Variance Component Analysis of Unbalanced Diallel Crosses
Other Title
不均衡全互交之變方成分分析
Journal
中華農業研究
Journal Volume
35
Journal Issue
4
Pages
460-474
Date Issued
1986-12-06
Date
1986-12-06
Author(s)
Ching Liu
劉清
Abstract
This paper presents an efficient and stable method for estimating variance components from an unbalanced diallel crosses. The method follows the general procedure for computing the sums of squares in a random model by formulating testable hypotheses as if all effects were fixed and then compute the corresponding sums of squares. Expected sums of squares are derived from the expectations of quadratic forms of the observations. Estimable functions for effects in the model are generated by using the Cholesky decomposition of the reduced X'X matrix on the grounds that the sequential reduction is suitable in obtaining the sums of squares of general combining abilities, specific combining abilities, maternal effects and reciprocal effects in an unbalanced diallel crosses. As far as the sampling properties of the estimated variance components are concerned, no other method has yet been proved to be more optimal uniformly than the present one. Same computational method can also be used to handle the mixed diallel model with a little modification in the expected values of the sums of squares. Computing covariance components can be done virtually the same way as computing the variance components. Numerical examples are given to illustrate the computational procedurs.
本文提出一種有效且穩定的方法來估算不均衡全互交資料之變方成分。本法先將所有效應視為固定型以構成可測擬說（testable hypothesis），後再計算逢機型模式中各項效應之平方和，平方和之期望值是由觀測值二次形（quadratic form）之期望值導出。模式中各項效應之可估函數（estimable function）是由減縮（reduced）X'X矩陣經Cholesky分解而得來，此因在不均衡全互交資料中，逐次減縮法（sequential reduction）最適合用來計算一般組合力、特殊組合力、母系效應及反交效應等之平方和。就估算所得之變方成分的取樣性質（sampling properties）而言，尚未有其它方法經證實較本法一致為優。本文之計算方法亦可應用於混雜型全互交模式，僅需將平方和之期望值部份作些許修改。由於變方成分計算與變積成分計算之共同性，本法亦可用來估算變積成分。文中附有數例以說明計算過程。
Publisher
農業試驗所
Type
journal article
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