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Cows are 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. The initial approach estimated a test-day yield with doubled 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 be different between day and night. Additive correction factors (ACF) are evaluated by the average differences between AM and PM milk yield for various milking interval classes (MIC). We show that an ACF model is equivalent to a regression model of daily yield on categorical regressor variables, and a continuous variable for AM or PM yield with a fixed regression coefficient. Similarly, a linear regression model can be implemented as an ACF model with the regression coefficient for AM or PM yield estimated from the data. Multiplicative correction factors (MCF) are ratio of daily yield to yield from single milkings, but their statistical interpretations vary. Overall, MCF were more accurate for estimating daily milk yield than ACF. MCF have biological and statistical challenges. An exponential regression model was proposed as an alternative model for estimating daily milk yield, which improved the accuracy in the present study. Characterization of ACF and MCF showed how ACF and MCF improved the accuracy compared to doubling AM or PM yield as the daily milk yield. The methods were explicitly described to estimate daily milk yield in AM and PM milking plans. Still, the principles are generally applicable to cows milked more than two times a day, and they apply similarly to the estimation of daily fat and protein yields with some necessary modifications., Comment: 14 pages, 2 tables, and 1 figure

Additional file 1: Supplementary Fig. 1. Alpha diversity metrics by health status group. Boxplots showing the distribution of fecal and rumen alpha diversity for each health group control (CON, n = 11), control-hyperketonemic (C-HYK, n = 9), and hyperketonemic (HYK, n = 10), as measured by Pielou’s evenness, Faith’s phylogenetic diversity, and the Shannon diversity index.

Additional file 3: Supplementary Fig. 3. Rumen microbiome convergence summaries. The A) cross-validation score and B) loss plots are shown for the Songbird multinomial regression model used to compute log-fold changes in rumen microbial abundance relative to health status. The blue line represents our model computing log-fold changes with respect to health status; the orange line represents the null or baseline model demonstrating log-fold changes due to random chance.

Additional file 3: Supplementary Fig. 3. Rumen microbiome convergence summaries. The A) cross-validation score and B) loss plots are shown for the Songbird multinomial regression model used to compute log-fold changes in rumen microbial abundance relative to health status. The blue line represents our model computing log-fold changes with respect to health status; the orange line represents the null or baseline model demonstrating log-fold changes due to random chance.

Additional file 2: Supplementary Fig. 2. Fecal microbiome convergence summaries. The A) cross-validation score and B) loss plots are shown for the Songbird multinomial regression model used to compute log-fold changes in fecal microbial abundance relative to health status. The blue line represents our model computing log-fold changes with respect to health status; the orange line represents the null or baseline model demonstrating log-fold changes due to random chance.