Realized Genome Sharing in Heritability Estimation Using Random Effects Models

For heritability estimation using a two-component random effects model, we provided formulas for the limiting distribution of the maximum likelihood estimate. These formulas are applicable even when the wrong measure of kinship is used to capture additive genetic correlation. When the model is correctly specified, we showed that the asymptotic sampling variance of heritability estimate is determined by both the study design and the extent of variation in the kinship measure that constitutes the additive genetic correlation matrix. When the correlation matrix is mis-specified, the extent of asymptotic bias depends additionally on how the fitted correlation matrix differs from the truth. In particular, we showed in a simulation study that estimating heritability using a population-based design and the classic GRM as the fitted correlation matrix can potentially contribute to the ”missing heritability” problem.