By C. R. Henderson (auth.), Prof. Dr. Daniel Gianola, Dr. Keith Hammond (eds.)
Developments in facts and computing in addition to their program to genetic development of cattle received momentum over the past two decades. this article stories and consolidates the statistical foundations of animal breeding. this article is going to turn out beneficial as a reference resource to animal breeders, quantitative geneticists and statisticians operating in those parts. it's going to additionally function a textual content in graduate classes in animal breeding method with prerequisite classes in linear versions, statistical inference and quantitative genetics.
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Additional resources for Advances in Statistical Methods for Genetic Improvement of Livestock
An extension of the Box-Cox theory of transformations to univariate mixed linear models is presented. The discussion includes estimation of the transformation and of the required variance components, including computing algorithms. An analysis of fixed effects and breeding values after the transformation involves the following steps: (1) estimate ratios of variance components and the transformation parameter from their joint posterior distribution; (2) conditionally on these values, integrate out the residual variance (O'~) from the joint posterior distribution of fixed, random effects and O'~, and (3) complete inferences using a multivariate-t distribution.
1) would hold and the "standard" analysis could be carried out. Unfortunately, the required transformation is not always known on theoretical grounds so it must be estimated using the available data and prior knowledge. As pointed out by Box and Tiao (1973), a transformation can be found when the problem arises because of an unsuitable choice of metric (in the example, testicular area rather than diameter), and this may not always be the case. , induce normality and remove heterogeneity of variance.
19). 35) 31 Evaluating these derivatives and their expectations is relatively easy under normality assumptions. 31), the second derivatives can be calculated readily and their expectations evaluated. 35) is more involved because results for the variance of quadratic forms under normality need to be invoked. With all derivatives and expectations evaluated, the Newton-Raphson algorithm (Dahlquist and Bjorck 1974) can be constructed. 6 Analysis of the Effects After Transformation We have addressed so far the situation where fInding the transformation (marginally or in conjunction with all or some of the dispersion parameters) is the focal point of the analysis.