[R-sig-Geo] The sum.w Field in SDF

[Roger Bivand]

On Wed, 18 Jul 2007, Ryan Rosario wrote:

> I understand that the sum.w field is the sum of the weights associated with
> a particular observation/location.

This is apparently a follow-up to a question on 15 July about robust GWR. 
GWR is seriously affected by multicollinearity anyway (see Wheeler & 
Tiefelsdorf refered to on the gwr() help page), so trying this may be a 
waste of time.

>
> But what is this sum taken over? Is there a way to access the individual
> weights before they are summed?
>

It is simply the sum of weights for that fit point - with fixed bandwidth, 
the weights sums vary, so that is why it is reported.

> Basically, I need a single weight for each observation (not a sum), so that
> I can use the robust GWR method presented by Brundsdon et. al. So I need to
> divide sum.w by some number N. This will give me an average weight (more
> importantly, it is a single weight). In this case, what does N represent?
> The number of observations, or is it some number of iterations for a
> numerical method used in GWR?

No, you need to modify both gwr.sel() and gwr() to take a weights= 
argument like lm, and them multiply the geographical weights by the case 
weights for each fit point. Then you can use the formula you cite to 
construct case weights, but only for data points.

Note that you are mixing up data points and fit points - there are *no* 
residuals at fit points unless the fit points are data points. You can 
only try this trick if you force data and fit points to be the same (as 
when computing the hat matrix).

If you'd like to contribute patches for adding a weights= argument, I 
could look and see if they seem to work.

Roger

>
> Ryan
>
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-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, 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