The spatial extent - with - index autocorrelation is always responds the same principle: To relate the differences in the thematic values between two locations or cases, with the corresponding geometric distance between them . Therefore, there is a common framework to an index of spatial autocorrelation .
In the Local Moran 's I index , like the Pearson correlation coefficient , the results vary between -1 and 1 , representing the maximum negative and positive autocorrelation , zero means a completely random spatial pattern .
Meanwhile, the Getis and Ord G , is an index of spatial association to different Moran's I , indeed, be said that the inference resulting from G is complementary to I. A significant positive value of G ( G> 0) indicates that there is a " cluster" of high values of the variable analyzed with reference to their average. Also, a significant but negative index value of G (G < 0) is shown a group of low values relative to the average of the variable analyzed .
* The index would Gi : Gi * > 0: significant cluster of similar high values around i , while Gi * < 0: significant cluster of low values around i like .
To complement to the previous answer with respect to the G-statistics:
The G-Statistics is (like Moran's I) available in both, a global as well as a local fashion. The global G indicates a general behaviour of the dataset. It either indicates tendency towards clustering of low values (negative G), high values (positive G) or none of both. In the latter case it is still possible to have clustering of similar values. However, these are not considerably high or low, compared to the overall dataset.
The local Gi (and Gi*) can be interpreted in the same manner. The difference between both versions is that Gi excludes the value that is currently under investigation. In contrast, Gi* takes this value into account.
In terms of significance assessment, one usually uses z-scores. These are (due to the well-known central limit theorem) apprpximately normal. Thus, it is quite easy to assess significance by means of normal theory. A z-score > 1.68 indicates significance (alpha = 0.1). The same goes for negative values, where you would watch out for values below -1.68 respectively.
However, I'd like to point out that when using local statistics, you should be aware of alpha-error inflation. That appears because you are conducting multiple hypothesis tests on one sample. You should consider Bonferroni correction (or some related method) in that case.
I hope that added to the previous answer.
I found all answers are interesting since they are based on the life experience of people using the spatial-temporal cluster analysis. When I read articles that aimed to evaluate the similarity and differences between traditional and new spatial -temporal analysis, most appreciated their importance to the analysis and recommend to use mixed methods of analysis and appreciate the values. Also, the objective of the authors is important to choose the method of spatial data analysis.
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