Investigating the Genetic Architecture of Non-Cognitive Skills Using GWAS-by-Subtraction

<jats:title>Abstract</jats:title><jats:p>Educational attainment (EA) is influenced by cognitive abilities and by other characteristics and traits. However little is known about the genetic architecture of these “non-cognitive” contributions to EA. Here, we use Genomic Structural Equation Modelling and results of prior genome-wide association studies (GWASs) of EA (N = 1,131,881) and cognitive test performance (N = 257,841) to estimate SNP associations with variation in EA that is independent of cognitive ability. We identified 157 genome-wide significant loci and a polygenic architecture accounting for 57% of genetic variance in EA. Phenotypic and biological annotation revealed that (1) both cognitive and non-cognitive contributions to EA were genetically correlated with socioeconomic success and longevity; and (2) non-cognitive contributions to EA were related to personality, decision making, risk-behavior, and increased risk for psychiatric disorders; (3) non-cognitive and cognitive contributions to EA were enriched in the same tissues and cell types, but (4) showed different associations with gray-matter neuroimaging phenotypes.</jats:p>

section_content: approach: We focused on genetic variation in educational outcomes not explained by genetic variation in cognitive ability. Specifically, we applied Genomic Structural Equation Modeling (Genomic-SEM) 22 to summary statistics from GWASs of educational attainment (EA) 23 and CP 23 (Figure 1 ). Both EA and CP were regressed on a latent factor, which captured genetic variance in CP (hereafter "Cog"). EA was further regressed on a second latent factor capturing genetic variance in EA independent of CP, hereafter "NonCog". By construction, genetic variance in NonCog was independent of genetic variance in Cog (rg=0). In other words, the NonCog factor represents residual genetic variation in educational attainment that is not accounted for by the Cog factor. These two latent factors were then regressed on individual SNPs, yielding a GWAS of the latent constructs Cog and NonCog. 

The NonCog latent factor accounted for 57% of genetic variance in EA. LD Score regression analysis estimated the NonCog SNP-heritability as h 2 NonCog=. 0637 (SE=. 0021). After Bonferroni correction, GWAS of NonCog identified 157 independent genome-wide significant lead SNPs (Figure 2 ) (independent SNPs defined as outside a 250Kb window, or within a 250Kb window and r 2 < 0. 1). As SNP associations on CP are entirely mediated by the Cog latent factor, results from the GWAS of Cog parallel the original GWAS of CP reported by Lee et al. (2018) 23 and are reported in Supplementary Note 1.

section_content: Cholesky model as fitted in Genomic SEM, with path estimates for a single SNP included as illustration. SNP, Cognitive performance (CP) and Educational attainment (EA) are observed variables based on GWAS summary statistics. The genetic covariance between CP and EA is estimated based on GWAS summary statistics for CP and EA. The model is fitted to a 3x3 observed variancecovariance matrix (i. e. SNP, CP, EA). Cog and Non-Cog are latent (unobserved) variables. The covariances between CP and EA and between Cog and NonCog are fixed to 0. The variance of the SNP is fixed to the value of 2pq (p = reference allele frequency, q = alternative allele frequency, based on 1000 Genomes phase 3). The variances of CP and EA are fixed to 0, so that all variance is explained by the latent factors. The variances of the latent factors are fixed to 1. The observed variables CP and EA were regressed on the latent variables resulting in the estimates for the path loadings: λCog-CP=. 4465; λCog-EA=. 2305; λNonCog-EA=. 2432. ) and independent (within a 250Kb window and r 2 <. 1) associations.
section_name: Figure 1. GWAS-by-subtraction Genomic-SEM model.

section_name: Figure 2. Manhattan plot of SNP associations with NonCog. Plot of the -log10(p-value) associated with the Wald test of βNonCog for all SNPs, ordered by chromosome and base position. Purple triangles indicate genome-wide significant (p < 5e10

section_content: To establish if the Genomic-SEM GWAS-by-subtraction succeeded in isolating genetic variance in education that was independent of cognitive function, we investigated whether NonCog genetically correlated with measures related to educational attainment and cognitive function and compared genetic correlations with Cog. We also confirm these results by conducting polygenic score (PGS) meta-analysis in 6 independent cohorts from the Netherlands (Netherlands Twin Register 24 [NTR]), the U. S. (Texas Twin Project 25 ; National Longitudinal Study of Adolescent to Adult Health 26 [AddHealth], Wisconsin Longitudinal Study 27 [WLS]), New Zealand (Dunedin Longitudinal Study 28 ), and the United Kingdom (E-Risk 29 ). Results reported in this preprint omit polygenic score analysis of the Dunedin and E-Risk cohorts. Effect-sizes for rg and PGS analysis are reported in Figure 3 and Supplementary Figure 2 and Supplementary Tables 4, 5 and 9. Findings were parallel for analysis of educational attainment. To compute rg among NonCog, Cog, and educational attainment, we re-ran the Genomic-SEM model using summary statistics that omitted the 23andMe sample from the EA GWAS. We then computed the rg between NonCog (estimated without 23andMe) and EA in the 23andMe sample. NonCog was more strongly associated with EA than was Cog (NonCog rg =. 71 (SE=. 02), Cog rg=. 57 (SE=. 02), pdiff <. 0001). In PGS analysis based on the full Genomic-SEM model including 23andMe, effect-sizes for associations with educational attainment were similar for NonCog and Cog (AddHealth, WLS and NTR meta-analysis NonCog =. 22 (SE=. 03), Cog =. 22 (SE=. 02), pdiff=. 63, total N=21,365; Dunedin and E-Risk analysis pending). 

NonCog genetics have similar associations with socioeconomic attainment and longevity as compared to Cog genetics. The public-health significance of educational attainment is partly due to its relationship with long-term economic and health outcomes 31, 32. 

We therefore tested if NonCog was related to these long-term outcomes and if magnitudes of associations were similar to those for Cog. Socioeconomic Attainment. In genetic correlation analysis, NonCog was as stronglyor more stronglyassociated with socioeconomic attainment outcomes, as compared to Cog (for income 33 Longevity. We estimated rg with longevity as proxied by parental lifespan 34. Genetic correlations were similar for NonCog and Cog (NonCog rg=. 32 (SE=. 07); Cog rg=. 36 (SE=. 07); pdiff_fdr=. 71). In Genomic-SEM analysis, NonCog explained 50% of the rg between EA and longevity. 

In sum, validation analysis found NonCog genetics were less-related to cognitive-and academic-ability phenotypes as compared to Cog genetics, but showed comparable associations with academic-, economic-and health-attainment phenotypes. These findings are consistent with GWAS-by-subtraction analysis having identified genetic influences on noncognitive skills important to achievement in school and beyond.
section_name: Phenotypic Annotation I: Validating the NonCog Factor

section_content: Our next set of phenotypic annotation analyses investigated connections between the NonCog factor and phenotypes linked with non-cognitive skills within the disciplines of economics and psychology (Figure 3 ). NonCog genetics were associated with decision-making preferences. In economics, non-cognitive influences on achievement and health are often studied in relation to decisionmaking preferences [35] [36] [37] [38]. NonCog was genetically correlated with higher levels of comfort with risk-taking 39 (risk tolerance rg=. 10 (SE=. 03)) and willingness to forego immediate gratification in favor of a larger reward at a later time 40 (delay discounting rg=-. 52 (SE=. 08)). In contrast, Cog was genetically correlated with generally more cautious decision-making characterized by lower levels of risk tolerance (rg=-. 35 (SE=. 07), pdiff_fdr<. 0001) and moderate delay discounting (rg=-. 10 (SE=. 02), pdiff_fdr=. 0852).
section_name: Phenotypic Annotation II. Exploring Genetic Correlates of the NonCog Factor

section_content: fertility. An alternative approach to studying non-cognitive skills in economics and other social sciences is to infer individual differences in non-cognitive skills from patterns of risk behavior. In genetic correlation analysis of obesity 41, substance use 39, [42] [43] [44] [45], and sexual behaviors and early fertility 39, 46, 47, NonCog was consistently genetically correlated with lower levels of risk (rg range. 2-. 5), with the exception that the rg with alcohol use was not different from zero and rg with cannabis use was positive. Genetic correlations for Cog were generally in the same direction but of smaller magnitude. 

NonCog genetics were associated with a broad spectrum of personality characteristics linked with social and professional competency. In psychology, noncognitive influences on achievement are conceptualized as personality traits, i. e. patterns of stable individual differences in emotion and behavior. The model of personality that has received the most attention in genetics is a five-factor model referred to as the Big-5. Genetic correlation analysis of the Big-5 personality traits [48] [49] [50] revealed NonCog genetics were most strongly associated with Openness to Experience (being curious and eager to learn; rg=. 30 (SE=. 04)) and were further associated with a pattern of personality characteristic of changes that occur as people mature in adulthood 51 In contrast, genetic correlations of Cog with Conscientiousness, Extraversion, and Agreeableness were in the opposite direction (rg=-. 12 to -. 25, pdiff_fdr<. 0005). 

We conducted PGS analysis of Big-5 personality in the NTR, Texas Twin, AddHealth, and WLS cohorts (N = 21,203 -21,290 across personality traits) (Supplementary Figure 3 ). 

NonCog PGS associations with personality traits paralleled genetic correlations, but were smaller in magnitude and were statistically different from zero at the alpha=0. 05 threshold only for Openness (meta-analytic =. 13 (SE=. 02)) and Agreeableness (meta-analytic =. 04 (SE=. 02)). Also parallel to genetic correlation analysis, the Cog PGS associations with openness and neuroticism were in the same direction but smaller in magnitude as compared to NonCog associations, and were in the opposite direction for conscientiousness, extraversion, and agreeableness, although only associations with openness, conscientiousness, and neuroticism were statistically different from zero at the alpha=0. 05 level (meta-analytic βNeuroticism=-. 05, pdiff=<. 0001; βOpenness=. 08, pdiff=. 152; βConscientiousness=-. 03, pdiff=. 001). NonCog genetics were associated with higher risk for multiple psychiatric disorders. In clinical psychology and psychiatry, research is focused on mental disorders. 

Mental disorders are generally associated with phenotypic impairments in academic achievement and social role functioning, 52, 53 but positive genetic correlations with educational attainment and creativity have been reported for some disorders 54, 55. We therefore tested NonCog rg with psychiatric disorders based on published case-control GWAS [56] [57] [58] [59] [60] [61] [62] In sum NonCog genetics were associated with phenotypes from economics and psychology thought to mediate non-cognitive influences on educational success. These associations contrasted with associations for Cog genetics, supporting distinct pathways of influence on achievement in school and later in life. Opposing patterns of association were also observed for psychiatric disorders, suggesting that the unexpected positive genetic correlation between educational attainment and mental health problems uncovered in previous studies arises from non-cognitive genetic influences on educational attainment.
section_name: NonCog genetics were associated with less risky health behavior and delayed

section_content: NonCog and Cog genetics were enriched in similar tissues and cells. We tested whether common variants in genes specifically expressed in 53 GTEx tissues 63 or in 152 tissues captured in a previous aggregation of RNA-seq studies 64, 65 were enriched in their effects on Cog or NonCog. Genes predominantly expressed in the brain rather than peripheral tissues were enriched in both NonCog and Cog (Supplementary Table 10 ). 

To examine expression patterns at a more granular level of analysis, we used MAGMA 66 and stratified LD score regression 67 to test enrichment of common variants in 265 brain cell-type-specific gene-sets 68. In MAGMA analysis, common variants in 95 of 265 genesets were enriched for association with NonCog. The enriched cell-types were predominantly neurons (97%), with enrichment most pronounced for telencephalon-projecting neurons, diand mesencephalon neurons, and to a lesser extent, telencephalon interneurons (Supplementary Figure 4 and Table 12 ). As measured by correlation between Z-statistics, enrichment for Cog was similar to NonCog (r=. 85) and there were no differences in cell-typespecific enrichment, suggesting little differentiation between cognitive ability and non-cognitive traits at the level of cell-type (Supplementary Figure 5 ). Stratified LDSC results were similar to results from MAGMA (Supplementary Note 2, Supplementary Figure 6 and Table 13 ). While the same gene-sets, based on scRNA-seq expression in neuronal cell-types, are enriched for NonCog and Cog, gene-level analysis 69 (Supplementary Note 3) confirms the specific genes driving this enrichment do not necessarily affect the two traits in the same direction. 

NonCog and Cog genetics show diverging associations with total and regional brain volumes. EA is genetically correlated with greater total brain volume 70, 71. We therefore compared the rg of NonCog and Cog with total brain volume and with 100 regional brain volumes (99 gray matter volumes and white matter volume) controlling for total brain volume (Supplementary Table 15 ) 72. For total brain volume, genetic correlation was stronger for Cog NonCog was not associated with any of the regional gray-matter volumes after FDR correction. In contrast, Cog was significantly associated with regional gray-matter volumes for the bilateral fusiform, insula and posterior cingulate (rg range. 11-. 17), as well as left superior temporal (rg=. 11 (SE=. 04)), left pericalcarine (rg=-. 16 (SE=. 05)) and right superior parietal volumes (rg=-. 22 (SE=. 06)) (Figure 5 ). 

NonCog and Cog genetics were weakly associated with white matter microstructure. We tested genetic correlation of NonCog and Cog with white matter tract integrity as measured using diffusion tensor imaging (DTI) 73. Analyses included 5 DTI parameters in each of 22 white matter tracts (Supplementary Table 16 ): fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), radial diffusivity (RD), and mode of anisotropy (MO). 

We first analyzed tract-wide association of NonCog and Cog with the five DTI parameters. Cog was nominally associated with global white matter microstructure for two DTI parametersaverage AD (rg=. 09 (SE=. 04); greater diffusion of water along the principal axis of diffusion) and average MO (rg=. 11 (SE=. 04); more tubular, as opposed to planar, water diffusion). Only average MO survived FDR correction (q=. 014). These genetic correlations did not differ from genetic correlations with the NonCog factor (χ 2 p >. 324). 

Next, we analyzed tract-specific genetic correlations for each of the 5 DTI parameters. 

NonCog was positively associated with MO in the corticospinal tract (rg=. 14 (SE=. 05)), retrolenticular limb of the internal capsule (rg=. 12 (SE=. 04)) and splenium of the corpus callosum (rg=. 10 (SE=. 04); Figure 5 ), whereas the Cog factor was not associated with any specific tracts. However, none of the FDR-significant associations for NonCog were statistically different from associations for Cog (pdiff_fdr=. 89-. 99), possibly reflecting a lack of power to detect differences in small effects.
section_name: Biological Annotation Analysis Reveal Shared and Specific Neurobiological Correlates

section_content: http://mindboggle. info). Cog showed significant associations with gray matter volume for the bilateral fusiform, insula and posterior cingulate, the left superior temporal and left pericalcarine and right superior parietal volumes. NonCog was not associated with any of the regional brain volumes. b. White matter tract patterning of FDR-corrected significant genetic correlations with regional mode of anisotropy (MO) for Cog versus NonCog. White matter tract probability maps are plotted according to the Johns Hopkins University DTI atlas (https://neurovault. org/). Cog was not associated with regional MO. NonCog showed significant associations with MO in the corticospinal tract, the retrolenticular limb of the internal capsule and the splenium of the corpus callosum.
section_name: Figure 5. Genetic correlations with regional gray matter volumes and white matter tracts. a. Cortical patterning of FDR-corrected significant genetic correlations with regional gray matter volumes for Cog versus NonCog, after correction for total brain volume. Regions of interest are plotted according to the Desikan-Killiany-Tourville atlas, shown on a single manually-edited surface (Klein & Tourville, 2012;

section_content: GWAS of non-cognitive influences on educational attainment (EA) identified 157 independent loci and polygenic architecture accounting for more than half the genetic variance in EA. In genetic correlation and PGS analysis, these non-cognitive (NonCog) genetics showed similar magnitude of associations with EA, economic attainment and longevity to genetics associated with cognitive influences on EA (Cog). As expected, NonCog genetics had much weaker associations with cognition phenotypes as compared to Cog genetics. These results contribute new GWAS evidence in support of the hypothesis that heritable non-cognitive skills influence educational attainment and downstream life-course economic and health outcomes. 

Phenotypic and biological annotation analyses shed light on the substance of heritable non-cognitive skills influencing education. Economists hypothesize that preferences that guide decision-making in the face of risk and delayed rewards represent non-cognitive influences on educational attainment. Consistent with this hypothesis, NonCog genetics were associated with higher risk tolerance and lower time discounting. These decision-making preferences are associated with financial wealth, whereas opposite biases are hypothesized to contribute to a feedback loop perpetuating poverty 74. Consistent with results from analysis of decision-making preferences, NonCog genetics were also associated with healthier behavior and later fertility. 

Psychologists hypothesize that the Big Five personality characteristics of conscientiousness and openness are the two "pillars of educational success" 2,3,75. Our results provide some support for this hypothesis, with the strongest genetic correlation evident for openness. But they also show that non-cognitive skills encompass the full range of personality traits, including agreeableness, extraversion, and the absence of neuroticism. This pattern mirrors the pattern of personality change that occurs as young people mature into adulthood 51. Thus, non-cognitive skills share genetic etiology with what might be termed as "mature personality". The absolute magnitudes of genetic correlations between NonCog and individual personality traits are modest. This result suggests that the personality traits described by psychologists capture some, but not all genetic influence on non-cognitive skills. 

Although the general pattern of findings in our phenotypic annotation analysis indicated non-cognitive skills were genetically related to socially desirable characteristics and behaviors, there was an important exception. Genetic correlation analysis of psychiatric disorder GWAS revealed positive associations of NonCog genetics with schizophrenia, bipolar disorder, anorexia nervosa, and obsessive-compulsive disorder. Previously, these psychiatric disorders have been shown to have a positive rg with EA, a result that has been characterized as paradoxical given the impairments in educational and occupational functioning typical of serious mental illness. Our results clarify that these associations are driven by non-cognitive factors associated with success in education. These results align with the theory that clinicallydefined psychiatric disorders represent extreme manifestations of dimensional psychological traits, which might be associated with adaptive functioning within the normal range [76] [77] [78]. 

Our analysis found little support for the hypothesis that physical attributes, such as attractive appearance, might be associated with academic success because of social biases. 79 ere are not yet well-powered GWAS of physical attractiveness. However, tissue enrichments for NonCog genetics were found only in the brain and not in any peripheral tissues and genetic correlation with stature, a generally socially desirable physical attribute, were much smaller than for behavioral and psychological phenotypes. 

Finally, biological annotation analyses suggest similarities in the cellular mediators of NonCog and Cog influences on educational attainment. In tissue-enrichment analysis, GWAS results for both Cog and NonCog were enriched for gene-sets predominantly expressed in the brain. In gene-set enrichment analysis, there were no statistically significant differences between NonCog and Cog. Thus, while the effects of genetic variation on NonCog and Cog are uncorrelated, the variation resides in the same (functional) regions of the genome that play a role in specific types of neurons. We found some evidence of differences between NonCog and Cog in associations with brain structure: NonCog was more strongly associated with white matter microstructure as compared to Cog, whereas Cog was more strongly associated with gray matter volumes as compared to NonCog. Moderate sample sizes in neuroimaging GWAS mean these results must be treated as preliminary, requiring replication with data from largerscale GWAS of white-matter and gray-matter phenotypes. Results also illustrate how Genomic-SEM can be used to conduct GWAS of phenotypes not directly measured in largescale databases, an application that might have broad utility beyond the genetics of educational attainment. 

We acknowledge limitations. Genomic-SEM analysis to isolate non-cognitive genetic influences on educational attainment relies on a statistical model of a complex developmental process. Cognitive and non-cognitive skills develop in interaction with one another. For example, the dynamic mutualism hypothesis 80 proposes that non-cognitive characteristics shape investments of time and effort, leading to differences in the pace of cognitive development 81, 82. In Genomic-SEM analysis, the NonCog factor is, by construction, uncorrelated with adult cognition. Thus, the statistical model is an imperfect representation of etiology. Nevertheless, statistical separation of NonCog from Cog, although artificial, allows us to test if heritable traits other than cognitive ability influence educational attainment and to explore what those traits may be. Our finding that NonCog genetics account for roughly half of all genetic variance in EA should motivate future longitudinal studies to collect repeated measures of cognitive and non-cognitive skills in order to study their reciprocal relationship across development 83, 84. 

Our use of Genomic-SEM to perform GWAS-by-subtraction relied on published GWASs of adult cognitive performance and of educational attainment. Biases and limitations in these GWASs will also affect our results. For example, a large portion of data in the cognitive performance GWAS came from UK Biobank, which administered only a limited battery of cognitive tests. This limited battery could fail to capture genetic influences on some cognitive functions, resulting in incomplete separation of cognitive from non-cognitive genetics within the Genomic-SEM analysis. Genomic-SEM analysis of NonCog genetics using data from GWAS with more comprehensive cognitive testing is needed. 

In the case of GWAS of educational attainment, the included samples were drawn mainly from Western Europe and the U. S., and participants completed their education in the late 20 th and early 21 st centuries. The phenotype of educational attainment reflects an interaction between an individual and the social system in which they are educated. Differences across social systems, including education policy, culture, and historical context, may result in different heritable traits having influence on educational attainment 85. As a result, the GWAS results for educational attainment and the Genomic-SEM results for non-cognitive skills based on these results may not generalize beyond the times and places when and where GWAS samples were collected. Follow-up analysis in cohorts drawn from other contexts are needed to clarify how findings for NonCog genetics generalize. Generalization of the NonCog factor is also limited by the homogeneity of ancestry in the educational attainment and cognitive performance GWASs. Analysis included only participants of European descent. Although this restricted sample is necessary given the lack of methods for integrating genome-scale genetic data across populations with different ancestries 86, 87, it raises a potential threat to external validity. Analysis of (Non)Cog in non-European populations should be a priority following either the conduct of GWAS in other ancestries or the refinement of methods to better integrate data across samples drawn from different ancestries. 

Within the bounds of these limitations, our analysis provides a first view of the genetic architecture of non-cognitive skills influencing educational success. These skills are central to theories of human capital formation within the social and behavioral sciences and are increasingly the targets of social policy interventions. Our results establish that non-cognitive skills are central to the heritability of educational attainment and illuminate connections between genetic influences on these skills and social and behavioral science phenotypes.
section_name: Discussion

section_name: Methods

section_content: We reproduced the Social Science Genetic Association Consortium (SSGAC) 2018 GWAS of educational attainment 23 by meta-analyzing published summary statistics for N=766,345 (www. thessgac. org/data) with summary statistics obtained from 23andMe, Inc. 

(N=365,538). We included SNPs with sample-size > 500,000 and MAF > 0. 005 in the 1000 Genomes reference set (10,101,243 SNPs). We did not apply genomic control, as standard errors of publicly available and 23andMe summary statistics were already corrected 23. Metaanalysis was performed using METAL 88.
section_name: Meta-analysis of educational attainment GWAS

section_content: The objective of our GWAS-by-subtraction analysis was to estimate, for each SNP, the association with educational attainment that was independent of that SNP's association with cognition (hereafter, the NonCog SNP effect). We used Genomic-SEM 22 to analyze GWAS summary statistics for the educational attainment and cognitive performance phenotypes in the SSGAC's 2018 GWAS (Lee et al. 2018 23 ). The model regressed the educational-attainment and cognitive-performance summary statistics on two latent variables, Cog and NonCog (Figure 1 ). Cog and NonCog were then regressed on each SNP in the genome. This analysis allowed for two paths of association with educational attainment for each SNP. One path was fully mediated by Cog. The other path was independent of Cog and measured the non-cognitive SNP effect, NonCog. To identify independent lead hits with p <5e-8 (the customary p-value threshold to approximate an alpha value of 0. 05 in GWAS), we pruned the results using a radius of 250 kb and an LD threshold of r 2 <0. 1 (Supplementary Tables 1 and 2 ).
section_name: GWAS-by-subtraction

section_content: We use Genomic-SEM to compute genetic correlations of Cog and NonCog with other education-linked traits for which well-powered GWAS data were available (SNP-h 2 z-score >2; Supplementary Table 3 ) and to test if genetic correlations with these traits differed between Cog and NonCog. Specifically, models tested the null hypothesis that trait genetic correlations with Cog and NonCog could be constrained to be equal using a chi-squared test with FDR adjustment to correct for multiple testing. The FDR adjustment was conducted across all genetic correlation analyses reported in the article excluding the analyses of brain volumes described below. Finally, we used Genomic-SEM analysis of genetic correlations to estimate the percentage of the genetic covariance between educational attainment and the target traits that was explained by Cog and NonCog using the model illustrated in Supplementary Figure 8.
section_name: Genetic correlations

section_content: Polygenic score analyses were conducted in data drawn from six population-based cohorts from the Netherlands, the U. K., the U. S., and New Zealand: (1) the Netherlands Twin Register (NTR) 24, 89, (2) E-Risk 29, (3) the Texas Twin Project 25, (4) the National Study of Adolescent to Adult Health (AddHealth) 26, 90, dbGaP accession phs001367. v1. p1; (5) Wisconsin Longitudinal Study on Aging (WLS) 27, dbGaP accession phs001157. v1. p1; and (6) the Dunedin Multidisciplinary Health and Development Study 28. (At the time this preprint was posted, Dunedin and E-Risk analyses were not yet complete and data from these studies is not included in the reported analysis. ) Supplementary Tables 6 and 7 describe cohort-specific metrics. Polygenic scores were computed based on weights derived using the LD-pred 91 software with an infinitesimal prior and the 1000 Genomes phase 3 sample as a reference for the LD structure. LD-pred weights were computed in a shared pipeline to ensure comparability between cohorts. Each outcome (e. g., IQ score) was regressed on the Cog and NonCog polygenic scores and a set of control variables (sex, 10 principal components derived from the genetic data and, for cohorts in which these quantities varied, genotyping chip and age). In cohorts containing related individuals, non-independence of observations from relatives were accounted for using mixed linear models (MLM), generalized estimation equations (GEE), or by clustering of standard errors at the family level. We used a random effects meta-analysis to aggregate the results across the cohorts. This analysis allows a cohort-specific random intercept. Individual cohort results are in Supplementary Table 8 and meta-analytic estimates in Supplementary Table 9.
section_name: Polygenic score analysis

section_content: Enrichment of tissue-specific gene expression. We used gene-sets defined in Finucane et al. 2018 92 to test for the enrichment of genes specifically expressed in one of 53 GTEx tissues 63, or 152 tissues captured by the Franke et al. aggregation of RNA-seq studies 64, 65. This analysis seeks to confirm the role of brain tissues in mediating Cog and NonCog influences on educational attainment. The exact analysis pipeline used is available online (https://github. com/bulik/ldsc/wiki/Cell-type-specific-analyses). 

Enrichment of cell-type specific expression. We leveraged single cell RNA sequencing (scRNA-seq) data of cells sampled from the mouse nervous system 68 to identify cell-type specific RNA expression. Zeisel et al. 68 11 ). We restricted analysis to genes with expression levels above the 25 th percentile. For each gene in each cell-type, we computed the cell-type specific proportion of reads for the gene (normalizing the expression within cell-type). We then computed the proportion of proportions over the 265 cell-types (computing the specificity of the gene to a specific cell-type). We ranked the 12,119 genes retained in terms of specificity to each cell-type and then retained the 10% of genes most specific to a cell-type as the "cell-type specific" gene-set. We then tested whether any of the 265 cell-type specific gene-sets were enriched in the Cog or NonCog GWAS. This analysis sought to identify specific cell-types and specific regions in the brain involved in the etiology of Cog and NonCog. We further computed the difference in enrichment for Cog and NonCog to test if any cell types were specific to either trait. For these analyses, we leveraged two widely used enrichment analysis tools: MAGMA 66 and stratified LD score regression 67 MAGMA. We used MAGMA (v1. 07b 66 ), a program for gene-set analysis based on GWAS summary statistics. We computed gene-level association statistics using a window of 10kb around the gene for both Cog and NonCog. We then used MAGMA to run a competitive gene-set analysis, using the gene p-values and gene correlation matrix (reflecting LD structure) produced in the gene-level analysis. The competitive gene-set analysis tests whether the genes within the cell-type-specific gene-set described above are more strongly associated with Cog/NonCog than other genes. 

Stratified LDscore regression. We used LD-score regression to compute LD scores for the SNPs in each of our "cell-type specific" gene-sets. Parallel to MAGMA analysis, we added a 10kb window around each gene. We ran partitioned LD-score regression to compute the contribution of each gene-set to the heritability of Cog and NonCog. To guard against inflation, we use LD score best practices, and include the LD score baseline model (baselineL2. v2. 2) in the analysis. We judged the statistical significance of the enrichment based on the p-value associated with the tau coefficient. 

Difference in enrichment between Cog and NonCog. To compute differences in enrichment we compute a standardized difference between the per-annotation enrichment for

Cog and NonCog as:

Where is the enrichment of a particular gene-set for Cog, is the enrichment for the same gene-set for NonCog, is the standard error of the enrichment for Cog, is the standard error of the enrichment for NonCog, and CTI is the LD score cross-trait intercept, a metric of dependence between the GWASs of Cog and NonCog. 

Enrichment of gene expression in the brain. We performed a transcriptome-wide association study (TWAS) using Gusev et al. 69 (FUSION: http://gusevlab. org/projects/fusion/). We used pre-computed brain-gene-expression weights available on the FUSION website, generated from 452 human individuals as part of the CommonMind Consortium. We then superimposed the bivariate distribution of the results of the TWAS for Cog and NonCog over the bivariate distribution expected given the sample overlap between EA and CP (the GWAS on which our GWAS of Cog and NonCog are based, see Supplementary Note 2).
section_name: Biological annotation

section_content: Brain volumes. We conducted genetic correlation analysis of brain volumes using GWAS results published by Zhao et al. 72. Zhao et al. performed GWAS of total brain volume and 100 regional brain volumes, including 99 gray matter volumes and total white matter volume (Supplementary Table 15 ). Analyses included covariate adjustment for sex, age, their square interaction and 20 principle components. Analyses of regional brain volumes additionally included covariate adjustment for total brain volume. GWAS summary statistics for these 101 brain volumes were obtained from https://med. sites. unc. edu/bigs2/data/gwassummary-statistics/. Summary statistics were filtered and pre-processed using Genomic SEM's
section_name: Brain modalities

section_name: Acknowledgements

section_content: This study was developed with support from the Jacobs Foundation at a meeting organized by DWB and KPH with support from ETD and CM and attended by PB, BWD, JW, and others. 

We gratefully acknowledge contributions to the meeting from Katrin Mannik and Felix Tropf, and the Jacobs Foundation Fellowship team who made the meeting possible. DWB, KPH, MGN, ETD, CM are fellows of the Foundation. JW is a Jacobs Foundation Young Scholar. 

We would like to thank the research participants and employees of 23andMe for making this work possible. The study also used data from the Netherlands Twin Register (NTR), the Texas
section_name: Acknowledgements

section_name: Data and Resources

section_content: An FAQ on why, how and what we studied: https://medium. com/@kph3k/investigating-thegenetic-architecture-of-non-cognitive-skills-using-gwas-by-subtraction-b8743773ce44 GWAS summary data for Cog & NonCog: https://www. dropbox. com/s/cvzcedsfhbznv36/GWAS_sumstats_Cog_NonCog_Demange_et _al. zip?dl=0 A tutorial on how to perform GWAS-by-subtraction: http://rpubs. com/MichelNivard/565885
section_name: Data and Resources

section_content: region. We used Genomic-SEM to compute the genetic correlations between Cog, NonCog and brain volumes. Analyses of regional volumes controlled for total brain volume. For each volume, we tested if correlations differed between Cog and NonCog. Specifically, we used a chi-squared test to evaluate the null hypothesis that the two genetic correlations were equal. 

We used FDR adjustment to correct for multiple testing. The FDR adjustment is applied to the results for all gray matter volumes for Cog and NonCog separately. 

White matter structures. We conducted genetic-correlation analysis of white-matter structures using GWAS results published by Zhao et al. 73. Zhao et al. performed GWAS of diffusion tensor imaging (DTI) measures of the integrity of white-matter tracts. DTI parameters were derived for fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), radial diffusivity (RD), and mode of anisotropy (MO). Each of these parameters were measured for 22 white matter tracts of interests (Supplementary Table 16 ) resulting in 110 GWAS. GWAS summary statistics for these 110 GWAS were obtained from https://med. sites. unc. edu/bigs2/data/gwas-summary-statistics/. Summary statistics were filtered and processed using Genomic SEM's "munge" function; retaining all HapMap3 SNPs with allele frequency >. 01 outside the MHC region. For each white matter structure, we tested if genetic correlations differed between Cog and NonCog. Specifically, we used a chi-squared test to evaluate the null hypothesis that the two genetic correlations were equal. We used FDR adjustment to correct for multiple testing. As these different diffusion parameters are statistically and logically interdependent, having been derived from the same tensor, FDR adjustment was applied to the results for each type of white matter diffusion parameter separately. FDR correction was applied separately for Cog and NonCog.