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2018 Statistical properties of simple random-effects models for genetic heritability
David Steinsaltz, Andrew Dahl, Kenneth W. Wachter
Electron. J. Statist. 12(1): 321-358 (2018). DOI: 10.1214/17-EJS1386


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.


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David Steinsaltz. Andrew Dahl. Kenneth W. Wachter. "Statistical properties of simple random-effects models for genetic heritability." Electron. J. Statist. 12 (1) 321 - 358, 2018.


Received: 1 November 2016; Published: 2018
First available in Project Euclid: 15 February 2018

zbMATH: 1383.92051
MathSciNet: MR3763909
Digital Object Identifier: 10.1214/17-EJS1386

Primary: 92D10
Secondary: 60B20 , 62F10 , 62P10

Keywords: GCTA , heritability , Marčenko–Pastur distribution , random matrices , random-effects models


Vol.12 • No. 1 • 2018
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