J. Dairy Sci. 87:1908–1916 American Dairy Science Association, 2004. Estimated Heterogeneity of Phenotypic Variance of Test-Day Yield with a Structural Variance Model

First-lactation test-day milk, fat, and protein yields from New York, Wisconsin, and California herds from 1990 through 2000 were adjusted additively for age and lactation stage. A random regression model with third-order Legendre polynomials for permanent environ-mental and genetic effects was used. The model in-cluded a random effect with the same polynomial re-gressions for 2 yr of calvings within herd (herd-time effect) to provide herd-specific lactation curves that can change every 2 yr. (Co)variance components were esti-mated using expectation-maximization REML simulta-neously with phenotypic variances that were modeled using a structural variance model. Maximum heritabil-ity for test-day milk yield was estimated to be ∼20% around 200 to 250 d in milk; heritabilities were slightly lower for test-day fat and protein yields. Herd-time ef-fects explained 12 to 20 % of phenotypic variance and had the greatest impact at start of lactation. Variances of test-day yields increasedwith time, subclass size, and milking frequency. Test month had limited influence on variance. Variance increased for cows in herds with low and high milk yields and for early and late lactation stages. Repeatabilities of variances observed for a given class of herd, test-day, and milking frequency were 14 to 17 % across nested variance subclasses based on lac-tation stage. (Key words: heterogeneity of variance, (co)variance structure, test-day yield) Abbreviation key: EM = expectation maximization