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