compositions (version 2.0-8)

CompLinModCoReg: 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))

Value

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

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.

Author

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

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(...))

References

What to cite??

See Also

vgram2lrvgram, vgmFit2lrv

Examples

if (FALSE) {
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)
}