Assuming a specific type of data in the field of animal breeding, the iteration equations based on the expectation-maximization algorithm are derived for the restricted maximum likelihood estimation of variance components in a Sire and Dam Model. The application of the iteration equations to the data leads to the same estimates of additive genetic and environmental variances as those under the lndividual Animal Model. With the procedure using the iteration equations, compared to the case for the lndividual Animal Model, the size of the coefficient matrix to be inverted of the mixed model equations relatively becomes small, and the speed of convergence of the estimates becomes rather fast. Consequently, the total computational burden to obtain the proper estimates of additive genetic and environmental variances is expected to be considerably reduced in the proposed procedure. A numerical illustration, comparing the proposed procedure with the lndividual Animal Model procedure, is given using simulated carcass data on beef cattle.
We derive an expression of sampling (co) variances of the restricted maximum likelihood estimators of variance components in a mixed linear model with one random effect except for the residual term. The given matrix describing the sampling (co) variances is not a log likelihood-based one, but is rather developed noticing the equivalence between the restricted maximum likelihood estimators and the corresponding estimators by a minimum variance quadratic unbiased estimation in which the prior information for the variance ratio is based on the restricted maximum likelihood estimators of variance components. The current approach takes account of the exact (co) variances of the quadratics for the minimum variance quadratic unbiased estimation under normality, and the matrix derived is different from the inverse of the so-called information matrix which represents the large-sample, asymptotic dispersion matrix of the restricted maximum likelihood estimators. A numerical comparison is conducted to confirm the validity of our approach.
Overdispersion data of chromosome-aberration rates from atomic-bomb survivors were analyzed by the quasilikelihood/pseudolikelihood (QL/PL) estimating equation method (Breslow 1990). The variance function was composed of two extra-binomial variations: one is an intra-individual correlation, the other is a variation from dosimetry error. This dose-error-variance component was derived using the quasi-structural method (Pierce, Stram, Vaeth and Schafer 1992) that incorporates large-scale external dosimetry information. Using the results of fitting the QL/PL estimating equation, the Wald test revealed that the dose-estimation error is a significant source of overdispersion.