Exploratory factor analysis tested four factor solutions, specifying 1 to k + 1 factors with the factanal function of R (“stats” package version 3.5.1) (Supplementary Information section 3.2), where k is the number of clusters identified in the genetic correlation matrix, while retaining factors that explained ≥15% variance (preregistered threshold). The fourth factor explained only 12.5% variance, and thus, the three-factor solution was considered the best-fitting exploratory model (Supplementary Table 6). The factor loadings were consistent with the hierarchical clustering. However, as detailed in Supplementary Information section 3.2, the second and third factor accounted for complex residual variation and divergent residual cross-trait correlations among the subset of phenotypes that had the weakest loadings on the single common factor. Thus, we learned from exploratory analysis that some of the 11 indicators may not be optimal for identifying a common genetic liability to externalizing, and that a less complex model with fewer indicators may perform better in subsequent confirmatory analyses.
