GSTAT - singular in meters not km

Zev, if you do a

v.fit<-fit.variogram(v, vgm(0.0005, "Sph", 40000, 
0.00001),debug.level=32)

you'll see that the X matrix of the Gauss-Newton iteration with the 
derivatives of the parameters to the error sum of squares is nearly 
singular. The condition number of this matrix is so large that it 
makes the problem ill-conditioned. If you add argument 
fit.ranges=FALSE it will not be singular anymore.

In the end, this problem is similar to e.g. regression of polynomials 
on coordinates without standardizing the coordinates.

I'll add a warning message to fit.variogram to suggest the two 
solutions, for this case.
-- 
Edzer

Zev Ross wrote:

Edzer (and all),

I don't think that it's related to an unrealistic range. I've tried a 
lot of different realistic and non-realistic values and get singular 
results each time. If I divide the X and Y coordinates by 10, 100, 
1000 or 10000 I don't get singularity. Using Lat and Long works fine. 
Code is below and I included a link to a workspace with the "pol" 
data set at the bottom.

Zev

polA<-pol
coordinates(polA)<-~x+y
v<-variogram(pollutant~1, data=polA)
v.fit<-fit.variogram(v, vgm(0.0005, "Sph", 40000, 0.00001))
attributes(v.fit)$singular # TRUE

polB<-pol
polB$x<-polB$x/1000
polB$y<-polB$y/1000
coordinates(polB)<-~x+y
v<-variogram(pollutant~1, data=polB)
v.fit<-fit.variogram(v, vgm(0.0005, "Sph", 40, 0.00001))
attributes(v.fit)$singular #FALSE

polC<-pol
coordinates(polC)<-~longitude+latitude
v<-variogram(pollutant~1, data=polC)
v.fit<-fit.variogram(v, vgm(0.0005, "Sph", .4, 0.00001))
attributes(v.fit)$singular # FALSE

http://www.zevross.com/temp2/singular_or_not.RData

Edzer Pebesma wrote:

Hi Zev, it is hard to see what happens without seeing your data or R 
commands.

Is it possible that you passed an unrealistic value for the range 
parameter, as starting value for the variogram model argument of 
fit.variogram?
-- 
Edzer

Zev Ross wrote:

Hi All,

I'm fitting variograms in GSTAT with fit.variogram and I was 
surprised to find that all my fits were singular. I experimented 
with converting the data to unprojected data (decimal degrees) and 
with dividing my X and Y coordinates, which are in meters, by 1000 
(to get KM). In both cases the fitting procedure worked with no 
singularity. Based on the numbers of pairs the bins appeared to be 
about the same so it appears to be a matter of the coordinates 
themselves.

I'd prefer not to have to convert the coordinates back and forth 
between meters and KM, any suggestions?

Zev