An exponential regression model to estimate daily milk yields

Authors: WU, XIAO-LIN - Council On Dairy Cattle Breeding; WIGGANS, GEORGE - Council On Dairy Cattle Breeding; NORMAN, HOWARD - 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: Interbull Annual Meeting Proceedings
Publication Type: Proceedings
Publication Acceptance Date: 10/5/2022
Publication Date: 10/5/2022
Citation: Wu, X.-L., Wiggans, G.R., Norman, H.D., Miles, A.M., Van Tassell, C.P., Baldwin, R.L., Burchard, J., Durr, J. 2022. An exponential regression model to estimate daily milk yields. Interbull Bulletin. 57:67-73.

Interpretive Summary: Cows are typically milked two or more times on a test day, but not all these milkings are sampled and weighed. There are a number of methods used to estimate their total yields, and this accurate estimation impacts nearly every element of dairy farm management. Here, exponential regression models are proposed as a promising alternative tool for estimating total daily milk yields.

Technical Abstract: Accurate milking data are essential for herd management and genetic improvement in dairy cattle. Cows are typically milked two or more times on a test day, but not all these milkings are sampled and weighed. This practice started to supplement the standard supervised twice-daily monthly testing scheme in the 1960s, motivated by lowering the costs to the dairyman. The initial approach estimated a test-day yield by doubling the morning (AM) or evening (PM) yield in the AM-PM milking plans, assuming equal AM and PM milking intervals. However, AM and PM milking intervals can vary, and milk secretion rates may change between day and night. Statistical methods have been proposed to estimate daily yields in dairy cows, focusing on various correction factors. Additive correction factors (ACF) are evaluated by the average differences between AM and PM milk yield for different milking interval classes (MIC) and other categorical variables. Multiplicative correction factors (MCF) are ratio of daily yield to yield from single milkings, but their precise statistical interpretations vary. MCF have biological and statistical challenges. An exponential regression model was proposed as an alternative model for estimating daily milk yield, which was analogous to an exponential growth function with a partial yield as the initial state and the change of rate tuned by a linear function of milking interval. The results showed that the existing MCF model performed similarly, with substantially lower MSE and, therefore, greater accuracies over the initial approach of doubling AM or PM milk yields as the test-day milk yields. Two times AM or PM milk yields as the test-day milk yields were a reasonable approximation with equal AM and PM milking intervals but were subject to large errors with unequal AM and PM milking intervals. Discretizing milking interval into categorical MIC when computing MCF led to a loss of accuracy. The exponential regression models (Wu et al., 2022) had the smallest MAE and the greatest accuracies, representing a promising alternative tool for estimating DMY. The statistical methods were explicitly described to estimate daily milk yield in AM and PM milking plans. Still, the principles generally apply to cows milked more than twice daily.