
Post by Jian Yang on Dec 2, 2015 0:30:38 GMT
Heritability ( h^{2}) is per definition nonnegative. However, the estimate of h^{2} is supposed to be following a normal distribution with mean h^{2} and variance SE ^{2} where SE is the standard error of the estimate of h^{2}. Therefore, to get an unbiased estimate of h^{2}, we should allow the estimate to be negative (remlnoconstrain option in GCTAGREML analysis). In practice, there are a least two scenarios when we would see negative estimate of h^{2}1) Small sample size. If the sample size is small, the sampling variance (SE ^{2}) will be large. In this case, the estimate of h^{2} will fluctuate a lot and therefore has a certain chance to jump out of the parameter space (between 0 and 1). 2) The true h^{2} parameter is small. If h^{2} is very small, then even if the sample size is large, we will still have a certain probability to see negative estimate. In the Yang et al. (2013 PLoS Genet) and Zhu et al. (2015 AJHG) papers, to get an unbiased estimate of the mean estimate of h^{2}, we did not constrain the estimate to 0.

