Accounting for sampling error in genetic eigenvalues using random matrix theory

Sztepanacz, Jacqueline L. and Blows, Mark W. (2017) Accounting for sampling error in genetic eigenvalues using random matrix theory. Genetics, 206 3: 1271-1284. doi:10.1534/genetics.116.198606

Author Sztepanacz, Jacqueline L.
Blows, Mark W.
Title Accounting for sampling error in genetic eigenvalues using random matrix theory
Journal name Genetics   Check publisher's open access policy
ISSN 1943-2631
Publication date 2017-07-01
Sub-type Article (original research)
DOI 10.1534/genetics.116.198606
Open Access Status Not yet assessed
Volume 206
Issue 3
Start page 1271
End page 1284
Total pages 14
Place of publication Bethesda, MD, United States
Publisher Genetics Society of America
Language eng
Abstract The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix.
Keyword Eigenvalues
Genetic variance
Random matrix theory
Tracy-Widom distribution
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
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School of Biological Sciences Publications
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