I created a spatial weight matrix table using the "Inverse distance" in Conceptualization of Spatial Relationships. I set the "Nearest Neighbors" as 8. It's weird that in each neighboring region, the weights for every pair of features are exactly same! For example:

Feature from i to j and weight:

20 22 0.0769

20 21 0.0769

20 9 0.0769

.... ... ....

20 29 0.0769

the weight sum is 1. But I thought under the "Inverse distance" option, weights should reflect the distances between features. Apparently, the distance of feature 20 to 22 is different with feature 20 to feature 21, but why same weights were given...???

Thanks so much!!

Feature from i to j and weight:

20 22 0.0769

20 21 0.0769

20 9 0.0769

.... ... ....

20 29 0.0769

the weight sum is 1. But I thought under the "Inverse distance" option, weights should reflect the distances between features. Apparently, the distance of feature 20 to 22 is different with feature 20 to feature 21, but why same weights were given...???

Thanks so much!!

I think I may know why you are getting those results, but let's make sure I understand what you've done first:

1) Your Conceptualization of Spatial Relationships is Inverse Distance

2) You've set Number of Neighbors to 8 to ensure each feature has at least 8 neighbors

3) You are taking the default threshold distance (you didn't enter anything for Threshold Distance)

4) Row Standardization was checked ON

I did the above and got expected results with and without Row Standardization. As expected, the weights were different for feature pairs.

You, however, are seeing identical weights for all neighbors associated with a particular feature.

This is what I think might be happening: Because Inverse Distance is unstable for distances less than 1, our inverse distance calculation treats all distances less than 1 as 1. Suppose you are working in a small-ish study area and are using unprojected data (Geographic Coordinate System instead of a Projected Coordinate System) so that your units are in Degrees. With unprojected data, for a study area that has less than a 1 degree extent, all of your distances will be less than 1.0. All of the weights will get set to 1.0, and when you row standardize all of the weights for a feature's neighbors will be equal. To remedy, please project your data prior to analysis (always a good idea, but especially a good idea when your analyses involve distance measurements).

If this is *not* what's happening I will need additional information so that I can try to reproduce the problem. What version of ArcGIS are you using? Might you be able to send me your data? (I would not need any of the attributes, only the feature geometry).

Thanks for asking your question! I hope this resolves your problem; if not we'll try again :)

Best wishes,

Lauren M. Scott, PhD

ESRI

Geoprocessing, Spatial Statistics