Monte Carlo Comparison of Four Methods for Estimation of Genetic Parameters in the Univariate Case

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Abstract
Computer simulation was used to generate replicates of 2-way mixed-model data sets for comparing Henderson''s Method 3, maximum likelihood, restricted maximum likelihood and minimum norm quadratic unbiased estimation methods of variance component estimation. Estimates of sire and error variances and heritabilities by these statistical procedures were compared with parameters in unselected and selected dairy cattle data. Selection of records across fixed effects and selection within fixed effects were considered. Under a model of no selection, restricted and quadratic estimators of sire variances and heritability agreed more closely with parameters than those by maximum likelihood or Method 3. The mean square error for sire variance components was greater for Method 3 than for mixed model procedures, because random effect of sire was treated as fixed by Method 3 in obtaining the sum of squares for sire. Maximum likelihood estimators of error variance were biased downward, resulting in overstimation of heritability. Skewed distribution of sire effects did not seem to affect relative accuracy of estimates. Selection across fixed effects and selection within fixed effects reduced estimates in the univariate case regardless of estimation procedure. Selection within fixed effects affected estimates more seriously than selection across fixed effects. The restricted procedure generally converged faster than the maximum likelihood procedure.