An exponential regression model to estimate daily milk yields

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 afterwards, focusing on various forms of correction factors. Additive correction factors (ACF) are evaluated by the average differences between AM and PM milk yield for different milking interval classes (MIC), coupled with other categorical variables. Multiplicative correction factors (MCF) are ratios of daily yield to yield from single milkings, with varied statistical interpretations. MCF are now commonly used, but they 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. They all had substantially lower MSE and, therefore, greater accuracies than 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. For computing MCF, discretizing the milking interval into categorical MIC led to a loss of accuracy. The exponential regression models had the smallest MAE and the greatest accuracies, representing a promising alternative for estimating daily milk yields. 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.