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

### 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)
```

*compositions*version 2.0-8 Index]