Lactation yields and accuracies computed from test day yields and (co)variances by best prediction

Lactation records are calculated from data on milk, fat, and protein obtained from one or more milkings on several days during the lactation. The test interval method, which estimated missing daily milk yields by simple interpolation, was used for many years for standard monthly data but may not be as useful for the wider variety of test plans now being proposed. More accurate 305-d yields can be computed using best prediction, which has optimum properties if means and (co)variances are known and distribution is multivariate normal. The covariance of test day and 305-d yields is multiplied by the inverse of the test day (co)variance matrix, which is then multiplied by the test day deviation vector. This predicted 305-d deviation plus the mean 305-d yield equals the predicted 305-d yield. Similar algebraic methods are used to compute the correlation of true and estimated 305-d yields, which is needed to calculate lactation weights. Computation times were affordable but not trivial; they ranged from 0.001 to 1 s per lactation. Equations were modified to account for differing accuracies of data for partial days, means for multiple days, and data for unsupervised tests. Complete or incomplete lactations recorded with very different testing plans can be graphed and compared by best prediction.