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Just notes.
Mossa Merhi Reimert

2021-09-21

Maj & Mossa;

The current model that we are going with for SCC curves (or $\log(SCC)$) curves is called Wood's Model, i.e.

$$ y_t = a t ^ {b} \exp(-c t) $$

where $t$ is lactation day, and $a,b,c > 0$. Peak lactation day is $t_\texttt{peak} = b/c$.

Total yield is $y = \dfrac{a}{c^{b+1}} \Gamma(b+1)$; See Algebraic Model of the Lactation Curve in Cattle

The areas that can be improved are many, and these are just some of them:

  • Missing data overall: Since we only observe 10 measurements (at most) across across the entire lactation period (5, 305), there ought to be issues with low sample size here.
  • Missing data early in the lactation: The peak period might not not be captured at all, and the missing information here matters; One can choose to reduce the leverage of these observations on overall estimation; Or install prior knowledge about the expected peak $b/c$; Etc.
  • Influences from previous lactation period, like treatment, etc.
  • Affects of treatment on the SCC curves.