[R-sig-Geo] Simulation of spatially autocorrelated values

[Roger Bivand]

On Mon, 29 Mar 2010, Michael Haenlein wrote:

> Dear all,
>
> my name is Michael Haenlein and I am Associate Professor of Marketing at
> ESCP Europe in Paris, France.
>
> For a research project I'm currently working on, I would like to simulate a
> given degree of spatial auto correlation within an artificial network. The
> problem is as follows: I have a network with a given number of nodes
> (locations) and a given number of relationships between those nodes. Each
> node i has a value xi of a certain type of metric. Assume for example that
> the nodes are different cities and the xi is the average income of people
> living in the respective city. I have drawn the xi independently from a
> probability distribution so that there is no spatial auto correlation in the
> data set. I now would like to "adjust" the individual xi in order to reach a
> predefined level of spatial auto correlation such as a pre-defined level of
> Moran's I. So starting from a situation without spatial auto correlation,
> I'd like to use some iterative process to reach a Moran's I value of let's
> say 0.60.
>
> Can anyone give me advice on how this can be done?

Michael,

Please look at ?invIrW in spdep and its references, and possibly also the 
notes on p. 30 of:

http://www.bias-project.org.uk/ASDARcourse/unit6_slides.pdf

which use an alternative approach to the same question. Here \rho is the 
autoregressive coefficient, not I, and you might need to use some tricks 
to get to a specified global I.

You could treat APLE ?aple as half-way-house, or consider using the set of 
eigenvectors that whitens out equivalent autocorrelation - see 
?SpatialFiltering for references about the links between the solution to 
the eigenproblem of a doubly-centred W and autocorrelation.

Hope this helps,

Roger

>
> Any help is very much appreciated!
>
> Thanks in advance,
>
> Michael
>
>
>
> Michael Haenlein
> Associate Professor of Marketing
> ESCP Europe
> Paris, France
>
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>
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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