Estimating Parameters of a Random Regression Test Day Model for First Three Lactation Milk Production Traits Using the Covariance Function Approach

Estimating (co)variance parameters of a random regression model for test day yields of dairy cattle has been proven to be a challenging task due to the complexity of (co)variance structure of the test day yields. Two common approaches have been practised so far for the estimation of parameters: direct random regression model approach and indirect covariance functions (CF) approach. Animal genetic and permanent environmental effects are modelled in the direct approach with a lactation curve function and (co)variance components of random regression coefficients (RRC) for both effects are estimated jointly with other effects in the model. By contrast, in the indirect CF approach (co)variance parameters of genetic and residual effects are estimated using a multivariate model that treats test day yields of different lactation stages as genetically distinct traits, and then CF are fitted to the estimated (co)variance matrices from the first step to obtain (co)variances of RRC for additive genetic as well as permanent environmental effects. The objective of this study was to estimate (co)variance components of RRC of a random regression test day model for first three lactation test day yields via the CF approach.