Best Linear Unbiased Prediction of Breeding Values Not in the Model for Records

Methods for computing best linear unbiased predictions of random variables (breeding values or sire values) not appearing in the model for records are presented.One method involves taking linear functions of best linear unbiased predictions of variables appearing in the model for records.The second method involves expanding the usual mixed model equations to include variables not in the model. iNTRODUCTIONA common problem in animal breeding is evaluation of breeding values or other random variables (e.g., sire values) which do not appear in the linear model describing the records in the evaluation, if all fixed effects in the model are known, selection index (best linear prediction) can be used.Let y* be the vector of records corrected to zero means, ui the variable to be predicted, V the variance-covariance matrix of y*, and c the vector of covariances between y* and u i.The BLP (best linear predictor) of u i is u i = b y* where b is the vector of weights computed by solving Vb= e.In practice, all fixed effects are seldom, if ever, known, and consequently selection index is not appropriate.One should, of course, utilize any prior knowledge of fixed factors, e.g., age effects, and adjust the records accordingly.This done, there still will be unknown fixed factors in the model, # as a minimum.Then a modification of selection index, BLUP (best linear unbiased prediction), can be used (1).