Incremental spatial autocorrelation (ISA) uses Moran’s I to test for spatial autocorrelation within distance bands. Analysis is run on a given parameter (eg. percent cover, elevation).
Interpratation
- ISA returns z-score and p-values
- Significant p-value indicates spatial clumping
- Non-significant p-value indicates random processes at work
- Indicates significant peaks in z-score
- Higher z-score indicates more spatial clumping
- Distance of first peak in z-score usually used for further analysis
- Useful for determining the appropriate scale for further analysis
- Hot Spot Analysis
- Density tools which ask for a radius
- Determine whether a subsample should be taken to remove autocorrelation
Hey Kevin!
This summary was really helpful for me! I’m interested to know more about why you would use the distance at the first peak in z-scores for further analysis. Would you mind elaborating on that? Is it because this peak would be the closest distance at which a spatial clustering pattern is detected?
Sophie– I am wondering the same thing actually. I got the info about the tool from the Arc help and it suggested using the first peak for analysis without any justification. I added a graph of z-score by distance, and it shows that closer distances also show significant clustering, so I’m not sure what to make of the peaks. Perhaps, in cases where z-scores increase with distance, there is an inherent correlation involved, making a peak more interesting. Just pulling at straws though, I won’t pretend to know what’s going on here, at least not yet…
The peaks represent the entire dataset at a particular distance increment. A peak in the graph indicates a distance at which the clustering is the most pronounced. So, if you have several peaks that means that there are several distances that reflect pronounced clustering. That distance increment can then be used as the distance increment for further analysis, e.g. in a Hot Spot Analysis.
Source: Lauren Scott at http://forums.arcgis.com/threads/25649-Incremental-Spatial-Autocorrelation-(ISA)
Source: http://resources.arcgis.com/en/help/main/10.1/index.html#/Incremental_Spatial_Autocorrelation/005p0000004z000000/
Kuuipo
I will need to make that documentation clearer it seems 🙂
Yes, as Kuuipo says, ALL peaks reflect distances where the spatial processes promoting clustering are most pronounced. You should select the distance that best corresponds to the question you are asking… Uhmmm… so for tree distribtutions, for example… do you know something about distances with regard to seed propagation? … a disease spread by an insect vector… do you know anything about the range that the insect operates over?
Often what you will find is that the strongest peak is at a very large distance/scale… suppose I am looking at across the United States… often the strongest peak will be an East-West or a North-South pattern… mapping the variable of interest you will clearly see that the value is high (or low) in the East, and the value is low (or high) in the West. While this is indeed the strongest spatial pattern, it generally is not very interesting. By analyzing our data at a smaller spatial scale (the first peak distance) we get insights into the more subtle neighborhood or track or county level patterns and this is often what we are really interested in.
Very good summary!
Best wishes,
Lauren
hmmm… that should have said:
Suppose I am looking at population densities, for example, across the United States…