The LCV random effects model assumes that the distribution of marginal effect sizes for the two traits can be written as the sum of two independent bivariate distributions (visualized in Figure 1c-e in orange and blue respectively): (1) a shared genetic component (q1π, q2π) whose values are proportional for both traits; and (2) an even genetic component (γ1, γ2) whose density is mirror symmetric across both axes. Distribution (1) resembles a line through the origin, and we interpret its effects as being mediated by a latent causal variable (L) (Figure 1a); distribution (2) does not contribute to the genetic correlation, and we interpret its effects as direct effects. Informally, the LCV model assumes that any asymmetry in the shared genetic architecture arises from the action of a latent variable.
