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 <[email protected]> > An: Marco Helbich <[email protected]> > CC: [email protected] > 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/[email protected]/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: [email protected] -- Jetzt kostenlos herunterladen: Internet Explorer 8 und Mozilla Firefox 3.5 - sicherer, schneller und einfacher! http://portal.gmx.net/de/go/atbrowser _______________________________________________ R-sig-Geo mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-geo
