Estimating test-day milk yields by modeling proportional daily yields: Going beyond linearity

In the United States, lactation milk yields are not measured directly but are calculated from the test-day milk yields. Still, test-day milk yields are estimated from partial yields obtained from single milkings. Various methods have been proposed to estimate test-day milk yields, primarily to deal with unequal milking intervals dating back to the 1970s and 1980s. The Wiggans model is a de facto method for estimating test-day milk yields in the United States, which was initially proposed for cows milked 3 times daily, assuming a linear relationship between a proportional test-day milk yield and milking interval. However, the linearity assumption did not hold precisely in Holstein cows milked twice daily because of prolonged and uneven milking intervals. The present study reviewed and evaluated the nonlinear models that extended the Wiggans model for estimating daily or test-day milk yields. These nonlinear models, except step functions, demonstrated smaller errors and greater accuracies for estimated test-day milk yields compared with the conventional methods. The nonlinear models offered additional benefits. For example, the locally weighted regression model (e.g., locally estimated scatterplot smoothing) could utilize data information in scalable neighborhoods and weigh observations according to their distance in milking interval time. General additive models provide a flexible, unified framework to model nonlinear predictor variables additively. Another drawback of the conventional methods is a loss of accuracy caused by discretizing milking interval time into large bins while deriving multiplicative correction factors for estimating test-day milk yields. To overcome this problem, we proposed a general approach that allows milk yield correction factors to be derived for every possible milking interval time, resulting in more accurately estimated test-day milk yields. This approach can be applied to any model, including nonparametric models.