[R-sig-Geo] scaling response variable in a GWR

[Roger Bivand]

On Tue, 11 Dec 2012, Jean-Yves Barnagaud wrote:

> Dear listers;
>
> I'm wondering about how to scale variables to get meaningful results in a 
> geographically weighted regression. Apologies if this topic has already been 
> adressed on the list, I didn't find out.
>
> My aim is to study spatial patterns in the temporal trend of a variable, say 
> Y, through a GWR - in a nutschell as far as I understand the model is like:
>
> Y[x,y,t] = alpha[x,y] + beta[x,y]*time[t]
>
> where beta[x,y] and alpha[x,y] are computed as a bandwidth function of 
> neighbouring points -> am I right in my summary here?

I'm not sure that you are. This feels a bit like an attempt to look at the 
separability of spatial and temporal processes, where you could also 
include a process in [t] too. A separable setting would have only alpha 
and time, while their interaction is beta, perhaps? I don't think that 
scaling is central to the problem as such, although this may depend on 
the empirical configuration of Y.

Roger

>
> Y is a continuous normally distributed variable, and I'm interested in a way 
> of scaling Y which would allow to compare alpha and beta across localities. 
> As my reseearch question is related to whether and where Y increases more or 
> less, I'm particularly interested in the magnitude of beta, not just its 
> sign.
>
>> Do I need any kind of scaling ever? I mean, would I be able to compare 
> beta[x,y] between sites in which the mean Y differs (and thus ground my gwr 
> on raw Y values)? Or should I expect some kind of relationship between alpha 
> and beta (something like localities with higher Y have higher betas)? I'm not 
> too sure about whether what I know from standard linear regression holds for 
> GWR.
>
>> If I do need a scaling what would be wise to do?
>
> - scaling Y across sites, or within sites?
> - scaling by standardizing ((Y-mean(Y)) / sd(Y)) or something else, like 
> Y/max(Y) ? or something else?
>
> Any justified advice appreciated :o)
>
> Thanks a lot in advance;
>
> Best
>
> JY Barnagaud
>
>

-- 
Roger Bivand
Department of Economics, NHH Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no