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

[Jean-Yves Barnagaud]

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?

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

-- 
Jean-Yves Barnagaud
postdoctoral researcher
macroecology - community ecology - ornithology
Institut for Bioscience - Ecoinformatics and Biodiversity
Ny Munkegade 116
building 1540, office 321
8000, Aarhus C - Danemark
phone (+0045) 87156126
http://sites/google/com/site/jybarnagaud