[R-sig-Geo] mixed geographically weighted regression

[Marco Helbich]

Dear Roger,

thank you for your quick response! 

If I understand it correctly, the hat matrix is calculated using all explanatory variables. In my case, however, I would need to restrict the column space to those covariates where I assume varying coefficients (as in eq. (3)), and for this purpose I would need to calculate S_v by hand. Therefore, I would need the weight matrices for every observation. Or is there an easier way? 

Kind regards,

Marco


-------- Original-Nachricht --------
> Datum: Tue, 5 Jan 2010 18:00:50 +0100 (CET)
> Von: Roger Bivand <Roger.Bivand at nhh.no>
> An: Marco Helbich <marco.helbich at gmx.at>
> CC: r-sig-geo at stat.math.ethz.ch
> Betreff: Re: [R-sig-Geo] mixed geographically weighted regression

> On Tue, 5 Jan 2010, Marco Helbich wrote:
> 
> > Dear list,
> >
> > I am trying to fit a mixed geographically weighted regression model
> (with adaptive kernel) using the spgwr package, i.e. I want to hold some of the
> coefficients fixed at the global level. Thus, I have the following
> questions:
> >
> > 1. Which is the most efficient way to estimate such a model?
> > a) I found the posting
> http://www.mail-archive.com/r-sig-geo@stat.math.ethz.ch/msg00984.html where Roger recommended to first fit a global model,
> then the GWR using the residuals.
> > b) The method proposed in Mei et al. (2006,  pp. 588-589, see
> http://www.envplan.com/abstract.cgi?id=a3768) first computes the projection matrix of
> the locally varying part (called S_v) and uses this in a second step to
> derive the fixed coefficients (this seems to me like an application of the
> FWL-theorem see http://en.wikipedia.org/wiki/FWL_theorem).
> >
> > 2. In order to follow this method, I first have to find the kernel 
> > weights at each point. The help-file says that these can be found in the
> > SpatialPointsDataFrame (SDF), but I could not get it from there. Where 
> > can I extract them?
> 
> The sums of weights for each fit point are in the returned object, but 
> this is not what you (do not) want. The S_v matrix in the paper (eq. 3) is
> returned as the hat matrix, I believe. Since you have S_v, you do not need
> the W(u_i, v_i) weights (a diagonal matrix for each fit (and data) point 
> i). Given S_v, the unnumbered equation in the middle of the page gives you
> \hat{\beta_c}, doesn't it? I think that I would pre-multiply X_c and Y by 
> (I - S_v), then use QR methods to complete, if I wanted to proceed with 
> this.
> 
> Because of concerns about how these things are done, and how they are 
> represented in the literature, I'd look for corrobotation - being able to 
> reproduce others' published results for example.
> 
> Hope this helps,
> 
> Roger
> 
> >
> > We are using such a code:
> > library(spgwr)
> > 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$SDF
> >
> > I hope my problem is clear and appreciate every hint! Thank you!
> >
> > Best regards
> > Marco
> >
> >
> 
> -- 
> 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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