How to get the Coefficient of Determination in the results of GWR

Hi,

My coordinates geographical are decimal degrees. I am soryy I donot know 
how to and what do copy and paste from SAM to gwr()? I cannot see the 
code of SAM.

Thanks a lot.

Cheers.



?2010-05-13 17:43:06?"Roger Bivand" <Roger.Bivand at nhh.no> ???

On Thu, 13 May 2010, huangykiz wrote:

Hi,

I am sorry I say that I cannot get the same R^2 between in R/spgwr and 
SAM in my data.

Establish that the adaptive proportion is exactly the same.

You haven't done that - copy and paste from SAM to gwr(), not using 
gwr.sel(). Do it first for fixed Gaussian, then if you get a sensible 
figure from SAM for adaptive, do the same there. I see very different 
bandwidths chosen by SAM and by gwr.sel() and GWR3 - gwr.sel() and GWR3 
usually agree fairly well for CV fixed bandwidths, but gwr.sel() typically 
continues its search a little longer than GWR3.

I don't know how SAM chooses its bandwidth or adaptive proportion, it is 
closed source, so only its authors know.

Is SAM using Great Circle distances, if so, you should set longlat=TRUE in 
gwr.sel() and gwr()? Are your coordinates geographical (decimal degrees) 
or projected (metres)?

Roger

In R/spgwr
R^2:    0.972989;
AICc (GWR p. 61, eq 2.33; p. 96, eq. 4.21): 4668.92
Effective number of parameters (model: traceS): 435.7586; 
Effective number of parameters (residual: 2traceS - traceS'S): 582.3581;
Sigma (residual: 2traceS - traceS'S): 2.437066;
Sigma (model: traceS): 1.927127;
Sigma (ML): 1.325501;

In SAM,
Coefficient of Determination :           0.696 
Adjusted r-square (r?Adj):                 0.693 
Sigma:                                             20.058 
Effective Number of Parameters:          10.002 
Akaike Information Criterion (AICc):      4838.299 
Correlation Coefficient (r):                    0.834 
F:                                                   207.852 

Here are my code:
PET.adapt.gauss <- gwr.sel(SPECIES_RI ~ PET, data=Environmental_variables, coords=cbind(Environmental_variables$LONGX, 
Environmental_variables$LATY),adapt=TRUE)

PET.gauss<- gwr(SPECIES_RI ~ PET, data=Environmental_variables, coords=cbind(Environmental_variables$LONGX, 
Environmental_variables$LATY), gweight=gwr.Gauss,adapt=PET.adapt.gauss,hatmatrix=TRUE)

1 - (PET.gauss$results$rss/crossprod(scale(Environmental_variables$SPECIES_RI, scale=FALSE)))

In SAM, I selecte "spatial Weighting Function"=gaussian, adaptive 
Spatial Kernel, and compute Geographical Distances based on longitudinal 
coordinate(X) and latitudinal coordinate(Y). I donot select method for 
AIC optimisation.

So I donot know where is wrong.

Thank you very much for your great helps.






?2010-05-13 00:07:23?"Roger Bivand" <Roger.Bivand at nhh.no> ???

On Wed, 12 May 2010, Roger Bivand wrote:

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?

I have now compared the same data in R/spgwr and SAM for effective number 
of parameters, sigma, and your questionable R^2, and they agree adequately 
when the kernel and the bandwidth are the same. Having the algorithm 
choose the bandwidth does obscure what is going on. You should use SAM if 
you prefer GUI and not needing to know how things work, and remember that 
GWR is a very doubtful approach for anything beyond exploring 
non-stationarity, its original motivation.

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.



?2010-05-12 20:28:47?"Roger Bivand" <Roger.Bivand at nhh.no> ???

On Wed, 12 May 2010, huangykiz wrote:

Hi,
One of SAM author ("Jos? 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

?2010-05-12 20:28:47?"Roger Bivand" <Roger.Bivand at nhh.no> ???

On Wed, 12 May 2010, huangykiz wrote:

Hi,
One of SAM author ("Jos? 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.

?2010-05-12 15:27:58?"Roger Bivand" <Roger.Bivand at nhh.no> ???

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

?2010-05-12 01:16:18?"Roger Bivand" <Roger.Bivand at nhh.no> ???

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,





?2010-05-11 23:59:44?"Roger Bivand" <Roger.Bivand at nhh.no> ???

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.





?2010-05-11 22:33:59?"Roger Bivand" <Roger.Bivand at nhh.no> ???

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.





?2010-05-11 18:28:44?"Roger Bivand" <Roger.Bivand at nhh.no> ???

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

-- 
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