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 covaria
nce 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 depen
ded 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 co
variance. Similar curves were observed in analyses of simulated data sets.
Because of the observed discontinuity, algorithms implementing Method R tha
t require a continuous regression curve would not work in models with: cova
riances. An alternative algorithm was based on a transformation matrix obta
ined by multiplying a matrix of numerators with the inverse of a matrix of
denominators of the regression factors. Such an algorithm converged reliabl
y for all models tested. Method R can be modified to estimate covariances i
n models too large for other methods.