[R-sig-Geo] variance estimation in spgwr

[Roger Bivand]

On Sun, 17 Feb 2008, Takatsugu Kobayashi wrote:

> 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.

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

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

-- 
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