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matern – Matern variance structure


matern is a model function for an extended Matern class.

mtrn(x, y, phi=NA, nu=0.5, delta=1.0, alpha=0.0, lambda=2)

mtrnv(x, y, phi=NA, nu=0.5, delta=1.0, alpha=0.0, lambda=2, init=0.1)

mtrnh(x, y, phi=NA, nu=0.5, delta=1.0, alpha=0.0, lambda=2, init=0.1)
x An object in data containing the x coordinates.
y An object in data containing the y coordinates.
phi The range parameter; default NA.
nu The smoothness parameter; default 0.5.
delta Governs geometric anisotropy; default 1.0.
alpha Governs geometric anisotropy; default 0.0.
lambda Specifies the choice of metric: 2 is Euclidean distance (default), and 1 is city block
init An optional vector of initial values for any variance parameters, with an optional names attribute from the set {P, U, F} specifying the boundary constraint as positive, unconstrained or fixed, respectively.

The mtrn special function implements an extended Matern class which accomodates geometric anisotropy and a choice of metrics for random fields observed in two dimensions (Haskard et al., 2007). See the User Guide for details.

If an argument to mtrn is numeric, it is treated as a starting value for estimation and given the constraint code P (positive). This behaviour can be altered by concatenating the numeric value followed by the constraint code (“P”, “U” or “F”) into a character string. If an argument is absent from the call, the corresponding parameter is held fixed at its default value.

asr_mtrnv: Matern variance model, homogeneous variance form.
asr_mtrnh: Matern variance model, heterogeneous variance form.

Haskard KA, Cullis BR and Verbyla AP (2007). “Anisotropic Matern correlation and spatial prediction using REML.” Journal of Agricultural and Biological Sciences, 12, pp. 147-160.

Updated on August 7, 2018

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