Number of neighbors with "Cluster and Outlier Analysis (Anselin Local Moran's I)"

[MircoAckermann]

Hello everyone,

When running the tool "Cluster and Outlier Analysis (Anselin Local Moran's I)", the random expected value can be determined by permutation. The values of the relevant neighbors are exchanged according to the number of permutations. What does the tool calculate if there are not enough neighbors to carry out the corresponding number of permutations? I usually have individual features which only have one neighbor. How can I interpret the z and p values in this case?

[DanPatterson]

Did you see

How Cluster and Outlier Analysis (Anselin Local Moran's I) works—ArcGIS Pro | Documentation

and the COType field in the Interpretation section?

[MircoAckermann]

That's not exactly what I meant. I'm interested in how the algorithm works when not many neighbors are available. So if there is a feature with 4 neighbors, only 4*3*2*1 = 24 permutations are possible. How does the tool perform 999 permutations in this case? Or does it only perform the possible 24 permutations, making the expected value more uncertain? In the case that there is only one neighbor: Is an asymptotic test performed?

[DanPatterson]

My reading of the permutations section suggests it isn't the actual number of possible permutations but the number of random permutations of the data that is run

[MircoAckermann]

I am not sure if I have understood you correctly. In the section on permutations, it says that "...each permutation randomly rearranges the neighborhood values around each feature and calculates the Local Moran's I value of this random data." If you perform more permutations than are possible, you would perform the same combination of values multiple times. This would affect the interpretation of z and pseudo p.