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7 Command file: Specifying variance structures 129which is the correlation function of a random field which is continuous and oncedifferentiable. This has been used recently by Kammann and Wand (2003).As ν → ∞ then ρ M (·) tends to the gaussian correlation function.The metric parameter λ is not estimated by ASReml ; it is usually set to 2for Euclidean distance. Setting λ = 1 provides the cityblock metric, whichtogether with ν = 0.5 models a separable AR1×AR1 process. Cityblock metricmay be appropriate when the dominant spatial processes are aligned withrows/columns as occurs in field experiments. Geometric anisotropy is discussedin most geostatistical books (Webster and Oliver, 2001, Diggle et al., 2003) butrarely are the anisotropy angle or ratio estimated from the data. Similarly thesmoothness parameter ν is often set a-priori (Kammann and Wand, 2003, Diggleet al., 2003). However Stein (1999) and Haskard (2006) demonstrate thatν can be reliably estimated even for modest sized data-sets, subject to caveatsregarding the sampling design.The syntax for the Matérn class in ASReml is given by MATk where k is thenumber of parameters to be specified; the remaining parameters take theirdefault values. Use the !G qualifier to control whether a specified parameter isestimated or fixed. The order of the parameters in ASReml, with their defaults,is (φ, ν = 0.5, δ = 1, α = 0, λ = 2). For example, if we wish to fit a Matérnmodel with only φ estimated and the other parameters set at their defaultsthen we use MAT1. MAT2 allows ν to be estimated or fixed at some other value(for example MAT2 .2 1 !GPF). The parameters φ and ν are highly correlatedso it may be better to manually cover a grid of ν values.We note that there is non-uniqueness in the anisotropy parameters of thismetric d(·) since inverting δ and adding π 2to α gives the same distance. Thisnon-uniqueness can be removed by considering 0 ≤ α < π 2and δ > 0, or byconsidering 0 ≤ α < π and either 0 < δ ≤ 1 or δ ≥ 1. With λ = 2, isotropyoccurs when δ = 1, and then the rotation angle α is irrelevant: correlationcontours are circles, compared with ellipses in general. With λ = 1, correlationcontours are diamonds.• power models rely on the definition of distance for the associated term, forexample,– the distance between time points in a one-dimensional longitudinal analysis,– the spatial distance between plot coordinates in a two-dimensional field trialanalysis.Information for determining distances is supplied by the key argument on thestructure line.– For one dimensional cases, key may be