stepwise algorithm for GWR
Marco, I agree with Danlin. You can use AIC to compare models of the same type (i.e. OLS) with different model specifications, or, you can use AIC to compare models of different types (SAR, OLS, GWR) but with the same model specification. Alternatively, RMSE can be used to compare models of any type together no matter what specification, but there is no penalization for number of parameters used. Oftentimes, we either have a fixed number of parameters or we have a good idea which parameters are best or interesting, so we are able to cut down on some of the many possible specification options. -Josh -----Original Message----- From: Danlin Yu [mailto:yud at mail.montclair.edu] Sent: Wednesday, May 13, 2009 2:12 PM To: Marco Helbich Cc: r-sig-geo at stat.math.ethz.ch; Myers, Joshua Subject: Re: [R-sig-Geo] stepwise algorithm for GWR Marco: That's the point - I don't think such comparison is quite appropriate (I might be wrong) since the model specifications are not the same. You can compare AICs across OLS, SAR, and GWR with the same specification (same set of dependent and independent variables), but it's quite doubtful to compare AICs across any of these with different specifications. It really depends upon what's the purpose of your analysis. I assume you were trying to find the best model to fit your data. Maybe using all the models to do a prediction and calculate the RMSE could give you some hints? Hope this helps. Danlin Marco Helbich ??:
Dear Danlin and Joshua, first of all thank you for your replies! Here some further notes for clarification: I have already estimated a global ols model (based on stepwise model selection) and because of some spatial effects I recalculated it as simultaneous autoregressive model. After that I tested this model for non-stationarity... and voil? there is one. Now I want to compare this one with the one offering the lowest aic. All the best Marco -------- Original-Nachricht --------
Datum: Wed, 13 May 2009 10:04:22 -0400
Von: Danlin Yu <yud at mail.montclair.edu>
An: Marco Helbich <marco.helbich at gmx.at>
CC: r-sig-geo at stat.math.ethz.ch
Betreff: Re: [R-sig-Geo] stepwise algorithm for GWR
Dear Marco:
Before doing so, you'll have to ask yourself that whether all those AICs
are comparable among different model specifications. As a matter of
fact, I believe it might be more plausible if you stepwise it first as a
global model (OLS, after all, global models are an "averaged" view of
the local models), and then work with the selected specification.
Hope this helps,
Danlin
Marco Helbich ??:
Dear list!
I am doing some geographically weighted regression and I am intersted in
the most suitable model (the one with the lowest AIC). Because there is no
stepwise algorithm, I am trying to write a "brute force" function, which
uses all possible variable combination, applies the gwr and returns the AIC
value with the used variable combination in a dataframe.
For instance the model below: gwr1: crime ~ income, gwr2: crime ~
housing, gwr3: crime ~ var1, gwr4: crime ~ income + housing, ...
I hope my problem is clear and appreciate every hint! Thank you!
All the best
Marco
library(spgwr)
data(columbus)
columbus[,"var1"] <- rnorm(length(columbus[,1]))
col.bw <- gwr.sel(crime ~ income + housing + var1, data=columbus,
coords=cbind(columbus$x, columbus$y))
col.gauss <- gwr(crime ~ income + housing + var1, data=columbus,
coords=cbind(columbus$x, columbus$y), bandwidth=col.bw,
hatmatrix=TRUE)
col.gauss --
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___________________________________________
Danlin Yu, Ph.D.
Assistant Professor of GIS and Urban Geography
Department of Earth & Environmental Studies
Montclair State University
Montclair, NJ, 07043
Tel: 973-655-4313
Fax: 973-655-4072
email: yud at mail.montclair.edu
webpage: csam.montclair.edu/~yu
___________________________________________ Danlin Yu, Ph.D. Assistant Professor of GIS and Urban Geography Department of Earth & Environmental Studies Montclair State University Montclair, NJ, 07043 Tel: 973-655-4313 Fax: 973-655-4072 email: yud at mail.montclair.edu webpage: csam.montclair.edu/~yu