de Los Campos Gustavo, Gianola Daniel
Department of Animal Sciences, University of Wisconsin-Madison, WI 53706, USA.
Genet Sel Evol. 2007 Sep-Oct;39(5):481-94. doi: 10.1186/1297-9686-39-5-481. Epub 2007 Sep 27.
Multivariate linear models are increasingly important in quantitative genetics. In high dimensional specifications, factor analysis (FA) may provide an avenue for structuring (co)variance matrices, thus reducing the number of parameters needed for describing (co)dispersion. We describe how FA can be used to model genetic effects in the context of a multivariate linear mixed model. An orthogonal common factor structure is used to model genetic effects under Gaussian assumption, so that the marginal likelihood is multivariate normal with a structured genetic (co)variance matrix. Under standard prior assumptions, all fully conditional distributions have closed form, and samples from the joint posterior distribution can be obtained via Gibbs sampling. The model and the algorithm developed for its Bayesian implementation were used to describe five repeated records of milk yield in dairy cattle, and a one common FA model was compared with a standard multiple trait model. The Bayesian Information Criterion favored the FA model.
多变量线性模型在数量遗传学中日益重要。在高维设定中，因子分析（FA）可能为构建（协）方差矩阵提供一条途径，从而减少描述（协）离散所需的参数数量。我们描述了如何在多变量线性混合模型的背景下使用FA来对遗传效应进行建模。在高斯假设下，使用正交公共因子结构对遗传效应进行建模，使得边际似然是具有结构化遗传（协）方差矩阵的多元正态分布。在标准先验假设下，所有完全条件分布都具有封闭形式，并且可以通过吉布斯采样从联合后验分布中获得样本。为其贝叶斯实现而开发的模型和算法被用于描述奶牛产奶量的五个重复记录，并将一个公共FA模型与标准多性状模型进行了比较。贝叶斯信息准则支持FA模型。
