[R-sig-Geo] mixed geographically weighted regression

[Marco Helbich]

Great, thank you for giving me a hand!

Best regards
Marco


-------- Original-Nachricht --------
> Datum: Tue, 5 Jan 2010 18:54:08 +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 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?
> 
> Naturally. Use the hat matrix from a regular GWR fit with only X_v 
> included, as the paper (seems to) describe.
> 
> Roger
> 
> >
> > 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
> >
> >
> 
> -- 
> 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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