We formally modelled genetic covariances (rather than rg) in confirmatory factor analyses using genomic structural equation modeling (Genomic SEM, versions 0.0.2a-c)10 (Supplementary Information section 3.3). Genomic SEM is unbiased by sample overlap and imbalanced sample size, and by applying to summary statistics allows for genetic analyses of latent factors with more observations than is typically possible with individual-level data10. We estimated and benchmarked four models: (1) a common factor model with the 11 phenotypes, (2) a correlated three-factors model with the 11 phenotypes (with and without cross-loadings), (3) a bifactor model with the 11 phenotypes, and finally, (4) a revised common factor model that only included seven of the phenotypes that satisfied moderate-to-large (i.e., ≥ 0.50) loadings on the single latent factor in model (1) (Supplementary Table 7). We found that model (4) was the only model that closely approximated the observed genetic covariance matrix (χ2(12) = 390.234, AIC = 422.234, CFI = 0.957, SRMR = 0.079), fulfilled our preregistered model fit criteria, and coalesced with theoretical expectations of a common genetic liability to externalizing. This model was selected as
