R: Fit a Linear Model of Coregionalization to a Multivariable...

fit.lmc {gstat} | R Documentation

## Fit a Linear Model of Coregionalization to a Multivariable Sample Variogram

### Description

Fit a Linear Model of Coregionalization to a Multivariable Sample Variogram; in case of a single variogram model (i.e., no nugget) this is equivalent to Intrinsic Correlation

### Usage

    fit.lmc(v, g, model, fit.ranges = FALSE, fit.lmc = !fit.ranges,
    correct.diagonal = 1.0, ...)

### Arguments

`v` | multivariable sample variogram, output of variogram
`g` | gstat object, output of gstat
`model` | variogram model, output of vgm; if supplied this value is used as initial value for each fit
`fit.ranges` | logical; determines whether the range coefficients (excluding that of the nugget component) should be fitted; or logical vector: determines for each range parameter of the variogram model whether it should be fitted or fixed.
`fit.lmc` | logical; if TRUE, each coefficient matrices of partial sills is guaranteed to be positive definite
`correct.diagonal` | multiplicative correction factor to be applied to partial sills of direct variograms only; the default value, 1.0, does not correct. If you encounter problems with singular covariance matrices during cokriging or cosimulation, you may want to try to increase this to e.g. 1.01
`...` | parameters that get passed to fit.variogram

### Value

returns an object of class `gstat`, with fitted variograms;

### Note

This function does not use the iterative procedure proposed by M. Goulard and M. Voltz (Math. Geol., 24(3): 269-286; reproduced in Goovaerts' 1997 book) but uses simply two steps: first, each variogram model is fitted to a direct or cross variogram; next each of the partial sill coefficient matrices is approached by its in least squares sense closest positive definite matrices (by setting any negative eigenvalues to zero).

The argument `correct.diagonal` was introduced by experience: by zeroing the negative eigenvalues for fitting positive definite partial sill matrices, apparently still perfect correlation may result, leading to singular cokriging/cosimulation matrices. If someone knows of a more elegant way to get around this, please let me know.

### Author(s)

Edzer Pebesma

### References

http://www.gstat.org/

### See Also

variogram, vgm, fit.variogram, `demo(cokriging)`

[Package gstat version 2.0-3 Index]