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Estimation of Variances in Animal Model and Reduced Animal Model for Single Traits and Single Records

Department of Animal Sciences, University of Illinois, Urbana 61801

ABSTRACT

A reduced animal model can be used for best linear unbiased prediction, and this results in a large reduction in number of equations to be solved compared with the animal model. Similarly, the reduced animal model can be used for estimation of variances by minimum variance quadratic unbiased estimation and by restricted maximum likelihood. Generalized inverses of coefficient matrices of mixed model equations are required for these methods of estimation of variances under both the animal and the reduced animal model. Consequently, use of the reduced animal model can markedly reduce the order of such matrices. Simple examples are presented for these methods of estimation under both the animal model and the reduced animal model.