Faculdade de Ciências Agrárias e Veterinárias, UNESP, Jaboticabal (SP), Brazil.
J Anim Breed Genet. 2010 Dec;127(6):433-41. doi: 10.1111/j.1439-0388.2010.00873.x. Epub 2010 Oct 28.
The objective of this work was to estimate covariance functions using random regression models on B-splines functions of animal age, for weights from birth to adult age in Canchim cattle. Data comprised 49,011 records on 2435 females. The model of analysis included fixed effects of contemporary groups, age of dam as quadratic covariable and the population mean trend taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were modelled through a step function with four classes. The direct and maternal additive genetic effects, and animal and maternal permanent environmental effects were included as random effects in the model. A total of seventeen analyses, considering linear, quadratic and cubic B-splines functions and up to seven knots, were carried out. B-spline functions of the same order were considered for all random effects. Random regression models on B-splines functions were compared to a random regression model on Legendre polynomials and with a multitrait model. Results from different models of analyses were compared using the REML form of the Akaike Information criterion and Schwarz' Bayesian Information criterion. In addition, the variance components and genetic parameters estimated for each random regression model were also used as criteria to choose the most adequate model to describe the covariance structure of the data. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most adequate to describe the covariance structure of the data. Random regression models using B-spline functions as base functions fitted the data better than Legendre polynomials, especially at mature ages, but higher number of parameters need to be estimated with B-splines functions.
本研究旨在使用动物年龄 B 样条函数的随机回归模型来估计协方差函数，应用于 Canchim 牛从出生到成年的体重数据。数据包含 2435 头母牛的 49011 条记录。分析模型包括群体固定效应、母体年龄的二次协变量效应以及通过动物年龄的正交多项式三次回归考虑的群体均值趋势。残差方差通过具有四个类别的阶跃函数进行建模。直接和母体加性遗传效应以及动物和母体持久环境效应被作为随机效应包含在模型中。共进行了十七次分析，考虑了线性、二次和三次 B 样条函数以及最多七个节点。对于所有随机效应，都考虑了相同阶次的 B 样条函数。将 B 样条函数随机回归模型与 Legendre 多项式随机回归模型和多性状模型进行了比较。使用 REML 形式的 Akaike 信息准则和 Schwarz 贝叶斯信息准则比较了不同分析模型的结果。此外，还使用每个随机回归模型估计的方差分量和遗传参数作为标准，选择最适合描述数据协方差结构的模型。拟合二次 B 样条的模型，直接加性遗传效应和动物持久环境效应有四个节点或三个段，母体加性遗传效应和母体持久环境效应有两个节点，是最适合描述数据协方差结构的模型。使用 B 样条函数作为基函数的随机回归模型比 Legendre 多项式更适合拟合数据，尤其是在成熟年龄时，但 B 样条函数需要估计更多的参数。
