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- Title
Better Estimates of Genetic Covariance Matrices by "Bending" Using Penalized Maximum Likelihood.
- Authors
Meyer, Karin; Kirkpatrick, Mark
- Abstract
Obtaining accurate estimates of the genetic covariance matrix ΣG for multivariate data is a fundamental task in quantitative genetics and important for both evolutionary biologists and plant or animal breeders. Classical methods for estimating ΣG are well known to suffer from substantial sampling errors; importantly, its leading eigenvalues are systematically overestimated. This article proposes a framework that exploits information in the phenotypic covariance matrix ΣP in a new way to obtain more accurate estimates of ΣG. The approach focuses on the ''canonical heritabilities'' (the eigenvalues of ΣP-1 ΣG), which may be estimated with more precision than those of ΣG because ΣP is estimated more accurately. Our method uses penalized maximum likelihood and shrinkage to reduce bias in estimates of the canonical heritabilities. This in turn can be exploited to get substantial reductions in bias for estimates of the eigenvalues of ΣG and a reduction in sampling errors for estimates of ΣG. Simulations show that improvements are greatest when sample sizes are small and the canonical heritabilities are closely spaced. An application to data from beef cattle demonstrates the efficacy this approach and the effect on estimates of heritabilities and correlations. Penalized estimation is recommended for multivariate analyses involving more than a few traits or problems with limited data.
- Subjects
QUANTITATIVE genetics; GENETICS; BOTANISTS; ANIMAL breeders; EIGENVALUES; HERITABILITY; MULTIVARIATE analysis; ANALYSIS of covariance
- Publication
Genetics, 2010, Vol 185, Issue 3, p1097
- ISSN
0016-6731
- Publication type
Article
- DOI
10.1534/genetics.109.113381