Models utilizing a first order autoregressive - AR(1) - error structure were examined with a view to implementation in sire evaluation. The model comprised a fixed effect, a random [AR(1) covariance structure] effect within the fixed effect, and a residual. There were, therefore, three parameters to be estimated; the variance components associated with the random and the residual effects, and the correlation coefficient (p). Restricted Maximum Likelihood was used as the method of estimation and achieved via an Expectation Maximization algorithm. In the case of the latter, updates for the two variance components were achieved by closed form estimation, based on the assumption that p was known. The update of p, however, could not be found in this manner and was achieved by Fisher scoring, using the updated variance component associated with the random effect. For the (co)variance matrix associated with the random effect, direct methods were derived for finding elements of its inverse, and of the derivative of that inverse with respect to p. Simulation was used to test those methods, and the procedure was found to be robust as long as p was not close to ± unity. These results, along with some preliminary investigations of field data, suggest that the procedures developed may be beneficial in the modelling of nonzero covariances among records of animals in the same contemporary group.

K. M Wade, R. L Quaas, L. D van Vleck

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume XIII. Plenary lectures, molecular genetics and mapping, selection, prediction and estimation., , 508–511, 1990
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