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7 Command file: Specifying variance structures 131the elements of F are required, see Table 7.5,• FACVk models (CV for covariance) are an alternative formulation of FA modelsin which Σ is modelled as Σ = ΓΓ ′ + Ψ where Γ (ω×k) is a matrix of loadingson the covariance scale and Ψ is diagonal. The parameters in FACV– are specified in the order loadings (Γ) followed by variances (Ψ); when k isgreater than 1, constraints on the elements of Γ are required, see Table 7.5,– are related to those in FA by Γ = DF and Ψ = DED,difficult• the OWN variance structure is a facility whereby users may specify their own vari-ance structure. This facility requires the user to supply a program MYOWNGDGthat reads the current set of parameters, forms the G matrix and a full set ofderivative matrices, and writes these to disk. Before each iteration, ASRemlwrites the OWN parameters to a file, runs MYOWNGDG (which it presumes formsthe G and derivative matrix) and then reads the matrices back in. An exampleof MYOWNGDG.f90 is distributed with ASReml. It duplicates the AR1 and AR2structures. The following job fits an AR2 structure using this program.difficult• XFAk (X for extended) is the third form of the factor analytic model and hasthe same parameterisation as for FACV, that is, Σ = ΓΓ ′ + Ψ. However, XFAmodels– have parameters specified in the order diag (Ψ) and vec(Γ); when k is greaterthan 1, constraints on the elements of Γ are required, see Table 7.5,– may not be used in R structures,– are used in G structures in combination with the xfa(f,k) model term,– return the factors as well as the effects.– permit some elements of Ψ to be fixed to zero,– are computationally faster than the FACV formulation for large problemswhen k is much smaller than ω,Special consideration is required when using the XFAk model. The SSP mustbe expanded to have room to hold the k factors. This is achieved by using thexfa(f,k) model term in place of f in the model. For example,y ∼ site !r geno.xfa(site,2)0 0 1geno.xfa(site,2) 2genoxfa(site,2) 0 XFA2Example of using the OWN structurerepblcol