Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: An ’average information’ restricted maximum likelihood algorithm for estimating reduced rank genetic covariance matrices or covariance functions for animal models with equal design matrices | Genet Sei Evol 1997 29 97-116 Elsevier INRA 16 HAỈ 1997 .rngnt Gt q . Anlmefe 97 Original article An average information restricted maximum likelihood algorithm for estimating reduced rank genetic covariance matrices or covariance functions for animal models with equal design matrices K Meyer Animal Genetics and Breeding Unit University of New England Armidale NSW 2351 Australia Received 21 May 1996 accepted 17 January 1997 Summary - A quasi-Newton restricted maximum likelihood algorithm that approximates the Hessian matrix with the average of observed and expected information is described for the estimation of covariance components or covariance functions under a linear mixed model. The computing strategy outlined relies on sparse matrix tools and automatic differentiation of a matrix and does not require inversion of large sparse matrices. For the special case of a model with only one random factor and equal design matrices for all traits calculations to evaluate the likelihood first and average second derivatives can be carried out trait by trait collapsing computational requirements of a multivariate analysis to those of a series of univariate analyses. This is facilitated by a canonical decomposition of the covariance matrices and corresponding transformation of the data to new uncorrelated traits. The rank of the estimated genetic covariance is determined by the number of nonzero eigenvalues of the canonical decomposition and thus can be reduced by fixing a number of eigenvalues at zero. This limits the number of univariate analyses needed to the required rank. It is particularly useful for the estimation of covariance function when a potentially large number of highly correlated traits can be described by a low order polynomial. REML average information covariance components reduced rank covariance function equal design matrices Resume Algorithme de maximum de vraisemblance restreint base sur l information moyenne pour estimer les matrices de covariance .
