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about global getis g

3 messages · kun17, Roger Bivand

#
cold.zip <http://r-sig-geo.2731867.n2.nabble.com/file/n7587571/cold.zip>  

hello everyone,

I have designed a random grid file and put a 'cold spots' in the center, I
used globalG.test in spdep package to test the 'cold spots',but the results
made me confused, below is my code:

library(spdep)
library(maptools)
simu=readShapeSpatial("C:/GridCold.shp")
dists=1:12 
n=length(dists)
GG=EG=VG=ZG=pvalue=numeric(length=n)

coord=coordinates(simu)
for(i in 1:n){
	dnb=dnearneigh(coord,0,dists[i]) 
	simu.w=nb2listw(dnb,style="B",zero.policy=TRUE)	
	G=globalG.test(simu$value,simu.w,zero.policy=TRUE,alternative="two.sided")
	GG[i]=G$estimate[1]
	EG[i]=G$estimate[2]
	VG[i]=G$estimate[3]
	ZG[i]=G$statistic
	pvalue[i]=G$p.value
}
cbind(dists,GG,EG,VG,ZG,pvalue)

the results is:

    dists         GG         EG           VG         ZG       pvalue
 [1,]     1 0.01326694 0.01307190 1.127119e-09  5.8097284 6.257426e-09
 [2,]     2 0.03791890 0.03762976 1.456950e-08  2.3954667 1.659922e-02
 [3,]     3 0.08282060 0.08294887 1.127367e-07 -0.3820144 7.024507e-01
 [4,]     4 0.13412895 0.13528451 3.728269e-07 -1.8925080 5.842333e-02
 [5,]     5 0.20749034 0.21073626 1.131177e-06 -3.0519145 2.273869e-03
 [6,]     6 0.27401114 0.27974817 2.170007e-06 -3.8945442 9.838356e-05
 [7,]     7 0.34154256 0.35049020 3.542196e-06 -4.7541397 1.992932e-06
 [8,]     8 0.42087567 0.43444829 5.557734e-06 -5.7572477 8.549642e-09
 [9,]     9 0.50377144 0.52100154 7.538721e-06 -6.2753643 3.488166e-10
[10,]    10 0.58757397 0.60659362 8.890566e-06 -6.3787831 1.785007e-10
[11,]    11 0.65976673 0.67685506 8.894732e-06 -5.7297151 1.005995e-08
[12,]    12 0.72722625 0.74144560 8.057964e-06 -5.0091840 5.466130e-07

the first two rows with distance 1 and 2 indicate significant 'hot spots'!
when I use CrimeStat to calculate global G, when distance is 1 and 2,the
results are both not significant.

Could someone explain the difference?

thank you!

Kun



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1 day later
#
On Sun, 21 Dec 2014, kun17 wrote:

            
The Crimestat IV values are:
d        G       EG      SEG        ZG
V2  1 0.013267 0.013072 0.000262  0.745199
V3  2 0.037919 0.037630 0.000457  0.632980
V4  3 0.082821 0.082949 0.000736 -0.174370
V5  4 0.134129 0.135285 0.001036 -1.115844
V6  5 0.207490 0.210736 0.001491 -2.176953
V7  6 0.274011 0.279748 0.001903 -3.014358
V8  7 0.341543 0.350490 0.002316 -3.862926
V9  8 0.420876 0.434448 0.002797 -4.852804
V10 9 0.503771 0.521002 0.003203 -5.378934

which agree on G and E(G), but not beyond that. Ch 5 of the Crimestat 
manual has an error for B1, equation 5.21, which does not take into 
account the erratum published by the authors in 1993: "On page 195, the 
coefficient of W2 in B1, (just below center of the page) should be 6, not 
3.". However, this doesn't seem to be the only problem, as the spdep code 
when modified not to correct B1 doesn't reproduce the CrimeStat Standard 
error of "G" values.

Since CrimeStat is closed-source, and since we can show an error in their 
documentation, I suggest that you take this up with them, pointing out 
their not accommodating an erratum (there were more) published over twenty 
years ago, ask for a clarification, and report back here when they say 
what they are actually doing. The source to globalG.test() is readable, so 
they can readily check what it does.

Hope this helps,

Roger

  
    
1 day later
#
Thank you Roger, your professional knowledge has rebuilt my confidence in
spdep.

As to the example, I have a new understanding: when a 'cold spots' was put
in the center, the surrounding grids became 'hot spots' relatively, it
explained the result when distance was set to 1 unit. The idea of 'high' and
'low' in global G is comparative, not measured by mean value.

I will take the example to CrimeStat.

Merry Chrismas everyone!



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