fit.variogram: Fit a Variogram Model to a Sample Variogram

Description

Fit ranges and/or sills from a simple or nested variogram model to a sample variogram

Usage

fit.variogram(object, model, fit.sills = TRUE, fit.ranges = TRUE,
	fit.method = 7, debug.level = 1, warn.if.neg = FALSE, fit.kappa = FALSE)

Arguments

object

sample variogram, output of variogram

model

variogram model, output of vgm; see Details below for details on how NA values in model are initialised.

fit.sills

logical; determines whether the partial sill coefficients (including nugget variance) should be fitted; or logical vector: determines for each partial sill parameter whether it should be fitted or fixed.

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 whether it should be fitted or fixed.

fit.method

fitting method, used by gstat. The default method uses weights $N_h/h^2$ with $N_h$ the number of point pairs and $h$ the distance. This criterion is not supported by theory, but by practice. For other values of fit.method, see details.

debug.level

integer; set gstat internal debug level

warn.if.neg

logical; if TRUE a warning is issued whenever a sill value of a direct variogram becomes negative

fit.kappa

logical; if TRUE, a sequence of 0.3, 0.4,...,5 will be searched for optimal fit; alternatively another sequence can be given to this argument

Value

returns a fitted variogram model (of class variogramModel).

This is a data.frame with two attributes: (i) singular a logical attribute that indicates whether the non-linear fit converged (FALSE), or ended in a singularity (TRUE), and (ii) SSErr a numerical attribute with the (weighted) sum of squared errors of the fitted model. See Notes below.

Details

If any of the initial parameters of model are NA, they are given default values as follows. The range parameter is given one third of the maximum value of object$dist. The nugget value is given the mean value of the first three values of object$gamma. The partial sill is given the mean of the last five values of object$gamma.

Values for fit.method are 1: weights equal to $N_j$; 2: weights equal to $N_j/((gamma(h_j))^2)$; 5 (ignore, use fit.variogram.reml); 6: unweighted (OLS); 7: $N_j/(h_j^2)$. (from: http://www.gstat.org/gstat.pdf, table 4.2).

References

http://www.gstat.org/

Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers \& Geosciences, 30: 683-691.

Examples

Run this code

# NOT RUN {
library(sp)
data(meuse)
coordinates(meuse) = ~x+y
vgm1 <- variogram(log(zinc)~1, meuse)
fit.variogram(vgm1, vgm(1, "Sph", 300, 1))
fit.variogram(vgm1, vgm("Sph"))

# optimize the value of kappa in a Matern model, using ugly <<- side effect:
f = function(x) attr(m.fit <<- fit.variogram(vgm1, vgm(,"Mat",nugget=NA,kappa=x)),"SSErr")
optimize(f, c(0.1, 5))
plot(vgm1, m.fit)
# best fit from the (0.3, 0.4, 0.5. ... , 5) sequence:
(m <- fit.variogram(vgm1, vgm("Mat"), fit.kappa = TRUE))
attr(m, "SSErr")
# }

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