The total genetic covariation between MDD and AUD is the sum of pathways (a13 × a14), (a23 × a24), and (a33 × a34). The proportion of genetic covariation between MDD and AUD that is attributable to CON (after accounting for genetic variation shared with SR) is [(a23 × a24)/(a13 × a14 + a23 × a24 + a33 × a34)] and the covariation not explained by CON or SR is [(a33 × a34)/(a13 × a14 + a23 × a24 + a33 × a34)]. The proportion of phenotypic covariation between MDD and AUD that is explained by variance specific to CON is [(a23 × a24) + (e23 × e24)/(a13 × a14 + a23 × a24 + a33 × a34) + (e13 × e14 + e23 × e24 + e33e34)]. To determine the proportion of phenotypic, genetic, and environmental covariation that was unique to SR (i.e. after accounting for CON), the quadrivariate model was re-run with CON entered first and SR entered second. Therefore, the quadrivariate models estimated the proportion of phenotypic, genetic, and environmental covariation between MDD and AUD due to (1) SR only, (2) CON only, (3) both SR and CON, and (4) neither SR nor CON.
