Bayesian comparison of test‐day models under different assumptions of heterogeneity for the residual variance: the change point technique versus arbitrary intervals

Abstract

SummaryTest‐day milk yields from Spanish Holstein cows were analysed with two random regression models based on Legendre polynomials under two different assumptions of heterogeneity of residual variance which aim to describe the variability of temporary measurement errors along days in milk with a reduced number of parameters, such as (i) the change point identification technique with two unknown change points and (ii) using 10 arbitrary intervals of residual variance. Both implementations were based on a previous study where the trajectory of the residual variance was estimated using 30 intervals. The change point technique has been previously implemented in the analysis of the heterogeneity of the residual variance in the Spanish population, yet no comparisons with other methods have been reported so far. This study aims to compare the change point technique identification versus the use of arbitrary intervals as two possible techniques to deal with the characterization of the residual variance in random regression test‐day models. The Bayes factor and the cross‐validation predictive densities were employed for the model assessment. The two model‐selecting tools revealed a strong consistency between them. Both specifications for the residual variance were close to each other. The 10 intervals modelling showed a slightly better performance probably because the change point function overestimates the residual variance values at the very early lactation.