The genetic causality proportion (gcp) is defined as: (4)gcp=log∣q2∣−log∣q1∣log∣q2∣+log∣q1∣ which satisfies equation (1). gcp is positive when trait 1 is partially genetically causal for trait 2. When gcp = 1, trait 1 is fully genetically causal for trait 2: q1 = 1 and the causal effect size is q2 = ρg (Figure 1b,e). The LCV model is broadly related to dimension reduction techniques such as Factor Analysis[67] and Independent Components Analysis[68], although it differs in its modeling assumptions as well as its goal (causal inference); our inference strategy (mixed fourth moments) also differs.
