Modified Equations for Sire Models with Groups

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Abstract
Sire [dairy] evaluation by best linear unbiased prediction for models including groups is considered in an alternative formulation of mixed model equations. Sires'' evaluations are solutions to this modified system of equations in contrast to regular mixed model equations where evaluations are linear functions of group and sire solutions. The major advantage of modified equations is theoretical. To illustrate this advantage, the modified equations are used to show a relationship between group models and selection models.