** X. Wu ^{1,2}, G.R. Wiggans^{1}, H.D. Norman^{1}, A.M. Miles^{3}, C.P. Van Tassell^{3}, R.L. Baldwin^{3}, P.M. VanRaden^{3}, Javier Burchard^{1}, and J. Durr^{1}**

2022 J. Dairy Sci. Commun.

Cost-effective milking plans has been used to supplement the standard supervised four-weekly testing scheme since the 1960s. A cow is typically milked two or more times on a test day, but not all these milkings are sampled and weighed. Statistical methods have been proposed to estimate daily yields in dairy cows, centering on various yield correction factors in two broad categories. This technical note presents a systematic review about additive and multiplicative correction factors concerning their statistical interpretations, model assumptions, and challenges. The initial approach of doubling morning (AM) or evening (PM) milk yield as a test-day yield in an AM-PM plan was inaccurate because it assumed an over-simplified, fixed multiplicative correction factor for all cows. Additive correction factors provide additive adjustments to two times AM or PM yields, based on the differences between AM and PM milk yield for varied milking interval classes, coupled with other categorical variables whenever applicable. Hence, an equivalent additive correction factor regression model assumes a fixed regression coefficient (2.0) for the yield from single milkings. A linear regression model implemented as an additive correction factor model assumes an unknown regression coefficient for yields from a single milking and estimate it from the data. The latter improved the accuracy. Multiplicative correction factors are ratios of daily yields to yields from single milkings but their statistical interpretations differ. Overall, multiplicative correction factors are more accurate than additive correction factors. Biological and statistical challenges with the current yield factors are discussed. Systematic biases from discretizing milking interval are shown analytically compared to the corresponding linear regression models. An alternative model is proposed, which improved the estimation accuracy based on the simulation data. This new model postulates an exponential function for the daily milk yield curve. It is also analogous to an exponential growth function with a change rate tuned by a meta time as a linear function of milking interval. The methods and principles, though reviewed and evaluated on daily milk yield, similarly apply the estimation of daily fat and protein yields.

**Key words:** dairy cattle, daily milk yield curve, exponential function, milking interval, statistical models, yield correction factors