On Some Results of C. Radhakrishna Rao Applicable to the Analysis of Multi-Environment Variety Trials
The analysis of results of a series of experiments repeated at several environments with the same set of plant varieties (genotypes) is usually based on a mixed effects model. Because of possible different responses of the varieties to variable environmental conditions, the standard mixed model for that analysis becomes questionable. Therefore, a more general mixed model is to be considered. However, in its most general form it involves usually a large number of variance and covariance components to be estimated. This causes computational problems, even when using advanced algorithms, unless some simplifying structures are imposed on the general covariance matrix. It has appeared, that these problems can be avoided when adopting a classic method proposed by Rao (1972). This method has been explored recently by Calinski, Czajka, Kaczmarek, Krajewski, and Pilarczyk (2005). The purpose of the present paper is to show the use of that and some other theoretical results of C. Radhakrishna Rao in detail.
AMS Subject Classification62F10 and 62K10
KeywordsGeneral mixed effects model Generalized lattice design Series of experiments Variance-covariance components estimation
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