Fit a Linear Model of Coregionalization to a Multivariable Sample Variogram

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;

References

http://www.gstat.org/

Author

Edzer Pebesma

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.