Here αk is the random marginal effect of a SNP of trait k, π is interpreted as the marginal effect of a SNP on L, and γk is interpreted as the non-mediated effect of a SNP on trait k. α and π (but not γ) are normalized to have unit variance, and all random variables have zero mean. (The symbol ``~" means ``has the same distribution as.") q1, q2 are the model parameters of primary interest, and we can relate them to the mixed fourth moments, which are observable (equation 2). In particular, this implies that the model is identifiable (except when the excess kurtosis κπ = 0; see Supplementary Note). We do not expect that κπ will be exactly zero for any real trait, but there will be lower power for traits with higher polygenicity. Note that we have avoided assuming any particular parametric distribution.
