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.biv...@nhh.no> > An: Marco Helbich <marco.helb...@gmx.at> > CC: r-sig-geo@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.biv...@nhh.no> > >> An: Marco Helbich <marco.helb...@gmx.at> > >> CC: r-sig-geo@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.biv...@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.biv...@nhh.no -- Preisknaller: GMX DSL Flatrate für nur 16,99 Euro/mtl.! http://portal.gmx.net/de/go/dsl02 _______________________________________________ R-sig-Geo mailing list R-sig-Geo@stat.math.ethz.ch https://stat.ethz.ch/mailman/listinfo/r-sig-geo