For a bivariate analysis where the two traits are measured on different sets of individuals, e.g. height in males and blood pressure in females, the variance-covariance matrix is [6] where y 1 is an N 1×1 vector of phenotypes in sample set #1 (e.g. males), and y 2 is an N 2×1 vector of phenotypes for in sample set #2 (e.g. females), with N 1 and N 2 being the sample sizes of the two sets. A 1 is an N 1×N 1 GRM for individuals in sample set #1, A 2 is an N 2×N 2 GRM in sample set #2 and A 12 is an N 1×N 2 GRM between the two sets of samples. and are the genetic variance for the two traits. and are the residual variances with the corresponding identify matrix I 1 and I 2. is the genetic covariance between traits. Since the two traits are measured on different sets of samples, the residual covariance is ignored because it is assumed that there is no covariance between the unrelated individuals apart from that caused
