R: Fixed Covariance Matrix

RMfixcov {RandomFields} | R Documentation

## Fixed Covariance Matrix

### Description

`RMfixcov` is a user-defined covariance according to the given covariance matrix.

It extends to the space through a Voronoi tesselation.

### Usage

    RMfixcov(M, x, y=NULL, z=NULL, T=NULL, grid, var, scale, Aniso, proj,
    raw, norm)

### Arguments

`scale, Aniso, proj,var` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.
`M` | a numerical matrix defining the user-defined covariance for a random field; The matrix should be positive definite, symmetric and its dimension should be equal to the length of observation or simulation vector.
`x,y,z,T,grid` | optional. The usual arguments as in `RFsimulate` to define the locations where the covariates are given
`raw` | logical. If `FALSE` then the data are interpolated. This approach is always save, but might be slow. If `TRUE` then the data may be accessed when covariance matrices are calculated. No rescaling or anisotropy definition is allowed in combination with the model. The use is dangerous, but fast. Default: FALSE (outside mixed models)
`norm` | optional model that gives the norm between locations

### Details

The covariances passed are implemented for the given locations. Within any Voronoi cell (around a given location) the correlation is assumed to be one.

In particular, it is used in `RFfit` to define neighbour or network structure in the data.

### Value

`RMfixcov` returns an object of class `RMmodel`

### Note

Starting with version 3.0.64, the former argument `element` is replaced by the `general` option `set` in `RFoptions`.

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### References

- Ober, U., Ayroles, J.F., Stone, E.A., Richards, S., Zhu, D., Gibbs, R.A., Stricker, C., Gianola, D., Schlather, M., Mackay, T.F.C., Simianer, H. (2012): Using Whole Genome Sequence Data to Predict Quantitative Trait Phenotypes in Drosophila melanogaster. PLoS Genet 8(5): e1002685.

### See Also

`RMcovariate`, `RMmodel`, `RFsimulate`, `RFfit`, `RMuser`

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again

    ## Example 1 showing that the covariance structure is correctly implemented
    n <- 10
    z <- matrix(runif(n^2), nc=n)
    (z <- z %*% t(z))
    RFcovmatrix(RMfixcov(z), 1:n)

    ## Example 2 showing that the covariance structure is interpolated
    RFcovmatrix(RMfixcov(z, 1:n), c(2, 2.1, 2.5, 3))

    ## Example 3 showing the use in a separable space-time model
    model <- RMfixcov(z, 1:n, proj="space") * RMexp(s=40, proj="time")
    (z <- RFsimulate(model, x = seq(0,12, 0.5), T=1:100))
    plot(z)

[Package RandomFields version 3.1.50 Index]