[R-sig-Geo] localG {spdep} - critical values for Gi* statistics

[Roger Bivand]

On Wed, 21 Sep 2011, zbynek.janoska at centrum.cz wrote:

> Hello,
> I am wondering, if it is posiible to obtain critical values for Gi
> statistics calculated by localG {spdep} function.
>
> In manual there is (quoting): The critical values of the statistic under
> assumptions given in the references for the 95th percentile are for n=1:
> 1.645, n=50: 3.083, n=100: 3.289, n=1000: 3.886.
>
> However, I have n=77, right in the middle between values given, and also I
> wonder, whether critical values for Gi* and Gi are the same? I suppose they
> are, since the difference is only in spatial weights, is it not?
> Consequently, another percentile than 95th could be useful.

The help page does point to the references, so they are where you should 
go. I'm not aware of anything else in the literature, but see:

Tonglin Zhang, Limiting distribution of the G statistics, Statistics and 
Probability Letters 78 (2008) 1656–1661

In any case, the p-values you are looking for will need Bonferroni or 
other adjustment, and as Zhang notes, when there are few neighbours, the 
assumption of normality will probably fail. The local Moran's I case is 
known in more detail, see Tiefelsdorf (2000) and papers citing his 
monograph.

Hope this helps,

Roger

>
> Thank You,
> Zbynek
>
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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