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Proc Natl Acad Sci U S A. 2016 Jul 5;113(27):7377-82. doi: 10.1073/pnas.1510497113.

Linear mixed model for heritability estimation that explicitly addresses environmental variation.

Author information

Microsoft Research, Los Angeles, CA 90024;
Wellcome Trust Sanger Institute, Hinxton CB10 1SA, United Kingdom; Department of Medicine, University of Cambridge, Cambridge CB2 0SP, United Kingdom;
Microsoft Research, Redmond, WA 98052;
Wellcome Trust Sanger Institute, Hinxton CB10 1SA, United Kingdom;
MRC/UVRI Uganda Research Unit on AIDS, Uganda.
Microsoft Research, Los Angeles, CA 90024;


The linear mixed model (LMM) is now routinely used to estimate heritability. Unfortunately, as we demonstrate, LMM estimates of heritability can be inflated when using a standard model. To help reduce this inflation, we used a more general LMM with two random effects-one based on genomic variants and one based on easily measured spatial location as a proxy for environmental effects. We investigated this approach with simulated data and with data from a Uganda cohort of 4,778 individuals for 34 phenotypes including anthropometric indices, blood factors, glycemic control, blood pressure, lipid tests, and liver function tests. For the genomic random effect, we used identity-by-descent estimates from accurately phased genome-wide data. For the environmental random effect, we constructed a covariance matrix based on a Gaussian radial basis function. Across the simulated and Ugandan data, narrow-sense heritability estimates were lower using the more general model. Thus, our approach addresses, in part, the issue of "missing heritability" in the sense that much of the heritability previously thought to be missing was fictional. Software is available at


Gaussian radial basis function; environment; heritability estimation; linear mixed model; model misspecification

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