When the multivariate S-LDSC model is correct, Sτ is expected to produce unbiased estimates of the conditional contribution of an annotation to genetic covariance, after controlling for the effects of variants in all other annotation (i.e., accounting for the fact that variants can reside in multiple annotations). In comparison, S0 is expected to produce unbiased estimates of the total contribution of all genetic variants in an annotation to genetic covariance (i.e., irrespective of its overlap with the other annotations). S0 has two desirable properties. First, its estimate is not as directly contingent on which other annotations are included in the multivariate S-LDSC model. Second, because it does not decompose contributions of an annotation into those that are shared vs. unique of other annotations, it is expected to produce more stable estimates at small and moderate sample sizes. For this reason, the empirical Stratified Genomic SEM analyses reported here employ S0 matrices, and should be interpreted accordingly.
