Electronic Journal of Statistics

Statistical properties of simple random-effects models for genetic heritability

David Steinsaltz, Andrew Dahl, and Kenneth W. Wachter

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Random-effects models are a popular tool for analysing total narrow-sense heritability for quantitative phenotypes, on the basis of large-scale SNP data. Recently, there have been disputes over the validity of conclusions that may be drawn from such analysis. We derive some of the fundamental statistical properties of heritability estimates arising from these models, showing that the bias will generally be small. We show that the score function may be manipulated into a form that facilitates intelligible interpretations of the results. We go on to use this score function to explore the behavior of the model when certain key assumptions of the model are not satisfied — shared environment, measurement error, and genetic effects that are confined to a small subset of sites.

The variance and bias depend crucially on the variance of certain functionals of the singular values of the genotype matrix. A useful baseline is the singular value distribution associated with genotypes that are completely independent — that is, with no linkage and no relatedness — for a given number of individuals and sites. We calculate the corresponding variance and bias for this setting.

Article information

Electron. J. Statist., Volume 12, Number 1 (2018), 321-358.

Received: November 2016
First available in Project Euclid: 15 February 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 92D10: Genetics {For genetic algebras, see 17D92}
Secondary: 62P10: Applications to biology and medical sciences 62F10: Point estimation 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Heritability random-effects models random matrices Marčenko–Pastur distribution GCTA

Creative Commons Attribution 4.0 International License.


Steinsaltz, David; Dahl, Andrew; Wachter, Kenneth W. Statistical properties of simple random-effects models for genetic heritability. Electron. J. Statist. 12 (2018), no. 1, 321--358. doi:10.1214/17-EJS1386. https://projecteuclid.org/euclid.ejs/1518663656

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