[R-sig-Geo] How to get the Coefficient of Determination in the results of GWR

Roger Bivand Roger.Bivand at nhh.no
Wed May 12 17:29:00 CEST 2010 

On Wed, 12 May 2010, huangykiz wrote:

> Hi, Is "adapt=TRUE"(spgwr) not the same as "adaptive Spatial 
> Kernel"(SAM)?The result of "adaptive Spatial Kernel" may be better than 
> fixed bandwidth. If I want to ues "adaptive Spatial Kernel" in spgwr, 
> how to write the code?

READ THE HELP PAGES!

adaptive_proportion <- gwr.sel(...)

result <- gwr(..., adapt=adaptive_proportion; ...)

exactly as on the example om the help page:

data(georgia)
g.adapt.gauss <- gwr.sel(PctBach ~ TotPop90 + PctRural + PctEld + PctFB +
   PctPov + PctBlack, data=gSRDF, adapt=TRUE)
res.adpt <- gwr(PctBach ~ TotPop90 + PctRural + PctEld + PctFB + PctPov +
   PctBlack, data=gSRDF, adapt=g.adapt.gauss)
res.adpt

Clear?

> 
> Thanks a lot.
> 
> Cheers.
> 
> 
>> Hi,
>> I think that I use the same bandwidth and kernel. In SAM, I use "spatial Weighting Function"=gaussian, adaptive Spatial Kernel, and compute Geographical Distances based on longitudinal coordinate(X) and latitudinal coordinate(Y). In spgwr, gweight is gwr.Gauss and adapt is TRUE.
>> 
>> For example, this is my code:
>
>> PET.bw <- gwr.sel(SPECIES_RI ~ PET, data=variables, 
>> coords=cbind(variables$LONGX, variables$LATY),adapt=TRUE)
>
>> PET.gauss <- gwr(SPECIES_RI ~ PET, data=variables, 
>> coords=cbind(variables$LONGX, variables$LATY), bandwidth=PET.bw, 
>> gweight=gwr.Gauss,adapt=TRUE,hatmatrix=TRUE)
>
> So where do you pass PET.bw to the gwr() function? adapt=TRUE will treat 
> the adaptive proportion as 1, so include all data points. If you want to 
> compare, use a fixed bandwidth in both, with no CV selection. Then you 
> compare like with like.
>
> Note that your messages are *not* reaching the list, they must be sent to:
>
> r-sig-geo at stat.math.ethz.ch, not
>
> r-sig-geo-request at stat.math.ethz.ch
>
> You are not thinking carefully and are rushing into things and drawing 
> wrong conclusions.
>
>>
>> Thanks a lot.
>> 
>> Cheers.
>>
>>
>>
>> 在2010-05-12 20:28:47，"Roger Bivand" <Roger.Bivand at nhh.no> 写道：
>>> On Wed, 12 May 2010, huangykiz wrote:
>>>
>>>> Hi,
>>>> One of SAM author ("José Alexandre Felizola Diniz Filho"<diniz at icb.ufg.br>) say that they also base on GWR3 (the Fotherigham book)  and the data used within each kernel 
>>>> may be some slight differences
>>>
>>> Naturally, if you are not using exactly the same kernel and bandwidth, you 
>>> should not be surprised by differences in values. Please make sure that 
>>> the bandwidth and kernel are the same and try again.
>>>
>>> Roger
>>>
>>>> Cheers
>
>
>
>
> 在2010-05-12 20:28:47，"Roger Bivand" <Roger.Bivand at nhh.no> 写道：
>> On Wed, 12 May 2010, huangykiz wrote:
>>
>>> Hi,
>>> One of SAM author ("José Alexandre Felizola Diniz Filho"<diniz at icb.ufg.br>) say that they also base on GWR3 (the Fotherigham book)  and the data used within each kernel 
>>> may be some slight differences
>>
>> Naturally, if you are not using exactly the same kernel and bandwidth, you 
>> should not be surprised by differences in values. Please make sure that 
>> the bandwidth and kernel are the same and try again.
>>
>> Roger
>>
>>> Cheers.
>>>
>
>
>
>
>
> 在2010-05-12 15:27:58，"Roger Bivand" <Roger.Bivand at nhh.no> 写道：
>> On Wed, 12 May 2010, huangykiz wrote:
>>
>>> Hi,
>>> 
>>> I am sorry I donot know how to install module spgwr from sourceforge (I can find it on the web http://r-spatial.cvs.sourceforge.net/viewvc/r-spatial/spgwr/R/gwr.R?view=log). So I use the code sketch to calculate quasi-global R2. The results are different between SAM and spgwr(Attached are the results ). The quasi-global R2 in R is 0.4515894, but in SAM is 0.696.
>>> This is my code:
>>> 
>>> library(spgwr)
>>> Environmental_variables<-read.csv("Environmental_variables100.csv",header=TRUE)
>>> attach(Environmental_variables)
>>> region_PET.bw <- gwr.sel(SPECIES_RI ~ PET, data=Environmental_variables, coords=cbind(Environmental_variables$LONGX, Environmental_variables$LATY),adapt=TRUE)
>>> region_PET.gauss <- gwr(SPECIES_RI ~ PET, data=Environmental_variables, coords=cbind(Environmental_variables$LONGX, Environmental_variables$LATY), bandwidth=region_PET.bw, gweight=gwr.Gauss,adapt=TRUE,hatmatrix=TRUE)
>>> names(region_PET.gauss$SDF)
>>> region_PET.gauss$SDF$localR2
>>> 1 - (region_PET.gauss$results$rss/crossprod(scale(Environmental_variables$SPECIES_RI, scale=FALSE)))
>>> 
>>> Thank you very much.
>>
>> SAM is closed source - ask them how they compute it. For spgwr, the code 
>> is provided, so you can read it for yourself. For the record, the current 
>> gwr() code in spgwr gives the same value as GWR3, which is also closed 
>> source, and where the Effective number of parameters (model: traceS), 
>> Sigma, and Residual sum of squares also agree. I suppose SAM has a 
>> different understanding of GWR internals than the authors of the GWR book.
>>
>> Once again:
>>
>> Please *do* write to the R-sig-geo list rather than to me directly -
>> others can answer your question as well, perhaps better, and in a more
>> timely way than I can. In addition, threads in the list can be searched in
>> the archives, so others can avoid the same problem later.
>>
>> Please summarise to the list if this resolves the problem.
>>
>> Roger
>>
>>> 
>>> 
>>>
>>>
>>>
>>> 在2010-05-12 01:16:18，"Roger Bivand" <Roger.Bivand at nhh.no> 写道：
>>>> On Wed, 12 May 2010, huangykiz wrote:
>>>>
>>>>> Hi, I just need one for global, not *each* fit point. In this case, how 
>>>>> can I select or do? Why in other software such as SAM(Spatial Analysis 
>>>>> in Macroecology) just gives one R2?
>>>>
>>>> If you believe theirs, good luck! The authors of the GWR book have local 
>>>> R^2 values in GWR3 and formulae that are wrong by their own admission in 
>>>> private emails. The localR2 now agrees with the as-yet unreleased GWR4 
>>>> from the GWR authors. How SAM can be "better", I don't know. What you are 
>>>> suggesting is that the model fitted with fit points at data points (but 
>>>> not at other fit points) might have a "quasi-global" R^2, based on the RSS 
>>>> of the pooled fit. For the columbus case, that might be:
>>>>
>>>> 1 - (col.gauss$results$rss/crossprod(scale(columbus$crime, scale=FALSE)))
>>>>
>>>> but I don't know whether this is in any way correct. I've added it as:
>>>>
>>>> Quasi-global R2:
>>>>
>>>> to the print output of a GWR model fitted with a hatmatrix, and have 
>>>> committed it to sourceforge, project r-spatial, module spgwr. Arguably, it 
>>>> ought to be adjusted by the ratio of degrees of freedom, but I don't trust 
>>>> the DF either. Could you please check out spgwr from sourceforge ,install 
>>>> it from source, and confirm that the "quasi-global R2" does the same as 
>>>> SAM, or use the code sketch above to do the same, and report back?
>>>>
>>>> Roger
>>>>
>>>>> 
>>>>> Thanks a lot.
>>>>> 
>>>>> Cheers,
>>>>>
>>>>> 
>>>>>
>>>>>
>>>>>
>>>>> 在2010-05-11 23:59:44，"Roger Bivand" <Roger.Bivand at nhh.no> 写道：
>>>>>> On Tue, 11 May 2010, huangykiz wrote:
>>>>>>
>>>>>>> Hi,
>>>>>>> 
>>>>>>> There are 49  localR2 in the results. Which one do I need? The code "look for localR2:" cannot run.
>>>>>>
>>>>>> Well, how many do you want? There is one for each fit point, they are 
>>>>>> *local* R2. Please do try to grasp what GWR does - it fits one moddel for 
>>>>>> *each* fit point.
>>>>>>
>>>>>>> 
>>>>>>> Thans a lot
>>>>>>> 
>>>>>>> Cheers.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> 在2010-05-11 22:33:59，"Roger Bivand" <Roger.Bivand at nhh.no> 写道：
>>>>>>>> On Tue, 11 May 2010, huangykiz wrote:
>>>>>>>>
>>>>>>>>> Hi, OK. But I need it for compariation. In what some contexts to get it? 
>>>>>>>>> May you tell me how to get it?
>>>>>>>>
>>>>>>>> library(spgwr)
>>>>>>>> data(columbus)
>>>>>>>> col.bw <- gwr.sel(crime ~ income + housing, data=columbus,
>>>>>>>>  coords=cbind(columbus$x, columbus$y))
>>>>>>>> col.gauss <- gwr(crime ~ income + housing, data=columbus,
>>>>>>>>  coords=cbind(columbus$x, columbus$y), bandwidth=col.bw, hatmatrix=TRUE)
>>>>>>>> names(col.gauss$SDF)
>>>>>>>>
>>>>>>>> look for localR2:
>>>>>>>>
>>>>>>>> col.gauss$SDF$localR2
>>>>>>>>
>>>>>>>> But do not rely on it or use it for anything at all! Like all GWR, it is 
>>>>>>>> most unreliable!
>>>>>>>>
>>>>>>>> Roger Bivand
>>>>>>>>
>>>>>>>>> 
>>>>>>>>> Thank you very much for your great helps
>>>>>>>>> 
>>>>>>>>> Best regards.
>>>>>>>>> 
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> 在2010-05-11 18:28:44，"Roger Bivand" <Roger.Bivand at nhh.no> 写道：
>>>>>>>>>> On Tue, 11 May 2010, huangykiz wrote:
>>>>>>>>>>
>>>>>>>>>>> Dear professor Bivand,
>>>>>>>>>>> 
>>>>>>>>>>> I am a strudent. I recently use GWR(Geographically 
>>>>>>>>>>> weighted regression) model. May I ask you a question? There is not 
>>>>>>>>>>> Coefficient of Determination in the results of GWR. How can I get it? 
>>>>>>>>>>> What is the programs to get it?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Please address questions like this to the R-sig-geo list rather than to me 
>>>>>>>>>> directly in future.
>>>>>>>>>>
>>>>>>>>>> The local R2 values are available in some contexts when running gwr(), but 
>>>>>>>>>> are not well defined (neither in the GWR book nor in implementations). I 
>>>>>>>>>> advise against their use - they are most probably meaningless.
>>>>>>>>>>
>>>>>>>>>> Hope this helps,
>>>>>>>>>>
>>>>>>>>>> Roger Bivand
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> 
>>>>>>>>>>> Thank you very much for your any helps.
>>>>>>>>>>> 
>>>>>>>>>>> Best regards.
>>>>>>>>>>> 
>>>>>>>>>>> Yong Huang
>>>>>>>>>>
>>>>>>>>>> -- 
>>>>>>>>>> Roger Bivand
>>>>>>>>>> Economic Geography Section, Department of Economics, Norwegian School of
>>>>>>>>>> Economics and Business Administration, Helleveien 30, N-5045 Bergen,
>>>>>>>>>> Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
>>>>>>>>>> e-mail: Roger.Bivand at nhh.no
>>>>>>>>>>
>>>>>>>>
>>>>>>>> -- 
>>>>>>>> Roger Bivand
>>>>>>>> Economic Geography Section, Department of Economics, Norwegian School of
>>>>>>>> Economics and Business Administration, Helleveien 30, N-5045 Bergen,
>>>>>>>> Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
>>>>>>>> e-mail: Roger.Bivand at nhh.no
>>>>>>
>>>>>> -- 
>>>>>> Roger Bivand
>>>>>> Economic Geography Section, Department of Economics, Norwegian School of
>>>>>> Economics and Business Administration, Helleveien 30, N-5045 Bergen,
>>>>>> Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
>>>>>> e-mail: Roger.Bivand at nhh.no
>>>>
>>>> -- 
>>>> Roger Bivand
>>>> Economic Geography Section, Department of Economics, Norwegian School of
>>>> Economics and Business Administration, Helleveien 30, N-5045 Bergen,
>>>> Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
>>>> e-mail: Roger.Bivand at nhh.no
>>
>> -- 
>> Roger Bivand
>> Economic Geography Section, Department of Economics, Norwegian School of
>> Economics and Business Administration, Helleveien 30, N-5045 Bergen,
>> Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
>> e-mail: Roger.Bivand at nhh.no

-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no

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