I. Misztal

Indirect Solution of Mixed Model Equations

Abstract Large scale genetic evaluation of animals by best linear unbiased prediction can have a high computational cost. This is partly due to the need to set up mixed model equations, which are then solved in an iterative way. Solutions can also be obtained by succesive averaging without setting the mixed model equations directly. Formulas are presented for a class of models with fixed and random factors, including an additive relationship matrix. Two iterative procedures were investigated, Gauss-Seidel and Jacobi. With a balanced data set, putting restrictions on fixed effects is not effective for improving convergence rates in Gauss-Seidel but is essential in Jacobi. Computational techniques needed to implement the indirect procedures are discussed.

Approximation of Prediction Error Variance in Large-Scale Animal Models

Abstract Computation of prediction error variances for genetic evaluations estimated by mixed model methodology requires inversion of the coefficient matrix, which is not practical for large populations. Although methods have been developed to approximate prediction error variance for sire models, they are not suitable for animal models, because sizable effects of the relationship matrix are not considered. To approximate reciprocal of prediction error variance, an iterative algorithm was developed that combines contributions due to production records (if any) and due to relationships. Contribution due to production records is a weighted number of records; contribution due to relationships is sum of contributions from parents and offspring. Accuracy of the algorithm was investigated with a simulated data set for three generations of animals that included 1000 cows, 40 sires, 2315 records, and 100 herd-year-seasons. The model included herd-year-season and permanent environmental effects. Iteration involved reading the file with records once and reading the relationship file once per round (seven rounds were required in the simulation). Correlation between repeatability estimates obtained by the algorithm and by inversion was. 996.