REML Fit Direct Variogram Partial Sills to Data

Fit Variogram Sills to Data, using REML (only for direct variograms; not for cross variograms)

Usage

fit.variogram.reml(formula, locations, data, model, debug.level = 1, set, degree = 0)

Arguments

formula: formula defining the response vector and (possible) regressors; in case of absence of regressors, use e.g. z~1
locations: spatial data locations; a formula with the coordinate variables in the right hand (dependent variable) side.
data: data frame where the names in formula and locations are to be found
model: variogram model to be fitted, output of vgm
debug.level: debug level; set to 65 to see the iteration trace and log likelihood
set: additional options that can be set; use set=list(iter=100) to set the max. number of iterations to 100.
degree: order of trend surface in the location, between 0 and 3

Value

an object of class "variogramModel"; see fit.variogram

References

Christensen, R. Linear models for multivariate, Time Series, and Spatial Data, Springer, NY, 1991.

Kitanidis, P., Minimum-Variance Quadratic Estimation of Covariances of Regionalized Variables, Mathematical Geology 17 (2), 195--208, 1985

Author

Edzer Pebesma

Note

This implementation only uses REML fitting of sill parameters. For each iteration, an $n \times n$ matrix is inverted, with $n$ the number of observations, so for large data sets this method becomes demanding. I guess there is much more to likelihood variogram fitting in package geoR, and probably also in nlme.

Examples

library(sp)
data(meuse)
fit.variogram.reml(log(zinc)~1, ~x+y, meuse, model = vgm(1, "Sph", 900,1))
#>   model      psill range
#> 1   Nug 0.02549524     0
#> 2   Sph 0.61080053   900