Statistical methods revisited for estimating daily milk yields: how well do they work?

Cost-effective milking plans have been adapted to supplement the standard supervised twice-daily monthly testing scheme since the 1960s. Cows are often milked two or more times on a test day, but not all those milkings are measured. Various methods have been proposed to estimate daily yields, focusing on yield correction factors in two broad categories, additive (ACF) and multiplicative correction factors (MCF). The primary goal of the present study was to evaluate the performance of existing statistical methods, including a recently proposed exponential regression model, for estimating DMY using ten-fold cross-validation in Holstein and Jersey cows. The initial approach estimated daily yield to be twice the morning (AM) or evening (PM) yield in AM-PM plans, assuming equal 12-hour AM and PM milking intervals. In practice, however, AM and PM milking intervals can differ, and milk secretion rates may vary between day and night. ACF provide adjustments to two times AM and PM yields as the estimated daily yields, which is equivalent to a regression model assuming a fixed regression coefficient of 2.0 for AM or PM yields. Similarly, a linear regression model can be implemented as an additive correction factor model that estimates the regression coefficient for yield from single milking from the data. Relaxing the assumption for the fixed regression coefficient of partial yield allowed the linear model to fit and predict the data better. MCF are ratios of daily yield to yield from a single milking, also referred to as ratio factors. Multiplying a yield from a single milking by a corresponding ratio factor gives an estimate of daily milk yield. In the present study, all the methods had small variances and, therefore, high precision of the estimates, but they varied considerably in squared biases. Overall, the ACF models had larger squared biases and lower accuracies of estimated daily milk yield than the MCF models and the linear models. The exponential regression model had greatest accuracies and smallest squared biases of all the methods evaluated. Computed ACF or MCF on discretized milking interval time suffered from the loss of information, which in turn led to slightly larger errors and lower accuracies. ACF and MCF were characterized and model parameters were compared as well. The present study focused on estimating daily milk yields in AM-PM milking plans, yet the methods and relevant principles are generally applicable to cows milked more than two times a day, and they apply to estimating daily fat and protein yields.