Moran's I significant only when using 'Inverse Distance' conceptualization

Question

For a points file, I used 'conceptualization of spatial distance' for Moran's I as:

1 - Zone of indifference

2 - Inverse distance

3 - Inverse distance squared

The Moran's I was statistically significant only for 'inverse distance'.

Subsquently I used hot spot analysis and found statistically significant hot and cold spots.

Could someone please help me understand why Moran's I is only significant for 'inverse distance'?

Thanks!

MasoodShaikh · Answer

Thanks, this is very helpful indeed!

LaurenGriffin · Answer

Hi Masood,

When you use inverse distance for the conceptualization of spatial relationships parameter, you should also row standardize. This is because the scaling constant with Inverse Distance is very small (close to zero... especially with a large study area). All the other conceptualizations should have larger weights. Check to see that the Conceptualization of Spatial Relationship you are using is appropriate for the question you are asking. Also, determine if row standardization is appropriate or not. If it IS the most appropriate conceptualization of spatial relationship AND you feel confident row standardization is not appropriate, I would trust the conclusion you're getting.

Heads up: There will be new tool in ArcGIS Pro 3.4 called Compare Neighborhood Conceptualizations. It will provide one way to identify an appropriate Conceptualization of Spatial Relationships parameter based on your data. You would still want to decide if standardization is appropriate or not, and always do a gut check to make sure the recommendations make sense to what you know about your subject area. Optimized Hot Spot Analysis will also recommend a fixed distance conceptualization by looking for a distance that maximizes spatial autocorrelation.  I believe, but am not at all sure, Pro 3.4 will be available soon-ish.

Also, please note that it is not uncommon to have a global method like Moran's I indicate there is no statistically significant clustering at the global scale, then to find significant hot and/or cold spots using Hot Spot Analysis (local scale analysis). This is discussed here in the Global Moran's I documentation (see the first FAQ). It is also discussed in the 1992 seminal article for the Gi* statistic (called Hot Spot Analysis in ArcGIS). See page 199 and the SIDS example. When the authors analyze the data with a global method, there is no evidence of statistically significant clustering. When they use Gi*, they do find evidence of statistically significant clustering (see conclusions at the top of page 201).

I hope this helps!

Best wishes,

Lauren Griffin, Esri