Statistical modelling

Contents

Fitting Wood's curve
Milk curve comparisons
Concentrates and milk yield

Fitting Wood's curve

Here we repeat the analysis conducted in Romney et al.'s paper by fitting Wood's model:
y_n = an^be^-cn, where y_n is the milk yield on day n and a, b and c are constants.
This model has been successfully applied to milk yields of dairy cows raised in the developed world, and satisfactorily represents the peak yield that is commonly achieved around about six to seven weeks into lactation.

In sub-Saharan Africa, where smallholder farmers often cannot afford the optimal feeding levels required in early lactation, the early peak in milk yield often does not materialise, and so Wood's formula may not always provide such a good fit (Kamidi, 2005).

It is common to convert Wood's model to logarithms:
      log_e y_n = log_e a + b. log_e n - c.n

which can be fitted by a multiple regression analysis with independent variables
      x₁ = log_e n and x₂ = n.