Spatial Association Analysis

This module allows the user to perform some exploratory analysis techniques in spatial data (cadastral, having objects-areas). This module gives spatial association indexes and some visualization possibilities with the intention to allow the user to identify spatial groupings, atypical cases and different spatial regimes existing in the information layer. The central concept of this module is spatial autocorrelation.
 
 

Exploratory analysis techniques for AVAILABLE spatial data

The SPRING implemented techniques are direct and indirectly related to the local and global Moran index. This techniques combined with objects attributes visualization functions form a set of tools for exploratory analysis:

1 - Moran Index - I’Moran

2 - Local Index for Spatial Association (LISA)

3 - Moran Spreading Graph

4 - Z x WZ Bars Map

5 - Box map, Lisa map and Moran map

For the analysis attribute, 7 new columns are generated in the corresponding objects table, which has the necessary information for the visualization module.

To execute this module:

1 - Select the desired IL, it has to belong to the cadastral model and has spatially represented objects by polygons;
2 - Click on: Spatial Analysis – Spatial Statistics – Moran Spatial Association..., in the main menu;
3 - Define the object and the attribute for which the index will be generated;

4 - Define the number of permutations.
5 - Click on apply.

The result of the global index is presented in the footnote of the module window. Seven new columns are added to the objects table having the necessary information for the different ways for visualization.
 

1 -Moran Index - I’Moran

The Moran Index gives a general association spatial measure of the data set, ranging from [-1, 1]. Weak spatial association data, results in a small index value. Positive and negative values give a positive and negative spatial autocorrelation, respectively. The values for local indexes are added as a new column in the objects table (IMoran).

To visualize spatially the LISAs:
1- After executing the spatial association module, select the consulting... button in the control panel.
2 - In the objects visualization windows select: edit-grouping... Select the same step or quantil mode. Place over the IMORAN attribute. Click on grouping and wait for the result. Finally, click on apply.
 

2 - Local Index for Spatial Association (LISA)

While the global indicators, such as the Moran index, give a unique value as a spatial association measure for all data set, the local indicators produce an specific value for each object, which gives the grouping identification of objects with similar attributes values (clusters), irregular objects (outliers) and with more than one spatial regime. A local indicator has the following objectives:

i) allows the pattern identification of significant spatial association;

ii) be a decomposition of the global index of spatial association.

The local indicator used in the SPRING is named the Moran Local Index.
 

3 - Moran Spreading Graph

This device allows to visualize the data behavior using a spreading graph, where the objects attributes deviation values related to the average (Z), they are associated to X axis, and the average value of their neighbors (Wz), to the Y axis.
 

To visualize the graph in the SPRING:

1 - In the objects table, select the Z columns (attributes deviation related to the average) and WZ (average of the Z neighbors);
2 - Place the cursor over one of the selected columns and press the mouse right button. A new menu will show up, and then, select the graph option.
 

4 - Z x WZ Bars Map

This device allows the simultaneous visualization of the value related to the object attribute and the corresponding value to its respective neighborhood, using two graphical bars over a corresponding area in the object in the map. The bars height are proportional to the object attribute values (or a deviation) and to the neighbors average. Both information can be obtained from the objects table column: Z and WZ.
 

To generate the bars map in the SPRING:

1- After executing the spatial association module, select the consulting... button in the control panel.

2 - In the objects visualization window select: edit-grouping... Select the bar graph mode. Place over the Z attribute and click on the insert button. Repeat for the WZ attribute and click on apply.
 

5 - Box map, Lisa map and Moran map

These three visualization graphical devices are based on the LISA results and from the Moran spreading graph. In the box map, each object is classified according to its position related to the quadrants, receiving a corresponding color in the map to be generated. In the LISA map generation, the significance evaluation is performed comparing the LISA values, with a series of values, obtained by the neighbors attributes values permutation (number of permutations defined by the user). Under the null hypothesis (non-existence of the spatial autocorrelation).The significance values are then classified into four groups: non-significant, with significance value of 0.05, 0.01 and 0.001. The significance evaluation of 0.001 happens only for a permutation number greater or equals to 999.

In the Moran map, like the LISA map, only the objects for which the LISA values were considered significant (p < 0,05), are presented, however, they are classified into four groups, depending on the quadrant they belong to in the spreading graph. The other objects, are classified as "without significance".
 

To generate these maps in the SPRING window:

1 - After executing the spatial association module, select the consulting... button in the panel control.

2 - In the objects visualization window select: edit-grouping... select the same step or quantil mode. Place over the BOXMAP or LISAMAP or MORANMAP attributes, according to ones interest. Click on grouping and wait for the result. Finally, click on apply.