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# matern – Matern variance structure

###### Description

matern is a model function for an extended Matern class.

###### Usage
```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)```
###### Arguments
 `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.
###### Details

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.

###### Functions
 `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.