R: Matern variance structure

matern_vs {asreml} | R Documentation

## Matern variance structure

### Description

Model function for an extended Matern class The `mtrn` special function implements an extended Matern class (structure) which accommodates geometric anisotropy and a choice of metrics for random fields observed in two dimensions (Haskard et al., 2007). See the reference manual for further details.

### 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. Options are `1` for city block, and `2` for Euclidean distance (default = `2`).
`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

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_mtrn()`: Matern variance model; correlation form.

- `asr_mtrnv()`: Matern variance model; homogeneous variance form.

- `asr_mtrnh()`: Matern variance model; heterogeneous variance form.

[Package asreml version 4.2.0.480 Index]