Notice that the variance components are similar to, but not the same as, those obtained from the ANOVA. More importantly these estimators have known asymptotic statistical properties (permitting estimation of their standard errors) and have the properties of maximum likelihood – among all possible estimates they have the highest probabilities given the observed data and the assumption that the effects of the different levels of random factor are normally distributed.
The BLUPs for RILs are computed as before, and we compare them to the RIL LSmeans shown
above from the ANOVA: