Empirical algebraic modelling of live weight of Irish dairy cows over lactation

The aim of this study is to derive an equation that has the ability to model live weight of Irish dairy cows over lactation. The data set consisted of 6899 cows from 63 herds, of which 428 were from experimental herds and 6471 cows were from commercial herds. An initial examination focussed on time series techniques, as the data are of a time series nature. Splines were also examined to determine the dimensions of a model required to represent the data. As an incomplete gamma function, which was previously used to model milk yield, has been used in other studies to model live weight, various milk yield models were investigated. Finally, live weight changes between two calvings were modelled as a function of age, days in milk and pregnancy. As multicollinearity was evident in this function, the variance inflation factor was examined and principal component analysis was carried out on the variables responsible for multicollinearity. The proposed live weight model has a better fit than previous models, weak multicollinearity and the residuals are homoskedastic, independent and normally distributed. This live weight model therefore provides an acceptable level of accuracy in representing the shape of the live weight curve for Irish dairy cows and can be easily modified for different environmental scenarios.