Genomic structural equation modelling provides insights into the multivariate genetic architecture of complex traits

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Genetic correlations estimated from genome-wide association studies (GWASs) reveal pervasive pleiotropy across a wide variety of phenotypes. We introduce genomic structural equation modelling (genomic SEM): a multivariate method for analysing the joint genetic architecture of complex traits. Genomic SEM synthesizes genetic correlations and single-nucleotide polymorphism heritabilities inferred from GWAS summary statistics of individual traits from samples with varying and unknown degrees of overlap. Genomic SEM can be used to model multivariate genetic associations among phenotypes, identify variants with effects on general dimensions of cross-trait liability, calculate more predictive polygenic scores and identify loci that cause divergence between traits. We demonstrate several applications of genomic SEM, including a joint analysis of summary statistics from five psychiatric traits. We identify 27 independent single-nucleotide polymorphisms not previously identified in the contributing univariate GWASs. Polygenic scores from genomic SEM consistently outperform those from univariate GWASs. Genomic SEM is flexible and open ended, and allows for continuous innovation in multivariate genetic analysis.

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Fig. 1: Genomic SEM solutions for p- and neuroticism-factor models with SNP effect.
Fig. 2: Manhattan plots of unique, independent hits from genomic SEM.
Fig. 3: Out-of-sample prediction using genomic SEM- and univariate-based PGSs for psychiatric traits.

Data availability

The data that support the findings of this study are all publicly available. Links to the location of summary statistics, linkage disequilibrium scores, reference panel data and the code used to produce the current results can all be found at

Code availability

GenomicSEM software is an R package that is available from GitHub at The GenomicSEM R package can be installed directly at Example GenomicSEM code, including code used to produce the results, is provided for each set of analyses at


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E.M.T.-D., K.P.H. and A.D.G. were supported by NIH grant R01HD083613. E.M.T.-D., S.J.R. and I.J.D. were supported by NIH grant R01AG054628. E.M.T.-D. and K.P.H. were each supported by Jacobs Foundation research fellowships. E.M.T.-D. and K.P.H. are members of the Population Research Center at the University of Texas at Austin, which is supported by NIH grant P2CHD042849. M.G.N. is supported by a Royal Netherlands Academy of Science Professor Award to D. I. Boomsma (PAH/6635), ZonMw grant: ‘Genetics as a research tool: a natural experiment to elucidate the causal effects of social mobility on health’ (pnr: 531003014) and ZonMw project: ‘Can sex- and gender-specific gene expression and epigenetics explain sex-differences in disease prevalence and etiology?’ (pnr: 849200011). H.F.I. is supported by the ‘Aggression in children: unraveling gene–environment interplay to inform treatment and intervention strategies' (ACTION) project. ACTION receives funding from the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement number 602768. P.D.K. and R.d.V. were supported by ERC Consolidator Grant 647648 EdGe. I.J.D., A.M.M., S.J.R., R.E.M. and W.D.H. are members of the University of Edinburgh Centre for Cognitive Ageing and Cognitive Epidemiology, which is part of the cross-council Lifelong Health and Wellbeing Initiative (MR/K026992/1). W.D.H. is supported by a grant from Age UK (Disconnected Mind Project). PGS analyses for the p factor were conducted under UKB dataset resource–application number 4844. PGS analyses for neuroticism were conducted using data from Generation Scotland. Generation Scotland received core support from the Chief Scientist Office of the Scottish Government Health Directorates (CZD/16/6) and the Scottish Funding Council (HR03006). Genotyping of the Generation Scotland:Scottish Family Health Study samples was carried out by the Genetics Core Laboratory at the Wellcome Trust Clinical Research Facility, Edinburgh, Scotland, and was funded by the Medical Research Council UK and Wellcome Trust (Wellcome Trust Strategic Award ‘STratifying Resilience and Depression Longitudinally’ (STRADL) reference 104036/Z/14/Z). Ethical approval for the Generation Scotland:Scottish Family Health Study was obtained from the Tayside Committee on Medical Research Ethics (on behalf of the National Health Service). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

A.D.G., M.R., H.F.I., M.G.N. and E.M.T.-D. developed the software. A.D.G., M.G.N. and E.M.T.-D. developed the theory underlying genomic SEM. A.D.G., M.R., R.d.V., M.G.N. and E.M.T.-D. developed the techniques and mathematical derivations. A.D.G., T.T.M., M.G.N. and E.M.T.-D. performed the simulation studies. S.J.R., R.E.M. and E.M.T.-D. performed the polygenic prediction analyses. A.D.G., M.G.N. and E.M.T.-D. wrote the manuscript. M.R., S.J.R., T.T.M., W.D.H., A.M.M., I.J.D., R.E.M., P.D.K. and K.P.H. provided feedback and edited the manuscript.

Correspondence to Andrew D. Grotzinger.

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Supplementary information

Supplementary Information

Supplementary Methods, Supplementary Results, and Supplementary Figures 1–27.

Reporting Summary

Supplementary Dataset

Study raw data presented in Supplementary Tables 1–21.

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