matern {asreml} | R Documentation

## Matern variance structure.

### Description

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, Verbyla AP (2007). “Anisotropic Matern correlation and spatial prediction using REML.” Journal of Agricultural and Biological Sciences, 12, 147–160.

[Package asreml version 4.1.0.176 Index]