Spatial autocorrelation in GIS helps understand the degree to which one object is similar to other nearby objects.
Moran’s I (Index) measures spatial autocorrelation. Geographer Waldo R. Tobler stated in the first law of geography:
“Everything is related to everything else, but near things are more related than distant things.”
Spatial autocorrelation measures how close objects are in comparison with other close objects. Moran’s I can be classified as positive, negative, and with no spatial auto-correlation.
Why is Spatial Autocorrelation Important?
One of the main reasons why spatial auto-correlation is important is because statistics rely on observations being independent of one another. If autocorrelation exists in a map, then this violates the fact that observations are independent of one another.
Another potential application is analyzing clusters and dispersion of ecology and disease.
These trends can be better understood using spatial autocorrelation analysis.
Positive Spatial Autocorrelation Example
Positive spatial autocorrelation occurs when Moran’s I is close to +1. This means values cluster together. For example, elevation datasets have similar elevation values close to each other.
There is clustering in the land cover image above. This clustered pattern generates a Moran’s I of 0.60. The z-score of 4.95 indicates there is a less than 1% likelihood that this clustered pattern could be the result of a random choice.
Negative Spatial Autocorrelation Example
Negative spatial auto-correlation occurs when Moran’s I is near -1. A checkerboard is an example where Moran’s I is -1 because dissimilar values are next to each other. A value of 0 for Moran’s I typically indicates no autocorrelation.
Using the spatial autocorrelation tool in ArcGIS, the checkerboard pattern generates a Moran’s index of -1.00 with a z-score of -7.59.
(Remember that the z-score indicates the statistical significance given the number of features in the dataset).
This checkerboard pattern has a less than 1% likelihood that it is the result of a random choice. If you want to test this statistical technique, try GeoDa software for this and more.
What’s Next: Spatial Dependency
Spatial autocorrelation indicates if there is clustering or dispersion in a map. While a positive Moran’s I hints that data is clustered, a negative Moran’s I implies data is dispersed.
If you’ve tested this spatial autocorrelation guide, try to master spatial statistics widely used statistics in GIS: