Effects of data imbalance on estimation of heritability

Effects of data imbalance on bias, sampling variance and mean square error of heritability estimated with variance components were examined using a random two-way nested classification. Four designs, ranging from zero imbalance (balanced data) to "low", "medium" and "high" imbalance, were considered for each of four combinations of heritability (h(2)=0.2 and 0.4) and sample size (N=120 and 600). Observations were simulated for each design by drawing independent pseudo-random deviates from normal distributions with zero means, and variances determined by heritability. There were 100 replicates of each simulation; the same design matrix was used in all replications. Variance components were estimated by analysis of variance (Henderson's Method 1) and by maximum likelihood (ML). For the design and model used in this study, bias in heritability based on Method 1 and ML estimates of variance components was negligible. Effect of imbalance on variance of heritability was smaller for ML than for Method 1 estimation, and was smaller for heritability based on estimates of sire-plus-dam variance components than for heritability based on estimates of sire or dam variance components. Mean square error for heritability based on estimates of sire-plus-dam variance components appears to be less sensitive to data imbalance than heritability based on estimates of sire or dam variance components, especially when using Method 1 estimation. Estimation of heritability from sire-plus-dam components was insensitive to differences in data imbalance, especially for the larger sample size.