Evaluation of alternative methods for estimating the precision of REML-based estimates of variance components and heritability

Residual Maximum Likelihood (REML) analysis is the most widely used method to estimate variance components and heritability. This method is based on large sample theory under the assumption that the parameter estimates are asymptotically multivariate normally distributed with covariance matrix given by the inverse of the information matrix. Hence, these sampling variances could be biased if the assumption of asymptotic approximation is incorrect, especially when the sample size is small. Though it is difficult to assess the impact of sample size, an alternative option is to generate a full distribution of the parameters to determine the uncertainty of estimates. In this study, we compared the REML estimates of variance components, heritability and sampling variances of body-weight (BW), body-depth (BD), and condition-factor (K) with those obtained from four sampling-based methods viz., parametric and nonparametric bootstrap, asymptotic sampling and Bayesian estimation. The aim was to understand if a sample size of order 1413 was sufficient to contain adequate information for a reliable asymptotic approximation. The REML solution was close to values obtained from different sampling-based methods indicating that the present sample size was sufficient to estimate reliable genetic variation in different traits with varying heritability. The variance and heritability estimated by a nonparametric bootstrap estimate based on randomization of family effects gave comparable results as evaluated by REML for different traits. Hence, the nonparametric bootstrap estimate can be effectively used to understand whether the sample size is large enough to contain sufficient information under likelihood estimation assumptions.