Figure 2 ∣. Model comparisons for producing Q metrics.

Unstandardized path diagrams for common pathway (right) and independent pathways (left) models used to compute the Genomic SEM heterogeneity statistics for associations with external traits (Q_Trait, top) and individual SNPs (Q_SNP, bottom). In this example, F is a common genetic factor of the genetic components of three GWAS phenotypes (Y₁-Y₃). Observed variables are represented as squares, and latent variables are represented as circles. The genetic component of each phenotype is represented with a circle as the genetic component is a latent variable that is not directly measured, but is inferred using LDSC. SNPs are directly measured, and are therefore represented as squares. Single-headed arrows are regression relations, and double-headed arrows are variances. Paths labeled 1 are fixed to 1 for model identification purposes. All unlabeled paths represent freely estimated model parameters. Q represents the decrement in model fit of the common pathway model relative to the more restrictive independent pathways model. Q is a χ² distributed test statistic with k − 1 degrees of freedom, representing the difference between the k SNP-phenotype or Trait-phenotype b coefficients in the independent pathways model and the 1 SNP-factor or Trait-factor b coefficient in the common pathway model. Q is estimated here using a χ² difference test across the common and independent pathways models; this is statistically equivalent to the 2-step procedure outlined in the original Genomic SEM¹³ publication for calculating Q_SNP. Q_Trait indexes whether the pattern of genetic associations between the genetic component of an external trait (depicted as X_g) and the individual disorders is well accounted for by a given factor. Q_SNP indexes whether the associations between an individaul SNP (depicted as SNP_m) and the individual dissorders is well accounted for by the factor. For simplicity, we depict a stylized representation containing only one factor and three disorders. The full models used to derive Q_Trait and Q_SNP for the empirical analyses reported in this paper are presented in Supplementary Figures 5 and 38.