|Van Vleck, Lloyd|
Submitted to: Journal of Dairy Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 3/11/1999
Publication Date: N/A
Interpretive Summary: The method of calculating components of variation which seems to have the most optimal properties is called restricted maximum likelihood (REML). Be- cause by definition a variance cannot be negative, REML estimates must always be zero or greater; therefore, REML estimates of variability would be biased for factors which have no variation as only estimates that are zero or greater than zero would be accepted. The size of such bias cannot be determined analytically. This study estimated the bias epirically. The actual data were analayzed with the correct model including effects of cytoplasmic line which is likely to have small variance. The actual data were then reanalyzed 20 times with cytoplasmic lines assigned randomly to the records. The expectation was that variance due to cytoplasmic lines should be about zero. This procedure was repeated for 10 samples of records with each including about 7,000 animals. The estimates from the actual data were about 1.1% of total variance but from the same data with levels assigned randomly to cytoplasmic effects the estimates averaged .3%. Thus, estimates of cytoplasmic line effects are likely to be overestimated by up to .3%. Variance due to sire by herd interaction effects which was another factor to which levels were randomly assigned may have been biased by up to .4%.
Technical Abstract: A total of 138,869 lactation milk yields (305d, 2x, ME) from first three parities of 68,063 New York Holstein cows were used to estimate by REML variance components due to additive direct genetic, cow permanent environmental (cow within sire for sire model), sire by herd interaction, and cytoplasmic line effects. The original data were assigned to ten random msamples which were each analyzed using both an animal model and a sire model. For each sample of original data, twenty other analyses were done with levels assigned randomly to cytoplasmic and sire by herd interaction effects (simulated data) of which ten were analyzed with an animal and ten with a sire model. The models also included fixed effects of herd-year- seasons. Average fractions of phenotypic variance and average standard errors for animal and sire models respectively were: for additive direct genetic effects, .300 (.029) and .228 (.040) for original data and .325 (.025) and .262 (.039) for simulated data; for sire by herd interaction effects, .015 (.008) and .018 (.007) for original data and .003 (.007) and .004 (.009) for simulated data; and for cytoplasmic line effects, .011 (.007) and .043 (.008) for original data and .003 (.006) and .003 (.007) for simulated data. The differences between estimates of variance components for original data and the same data with randomly assigned levels of cytoplasmic and sire by herd interaction effects suggest that estimates of fractions of total variance due to sire by herd interaction and cytoplasmic effects estimated with REML may be biased upward by .003 to .004.