Linear mixed model for heritability estimation that explicitly addresses environmental variation

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


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

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

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Environment*
  • Humans
  • Inheritance Patterns
  • Linear Models*
  • Models, Genetic*
  • Phenotype*