Exceedance probability vs Getis Ord Gi*

[Pacharapol Withayasakpunt]

I understand Getis Ord Gi* as Hotspot analysis above baseline, but what are the differences from exceedance probability?

To add more to the confusion, there seems to be multiple kinds of local spatial statistic G, as seen in R language help for localG.

G and Gstar local spatial statistics

Description
The local spatial statistic G is calculated for each zone based on the spatial weights object used. The value returned is a Z-value, and may be used as a diagnostic tool. High positive values indicate the posibility of a local cluster of high values of the variable being analysed, very low relative values a similar cluster of low values. For inference, a Bonferroni-type test is suggested in the references, where tables of critical values may be found (see also details below).

Details
If the neighbours member of listw has a “self.included” attribute set to TRUE, the Gstar variant, including the self-weight w_{ii} > 0, is calculated and returned. The returned vector will have a “gstari” attribute set to TRUE. Self-weights can be included by using the include.self function before converting the neighbour list to a spatial weights list with nb2listw as shown below in the example.

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.

Value
A vector of G or Gstar values, with attributes “gstari” set to TRUE or FALSE, “call” set to the function call, and class “localG”.

Well, from Marcos Luna’s video, it was Gi* (G-I-star), but from our professor’s video, it was Gi (without star). I am not sure what is correct. it might even be simply local G statistics…

[Jarunee Siengsanan-Lamont]

Hi,

From the website: https://rpubs.com/quarcs-lab/spatial-autocorrelation

“Getis-Ord approach
The Getis-Ord Gi Statistic looks at neighbours within a defined proximity to identify where either high or low values cluster spatially.”

which is to identify hotspots among neighbourhoods. For exceedance probability, it implies probability (of mean versus estimate) above the threshold (c).

“6.6 Exceedance probabilities
We can also calculate the probabilities of relative risk estimates being greater than a given threshold value. These probabilities are called exceedance probabilities and are useful to assess unusual elevation of disease risk.”
from https://www.paulamoraga.com/book-geospatial/sec-arealdataexamplespatial.html#exceedance-probabilities

hope this help

[Pacharapol Withayasakpunt]

Thank you very much for sharing. It is always nice to see more code.

However, this makes it confusing with Local Moran’s I

– A positive value for Ii indicates that the unit is surrounded by units with similar values.
– The Getis-Ord Gi Statistic looks at neighbours within a defined proximity to identify where either high or low values cluster spatially.

The page also mentions Geary’s C which also found in Wikipedia some time ago.

Not sure if exceedance probability is considered a spatial statistics…

EDIT: The rpubs links to a lot of YouTube VDOs, which is very helpful 🙂

[Jarunee Siengsanan-Lamont]

my apologies: exceedance prob is prob of observed/ expected.

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