ASReml-S reference manual - VSN International

BAvailable variance modelsTable B.1 presents the full range of variance models available in asreml with their algebraicdescriptions and numbers of parameters. In most cases the algebraic form is forthe correlation model (id() to agau()). However, the models from diag() onwards areadditional heterogeneous variance models.Recall from Section 4.3 the algebraic forms of the homogeneous and heterogeneous variancemodels are determined as follows. Let C (ω×ω) = [C ij ] be the correlation matrixfor a particular correlation model. If Σ (ω×ω) is the corresponding homogeneous variancematrix thenΣ = σ 2 Cand has just one more parameter than the correlation model. For example, the homogeneousvariance model corresponding to the id() correlation model has variance matrixΣ = σ 2 I ω (specified idv() in the asreml function call, see below) and one parameter.Likewise, if Σ (ω×ω)his the heterogeneous variance matrix corresponding to C, thenΣ h = DCDwhere D (ω×ω) = diag (σ i ) . In this case there are an additional ω parameters. For example,the asreml function for the heterogeneous variance model corresponding to id()variance model has variance matrix⎡σ 2 0 . . . 0 ⎤1 0 σ 2 2Σ h = ⎢. . . 0⎣... .. .⎥⎦0 0 . . . σω2(specified idh() in the asreml command file, see below) and involves the ω parametersσ 2 1 . . . σ2 ω.