Submitted to: Journal of Dairy Science
Publication Type: Abstract Only
Publication Acceptance Date: March 25, 1996
Publication Date: N/A
Test-day yields with multivariate normal distribution and known means can be combined into a 305-day yield by best prediction. The many missing daily yields are predicted from their covariances with the few measured yields; then all are summed. A 305-day yield equals mean 305-day yield plus covariance between lactation and observed test-day yields multiplied by inverse of the variance for observed test days multiplied by observed test-day deviations. Dimensions of all vectors and matrices are usually <30 with multitrait prediction and <10 with single-trait prediction of 305-day milk, fat, or protein yields. Squared correlations of predicted and true 305-day yields and lactation weights are simple functions of these matrices. A FORTRAN program was developed and tested on an IBM 9370 computer. All covariances among test days could be stored initially, but memory was greatly reduced by generating them from a function as needed. Inversion of a 30x30 matrix and other algebraic steps required nearly 1 s per lactation. Inversion of three 10x10 matrices and other steps for single-trait prediction required only .05 s per lactation. Missing traits and fewer tests greatly reduce processing time. For efficiency, covariances of 305-day yield with any daily yield were computed just once at the beginning of the program and stored in a small vector. Covariances among a.m.-p.m. tests equal covariances among full-day tests except for an additional measurement error, which add to diagonals (variances) for a.m.-p.m. tests. Test-day means are assumed known in theory but in practice can be generated from lactation means for each herd. Best prediction provides very flexible theory to calculate 305-day yields and accuracies of those yields as measured under many different test plans.