Many economically important characteristics of agricultural crops are measured as ordinal traits. Statistical analysis of the genetic basis of ordinal traits appears to be quite different from regular quantitative traits. The generalized linear model methodology implemented via the Newton-Raphson algorithm offers improved efficiency in the analysis of such data, but does not take full advantage of the extensive theory developed in the linear model arena. Instead, we develop a multivariate model for ordinal trait analysis and implement an EM algorithm for parameter estimation. We also propose a method for calculating the variance-covariance matrix of the estimated parameters. The EM equations turn out to be extremely similar to formulae seen in standard linear model analysis. Computer simulations are performed to validate the EM algorithm. A real data set is analyzed to demonstrate the application of the method. The advantages of the EM algorithm over other methods are addressed. Application of the method to QTL mapping for ordinal traits is demonstrated using a simulated baclcross (BC) population.

译文

农业作物的许多经济上重要的特征被衡量为序数性状。序数性状的遗传基础的统计分析似乎与常规数量性状有很大不同。通过Newton-Raphson算法实现的广义线性模型方法在分析此类数据时提供了更高的效率,但并未充分利用线性模型领域中开发的广泛理论。相反,我们开发了用于顺序特征分析的多变量模型,并实现了用于参数估计的EM算法。我们还提出了一种计算估计参数的方差-协方差矩阵的方法。事实证明,EM方程与标准线性模型分析中的公式极为相似。进行计算机仿真以验证EM算法。分析了实际数据集以证明该方法的应用。讨论了EM算法相对于其他方法的优势。使用模拟的baclcross (BC) 种群证明了该方法在顺序性状的QTL映射中的应用。

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