Mixed Linear Model with Uncertain Paternity

SUMMARY In animal breeding applications, mixed linear models are often used to estimate genetic parameters and to predict the breeding value of sires, under the assumption that paternity can be attributed without error. This paper considers a mixed linear model for situations in which paternity is uncertain. It is shown how mixed model equations can be used to obtain the best linear unbiased predictors for sire evaluation in such situations. Minimum norm quadratic unbiased estimation {MINQUE} theory is used for estimating the unknown variance components. The methods are illustrated using data on birth weight. Empirical Bayes and iterated MINQUE procedures lead to quite different results in estimating variance components.