[R-sig-Geo] stepwise algorithm for GWR

[Myers, Joshua]

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 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 <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
>>> --
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> R-sig-Geo at stat.math.ethz.ch
>>> 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: 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