van der Werf J H, Goddard M E, Meyer K
Animal Genetics and Breeding Unit, University of New England, Armidale, New South Wales, Australia.
J Dairy Sci. 1998 Dec;81(12):3300-8. doi: 10.3168/jds.S0022-0302(98)75895-3.
In the analysis of test day records for dairy cattle, covariance functions allow a continuous change of variances and covariances of test day yields on different lactation days. The equivalence between covariance functions as an infinite dimensional extension of multivariate models and random regression models is shown in this paper. A canonical transformation procedure is proposed for random regression models in large-scale genetic evaluations. Two methods were used to estimate covariance function coefficients for first parity test day yields of Holsteins: 1) a two-step procedure fitting covariance functions to matrices with estimated genetic and residual covariances between predetermined periods of lactation and 2) REML directly from data with a random regression model. The first method gave more reliable estimates, particularly for the periphery of the trajectory. The goodness of fit of a random regression model based on covariables describing the shape of the lactation curve was nearly the same as random regression on Legendre polynomials. In the latter model, two and three regression coefficients were sufficient to fit the covariance structure for additive genetic and permanent environment, respectively. The eigenfunction pattern revealed the possibility of selection for persistency. Covariance functions can be usefully implemented in large-scale test day models by means of random regressions.
在奶牛产奶日记录分析中，协方差函数允许不同泌乳天数的产奶日产量的方差和协方差连续变化。本文展示了作为多元模型无穷维扩展的协方差函数与随机回归模型之间的等价性。针对大规模遗传评估中的随机回归模型，提出了一种规范变换程序。采用两种方法估计荷斯坦牛头胎产奶日产量的协方差函数系数：1）一种两步程序，将协方差函数拟合到具有泌乳预定时间段之间估计遗传和残差协方差的矩阵；2）直接使用随机回归模型从数据中进行限制最大似然估计（REML）。第一种方法给出了更可靠的估计，特别是对于轨迹的边缘部分。基于描述泌乳曲线形状的协变量的随机回归模型的拟合优度与基于勒让德多项式的随机回归几乎相同。在后者模型中，分别有两个和三个回归系数足以拟合加性遗传和永久环境的协方差结构。特征函数模式揭示了选择持久性的可能性。通过随机回归，协方差函数可有效地应用于大规模产奶日模型。
