Comparison of Three Methods of Sire Evaluation

Three methods of sire evaluation were compared empirically--herdmate comparison, least squares, and maximum likelihood. Michigan Dairy Herd Improvement Association Holstein data representing 10,620 first lactation records and 1,003 herd-year groups were analyzed. Forty individual bulls representing three artificial insemination units were evaluated. The rank correlations among herdmate comparison and ]east squares estinlates ranged from 0.94 to 0.97. The rank correlations between the maximum likelihood evaluations and those computed by least squares and herdmate comparisons were .99 and .97, respectively. The sampling errors of the maximum likelihood sire constants were about 1.5% smaller than those for least squares estimates. Most of the recent research in sire evaluation methodology has eentered on the herdmate comparison procedure. The evidence indicates that the herdmate comparison procedure gives a reasonably accurate assessment of bulls used in artificial insemination [Heidhues et al., (6), McDaniel et al. (13)]. However, little attention has been given to the development of possible alternative procedures which possess nmre desirable properties. One probable reason is that of computational limitations. The herdmate comparison is relatively easy to program and does not have elaborate computational requirelnents. The herdmate comparison can be computed on a sequential basis, thus reducing computer storage requirements in contrast to procedures which require a matrix inversion process. There are several classes of nongenetie effects which must be considered in sire evaluation. The number of sets of factors illv¢~lved causes a geometric increase in computer storage requirements for nonsequential processes, such as matrix inversion. Henderson and Carter (10) apportioned the total variation in age-adjusted dairy records as follows: Received for publication 5uly 3, 1967. Milk Fat ( % ) Sire 7 7 Herd 30 33 Year-season 4 5 Sire X herd 2 2 Herd X year-season 14 15 Residual 43 38 Obviously, any model for sire evaluation must contain herd and year-season effects. Given this model, one nmy proceed in one of two ways: a) Adjust the data for herd and year-season effects and then analyze the data ignoring herds and year-seasons, or b) obtain a sinmltaueous solution for the effects of sires, herds, and year-seasons. Procedure a) might be one as elaborate as Henderson's Method Two (8) or as Sinlple as the herdmate comparison. Procedure b) would involve the application of a linear model requiring matrix inversion for a solution (since the data are highly nonorthogonal). Cunningham (1) pointed out that the herdmate comparison procedure amounts to a twostage process in which herd and year-season effects are removed (by expressing the records as deviations from herd-year-season means) and sires are evaluated by analyzing these deviations, ignoring herds and year-seasons. This means that sires are compared on a withinherd-year-season basis. Possible interactions of sires with herds and year-seasons are ignored. Also, sire comparisons contained in differences among herd-year-season means are not used. Due to nonorthogonality, the herd-year-season means contain some information on sire effects. A variation on the herdmate comparison procedure [Henderson, (9)] does utilize a portion of the inter-herd-year-season variance, but for a different purpose. This adjustment (the adjusted daughter average) takes into account that a portion of this variation represents genetic differences among the cow groups in these herds. As an alternative to the herdmate comparison, Cunningham (1) suggested the sinmttaneous consideration of the sire, herd, and year-season effects by linear estimation. The model he suggested is