Spatial Statistics
The Spatial Statistics operation allows the user to calculate the following statistics:
Global Moran Index:
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.
Local Moran Index – LISA:
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:
Z: Vector with observed deviations;
Wz: Local weighted average vector;
MoranIndex: Local Moran Index;
LISASig: p statistics value;
BoxMap: Presented values correspond to the relation between Z and Wz values in a Dispersion Plot divided by quadrants (Q). Values range from 1 to 4, where:
1 corresponds to values in Q1 (high-high – high Z and Wz values),
2 (Q2, low-low),
3 (Q3, high-low),
4 (Q4, low-high);
LISAMap: This column values, ranging from 0 to 4, are created only if a level of significance is selected in the interface. During the creation of a LISAMap, local indices are classified as:
Non significant (0);
With 95% confidence (1, p=0.05);
With 99% confidence (2, p=0.01);
With 99.9% confidence (3, p=0.001).
MoranMap: This column values are generated only if a level of significance is selected in the interface. This result presents only regions where Ii values are significant (interval above 95%) while BoxMap does not consider significance. In this case, local indices Ii are associated to the Moran dispersion diagram. The values are:
0 (non significant),
1 – Q1 (high-high),
2 – Q2 (low-low),
3 – Q3 (high-low),
4 – Q4 (low-high).
Local Mean:
Spatial Local Mean method examines the mean value mi of an attribute in the study region (first order).
G and G* Functions:
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.
It is accessible through:
PROCESSING → SPATIAL ANALYSIS → SPATIAL STATISTICS
Input Information:
Layer Name: Select the input Layer.
Attribute Name: Defines the attribute from layer used to calculate the statistics.
Attribute Link: Defines the attribute that identifies the objects of this layer.
Load GPM: Opens a dialog to select a file with a desired proximity matrix.
Operation Parameters:
Global:
Moran Index.
Index Value: Calculated value for global moran index.
P-Value: Calculated value for p-value.
Evaluate Significance / Number of permutations.
Local:
G Statistics.
Local Mean.
Local Moran Index (LISA).
Evaluate Significance / Number of permutations.
Output Information:
Repository:
Select one type
of repository by clicking on the
button to save the output layer as a file or on the
button to save it in the database.
Layer Name: Defines the name to create the output layer.
Click on the OK button and then the spatial statistics will be calculated.