Spatial Autocorrelation and Moran’s I in GIS

Spatial Autocorrelation
A checkerboard pattern is an example where Moran’s I is -1 because dissimilar values are next to each other.

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’s stated in the first law of geography:

“Everything is related to everything else, but near things are more related than distant things.”

  • Positive spatial autocorrelation is when similar values cluster together on a map.
  • Negative spatial autocorrelation is when dissimilar values cluster together on a map.

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.

  • Is the disease an isolated case?
  • Is it clustered or spreading with dispersion?

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.

Clustered Image Spatial Autocorrelation
Clustered Image Spatial Autocorrelation

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.

Checkboard Pattern: Spatial Autocorrelation
Checkerboard Pattern: Spatial 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 at 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:

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