Kang et al. (2008) describe an efficient mixed model formulation for the special case of only one random effect, which avoids any matrix computation in the REML estimation of variance components. Piepho et al. (2011) re-parametrize their formulation to allow for a fixed residual variance. This re-parametrization might be especially useful in a plant breeding context. Here, the phenotypes used for estimation of marker effects are commonly the adjusted (for all other random and fixed effects) entry means, obtained beforehand from a one- or two-step adjustment procedure, most likely a mixed-model analysis (Moehring and Piepho, 2009). From this analysis, good estimates of the residual variance are usually available, so that it is not necessary and even counterproductive to re-estimate this parameter in RR-BLUP (Moehring and Piepho, 2009). Please see Piepho et al. (2011) for details.
The package
Moehring, J., Piepho, H. P. (2009): Comparison of weighting in two-stage analyses of series of experiments. Crop Science 49, 1977-1988
rrBlupM6