[R-sig-Geo] Local Moran's I spatial weights

[Roger Bivand]

On Tue, 12 Jun 2012, Daniel Wicks wrote:

> I have a number of random sample points across a study area.  At each 
> point an observation has been made as to the occurrence of an event, 
> marked accordingly with a 0 or 1 based on a presence or absence of the 
> event.

How were the observations made? Were the observation locations determined 
by you - a random sample, or by the phenomena (in which case it is more 
like a marked point process).

> I am interested in visualising the spatial association between 
> these points.  I therefore want to create a map showing local variation 
> of Moran's I but in the form of a continuous surface across the entire 
> study area.

Well, Moran's I is for a continuously valued observed variable (or 
residuals), not for a 0/1 variable. The equivalent measure is the join 
count, but this does not have a local version.

If your observations are 0/1, and have point support, it isn't obvious why 
you want a continuous surface. This would be nearest to some kind of odds 
interpolation (what is the chance of a 1 at an unobserved location, given 
the data and their locations). You have to be very careful indeed with 
inhomogeneity (that is here, spatially patterned omitted environmental 
variables influencing the 0 or 1 observations).

It is also possible that your sampling scheme is affecting the outcome - 
it is possible to sample to at least partially control for inhomogeneity.

> You can achieve this in GWR using the fit.points weighted 
> by distances from the data points to produce a map of local variation in 
> regression.  I am trying to do something similar with Moran's I.
>

GWR has nothing to do with this at all.

> I apologise for the confusion as I am not best sure how to express my 
> query.
>

Your data are probably rather different from your view of them. I'm not 
sure, but maybe a kernel ratio of 2D kernels for the 0 and 1 marked 
observations might help you visualise things, even though this isn't 
really a marked point process. You'd still risk falling into the trap of 
inhomogeneity (the apparently important features of the ratio map might 
correlate highly with missing variables).

Roger

> Dan.
>
>
> On 12 Jun 2012, at 12:37, Roger Bivand wrote:
>
>> On Tue, 12 Jun 2012, djrwicks wrote:
>>
>>> Thank you, a geographically weighted measure of Moran's I sounds like a
>>> sensible description of what I am trying to achieve.  Is it possible to
>>> calculate this using GW weights?
>>
>> Please do quote the thread, because nabble servers do go over capacity (as at present), and the context is lost.
>>
>> I replied to your first post by asking for more precision. I still don't have it. What do you mean by "a geographically weighted measure of Moran's I"? The spatial weights used in the global and local measures relate the observations of a variable, where the relationships are expressed by a weights matrix. The matrix of GW weights would look like this when the GW data points and fit points are the same points, because the weights are from fit point i to all data points.
>>
>> You have not made your needs plain at all, I'm afraid.
>>
>> Roger
>>
>>>
>>> Dan.
>>>
>>> --
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>>
>> --
>> 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
>>
>
>

-- 
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