Undesirable Properties of Regressed Least Squares Prediction of Breeding Values

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Abstract
Regressed least squares was defined, precautions required in computing it were described, the variances of errors of prediction were stated and some deficiencies of the methods were reported. These deficiencies were: predictors are not invariant; variances of prediction errors are not minimum; animals with no records (or with no progeny in progeny testing) cannot be evaluated; and computations are more difficult than those for the mixed model solution for best linear unbiased prediction. A modification of regressed least squares that does yield best linear unbiased prediction was described, but it was more difficult computationally than the mixed model solution.