Estimating a Genetic Covariance from Least Squares Solutions

Abstract

An unbiased and invariant procedure is described for estimating the covariance between effects of two traits or of random variables such as sires in two environments when the residual effects for one trait are not correlated with those of the other trait. When the covariance is desired between two classes in the model, such as sire of fetus and sire of cow, the data can be divided randomly into two sets to allow use of this procedure to estimate the covariance since the residuals in the two data sets would be uncorrelated. The method is to obtain solutions by ordinary least squares for each trait separately as if the random effects of interest were actually fixed and then to compute a sample covariance between the two sets of solutions.