. In this model, recruitment site and family common factors are treated as random effects
(i.e., as random samples from a population). We further report the dense numeric matrix results
for the regression models in Supplementary File 3.
The pooled data with both the regular ABCD baseline sample and the pooled twin samples
were used. As Heeringa and Berglund (2021) note, the specification replicates that used by the
ABCD Data Exploration and Analysis Portal (DEAP). Thus, the use of this multilevel model also
aids in replication. For the regression analyses on the SIRE subsamples, we ran four models. The
first model includes genetic ancestry and controls for both child and family immigrant status.
The second model adds a term for SIRE and ethnic attachment to capture SIRE specific cultural
effects. The third model adds terms to capture possible discrimination related effects: state-level
racism, child reported experiences of discrimination, and race-related phenotype. The fourth
model adds our general SES variable. Geographic effects are controlled for by including study
site as a random effect in the model.
For the regression analyses, general cognitive ability scores (g-scores) are used as the
dependent variable. This variable was standardized (M = 0.00; SD = 1.00) in the full sample. As
for the independent variables, both the ancestry and fractional SIRE variables were left
unstandardized. This allows the unstandardized beta coefficients for these variables to be
interpreted as the effect of a change in 100 percent ancestry/SIRE identity on one standardized
unit of cognitive ability. The rationale for this method has been detailed elsewhere (Lasker et al.,
2019). The Child_USA_Born and Immigrant_Family dummy variables were also left
unstandardized to retain interpretability. The three eye color and the three hair color variables,
which represent probabilities that sum to one in the full samples, are also not standardized to
retain interpretability. The remaining variables ethnic attachment, state racism, discrimination
factor, skin color, and SES are all standardized in the full sample. Thus, the unstandardized B
coefficient for these variables represents the change in g induced by a change of one standard
deviation in the independent variable.
1. Descriptive statistics
The descriptive statistics for the total sample and the four SIRE subsamples are shown in Table
1. Cohen’s d for the difference in g between Black and White Americans comes to 1.02 d. This
represents a large effect by conventional standards (Cohen, 1988) and is typically sized for
measured g differences across SIRE groups (Roth et al., 2017). The difference between Hispanic
and White Americans is 0.38 d, while that between Others and White Americans is 0.37 d. These
latter two differences represent small to medium sized effects (Cohen, 1988). The Hispanic-
White difference is smaller than usually reported (e.g., Roth et al., 2017). This could be due to
the exclusion of children who were not fluent in English.
Table 1. Total sample and subsample characteristics
Total sample
M ± SD
M ± SD
M ± SD
M ± SD
M ± SD
Age (in Months)
P_Brown Hair
Note: Nationality variables (Mexico, Cuba, Puerto Rico) were only computed for Hispanics.
In this sample, parent-identified Whites are 98% European in ancestry (1% African; 1%
Amerindian). Since this group has little admixture, we relegate the within SIRE admixture-
regression analyses to the supplementary file. Both the Black (82% African, 16% European, 1%
Amerindian) and the Other (62% European, 32% African, 4% Amerindian) groups are African-
European admixed groups. Hispanics additionally have a substantial Amerindian component
(60% European, 28% Amerindian, 10% African). Figure 1 shows the distribution of ancestry by
SIRE groups. These admixture percentages correspond with those typically reported in the
literature (e.g., Bryc et al., 2015).
Figure 1. Admixture triangle plot for SIRE groups in the ABCD sample
Regression Plots and Admixture Regression analyses
1. Black Americans
Figure 2 shows the regression plot for European ancestry and g-scores among Black children.
European ancestry is significantly (r = .10, N = 1690) associated with g scores. The R boxplot
function indicated 13 outliers. However, removing these had no effect on the bivariate
correlation (r = .10, N = 1677). Additionally, the Loess regression line indicated a possible
curvilinear relation with a slight uptick in scores at the lowest European ancestry decile. Further
analysis showed that this was due to relatively high scores of individuals from African immigrant
families (MAfrican_immigrant = -.28, N = 60). Limiting our scope to African Americans within US-
born families raises the correlation to r = .13 (N = 1475); for African Americans with 2% to 80%
European admixture, this correlation is r = .11 (N = 1635). These results are shown in Tab S4 of
Supplementary file 3 along with scores by African American subgroups. The full correlation
matrices are also provided in Supplementary File 3.
Figure 2. Regression plot of European ancestry and g in the Black American subsample (N =
We next proceed to the admixture-regression analyses. Since the Black SIRE category
excludes multi-racial individuals, we do not include a term for fraction SIRE in these models. As
seen in Table 2, African ancestry is strongly and significantly negatively related to cognitive
ability in all four models. Amerindian ancestry is also negatively related to g-scores; however,
owing to the low Amerindian admixture among non-Hispanic Blacks and consequently the
high standard errors these estimates are not reliable. Adding ethnic attachment scores in
Model 2 does not change the relationship with Amerindian and African ancestry. As seen in
Model 3, measures of racial discrimination do not mediate the relation between g and ancestry.
Of these variables added to Model 3, only experiences of discrimination had a significant
independent effect. Finally, as seen in Model 4, while SES was significantly related to g, it did
not substantially attenuate the association between African ancestry and g (bAfrican ancestry = -1.08
to -0.89).
Table 2. Regression results for the effect of genetic ancestry on g Among Black Americans (N =
Note: Shown are the beta coefficients (b) and p-values (p) from the mixed effects models with
recruitment site and family common factors treated as random effects. The values in parentheses
are standard errors. The marginal and conditional R2 are provided at the bottom.
2. Hispanic Americans
Figure 3 shows the regression plot for European ancestry and g scores among Hispanic
children. As seen, European ancestry is significantly (r = .23, N = 2021) associated with g scores.
While the R boxplot function indicates that there are 23 outliers, removing these had little effect
on the bivariate correlation (r = .22, N = 1998). The Loess regression line suggests a possible
slight uptick in scores at the lowest European ancestry decile. However, the 95% confidence
intervals of this line (not shown) overlapped with the linear regression line.
Figure 3. Regression plot of European ancestry and g in the Hispanic American subsample (N =
For the Hispanic admixture-regression analyses, we include a term for race because the
Hispanic ethnic category is inclusive of all self-identified racial groups. As shown in Table 3,
both Amerindian and African ancestry are strongly negatively associated with g in the first three
models. Adding SIRE ethnic identity and the ethnic attachment variable in Model 2 had little
effect on the beta for Amerindian ancestry. Doing so increases the effect of African ancestry. In
Model 3, both skin color and experiences of discrimination have significant independent effects
on g, but these variables only slightly attenuated the relation between g and Amerindian and
African ancestry. However, as seen in Model 4, SES attenuated the effect of Amerindian and
African ancestry (Model 3: bafrican ancestry = -0.96 →Model 4: bafrican ancestry = -0.58; Model 3:
bamerindian ancestry = -1.37 →Model 4: bamerindian ancestry = -0.86). Nonetheless, the magnitudes of the
Amerindian and African ancestry effects remained medium to large in size and statistically
Table 3. Regression results for the effect of genetic ancestry on g among Hispanic American
children (N = 2021).
Note: Shown are the beta coefficients (b) and p-values (p) from the mixed effects models with
recruitment site and family common factors treated as random effects. The values in parentheses
are standard errors. The marginal and conditional R2 are provided at the bottom.
3. Other Americans
Figure 4 shows the regression plot for European ancestry and g-scores among the Other group.
European ancestry is significantly (r = .19, N = 748) associated with g scores. Eight outliers were
identified using the R boxplot function. Removing these had little effect on the correlation (r =
.16, N = 740). The Loess regression line show a slight uptick in scores at the lowest European
ancestry decile. However, the 95% confidence intervals of this line overlapped with the linear
regression line. The correlation matrix is provided in the Supplementary File.
Figure 4. Regression plot of European ancestry and g in Other American subsample (N = 748).
As for Hispanics, we include a term for race because the Other American ethnic category is
inclusive of all self-identified racial groups. As seen in Table 4, both coefficients for Amerindian
and African ancestry show a strong negative association with g from Model 1 through Model 4.
Adding SIRE ethnic identity and the ethnic attachment variable in Model 2 has little effect on the
beta for Amerindian ancestry. Doing so increases the effect of African ancestry. In Model 3, only
experiences of discrimination has a significant independent effect on g. The discrimination
variables did not attenuate the relation between g and Amerindian and African ancestry. As seen
in Model 4, SES moderately attenuated the effects of Amerindian and African ancestry (Model
3: bafrican ancestry = -1.38 →Model 4: bafrican ancestry = -1.08; Model 3: bamerindian ancestry = -1.51 →Model
4: bamerindian ancestry = -1.09). Nonetheless, the magnitudes of these ancestry effects remained large
in magnitude and statistically significant.
Table 4. Regression Results for the Effect of Genetic Ancestry on g Among Other Americans
Children (N=748).
Note: Shown are the beta coefficients (b) and p-values (p) from the mixed effects models with
recruitment site and family common factors treated as random effects. The values in parentheses
are standard errors. The marginal and conditional R2 are provided at the bottom.
4. White Americans
We do not report the admixture regression results for the 5911 non-Hispanic White Americans.
These results are unreliable owing to the low dispersion in African and Amerindian ancestry
within this SIRE group (see: Table 1). Thus, we relegate these results to the supplemental
material. Briefly, though, in Model 4 for this subsample, both African ancestry (bAfrican ancestry = -
.85, p = .110) and Amerindian ancestry (bAmerindian ancestry = -.96) also have large negative effects.
However, this effect is only statistically significant for Amerindian ancestry (p = 0.012).
5. Full sample
The results above indicate that factors associated with genetic ancestry are related to g within
SIRE groups. These findings also suggest that these same factors explain differences between
SIRE groups (Halder et al., 2015). Using the full sample, we examine this implication. The
relation between European ancestry and g for the full sample is shown in Figure 5. As expected,
there is a strong positive association for the SIRE groups between ancestry and g (r = .36; N =
10370). Because the range of ancestry is not restricted restriction of range attenuates
correlations the correlation is high. In this plot, we again see the uptick at the lowest decile of
European admixture. This is due to the relatively high scores of children of recent African
Figure 5. Regression plot of European ancestry and g in the full sample (N = 10370).
To examine if SIRE differences can be accounted for by genetic ancestry, we construct a new
set of regression models using the full sample. As seen in Table 5 in the first two models, Model
1a and Model 1b, we include only genetic ancestry variables or alternatively SIRE variables
along with controls for migrant status. As seen in Model 2, none of the SIRE values remain
significant after adding genetic ancestry to the model. These results indicate that ancestry-
associated factors account for the SIRE differences in g. We additionally include a Model 3,
which adds the cultural, socioeconomic, and phenotypic indices. As seen in Model 3, these
variables attenuated the effect of African and Amerindian ancestry (Model 2: bafrican ancestry = -1.31
→Model 3: bafrican ancestry = -0.80; Model 2: bamerindian ancestry = -1.57 →Model 3: bamerindian ancestry = -
0.86), but the ancestry effects remain large. Note that the effects of East Asian and South Asian
ancestry are insignificant because there is little variance in these ancestry components. This is
because we excluded everyone identified as Asian and Pacific Islander.
Table 5. Regression results for the effect of ancestry on cognitive ability in the full sample (N =
Note: Shown are the beta coefficients (b) and p-values (p) from the mixed effects models with
recruitment site and family common factors treated as random effects. The values in parentheses
are standard errors. The marginal and conditional R2 are provided at the bottom.
Finally, we can check the extent to which eduPGS can explain ancestry effects. Before doing
so, we verify that eduPGS are associated with g within each of the SIRE groups. In doing so, we
include controls for the first 20 genetic principal components or, alternatively, continental
ancestry (with European ancestry left as the reference). Moreover, we run the analysis both using
all families and using only singleton families (i.e., families with only one child). The full results
are provided in the supplementary material. The results are summarized in Table 6. As
previously found, the eduPGS by g associations are attenuated among African Americans, but
not among Hispanic and Other Americans (Fuerst et al., 2021). Nonetheless, eduPGS are
significantly associated with g within all SIRE groups.
Table 6. Validities (b) of eduPGS by American SIRE groups from multilevel regression models
with g as a dependent variable and PGS as a predictor
20 PCs
Full sample
Full sample
20 PCs
Note: The samples sizes for the full samples are: Black (N = 1690), Hispanic (N = 2021), Other (N = 748) and White (N
= 5911). The sample sizes for the singletons subsamples are: Black (N = 1159), Hispanic (N = 1516), Other (N = 505)
and White (N = 3674). All betas were statistically significant at the p < .01 level. Singletons = single child families.
For further validation of the PGS, we correlated the eduPGS with the NIHTBX summary
scores which we had for all groups, including Asians. We computed mean scores for all ABCD
SIRE subgroups and combinations with N ≥ 50. There were 17 such groups. We then correlated
the eduPGS with the mean subgroup test scores. This correlation came to r = .93. Thus, we
conclude, in line with Chande et al. (2020), that “the general concordance seen between
genetically inferred (predicted) phenotypic differences and the observed differences for
anthropometric traits, or known prevalence differences in the case of disease traits, supports the
approach taken here” (p. 1525-6), despite concerns raised in the literature. The regression plot is
shown in Figure 6. The number of individuals in each SIRE group is represented by the size of
the associated data point.
Figure 6. Regression plot of eduPGS and NIHTBX scores for the 17 largest SIRE groups in the
ABCD sample with SIRE group sample sizes represented by the size of the data points.
Next, we include the PGS in the model, starting with Model 3 from Table 5. Comparing
Model 3 and Model 4 (which adds eduPGS) of Table 7, we see that eduPGS explains a
substantial portion of the residual effect of African and Amerindian ancestry after controls for
Table 7. Regression results for the effect of eduPGS and ancestry on cognitive ability in the full
Note: Shown are the beta coefficients (b) and p-values (p) from the mixed effects models with
recruitment site and family common factors treated as random effects. The values in parentheses
are standard errors. The marginal and conditional R2 are provided at the bottom.
We also examine the individual SIRE subsample results for eduPGS. The model adds
eduPGS to the respective Model 4s for each SIRE group (i.e., the model with potential
environmental factors included). The full results are provided in the Supplementary File. These
results are summarized in Table 8. Specifically, Table 8 shows the effects for Amerindian and
African ancestry on g with possible environmental controls. These come from the fourth models
of Tables 2, 3, 4, and S8 and the third model from Table 5. It next shows the effects when
eduPGS is added. As seen, eduPGS accounts for a portion of the ancestry by g association in all
SIRE subsamples.
Table 8. Effects (b) of Amerindian and African ancestry on g in multi-level models with
environmental controls (Model 4/3), and multi-level models with environmental controls and
eduPGS (Model 5)
Model 4
Model 5
Model 4
Model 5
Model 4
Model 5
Model 4
Model 5
Model 3
Model 5
It is conceptually possible that our eduPGS are just capturing global ancestry effects. Our
ancestry components are based on more SNPs. Moreover, they are not weighted by trait-
associations which will attenuate the association with ancestry. As such this is unlikely.
However, to test this possibility we created pseudoPGS. To do so, we used PLINK v1.90b6.8 to
select random sets of 8,898 variants to match the eduPGS. Then we randomly assigned the
eduPGS beta weights (from Lee et al., 2018) to the respective sets of SNPs.
Following this procedure, we create 10 pseudo eduPGS scores. This procedure produced
PGS with the same set of SNPs as the SNPs used to calculate genetic ancestry, but randomized
trait-association information. The full results are provided in Supplementary File 3, Table S17.
Unlike the real PGS, these pseudoPGS had no validity independent of genetic ancestry. This is
because of the random assignment of eduPGS betas to the SNP frequencies resulting in poor
indices of ancestry. Generally, we conclude that PGS will not necessarily capture effects of
global ancestry. This finding suggests that our eduPGS are in fact capturing causal genetic
effects on g both within and between ancestries.
Genetic ancestry measures provide very powerful scientific value in studying SIRE differences
in g. Using ancestry allows one to examine how the trait varies by genetic ancestry within self-
identified racial and ethnic groups. Doing so offers a potential solution to the problem of
decomposing genetic and environmental variance (Halder et al., 2015). Admixture regression has
been widely applied to medical and behavioral traits. This includes Type 2 Diabetes (Cheng et
al., 2013), asthma (Salari et al., 2005), blood pressure (Klimentidis et al., 2012), and sleep depth
(Halder et al. 2015). Admixture regression has a natural application to studying g.
Here we apply this technique to examine SIRE differences in g. We find that African and
Amerindian ancestry are strongly negatively associated with general cognitive ability among
African, Hispanic, and other American subsamples. This replicates previous research which
showed that genetic ancestry predicts cognitive ability, independent of social economic status
and phenotypic discrimination variables which are the usual suspects (Kirkegaard et al., 2019;
Lasker et al., 2019; Warne, 2020). The importance of such analyses within SIRE groups is that
they shed light on the cause of g differences between SIRE groups with respect to similarities in
developmental processes (Rowe, Vazsonyi, Flannery, 1994).
The ancestry effects are consistent in direction across subsamples and hold after controlling
for a wide array of economic and social factors, including migrant status, SIRE, ethnic
attachment, measures of discrimination, phenotypic indices of race, and general SES. These
results suggest that African, Hispanic, and other groups have inherited alleles from their African
and Amerindian ancestors which make them liable to lower levels of g. In fact, as seen in Table 5
(Model 2), 100%, 76%, 81%, and 100% of the respective Black, Native American, Other, and
Hispanic SIRE effects were explained by genetic ancestry. This association between genetic
ancestry and g suggests a partial genetic basis for observed SIRE differences.
This inference is supported by additional findings based on the eduPGS analyses. These
polygenic scores were found to be predictive of g within SIRE groups controlling for the first 20
principal components and for ancestry. Moreover, they explain a substantial portion of the
ancestry effects both in the full sample and all subsamples. Also, they were almost perfectly
correlated with SIRE group means in cognitive ability (r = .93). The most parsimonious
explanation for this, given the apparent absence of obvious forms of confounding (Fuerst et al.,
2021), would seem to be that eduPGS are capturing causal effects of genes on g both within and
between ancestry groups and thus also SIRE groups. Firm conclusions, though, will require a
better understanding of the relation between polygenic scores and ancestry (Lawson et al., 2020;
Fuerst et al., 2021).
It is worth emphasizing that our g scores were from a confirmatory factor model in which
strict factorial invariance (SFI) held between SIRE groups. SFI entails that the differences
between SIRE groups have the same psychometric meaning as the differences between
individuals within these groups (i.e., the scores are psychometrically unbiased). Moreover, SFI
implies that the causes of group differences are a subset of the causes of the individual
differences within groups (Lubke, Dolan, Kelderman, & Mellenbergh, 2003; Dalliard, 2014). In
this sample of children, individual differences in general cognitive ability are largely due to
genes (Freis, Morrison, Lessem, Hewitt, & Friedman, 2020).
It should be noted that the polygenic scores represent genetic variation that is caused by
common alleles, not genetic variation that is caused by rare alleles under mutation-selection
balance. The causal alleles that are tapped by polygenic scores are ancient. Most were already
polymorphic 60,000 years ago when people left Africa and spread all over Eurasia. Today’s
racial allele frequency differences are the cumulative effects of selection and genetic drift acting
over more than 2,000 generations, while rare variants under mutation-selection balance are much
younger, no more than one or two millennia or even less. Therefore it is predictable that genetic
race differences that evolved over a long time are differences in polygenic scores but not
necessarily differences in mutational load. The latter are the result of strength of selection during
the last centuries.
Overall, the results suggest that genetic variants related to general cognitive ability vary
between source genetic populations and have a causal effect on intelligence. Because individuals
within SIRE groups differ in their proportion of African, European and Amerindian ancestors,
general cognitive ability varies by genetic ancestry within SIRE groups.
This study advances over previous studies in that we used a diverse national sample, a good
measure of g, multiple indices of racial discrimination, including multiple race-associated
phenotype, a composite index of SES based on seven different indices. Moreover, our multilevel
model controlled for the effects of geography. Unfortunately, our index of skin color was
imperfect. However, it seems unlikely that skin color discrimination is a significant immediate
cause of g differences among 9-10 year old children. Such color discrimination explanations
usually propose labor market based discrimination (Hersch, 2011), which would be captured by
our index of SES. Regardless, admixture-regression results can only provide indirect evidence
for a genetic hypothesis since there could be unmeasured environmental factors that are related
to both ancestry and cognitive ability.
While the results also show that educational and intelligence-related polygenic scores can
account for some of the effects of ancestry on g, these results are only tentative. It is not certain
that these PGS are capturing genetic effects, at least between ancestries (Fuerst et al., 2021).
Thus these results do not provide definitive evidence for a genetic hypothesis. However,
following the methodology of genetic epidemiology, admixture regression analyses are just a
first step in elucidating the genetic and environmental causes of group differences.
Author Contributions
All analyses were conducted by JGRF under the guidance of BJP. MH and GC helped prepare
the manuscript.
Data used in the preparation of this article were obtained from the Adolescent Brain Cognitive
DevelopmentSM (ABCD) Study (, held in the NIMH Data Archive
(NDA). This is a multisite, longitudinal study designed to recruit more than 10,000 children age
9-10 and follow them over 10 years into early adulthood. The ABCD Study® is supported by the
National Institutes of Health and additional federal partners under award numbers
U01DA041048, U01DA050989, U01DA051016, U01DA041022, U01DA051018,
U01DA051037, U01DA050987, U01DA041174, U01DA041106, U01DA041117,
U01DA041028, U01DA041134, U01DA050988, U01DA051039, U01DA041156,
U01DA041025, U01DA041120, U01DA051038, U01DA041148, U01DA041093,
U01DA041089, U24DA041123, U24DA041147. A full list of supporters is available at A listing of participating sites and a complete listing
of the study investigators can be found at ABCD
consortium investigators designed and implemented the study and/or provided data but did not
necessarily participate in the analysis or writing of this report. This manuscript reflects the
research results and interpretations of the authors alone and may not reflect the opinions or views
of the NIH or ABCD consortium investigators. The ABCD data repository grows and changes
over time. The ABCD data used in this report came from Version 3.01. The raw data are
available at Instructions on how to create an
NDA study are available at Additional support
for this work was made possible from supplements to U24DA041123 and U24DA041147, the
National Science Foundation (NSF 2028680), and Children and Screens: Institute of Digital
Media and Child Development Inc.
Additionally, we thank Jordan Lasker for guidance with the MGCFA analysis code. We also
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Supplemental File 1: Supplemental Material for Global Ancestry and Cognitive Ability in a Sample of
American Youths: Multi-Group Confirmatory Factor Analysis
1. Data Preparation
The following variables were used to perform a multiple-group confirmatory factor analysis
(MGCFA) of the cognitive tests used in the Adolescent Brain Cognitive Development cohort.
Additional details about these tests and their battery can be found at the website for the study.
The tests used were:
Picture Vocabulary
List Sorting
Card Sorting
Pattern Comparison
Picture Sequence Memory
Oral Reading Recognition
The WISC Matrix Test
The Little Man Test
The Rey Auditory Verbal Learning Test (RAVLT): Immediate
RAVLT: Delayed
To delineate SIRE groups, we used ABCD’s race_ethnicity variable which organizes
individuals into 5 mutually exclusive categories (single race, non-Hispanic White, “White”;
single race, non-Hispanic Black, “Black”; Hispanic of any race, “Hispanic” (this group is known
to be very heterogeneous in self-description and ancestry as will be shown with ternary plots
and other methods); single race, non-Hispanic Asian; “Asian”; and a residual non-Hispanic
other groups, “Other”). These classifications were based on parental responses to 18 questions
asking about the child’s race and one question asking about ethnicity. Non-Hispanic children
who were reported to belong to two or more races were classified as Other (a heterogeneous
collection of different groups, primarily composed of individuals who identify as more than one
race. The Asian group was not included due to its minute sample size coupled with its
considerable ethnic heterogeneity (as it includes both South and East Asians). In addition to
removing the Asian category, we removed any individual who was identified as Asian with the
multiple choice SIRE questions. This includes Asians classified as Hispanic and also multi-racial
individuals, classified as Other, who were identified as being part Asian. For these MGCFA
analyses, we included individuals with missing admixture and genetic-based scores. However
we also verified that the results held for the subsets not missing these data.
Outlier detection was the first step of data preparation. Rosner tests were run to reduce
the possibility that observations near outliers would be masked (see Rosner, 1983). These were
conducted at the level of the individual test and indicated eighteen outliers in the dataset of, at
this point, n = 11,124. Eleven of these outliers were from the List Sorting test, while four of them
came from the Picture Vocabulary test, one of them came from the Flanker test, and one of them
was from the Little Man test. Removing only the outlier test scores for these individuals and
imputing their artificially missing scores did not affect the results1 because they made such a
minor contribution to the aggregate sample. Additionally, retaining these outliers did not affect
the results of any analyses, only affecting the assessment of differences between linear and
nonlinear age-score relationships. As such, primary analyses do not involve these eighteen
observations since we did not want to deal with assumptions about the reasons for their
outlying score. To some, the inclusion of these people would taint subsequent analyses even
though our results were robust to their imputation and inclusion.
The second step of data preparation was assessment of missingness and subsequent
imputation of missing data. The largest amount of missingness was observed for the Little Man
Test, with 2.84% of cells missing. This was followed by the Delayed RAVLT, which had 2.28% of
observations missing, then by the Matrix Test, which was missing 2.11% of observations, and
then by the Immediate RAVLT, which was missing 1.80% of observations. List Sorting was
missing 1.72%, followed by Pattern Comparison which was missing 1.49%, then Oral Reading
Recognition with 1.41%, Picture Sequence Memory with 1.40%, Flanker and Card Sorting with
the same 1.34%, and finally Picture Vocabulary, with 1.30%. Before imputation was conducted,
we assessed the possibility of score and demography-related patterns of missingness,
observing, firstly, that there were no differences in missingness for certain tests based on scores
on other tests, nor differences by age (average = 118.96 months, SD = 7.48, range = 107-133
months), broad race/ethnicity (see the description of the variable “race_ethnicity” for more
detail) or sex (n female = 5,299 and male = 5,807). With no pattern to demographic or score-
based missingness, we conclude that imputation is viable since it does not appear that there is
systematic missingness by any variable relevant to our focal analyses. For completeness’ sake,
we ran our analyses with the removal of all cells with missingness and there were no
differences. In virtually every case, there were no differences in results to three decimal places,
excepting those for χ2, which did not differ enough to affect the interpretation of our results.
After finding that missingness did not present any immediately discernible rhyme nor reason,
we utilized Iterative Robust Model-Based Imputation or IRMI (Templ et al., 2011) with our
convergence threshold set to 5, the number of multiple imputations set to 1, and our maximum
number of iterations set to 100 using the R package VIM (Kowarik & Templ, 2016). Two
observations had to be removed to make this possible, since they included no responses to any
cognitive test.
Subsequent aspects of data preparation involved adjustment for criteria like age, sex,
assessment site, and family ID, but all analyses were run with all combinations of these
adjustments and the lack thereof as well as adjustments on a per-group rather than an
1 This sort of remark refers to the results of supplementary analyses throughout this supplement.
aggregated basis, with no alteration of our ultimate results. Therefore, we consider these results
to be robust to these corrections, even if the results presented in this supplement are concerned
primarily with fully aggregately adjusted data.
Our first adjustment involved age. We investigated the possibility of nonlinear effects of
age by comparing linear regressions to Savitzsy-Golay filter (i.e., LOESS) results for the age-test
score relationship at the level of each individual test. There were no meaningful differences
between LOESS and linear regression. Next, we observed that all residuals were near-zero for
the linear regressions of age on test scores and that they were all nearly normal, though there
were clear ceiling and floor effects in the areas where observations were scant on many of the
tests. Trimming to remove those effects on a per-test basis where the ceiling or floor appear to
begin did not affect the results; this was rerun with trimming at plus and minus 0.1 standard
deviations from that point to no effect.
We assessed the same results for restricted cubic splines (RCS; with three to nine splines)
and generalized additive models (GAM) with little difference. We then compared the χ2 and
AIC values of these models, using a p value of 0.05 and a p value – adjusted to be comparable to
0.05 at our large sample size – of 0.000007 (see Naaman, 2016). When presented, p values are not
rounded based on the next significant digit to avoid improper rounding issues; when they are
highly significant or insignificant, however, they are presented based on a boundary p value
like 0.05. We focus on the scaled results, since those were more likely to be accurate given our
large sample. We reran models where possible if p values <0.05 were indicated and this did not
change our results. In terms of χ2, the RCS and GAM models did not fit better except for the
Matrix Test: the RCS fit best for the Matrix Test but adjusting for it did not affect our results, so
we residualized for it like the rest of the tests anyway. In terms of AIC, the GAM was the best fit
for Picture Vocabulary, the Matrix Test, and the Delayed RAVLT. The RCS fit best in terms of
AIC for Flanker. Adjusting for age based on GAMs or RCS did not change our ultimate results.
This may be because of the effect of sample size on AIC, where the differences of between six
and forty-six points ought to have been considered negligible. We did not consider the GAM a
better fit when indicated by AIC when the degrees of freedom of the GAM were also negative,
since this represented an invalid model. However, adjusting for those invalid GAMs also did
not affect results.
Regardless of the reasons for the lack of effect, it is beyond this paper to ascertain them.
What is certain, however, is that it ultimately did not affect results following adjustment.
Breusch-Pagan tests were insignificant for all regressions except for Picture Vocabulary and the
Little Man test. The same pattern was observed for non-constant variance score tests with the
addition of Flanker. Despite this, our MGCFA results did not differ whether they were typical
or robust, perhaps due to the small number of affected tests. The results also did not differ
when the three tests were excluded in pairs. This was a possibility for testing because they were
loaded on factors with three indicators without them, albeit with other biased indicators forced
to be included (i.e., Flanker plus Picture Vocabulary or Little Man plus Picture Vocabulary
removed). With the model refit with equal factor loadings for the two remaining subtests with
all of them excluded, results, surprisingly, differed only marginally. Finally, we fit a local
structural equation model (Hildebrandt et al., 2009, 2016) across our range of ages (in months,
with a bandwidth of two). RMSEA and CFI were not appreciably better or worse across the
range of ages and there was no change in BIC from the youngest to the oldest ages.
Our second adjustment involved correcting for sex in the outlier-pruned, age-adjusted
data. To qualify adjustment by sex, we tested an MGCFA by sex. We fit our model based on the
theoretical model of the tests in the ABCD (Citation Here). The group factors modeled were
dubbed Complex Cognition (COC), Memory (MEM), and Executive Function (EF); these are
pictured below. Because the number of factors was three, there were no differences in fit
between a higher-order factor model in which g sat atop the group factors and one in which a
model with correlated group factors was fit; a bifactor model did fit better, but we elected not to
pursue testing with this model because it is not acceptable on theoretical grounds (Hood, 2010),
although this can be subject to change given certain results not presently found in the literature
on intelligence (e.g., common pathway models supporting a bifactor model over a higher-order
one). The model required three residual covariances, between Picture Sequence Memory and
the Matrix Test, List Sorting, and Card Sorting. Model fits are provided in Table S1.
Table S1. Model Fit Statistics for the ABCD Sex MGCFA
Model Description
Partial Scalar*
Latent Variances
Latent Means
Partial Scalar*
Latent Variances
Latent Means
Latent Means Group Factors
Latent Means MEM and EXE**
Latent Means MEM, EXE, and g
* The intercepts for the Little Man Test, Matrix Test and Flanker were freed. ** We tested among
models of all possible individual group factor constraints and used BIC to decide among them.
In the higher-order model prior to any mean constraints, differences in g amounted to an
insignificant (p = 0.015) 0.053 g female advantage, a 0.165 g advantage in MEM and a 0.149 g
advantage in EXE with a 0.118 g deficit in COC. These came with Z values of 2.444, 9.365, 7.037
and 16.231, respectively. In a model without differences in g, the group differences in MEM,
COC, and EXE, respectively, were 0.198, -0.070 (not significant, p = 0.003), and 0.183 in favor of
the female group (Zs = 9.692, 2.994 and 7.374). The only major difference between the male and
female groups was in the variances of their factors. For example, the standard deviations for the
factor scores for g, COC, MEM, and EXE were 0.922, 2.314, 1.220, and 1.263 for males versus
0.837, 2.134, 1.176, and 1.098 for females. SDI2, an effect size for invariance violations proposed
by Gunn et al., (2020), yielded values of 0.140, -0.154 and -0.242 for the Matrix Test, Flanker, and
Little Man Test (positive = favors the female group and vice-versa). Thus, all the violations of
invariance observed had small-to-moderate effects. Since we aimed to use factor scores, which
are unaffected by this, and all groups had very similar sex ratios, we corrected for sex. We also
corrected for assessment site and family ID. Invariance by site could not be reasonably assessed
due to the small samples found in some sites. To the extent this was the case, family ID was
worse. Adjusting or not adjusting, the results were the same; adjustment was still done to
obviate concern about the results.
2. Multiple Group Confirmatory Factor Analysis for Blacks, Whites, Hispanics, and Other
After preparing the cognitive data for analysis by self-described race or ethnicity, we
performed an MGCFA with the same model used to assess invariance for sex. There were 6,176
participants in the White group, 1,780 in the Black group, 2,318 in the Hispanic group, and 830
in the “Other” group. With the full sample of 11,104 being used, the cutoff Z-value used was
4.34. Our MGCFA model fit results are as follows in Table S2. Table S5 contains the means and
standard deviations for the resulting factor scores with the latter in parentheses while Tables S3-
S4 contain the means from the MGCFA model in units of Hedge’s g. The Hispanic group’s
means were set to 0. The other groups are compared relative to them. The gaps from the best-
fitting mean model (i.e., the strong form of Spearman’s hypothesis where only g causes
differences; all results are in units of Hedge’s g) were -0.584 for Blacks, 0.022 for “Other”, and
0.523 for Whites. Both the strong form of Spearman’s hypothesis and the model with both the
MEM and EXE factors constrained (M6B) had nearly equivalent fits. CFI was lower for the
Table S2. Model Fit Statistics for the ABCD Race and Ethnicity MGCFA
Model Description
χ2 df CFI RMSE
Partial Scalar*
Partial Strict**
Latent Variances
Latent Means
Partial Scalar*
Partial Strict**
Latent Variances
Latent Means
Latent Means Group Factors
Latent Means MEM and EXE
Latent Means MEM, EXE,
and g
2125.01 239 0.934 0.053 306476
* The intercepts for the Picture Vocabulary and Picture Sequence Memory Tests were freed. ** The
variances for Flanker, Card Sorting and Pattern Comparison were freed.
Our criteria for not moving to partial invariance was stricter than what is typical in the
literature on MGCFA, but we believe it is justified to understand which tests might be biased
for users of the ABCD data. The page below contains a plot of factor scores for g by group.
Table S3. Group Differences in the ABCD (MGCFA; Latent Variance Model)
General Intelligence
Executive Function
Complex Cognition
The Hispanic group is the comparison group, whose means are set to 0.
Table S4. Group Differences in the ABCD (MGCFA; Spearman’s Weak Hypothesis Model)
General Intelligence
Executive Function
Complex Cognition
The Hispanic group is the comparison group, whose means are set to 0.
Table S5. Group Differences in the ABCD (Factor Scores from Latent Variance Model)
General Intelligence
Executive Function
Complex Cognition
0.306 (0.724)
0.235 (1.149)
0.312 (0.995)
1.090 (1.664)
-0.481 (0.897)
-0.537 (1.217)
-0.519 (1.057)
-1.140 (1.985)
0 (0.819)
0 (1.159)
0 (1.049)
0 (1.903)
0.017 (0.912)
-0.065 (1.246)
0.007 (1.104)
0.140 (2.117)
Note: Standard deviations (SDs) are in parentheses. Note, within SIRE groups the SDs are not 1.
Gunn, H. J., Grimm, K. J., & Edwards, M. C. (2020). Evaluation of Six Effect Size Measures of
Measurement Non-Invariance for Continuous Outcomes. Structural Equation Modeling: A
Multidisciplinary Journal, 27(4), 503–514.
Hildebrandt, A., Lüdtke, O., Robitzsch, A., Sommer, C., & Wilhelm, O. (2016). Exploring Factor
Model Parameters across Continuous Variables with Local Structural Equation Models.
Multivariate Behavioral Research, 51(2–3), 257–258.
Hildebrandt, A., Wilhelm, O., & Robitzsch, A. (2009). Complementary and competing factor
analytic approaches for the investigation of measurement invariance. Review of
Psychology, 16(2), 87–102.
Hood, S. B. (2010). Latent Variable Realism in Psychometrics.
Kowarik, A., & Templ, M. (2016). Imputation with the R Package VIM. Journal of Statistical
Software, 74(1), 1–16.
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paradox. Electronic Journal of Statistics, 10(1), 1526–1550.
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standard and robust methods. Computational Statistics & Data Analysis, 55(10), 2793–2806.
Supplemental File 2. Supplemental Material for Global Ancestry and Cognitive Ability in a Sample of
American Youths: Socioeconomic Status
1. Data
Seven indicators were used to compute socioeconomic status: financial adversity, area
deprivation index, neighborhood safety protocol, parental education, parental income, parental
marital status, and parental employment status. These are detailed below:
1. Financial Adversity: The seven item Financial Adversity Questionnaire (PRFQ) was
administered to parents. They were asked: “In the past 12 months, has there been a time when
you and your immediate family experienced any of the following:
(1) “Needed food but could not afford to buy it or could not afford to go out to get it?” (1 =
“yes”, 0 = “no”),
(2) “Were without telephone service because you could not afford it?” (1 = “yes”, 0 = “no”),
(3) “Did not pay the full amount of the rent or mortgage because you could not afford it?” (1 =
“yes”, 0 = “no”),
(4) “Were evicted from your home for not paying the rent or mortgage?” (1 = “yes”, 0 = “no”),
(5) “Had services turned off by the gas or electric company, or the oil company would not
deliver oil because payments were not made?” (1 = “yes”, 0 = “no”),
(6) “Had someone who needed to see a doctor or go to the hospital but did not go because you
could not afford it?” (1 = “yes”, 0 = “no”), and
(7) “Had someone who needed a dentist but could not go because you could not afford it?” (1 =
“yes”, 0 = “no”)
We summed responses (maximum: 7; minimum: 0) and reverse coded the variable so that
higher scores indicated less financial adversity, The results were then standardized.
2. Area Deprivation Index (ADI): Parents completed a residential history questionnaire including
residential addresses and the number of full years they lived at each residence. ABCD computed
Area Deprivation Index (ADI) for each residential address based on the following variables:
1. “Percentage of occupied housing units without complete plumbing (log)”
2. “Percentage of occupied housing units without a telephone”
3. “Percentage of occupied housing units without a motor vehicle”
4. “Percentage of single”
5. “Percentage of population below 138% of the poverty threshold”
6. “Percentage of families below the poverty level”
7. “Percentage of civilian labor force population aged >=16 y unemployed
(unemployment rate)”
8. “Percentage of occupied housing units with >1 person per room (crowding)”
9. “Percentage of owner
10. “Median monthly mortgage”
11. “Median gross rent”
12. “Median home value”
13. “Income disparity defined by Singh as the log of 100 x ratio of the number of
households with <10000 annual income to the number of households with >50000
annual income”
14. “Median family income”
15. “Percentage of population aged >=25 y with at least a high school diploma”
16. “Percentage of population aged >=25 y with <9 y of education”
Scores were provided in terms of national percentiles. We used scores for the most recent
residence (variable: reshist_addr1_adi_perc). The resultant values were reverse coded to make
higher values indicate better neighborhoods, and then standardized.
3. Neighborhood Safety Protocol: Parents were asked three Likert scale questions about
neighborhood safety: “I feel safe walking in my neighborhood, day or night,” “Violence is not a
problem in my neighborhood,” and “My neighborhood is safe from crime” (1 = strongly
disagree; 5 = strongly agree). ABCD pre-computed means scores based on these three questions
(Minimum =1; Maximum =5) (variable: nsc_p_ss_mean_3_items). We standardized these
4. Education: Parents were asked about educational attainment: “What is the highest grade or
level of school you have completed or the highest degree you have received.” We recoded
responses to create interval scores (ranging from 0 to 18): Never attended/Kindergarten only = 0,
1st grade = 1, 2nd grade = 2, 3rd grade = 3, 4th grade = 4, 5th grade = 5, 6th grade = 6, 7th
grade = 7, 8th grade = 8, 9th grade = 9, 10th grade = 10, 11th grade = 11, 12th grade = 12, High
school graduate =12, GED or equivalent Diploma General =12, Associate degree: Occupational
Program =14, Associate degree: Academic Program = 14, Bachelor's degree = 16, Master's
degree = 18, Professional school = 18, Doctoral degree = 18. We standardized the recoded
educational scores for each parent, averaged the standardized scores, and then standardized the
5. Income: Parents were asked about total family income in the past 12 months. We recoded the
variable to a dollar amount scale: 1.00 = less than $5000 (recode: 4,500); 2.00 = $5000 to 11,999
(recode: 5,000); 3.00 = $12,000 to 15,999 (recode: 12,000); 4.00 = $16,000 to 24,999 (recode:
16,000); 5.00 = $25,000 to 34,999 (recode: 25,000); 6.00 = $35,000 to 49,999 (recode: 35,000);
7.00 = $50,000 to 74,999 (recode: 50,000); 8.00 = $75,000, to 99,999 (recode: 75,000); 9.00 =
$100,000 to 199,999 (recode: 100,000); 10.00 = $200,000 and greater (recode: 200,000). The
recoded variable was standardized.
6. Marital Status: The responding parent was asked about their relationship status. Parental
marital status was coded as 1 if married and 0 for any other arrangement (widowed, divorced,
separated, never married, living with partner, or refused to answer)
7. Employment Status. The responding parent was asked about their and their partner’s
employment status. Parental employment was coded as 1 if at least one parent was working now
either full or part time and 0 for all other cases.
2. Analysis
SES: We imputed missing data for the 7 SES indicators using the mice package (df, m=5,
maxit = 50, method = 'pmm', seed = 500). We then standardized the five continuous variables
(i.e., everything except marital and employment status). After, we submitted the variables to
Principal Component Analysis (PCA), using the R package PCAmixdata to handle mixed
categorical and continuous data (Chavent, Kuentz-Simonet, & Saracco, 2014). The first
unrotated component explained 42% of the variance in the full sample. The loadings are shown
in Table S1 below. This summary SES score correlated at r = .38 with g in the full sample. The
correlation matrix for the full sample is shown in Table S1.
Table S1. Principal Component Loadings for the Seven Socioeconomic Indicators.
We also checked the congruent coefficients for the SIRE group PC_loadings. These were .97 or
greater indicating the same structures across SIRE groups.
Marie Chavent, Vanessa Kuentz-Simonet, Amaury Labenne, Jérôme Saracco. Multivariate
Analysis of Mixed Data: The R Package PCAmixdata. 2017. hal-01662595
ResearchGate has not been able to resolve any citations for this publication.
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