[R-sig-Geo] Moran's I with binary weights

[Roger Bivand]

On Tue, 6 Jul 2010, Michael Haenlein wrote:

> Dear all,
>
> I have a brief question regarding Moran's I: Is there any research on the
> behavior of Moran's I for situations where the spatial weights matrix is
> binary, i.e. only includes either 1 or 0? Does Moran's I require weights
> that are distributed in a certain way in the [0,1] interval? Or is it
> sufficient to know who is connected to whom (i.e., binary weights)?
> Specifically, I'm interested in the question whether the use of binary
> weights introduces any form of bias in the estimated value of Moran's I.

Moran's I is fine with binary weights, and was originally developed for 
them. The "bias" is that entities with many neighbours get up-weighted, 
just as row-standardisation down-weights those entities in favour of those 
with few neighbours.

Roger

>
> Thanks very much for your reply 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