To have your steak and eat it: Genetic principal component analysis for beef cattle data

Title
To have your steak and eat it: Genetic principal component analysis for beef cattle data
Publication Date
2006
Author(s)
Meyer, Karin
Type of document
Conference Publication
Language
en
Entity Type
Publication
Publisher
Sociedade Brasileira de Melhoramento Animal [Brazilian Society of Animal Breeding] (SBMA)
Place of publication
Brazil
UNE publication id
une:9989
Abstract
Quantitative genetic analyses usually deal with several, if not many, correlated traits or effects. Generally, the matrices of covariances among these effects are considered to be 'unstructured', i.e. for k traits we have k(k + 1)/2 distinct (co)variance components, and restrictions on estimates are imposed only to ensure that estimated matrices are positive semi-definite, i.e. do not have negative eigenvalues. In contrast, in other areas of statistics covariance matrices are often assumed to be structured. Parametric forms, such as compound symmetry or auto-regressive covariances (e.g. Jennrich and Schluchter 1986) are common assumptions for longitudinal or spatial data. Alternative parameterisations are based on the eigen-vectors and -values of the covariances matrices concerned. In particular, principal component (PC) analysis is widely utilised to summarise multivariate information and as a dimension reduction technique. So far, PC analyses (PCA) for genetic (or other random) effects have by and large been carried out in 2 steps, first obtaining full rank estimates of covariance matrices, and then performing an eigen-decomposition of the estimates. A better approach is to estimate the PCs directly and, at the same time, to restrict estimation to the most important components only (Kirkpatrick and Meyer 2004). This is readily accommodated within the usual linear, mixed model framework, requiring only a simple reparameterisation. This paper reviews direct estimation of PCs, and presents an application to an analysis of carcass traits of beef cattle.
Link
Citation
Proceedings of the 8th World Congress on Genetics Applied to Livestock Production

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