Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Inferences of betweenfamily components of variance and covariance among environments in balanced cross-classified designs | Genet Sei Evol 1994 26 117-136 Elsevier INRA 117 Original article Inferences on homogeneity of between-family components of variance and covariance among environments in balanced cross-classified designs JL Foulley1 D Hébert2 RL Quaas3 1 Institut National de la Recherche Agronomique Station de Génétique Quantitative et Appliquée Centre de Recherches de Jouy-en-Josas 78352 Jouy-en-Josas Cedex 2 Domaine Experimental Agronomic d Auzeville Centre de Recherches de Toulouse BP 27 31326 Castanet Tolosan Cedex France 3 Cornell University Department of Animal Science Ithaca NY 14853 USA Received 4 August 1993 accepted 29 November 1993 Summary - Estimation and testing of homogeneity of between-family components of variance and covariance among environments are investigated for balanced cross-classified designs. The variance-covariance structure of the residuals is assumed to be diagonal and heteroskedastic. The testing procedure for homogeneity of family components is based on the ratio of maximized log-restricted likelihoods for the reduced hypothesis of homogeneity and saturated models. An expectation-maximization EM algorithm is proposed for calculating restricted maximum likelihood REML estimates of the residual and between-family components of variance and covariance. The EM formulae to implement this are iterative and use the classical analysis of variance ANOVA statistics ie the between- and within-family sums of squares and cross-products. They can be applied both to the saturated and reduced models and guarantee the solutions to be in the parameter space. Procedures presented in this paper are illustrated with the analysis of 5 vegetative and reproductive traits recorded in an experiment on 20 full-sib families of black medic Medicago lupulina L tested in 3 environments. Application to pure maximum likelihood procedures extension to unbalanced designs and comparison with approaches relying on alternative models are also discussed. genotype X environment interaction
