![]() Spatial Association AnalysisThis 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; 4 - Define the number of permutations. 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. 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: 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);
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. ![]() |