Exact Confidence Intervals for a Variance Ratio (or Heritability) in a Mixed Linear Model

A family of procedures is given to construct confidence intervals for the heritability coefficient in a mixed linear model. The procedures are applicable for constructing confidence intervals for a ratio of variance components in a mixed linear model having two sources of variation. If the random effects are correlated, the procedure is valid even when there are zero degrees of freedom for error. The resulting intervals are evaluated in terms of bias and expected length. A sufficient condition for local unbiasedness is given and a numerical procedure is discussed for computing expected lengths. The investigator may select the best confidence interval procedure from the family of procedures based on these criteria. Computer software for obtaining the best interval is available from the authors.