Analogous to the univariate analysis, estimation of genetic covariance by a bivariate mixed linear model analysis is asymptotically equivalent to the following linear regression model(9)where i.e. the product of phenotypes between the i-th individual in set #1 and the j-th individual in set #2, and is the ij-th element of the GRM A 12, i.e. the genetic relationship between the i-th individual in set 1 and the j-th individual in sample set #2. The regression coefficient is equivalent to genetic covariance between the two traits becauseIf the two sample sets are independent and phenotypes for both traits have been standardized with mean of 0 and variance of 1, then and . Since is small, . We then have .
