What is Spatial Autocorrelation (Spatial Dependency)?
Spatial autocorrelation in GIS helps understand the degree to which one object is similar to other nearby objects. Moran’s I (Index) is used to measure spatial autocorrelation.
Geographer Waldo R. Tobler’s stated in the first law of geography:
“Everything is related to everything else, but near things are more related than distant things.”
Spatial autocorrelation definition measures how much close objects are in comparison with other close objects. Moran’s I can be classified as: positive, negative and no spatial auto-correlation.
- Positive spatial autocorrelation is when similar values cluster together in a map.
- Negative spatial autocorrelation is when dissimilar values cluster together in a map.
Why is spatial autocorrelation important?
One of the main reasons why spatial auto-correlation is important is because statistics relies on observations being independent from one another. If autocorrelation exists in a map, then this violates the fact that observations are independent from one another.
Another potential application is analyzing clusters and dispersion of ecology and disease.
Is the disease an isolated case or spreading with dispersion?
These trends can be better understood using spatial autocorrelation analysis.
Positive Spatial Autocorrelation Example
Positive spatial auto-correlation occurs when Moran’s I is close to +1. This means values are clustered together. An example of this would be an elevation dataset because we’d expect similar elevation values be 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 random choice.
Negative Spatial Autocorrelation Example
Negative spatial autocorrelation 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 random choice.