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

In gstat: Spatial and Spatio-Temporal Geostatistical Modelling, Prediction and Simulation

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 )

Arguments

object	sample variogram, output of variogram
model	variogram model, output of vgm
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

Details

Other 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)

Value

returns a fitted variogram model (of class variogramModel).

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

Note

If fitting the range(s) is part of the job of this function, the results may well depend on the starting values, given in argument model. This is nothing new, but generally true for non-linear regression problems. This function uses the internal gstat (C) code, which iterates over (a) a direct (ordinary or weighted least squares) fit of the partial sills and (b) an iterated search, using gradients, for the optimal range value(s), until convergence of after a combined step ((a) and (b)) is reached.

If for a direct (i.e. not a cross) variogram a sill parameter (partial sill or nugget) becomes negative, fit.variogram is called again with this parameter set to zero, and with a FALSE flag to further fit this sill. This implies that once at the search space boundary, a sill value does not never away from it.

On singular model fits: If your variogram turns out to be a flat, horizontal or sloping line, then fitting a three parameter model such as the exponential or spherical with nugget is a bit heavy: there's an infinite number of possible combinations of sill and range (both very large) to fit to a sloping line. In this case, the returned, singular model may still be useful: just try and plot it. Gstat converges when the parameter values stabilize, and this may not be the case. Another case of singular model fits happens when a model that reaches the sill (such as the spherical) is fit with a nugget, and the range parameter starts, or converges to a value smaller than the distance of the second sample variogram estimate. In this case, again, an infinite number of possibilities occur essentially for fitting a line through a single (first sample variogram) point. In both cases, fixing one or more of the variogram model parameters may help you out.

Author(s)

Edzer Pebesma

References

http://www.gstat.org/

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

See Also

variogram, vgm

Examples

library(sp)
data(meuse)
vgm1 <- variogram(log(zinc)~1, ~x+y, meuse)
fit.variogram(vgm1, vgm(1,"Sph",300,1))

Example output

  model      psill  range
1   Nug 0.05065547   0.00
2   Sph 0.59060085 896.97

gstat documentation built on May 2, 2019, 4:59 p.m.