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 a re applicable for constructing confidence intervals for a ratio of var iance components in a mixed linear model hating two sources of variati on. If the random effects are correlated, the procedure is valid even when there are zero degrees of freedom for error. The resulting interv als are evaluated in terms of bias and expected length. A sufficient c ondition 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 b ased on these criteria. Computer software for obtaining the best inter val is available from the authors.