[R-sig-Geo] GSTAT - singular in meters not km

[Zev Ross]

Edzer,

Glad to hear that I wasn't crazy -- thanks so much for looking into this 
(and so quickly). For now I'll divide by 1000 and use KM which is an 
easy and reasonable solution. Zev

Edzer Pebesma wrote:
> 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
>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> R-sig-Geo at stat.math.ethz.ch
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>>
>>
>