From: Edzer J. Pebesma <e.pebesma_at_geo.uu.nl>

Date: Fri 05 Jan 2007 - 12:12:08 GMT

**[1] TRUE
**
Here I try to fit a three-parameter model to two data (semivariance)
points. Can't be done, infinite number of solutions, indicated by the
singularity flag. Second example: bad initial value for range:

Date: Fri 05 Jan 2007 - 12:12:08 GMT

Javier, consider two examples. First:

> library(gstat)

Loading required package: sp

> data(meuse) > coordinates(meuse)=~x+y > variogram(log(zinc)~1,meuse,width=100,cutoff=200) np dist gamma dir.hor dir.ver id 1 52 77.01898 0.1299659 0 0 var1 2 263 156.23373 0.2091154 0 0 var1> v = variogram(log(zinc)~1,meuse,width=100,cutoff=200) > vm = fit.variogram(v, vgm(1, "Exp", 100, 1)) Warning: singular model in variogram fit > attr(vm, "singular")

> v = variogram(log(zinc)~1,meuse,width=100,cutoff=1000)
> vm = fit.variogram(v, vgm(1, "Sph", 10, 1))
Warning: singular model in variogram fit
> attr(vm, "singular")

**[1] TRUE
**
Starting with a range of 10, any combination of nugget and partial sill
that fit the total sill improve the fit equally, indicated by the
singularity. A larger value of the range (try 800) will lead to a good,
non-singular fit.

fit.variogram does usually a non-linear regression, so any problem in that area is potentially present. You may want to consider fixing certain parameters to avoid certain problems; look at the fit.sills and fit.ranges arguments of fit.variogram.

In some cases, a singular model does fit the sample variogram nicely, e.g. where you use spherical or exponential models to effectively fit a linear semivariogram model: two parameters can be identified (nugget, slope) but three are fitted. The problem is to tell such a case from the two above, without looking at plots (i.e., automatically).

-- Edzer javier garcia-pintado wrote:Received on Sat Jan 06 00:26:46 2007

> Hello,> I'm using the gstat package within R for an automated procedure that> uses ordinary kriging.> I can see that there is a logical ("singular") atrtibute of some> adjusted model semivariograms:>> .- attr(*, "singular")= logi TRUE>> I cannot find documentation about the exact meaning and the implications> of this attribute, and I dont know anything about the inner calculations> of model semivariograms.>> I guess that the inverse of some matrix need to be calculated , and> this matrix is singular, but I also see that the model semivariogram is> calculated anyway.>> Could you briefly tell me something about the significance of this> attribute and if I should not use these model semivariograms when the> "singular" attibute is true?>

> Thank you very much and best regards,

>> Javier>>>

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