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

Authors: WU, XIAO LIN - Council On Dairy Cattle Breeding; WIGGANS, GEORGE - Council On Dairy Cattle Breeding; NORMAN, H - Council On Dairy Cattle Breeding; ENZENAUER, HEATHER - Council On Dairy Cattle Breeding; Miles, Asha; Van Tassell, Curtis - Curt; Baldwin, Ransom - Randy; BURCHARD, JAVIER - Council On Dairy Cattle Breeding; DURR, JOAO - Council On Dairy Cattle Breeding

Submitted to: Journal of Dairy Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 6/6/2023
Publication Date: 12/13/2023
Citation: Wu, X., Wiggans, G.R., Norman, H.D., Enzenauer, H.A., Miles, A.M., Van Tassell, C.P., Baldwin, R.L., Burchard, J., Durr, J. 2023. Estimating test day milk yields by modeling proportional daily yields: Going beyond linearity. Journal of Dairy Science. 106(12):8979-9005. https://doi.org/10.3168/jds.2023-23479.
DOI: https://doi.org/10.3168/jds.2023-23479

Interpretive Summary: Few dairy farms have inline milk meters which give a precise measurement of the daily milk yields of their cows. Instead, most herds across the US and the world participate in programs where a technician will come and measure the yield from a single milking, and the total daily yields are estimated from this partial measurement. This research examined the Wiggans (1986) linear regression model, a de facto method for estimating test-day milk yields in the US, and further assessed the potentials of non-linear models to further enhance the estimation accuracy.

Technical Abstract: Lactation milk yields are not measured directly but instead calculated from the test-day milk yields. Still, test-day milk yields are estimated from partial yields obtained from a single milking. Various methods have been proposed to estimate test-day milk yields, dating back to the 1970s and 1980s, primarily to deal with unequal milking intervals. The Wiggans (1986) model is a de facto method for estimating test-day milk yields in the USA, which was initially proposed for cows milked three 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 the Holstein cows milked twice daily because the milking intervals tended to be prolonged and uneven. In the present study, we reviewed and evaluated the non-linear models that extended the Wiggans (1986) model for estimating daily milk yields. These non-linear models, except step functions, had smaller errors and greater accuracies for estimated test-day milk yields compared to the current methods. There are additional features that make non-linear model more appealing than the linear model. For example, the locally weighed regression model (e.g., LOESS) could utilize data information in scalable neighborhoods and weigh observations according to their distance in milking time. General additive models provide a flexibly unified framework to model non-linear predictor variables additively. Another disadvantage of the traditional methods is a loss of accuracy due to discretizing milking interval time into large bins when deriving multiplicative correction factors for estimating test-day milk yields. To overcomes the limitation of the traditional methods, a general approach was proposed that allows milk yield correction factors to be derived for every possible milking interval time, hence giving more accurately estimated test-day milk yields. This approach applies to any model, including non-parametric models.