| A block-band system of mixed model equations was proposed for the animal model with multiple genetic factors. The block-band system places non-zero submatrices of the coefficient matrix on the diagonal band, and has only two non-zero submatrices on the right hand side of the mixed model equations. A formulation was derived under certain conditions for REML using diagonal elements of the inverse coefficient matrix. To improve the convergence rate for REML estimation, a simple technique that does not require additional computations was presented. Limitations of the above two techniques were discussed. A property of REML estimation was proven. As a result of applying this property, substantial savings in computations can be achieved.;Formulations for prediction error variance and REML estimation under the animal model with genetic groups were derived. Genetic groups were extended to the multitrait animal model, including computationally feasible mixed model equations, canonical and triangular transformations, and REML estimation.;Heritability and repeatability for the simple and weighted average of test-day SCS were about the same,.12 for heritability and.35 for repeatability. Herd-sire interaction variance was small (.002). Genetic and phenotypic correlations between somatic cell score and production traits were positive, and genetic correlations (.24 to.39) were higher than phenotypic correlations (about.15). |
