Model Selection in Estimation of Covariance Functions for Growth of Angora Goats

Covariance functions have been proposed as an alternative to model longitudinal data in animal breeding because of their various merits in comparison to the classical analytical methods. In practical estimation, different models and polynomial orders fitted can influence the estimates of covariance functions and thus genetic parameters. The objective of this study was to select model for estimation of covariance functions for body weights of Angora goats at 7 time points. Covariance functions were estimated by fitting 6 random regression models with birth year, birth month, sex, age of dam, birth type, and relative birth date as fixed effects. Random effects involved were direct and maternal additive genetic, and animal and maternal permanent environmental effects with different orders of fit. Selection of model and orders of fit were carried out by likelihood ratio test and 4 types of information criteria. The results showed that model with 6 orders of polynomial fit for direct additive genetic and animal permanent environmental effects and 4 and 5 orders for maternal genetic and permanent environmental effects, respectively, were preferable for estimation of covariance functions. Models with and without maternal effects influenced the estimates of covariance functions greatly. Maternal permanent environmental effect does not explain the variation of all permanent environments, well suggesting different sources of permanent environmental effects also has large influence on covariance function estimates.