Local G Statistic Conversion Error?

[Carson Telford]

Hi all,

I am running a Local G analysis in GeoDa and confused that the G statistics are being reported as decimals (ex: 0.000619795, p-value 0.07), when I am expecting a standardized score similar to a Z-score. The same thing happens when I run the Local G*.

I am guessing these need to be converted, but do not know how. Can anyone provide insight as to why GeoDa is doing this, and how I can convert the output to a standarized G statistic that is interpretable?

Thank you!

[Julia Koschinsky]

from Luc Anselin:

GeoDa does not report Z-values for the Gi and Gi* statistics, since these are based on an analytical derivation

for the moments, which is unreliable in practice. Instead, inference for these statistics in GeoDa is based on a 

conditional permutation approach, the same as for all the other local statistics. Only significant locations are

shown on the cluster map, with a code 1 for hot spot and 2 for cold spot. The determination of the “sign” is by

comparing the calculated value to the mean of the randomly permuted values.

The actual value of the statistic is simply a rescaled sum of values, so if all the values are positive, there will be

no negative Gi statistics. The use of the Z-value is to determine significance, as such these values have no intrinsic

meaning. So, the “interpretation” of the Gi statistic is based on the pseudo p-value from the conditional permutation.

In GeoDa, and the sign (1 or 2), which is only reported for the significant locations, as it should be.

So, even though there is no Z-value, all the information for an “interpretable” statistic is there.

Hope this helps.

L.

Luc Anselin, PhD
Stein-Freiler Distinguished Service Professor of Sociology and the College
Director, Center for Spatial Data Science
Committee on Quantitative Methods in Social, Behavioral, and Health Sciences
Senior Fellow, NORC
University of Chicago
http://spatial.uchicago.edu