Spatial Statistics
The
Spatial Statistics operation allows the user to
calculate the following 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.
- 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),
- 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:
- 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:
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.
It is
accessible through:
Plugins > Spatial Analysis >
Spatial Statistics...
This
interface consists of the
following steps:
1.
Input Information:
- Layer Name: Select the
desired 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.
- GPM: Opens a dialog to
select a file with a desired proximity matrix.
2.
Operation Parameters:
- Index Value: Calculated
value for global moran index.
- P-Value: Calculated
value for p-value.
- Evaluate Significance /
Number of permutations.
- Local Moran Index (LISA).
- Evaluate Significance /
Number of permutations.
3. Output
Information:
- Repository: Defines
where the output data will be saved.
- Layer Name: Defines the
name to create the output layer.
Click OK and then the spatial
statistics will be calculated.