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variance estimation in spgwr

2 messages · Takatsugu Kobayashi, Roger Bivand

Original
Takatsugu Kobayashi
# 
Hi,

I am curious if spgwr or some other spatial packages estimate local 
variances. I am particularly interested if gwr residuals are locally 
siginificant or not.  In this case, I believe I should estimate local 
variances.  I though an alternative to spgwr is gam in mgcv.

Suppose I have xy coordinates and some values d1 and d2 attached to 
point(x,y). z1 is related to z2, but this relationship is not spatially 
stationary. So I would set this up using gam:

model1 <- gam(d1 ~ s(x, y, by=d2)) : I am not quite familiar with 
adaptive bandwidth selections in gam...

or using spgwr

bw <- gwr.sel(d1~d2, coords=cbind(x,y), apapt=T)
model2 <- gwr(d1~d2, coords=cbind(x,y), apapt=T, bandwidth=bw, 
hatmatrix=TRUE, lonlat =FALSE)

What I would like to know is 

d1(i)-hat{d1(i)}/hat{sigma(i)}
where i denotes the ith location in a map.

I did a bit of search and "lokern" pacakge came up, but this is only for 
bivarriate case and not particularly spatial-oriented.

Sorry for ambiguity of my question...  I appreciate if someone could 
give me some clues.....

thanks

tk
Roger Bivand
#
On Sun, 17 Feb 2008, Takatsugu Kobayashi wrote:

            

      
      
      
    

        
The components for a sigma(i) are not currently returned by .GWR_int(), 
the workhorse function inside gwr(). The local RSS is calculated to get to 
the local coefficient of determination, so it could be returned in one 
form or other (but what would be a sensible residual degrees of freedom?). 
Whether you should trust the output is a completely different question.

If you want to infer, it is perhaps reasonable to look at Bayesian GWR, 
which would give you a distribution of the local residual, but even so, 
until the collinearity problem is resolved, caution is still the key thing 
to keep in focus (in my opinion).

Roger