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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.
###### References

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