Spatial Statistics

This index is used to identify the spatial correlation structure that best describes the data. The basic principle is to characterize the spatial dependency by showing how values are spatially correlated.

In a general way, Moran index is useful to test if the null hypothesis is that there is spatial dependency; in this case the value is zero. Positive values (between 0 and +1) indicate a direct correlation and negative values (between 0 and -1) indicate inverse correlation.

Once the index is calculate, it is important to statistically validate it. To estimate the index significance, the most common approach is the pseudo-significance test.

Global autocorrelation indicators, such as Moran index, provide one value as the measure of spatial association for the whole area dataset. However, in many cases it is desirable to analyze patterns in a scale with more details to verify if the hypothesis of stationarity of the process is valid locally.

To verify, it is necessary to use spatial association indicators that can be associated to different location of a spatially distributed variable. This methodology uses the Local Moran Index to find spatial correlation in these areas. Given that it is a local indicator, there is a specific correlation value for each area, which allows the identification of spatial clusters and outliers.

This operation creates the following attributes:

Spatial Local Mean method examines the mean value mi of an attribute in the study region (first order).

Local Moran Index may present some issues for understanding given that the correct statistical distribution being unknown and requiring its estimation through simulations. Therefore, G and G* normalizing functions can be important for some analysis.

G and G* functions are two local spatial autocorrelation indices that allow the test of hypotheses about the spatial clustering of the values sum, associated to the neighbors points to the considered one.

Since this indicators are composed by the sum of attributes values, the observation of significant high values of Gi and Gi* indicates that this attributes occur in high values, and the opposite indicates clustering of low values.

The main difference between G and G* functions is that the former considers values of all neighbors while the later considers the region to calculate the index.