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7 Command file: Specifying variance structures 1123c Two-dimensional separable autoregressive spatial model with measurementerrorNIN Alliance Trial 1989variety !Aid.row 22column 11nin89aug.asd !skip 1yield ∼ mu variety !r units,!f mv1 2 011 column AR1 0.322 row AR1 0.3This model extends 3b by adding a randomunits term. ThusV = σe 2 (γ η I 242+ Σ c (ρ c ) ⊗ Σ r (ρ r )) . The reservedword units tells ASReml to constructan additional random term with one level foreach experimental unit so that a second (independent)error term can be fitted. A unitsterm is fitted in the model in cases like this,where a variance structure is applied to theerrors. Because a G structure is not explicitlyspecified here for units, the default IDVstructure is assumed. The units term is often fitted in spatial models for fieldtrial data to allow for a nugget effect.4 Two-dimensional separable autoregressive spatial model with randomreplicate effectsSee Section 7.4This is essentially a combination of 2b and 3cto demonstrate specifying an R structure anda G structure in the same model. The varianceheader line 1 2 1 indicates that there is one Rstructure (1) that involves two variance models(2) and is therefore the direct product oftwo matrices, and there is one G structure (1).The R structures are defined first so the nexttwo lines are the R structure definition linesfor e, as in 3b. The last two lines are the Gstructure definition lines for repl, as in 2b. Inthis case V = σe 2 (γ r I 242+ Σ c (ρ c ) ⊗ Σ r (ρ r )) .NIN Alliance Trial 1989variety !Aid.row 22column 11nin89aug.asd !skip 1yield ∼ mu variety !r repl,!f mv1 2 111 column AR1 0.322 row AR1 0.3repl 1repl 0 IDV 0.1