For example, an analysis of data from several sites might consider different error variances for each site, that is R = Σd R i, where Σd represents a direct sum (see any matrix algebra book for an explanation) and R i is the residual matrix for site i. However, there are several situations when the analysis require a more complex covariance structure, usually a direct sum or direct product of two or more matrices. For example, the residual covariance matrix in simple examples is R = I σ e 2, or the additive genetic variance matrix is G = A σ a 2 (where A is the numerator relationship matrix). Information, the covariance structure is the product of a scalar (a variance component) by a design matrix. This is because ASReml assumes that, in absence of any additional When fitting simple models (as in many examples of Univariate Analysis) one needs to specify only the model equation (the bit like y ~ mu…) but nothing about the covariances that complete the model specification.
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