Estimation of genetic covariances with method R.

Method R is a simple and computationally inexpensive method for estimating (co)variances. The objective of the study was to investigate properties of Method R for estimation of (co)variance components with emphasis on covariance estimation. Theoretical Method R formulas were developed for simplified single-variate and bivariate models. In single-trait models, the curve of the regression of Method R was continuous and monotonic and its slope depended on the amount of information on each animal and on the variance ratio. The curve became steeper as the number of records per animal decreased. For covariance, the curve of the regression was monotonic but not continuous. However, a regression coefficient of 1 still corresponded to the correct covariance. Similar curves were observed in analyses of simulated data sets. Because of the observed discontinuity, algorithms implementing Method R that require a continuous regression curve would not work in models with covariances. An alternative algorithm was based on a transformation matrix obtained by multiplying a matrix of numerators with the inverse of a matrix of denominators of the regression factors. Such an algorithm converged reliably for all models tested. Method R can be modified to estimate covariances in models too large for other methods.