[Openspace] significance of Moran's I

[Roger Bivand]

On Fri, 5 Sep 2008, Patrick Yang wrote:

> Dear List,
>
> I am using GeoDa to measure spatial correaltions. I am wondering
> whether there is a cut-value to say the strenghth of correlation, besides
> p-value. I feel it is difficult to say there is a correlation if I=0.05 (or
> I=0.0*). As Person correlation,  we can say if >0.3, it exisits correlation.
> Does anyone have idea about the cut value (like I>0.1 or 0.3) to let us
> safetly arrivie the conclusion that there is a spatial correation? Any
> reference provided?

Cliff & Ord (1981) is the one that is cited most often, but you'll find 
plenty of help in domain books, like Waller & Gotway (2004). The clearest 
advice is simply never to try to interpret the observed value of Moran's 
I, because it depends on the scaling of the weights. For the same set of 
neighbours and the same scaling of the weights (for example row 
standardisation), you can compare the values across variables. But if you 
change the scaling, the values change a little; if you change the 
neighbours (say from contiguous zones to distance-based neighbours), the 
values can change more. Consequently, you can't compare unless you are 
matching like with like for the same data set.

Comparison should be based on the standard deviate of the observed value, 
or equivalently on p-values from permutation tests in the univariate case. 
Li et al. (2007) try to elaborate a comparable APLE measure in 
Geographical Analysis (p. 357-375), but implementations are not yet 
available (and indeed its values will only be comparable for equivalent 
weights).

Finally, apparently "large" values of Moran's I can reflect 
misspecification as much as actual autocorrelation, for example a 
spatially patterned omitted variable.

Hope this helps,

Roger

>
> Best regards,
> Zhenshan
>
>
>
>
>
>
> Department of Human Geography & Urban and Regional Planning
> Utrecht University (UU)
>
> Urban and Regional Planning and Geo-Information Management
> International Institute for Geo-Information Science and Earth Observation
> (ITC)
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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