Multiple trait variance-covariance component estimation procedures with missing information for some traits

Restricted maximum likelihood was used to estimate variance and covariance components in a multiple trait unequal information setting. Estimates were obtained by two forms of an expectation maximization algorithm and a third shortcut algorithm, which uses expectation maximization for the within component and the method of scoring for the between sire component. Eleven data sets were simulated to establish the behavior of each algorithm under a variety of conditions. The shortcut algorithm converged uniformly faster than both expectation maximization algorithms. Priors close to the converged values were more helpful in reducing the number of iterations for the expectation maximization algorithms than the shortcut algorithm. Starting iteration with unknown covariances was more detrimental than values for the covariances which were one-half, twice, or three times the values at convergence, especially for the expectation maximization algorithms;Dairy Herd Improvement data from the Northeastern United States were analyzed. Data were 49,918 cows with mature equivalent 305 d milk yield (trait 1) and number of services (trait 2), of which 15,656 also had number of services as heifers (trait 3). Two separate analyses were conducted to study the effect of the unequal number of traits per cow. The missing data case included all cows, with or without number of services as heifers, and the equal data case included only cows with number of services as a heifer and cow. The model included fixed herd-year-seasons, random sires and error. There were 352 sires in the missing data case and 327 in the equal data case. Sires were assumed to be unrelated. Estimates of heritabilities, and genetic and error correlations for the equal data case were: h[subscript]sp12 =.14, h[subscript]sp22 =.02, h[subscript]sp32 =.01, r[subscript] g12 =.59, r[subscript] g13 =.07, r[subscript] g23 =.68, r[subscript] e12 =.15, r[subscript] e13 =.00, r[subscript] e23 =.03; and h[subscript]sp12 =.22, h[subscript]sp22 =.02, h[subscript]sp32 =.01, r[subscript] g12 =.30, r[subscript] g13 = -.24, r[subscript] g23 =.43, r[subscript] e12 =.15, r[subscript] e13 =.00, r[subscript] e23 =.03 for the missing data case. Parameter estimates changed by accounting for missing traits. Heritability increased for milk yield and decreased for number of services in heifers and cows. All estimates of genetic correlations decreased