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

Genomic SEM solutions for p-factor and neuroticism factor models with SNP effect.Standardized results from using Genomic SEM (with WLS estimation) to construct a genetically defined p-factor of psychopathology (panel a) and a genetic neuroticism factor (panel b) with a lead independent SNP predicting the factors. SEs are shown in parentheses. For a model that was standardized with respect to the outcomes only, the effect of the SNP was −.093 (SE = .017; SNP variance = .252) for the p-factor, and for neuroticism the SNP effect was −.042 (SE = .007, SNP variance = .432); this can be interpreted as the expected standard deviation unit difference in the latent factor per effect allele. SCZ = schizophrenia; BIP = bipolar disorder; DEP = major depressive disorder; PTSD = post-traumatic stress disorder; ANX = anxiety. Irr = irritability; Feel = sensitivity/hurt feelings; fed-up = fed-up feelings; emb = worry too long after embarrassment.

Manhattan plots of unique, independent hits from Genomic SEM.Genomic SEM (with WLS estimation) was used to conduct multivariate GWASs of the p-factor (panels a and c) and neuroticism (panels b and d). Manhattan plots are shown for SNP effects (top panels) and for QSNP (bottom panels). The gray dashed line marks the threshold for genome-wide significance (p < 5 × 10−8). In all four panels, black triangles denote independent hits for SNP effects from the GWAS of the general factor that were not in LD with independent hits for the univariate GWAS or hits for QSNP. In all four panels, purple diamonds denote independent hits for the SNP effects from univariate GWASs that were not in LD with independent hits from the GWAS of the general factor. Grey stars denote independent hits for QSNP.

Out-of-sample prediction using Genomic SEM based and univariate based polygenic scores for psychiatric traits.Polygenic scores (PGSs) were constructed using the same set of SNPs for all predictors. R2 (%) on the y-axis indicates the percentage of variance (possible range: 0-100) explained in the outcome unique of covariates. The summary statistics for Genomic SEM were estimated using WLS. The Genomic SEM-based PGS was derived from a model estimating SNP effects on a common “p”-factor, constructed from SCZ, BIP, MDD, PTSD, and ANX (as in Fig. 1a.). In order to prevent bias, the Genomic SEM summary statistics were produced using SCZ and MDD GWAS summary statistics that did not include UKB participants. Error bars indicate 95% confidence intervals estimated using the delta method. Phenotypes were constructed for European participants in the UKB for five symptom domains and for a general p factor spanning all five symptom domains.