[Comparison of MIVQUE and REML with Monte Carlo simulation]

A comparison of two methods for estimation of variance component, MIVQUE and REML, was carried out on four data sets with Monte Carlo simulation. The model used was the sire model containing herd-year-season(HYS) effect (fixed), sire group effect(fixed) and sire effect(random), which is widely used in dairy cattle breeding. The largest data set consisted of 12847 records with 47 sires and 778 HYSs, which is corresponding to the milk yield data available currently in Beijing area. The smallest data set comprised 200 records with 148 HYSs and 20 sires. The criterion for the comparison were the bias and variance, either theoretical or empirical based on 1000 repeated simulations, of the estimates. The results show that for the larger data sets the two methods are little different from each other: Bias < 1% of the true values, correlation approximately 1, and variance (MIVQUE) approximately variance (REML). For the smaller data sets the MIVQUE was significantly better than REML. It was also shown that for REML the sample size like the first data set can satisfy its large sample properties of asymptotical unbiasedness and efficiency.