R: Compositional Linear Model of Coregionalisation

CompLinModCoReg {compositions} | R Documentation

## Compositional Linear Model of Coregionalisation

### Description

Creates a Variogram model according to the linear model of spatial corregionalisation for a compositional geostatistical analysis.

### Usage

    CompLinModCoReg(formula,comp,D=ncol(comp),envir=environment(formula))

### Arguments

`formula` | A formula without left side providing a formal description of a variogram model.
`comp` | a compositional dataset, needed to provide the frame size
`D` | The dimension of the multivariate dataset
`envir` | The enviroment in which formula should be interpreted.

### Details

The linear model of coregionalisation uses the fact that sums of valid variogram models are valid variograms, and that scalar variograms multiplied with a positive definite matrix are valid variograms for vector-valued random functions.

This command computes such a variogram function from a formal description, via a formula without left-hand side. The right-hand side of the formula is a sum. Each summand is either a product of a matrix description and a scalar variogram description or only a scalar variogram description. Scalar variogram descriptions are either formal function calls to

- `sph(range)` for spherical variogram with range `range`

- `exp(range)` for an exponential variogram with effective range `range`

- `gauss(range)` for a Gaussian variogram with effective range `range`

- `gauss(range)` for a cardinal sine variogram with range parameter `range`

- `pow(range)` for an power variogram with range parameter `range`

- `lin(unit)` linear variogram 1 at `unit`.

- `nugget()` for adding a nuggeteffect.

Alternatively it can be any expression, which will be evaluated in envir and should depende on a dataset of distantce vectrs `h`. An effective range is that distance at which one reaches the sill (for spherical) of 95% of its values (for all other models). Parametric ranges are given for those models that do not have an effective range formula.
The matrix description always comes first. It can be `R1` for a rank 1 matrix; `PSD` for a Positive Semidefinite matrix; \(S\) for a scalar Sill factor to be multiplied with the identity matrix; or any other construct evaluating to a matrix, like e.g. a function of some parameters with default values, that if called is evaluated to a positive semidefinite matrix. `R1` and `PSD` can also be written as calls providing a vector or respectively a matrix providing the parameter.
The variogram is created with default parameter values. The parameters can later be modified by modifiying the default parameter with assignments like `formals(vg)$sPSD1 = parameterPosdefMat(4*diag(5))`. We would anyway expect you to fit the model to the data by a command like `fit.lmc(logratioVariogram(...),CompLinModCoReg(...))`

### Value

A variogram function, with the extra class "`CompLinModCoReg`".

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

### References

What to cite??

### See Also

`vgram2lrvgram`, `vgmFit2lrv`

### Examples

    ## Not run:
    data(juraset)
    X <- with(juraset,cbind(X,Y))
    comp <- acomp(juraset,c("Cd","Cu","Pb","Co","Cr"))
    CompLinModCoReg(~nugget()+sph(0.5)+R1*exp(0.7),comp)
    CompLinModCoReg(~nugget()+R1*sph(0.5)+R1*exp(0.7)+(0.3*diag(5))*gauss(0.3),comp)
    CompLinModCoReg(~nugget()+R1*sph(0.5)+R1(c(1,2,3,4,5))*exp(0.7),comp)

    ## End(Not run)

[Package compositions version 2.0-0 Index]