Estimation of genetic and phenotypic covariance functions for longitudinal or 'repeated' records by restricted maximum likelihood
Estimation of genetic and phenotypic covariance functions for longitudinal or 'repeated' records by restricted maximum likelihood
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DOI：
10.1016/s0301-6226(96)01414-5
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发表时间：
1997-03-01
期刊：
影响因子：
--
通讯作者：
Hill, WG
中科院分区：
文献类型：
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作者：
Meyer, K;Hill, WG
协方差函数相当于具有许多（可能是无限多）记录的性状的协方差矩阵，其中协方差被定义为年龄或时间的函数。它们可以适用于任何变化源，例如遗传、永久环境或表型。协方差函数的合适函数族是正交多项式。这些给出了任意两个年龄的测量值之间的协方差，作为记录时年龄的高阶多项式。多项式可以全阶或降阶拟合。前者相当于估计协方差分量的多变量分析。降阶拟合涉及较少的参数并平滑了协方差估计中的差异。它给出的预测协方差矩阵的秩等于拟合阶数。协方差函数的系数可以通过现有算法的重新参数化来估计协方差分量，通过限制最大似然来估计。对于所有性状具有相同设计矩阵的简单动物模型，估计协方差函数的计算要求与遗传协方差函数的拟合阶数成正比。显示了模拟数据和一组肉牛数据的应用。 (C) 1997 Elsevier Science B.V.
Covariance functions are the equivalent of covariance matrices for traits with many, potentially infinitely many, records in which the covariances are defined as a function of age or time. They can be fitted for any source of variation, e.g. genetic, permanent environment or phenotypic. A suitable family of functions for covariance functions are orthogonal polynomials. These give the covariance between measurements at any two ages as a higher order polynomial of the ages at recording. Polynomials can be fitted to full or reduced order. The former is equivalent to a multivariate analysis estimating covariance components, A reduced order fit involves less parameters and smoothes out differences in estimates of covariances. It gives predicted covariance matrices of rank equal to the order of fit. The coefficients of covariance functions can be estimated by restricted maximum likelihood through a reparameterisation of existing algorithms to estimate covariance components. For a simple animal model with equal design matrices for all traits, computational requirements to estimate covariance functions are proportional to the order of fit for the genetic covariance function. Applications to simulated data and a set of beef cattle data are shown. (C) 1997 Elsevier Science B.V.