fit.variogram {sgeostat}

Variogram Model Fit

Description

Fit variogram models (exponential, spherical, gaussian, linear) to empirical variogram estimates.

An object of class variogram.model represents a fitted variogram model generated by fitting a function to a variogram object. A variogram.model object is composed of a list consisting of a vector of parameters, parameters, and a semi-variogram model function, model.

Usage

fit.variogram(model="exponential", v.object, nugget, sill,
              range, slope, ...)
fit.exponential(v.object, c0, ce, ae, type='c', 
                iterations=10, tolerance=1e-06, echo=FALSE, plot.it=FALSE, weighted=TRUE)
fit.gaussian(v.object, c0, cg, ag, type='c', 
             iterations=10, tolerance=1e-06, echo=FALSE,  plot.it=FALSE, weighted=TRUE)
fit.spherical(v.object, c0, cs, as, type='c', iterations=10,
             tolerance=1e-06, echo=FALSE,  plot.it=FALSE, weighted=TRUE,
             delta=0.1, verbose=TRUE)
fit.wave(v.object, c0, cw, aw, type='c', 
         iterations=10, tolerance=1e-06, echo=FALSE,  plot.it=FALSE, weighted=TRUE)
fit.linear(v.object, type='c', plot.it=FALSE,iterations=1, c0=0, cl=1)

Arguments

model

only available for fit.variogram, switches what kind of model should be fitted ("exponential", "wave", "gaussian", "spherical", "linear").

v.object

a variogram object generated by est.variogram()

nugget, sill, range, slope

only available for fit.variogram, initial estimates for specified variogram model (slope only for fit.linear)

c0

initial estimate for nugget effect, valid for all variogram types, partial sill (cX) and (asymptotical) range (aX) as follows:

ce, ae

initial estimates for the exponential variogram model

cg, ag

initial estimates for the gaussian variogram model

cs, as

initial estimates for the sperical variogram model

cw, aw

initial estimates for the periodical variogram model

cl

initial estimates for the linear variogram model (slope)

type

one of 'c' (classic), 'r' (robust), 'm' (median). Indicates to which type of empirical variogram estimate the model is to be fit.

iterations

the number of iterations of the fitting procedure to execute.

tolerance

the tolerance used to determine if model convergence has been achieved.

delta

initial stepsize (relative) for pseudo Newton approximation, applies only to fit.spherical

echo

if TRUE, be verbose.

verbose

if TRUE, be verbose (show iteration for spherical model fit).

plot.it

if TRUE, the variogram estimate will be plotted each iteration.

weighted

if TRUE, the fit will be done using weighted least squares, where the weightes are given in Cressie (1991, p. 99)

...

only fit.variogram: additional parameters to hand through to specific model fit functions

Value

A variogram.model object:

parameters

vector of fitted model parameters

model

function implementing a valid variogram model

Note

fit.exponential, fit.gaussian and fit.wave use an iterative, Gauss-Newton fitting algorithm to fit to an exponential or gaussian variogram model to empirical variogram estimates. fit.spherical uses the same algorithm but with differential quotients in place of first derivatives. When weighted is TRUE, the regression is weighted by n(h)/gamma(h)^2 where the numerator is the number of pairs of points in a given lag.

Setting iterations to 0 means no fit procedure is applied. Thus parameter values from external sources can be plugged into a variogram model object.

References

http://www.gis.iastate.edu/SGeoStat/homepage.html

See Also

est.variogram

Examples

#
# automatic fit:
#
maas.vmod<-fit.gaussian(maas.v,c0=60000,cg=110000,ag=800,plot.it=TRUE,
                        iterations=30)
#
# iterations=0, means no fit, intended for "subjective" fit
#
maas.vmod.fixed<-fit.variogram("gaussian",maas.v,nugget=60000,sill=110000,
                               range=800,plot.it=TRUE,iterations=0)