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7 Command file: Specifying variance structures 127AR1V 0.3 0.50.3 is the initial spatial correlation parameter and 0.5 is the initial varianceparameter value.Similarly, 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 heterogeneous variance model corresponding to ID is specifiedIDH in the ASReml command file (see below), involves the ω parameters σ 2 . . . 1 σ2 ωand is the variance matrix⎡σ 2 ⎤0 . . . 01 0 σ 2 . . . 02 Σ h =⎢ .⎣ . . .. ⎥ . ⎦0 0 . . . σω2Notes on the variance modelsThese notes provide additional information on the variance models defined inTable 7.3.New• the IDH and DIAG models fit the same diagonal variance structure,• the CORGH and US models fit the same completely general variance structureparameterized differently,• in CHOLk models Σ = LDL ′ where L is lower triangular with ones on thediagonal, D is diagonal and k is the number of non-zero off diagonals in L,• in CHOLkC models Σ = LDL ′ where L is lower triangular with ones on thediagonal, D is diagonal and k is the number of non-zero sub diagonal columnsin L. This is somewhat similar to the factor analytic model.• in ANTEk models Σ −1 = UDU ′ where U is upper triangular with ones on thediagonal, D is diagonal and k is the number of non-zero off diagonals in U,• the CHOLk, CHOLkC and ANTEk models are equivalent to the US structure, thatis, the full variance structure, when k is ω − 1,• initial values for US, CHOLk CHOLkC and ANTEk structures are given in the formof a US matrix which is specified lower triangle row-wise, viz