Bauman L E, Almasy L, Blangero J, Duggirala R, Sinsheimer J S, Lange K
Department of Biomathematics, Box 951766, University of California Los Angeles, CA 90095, USA.
Ann Hum Genet. 2005 Sep;69(Pt 5):590-611. doi: 10.1111/j.1529-8817.2005.00181.x.
The application of factor analysis to human genetics has the potential to discover the coordinated control of multiple traits by common environment, common polygenes, or a single major gene. Classical factor analysis explains the covariation among the components of a random vector by approximating the vector by a linear transformation of a small number of uncorrelated factors. In the current paper we show how factor analysis dovetails with the classical variance decompositions of biometrical genetics. To explore the relationships between related quantitative variables, and avoid complicated positive definiteness constraints, we employ Cholesky and factor analytic decompositions. We derive an ECM algorithm and a competing quasi-Newton algorithm for estimating parameters by maximum likelihood and propose tactics for selecting initial parameter values. We also show how parameter asymptotic standard errors under these parameterizations propagate to asymptotic standard errors of the underlying variance components. Our genetic analysis program Mendel, which now incorporates the program Fisher, has performed well on a variety of data sets. We illustrate our methods, algorithms, and models on two data sets: a bivariate quantitative genetic example using total finger ridge count data and a multivariate linkage example using insulin resistance data.
将因子分析应用于人类遗传学有潜力发现共同环境、共同多基因或单个主基因对多个性状的协同控制。经典因子分析通过用少量不相关因子的线性变换来近似随机向量，从而解释该随机向量各分量之间的协方差。在本文中，我们展示了因子分析如何与生物统计学遗传学的经典方差分解相契合。为了探索相关定量变量之间的关系，并避免复杂的正定约束，我们采用乔列斯基分解和因子分析分解。我们推导了用于通过最大似然估计参数的期望条件最大化（ECM）算法和一种竞争性拟牛顿算法，并提出了选择初始参数值的策略。我们还展示了在这些参数化下参数的渐近标准误差如何传播到基础方差分量的渐近标准误差。我们的遗传分析程序Mendel（现在已并入Fisher程序）在各种数据集上都表现良好。我们在两个数据集上阐述我们的方法、算法和模型：一个使用总指嵴计数数据的双变量定量遗传示例，以及一个使用胰岛素抵抗数据的多变量连锁示例。
