Re: [R-sig-Geo] stepwise algorithm for GWR
Dear Joshua and Danlin, your remarks are right, but I am not fully convinced. What are the differences between using it in an ols framwork and using it in a GWR one under the same conditions (same bandwith, amount of neighbors...)? Any further hints? Thank you and best regards Marco Original-Nachricht > Datum: Wed, 13 May 2009 14:32:35 -0400 > Von: "Myers, Joshua" > An: "Danlin Yu" , "Marco Helbich" > > CC: [email protected] > Betreff: RE: [R-sig-Geo] 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:[email protected]] > Sent: Wednesday, May 13, 2009 2:12 PM > To: Marco Helbich > Cc: [email protected]; 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 voilà 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 > >> An: Marco Helbich > >> CC: [email protected] > >> 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=colu
Re: [R-sig-Geo] 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:[email protected]] Sent: Wednesday, May 13, 2009 2:12 PM To: Marco Helbich Cc: [email protected]; 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 voilà 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 >> An: Marco Helbich >> CC: [email protected] >> 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 >>> -- >>> >>> ___ >>> R-sig-Geo mailing list >>> [email protected] >>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo >>> >>> >> -- >> ___ >> 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: [email protected] >> 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: [email protected] webpage: csam.montclair.edu/~yu ___ R-sig-Geo mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-geo
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 voilà 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 An: Marco Helbich CC: [email protected] 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 -- ___ R-sig-Geo mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-geo -- ___ 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: [email protected] 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: [email protected] webpage: csam.montclair.edu/~yu ___ R-sig-Geo mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-geo
Re: [R-sig-Geo] stepwise algorithm for GWR
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 voilà 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 > An: Marco Helbich > CC: [email protected] > 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 > > -- > > > > ___ > > R-sig-Geo mailing list > > [email protected] > > https://stat.ethz.ch/mailman/listinfo/r-sig-geo > > > > -- > ___ > 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: [email protected] > webpage: csam.montclair.edu/~yu -- ___ R-sig-Geo mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-geo
Re: [R-sig-Geo] stepwise algorithm for GWR
Dear Marco, I think Danlin is more experienced with this than myself, but in my experience I have found that best global OLS model is usually at least somewhat different than the best GWR model. I have found that there is usually a slightly different variable set (at least in the two datasets that I have been working with). In my datasets I have also found that it yields better results to not use a log or square root (or any other like variable transformation) in the local model, whereas it might make a difference in a global model. I am not saying it will be the same for you, but I am cautioning you to not just take what you see the global case and apply it blindly to the local GWR case. I have actually thought a lot about what you are suggesting, a selection algorithm for gwr, but I haven't had the time to play with it yet. It can be noted, however, that any such search algorithm will take a log time. It will probably need to be run overnight, unless you have some kind supercomputing cluster. -Josh -Original Message- From: [email protected] [mailto:[email protected]] On Behalf Of Danlin Yu Sent: Wednesday, May 13, 2009 10:04 AM To: Marco Helbich Cc: [email protected] Subject: 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 > -- > > ___ > R-sig-Geo mailing list > [email protected] > https://stat.ethz.ch/mailman/listinfo/r-sig-geo > -- ___ 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: [email protected] webpage: csam.montclair.edu/~yu ___ R-sig-Geo mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-geo ___ R-sig-Geo mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-geo
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 -- ___ R-sig-Geo mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-geo -- ___ 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: [email protected] webpage: csam.montclair.edu/~yu ___ R-sig-Geo mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-geo
