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(...))