| fit.variogram {gstat} | R Documentation |
Fit ranges and/or sills from a simple or nested variogram model to a sample variogram
fit.variogram(object, model, fit.sills = TRUE, fit.ranges = TRUE,
fit.method = 7, debug.level = 1, warn.if.neg = FALSE )
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 table 4.2 in the gstat
manual. |
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 |
returns a fitted variogram model (of class variogram.model).
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.
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
interates over (a) a direct (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.
Edzer J. Pebesma
Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30: 683-691.
data(meuse) vgm1 <- variogram(log(zinc)~1, ~x+y, meuse) fit.variogram(vgm1, vgm(1,"Sph",300,1))