Interpretting differential Moran's I and Local Moran's I

[John Heppen]

I see that GeoDa 1.8.12 lacks bivariate Moran's I and Local Moran's I and it has been replaced with the differential Moran's I and Local differential Moran's I which allows for comparison over more than two time periods. I have a question about interpreting the results.

 

I used to use bivariate Moran's I to compare a variable for two different time periods.

 

I was under the assumption that:

 

Polygons that were high-high were polygons where the value of the variable was high in the past and high in the future.

 

Polygons that were low-low meant a value that was low in the past and low in the future.

 

Polygons that were low-high meant a value was low in the past and high in the future meaning a change

 

Polygons that were high-low mean a value was high in the past but low in the future meaning a change.

 

When I use differential local Moran's I to compare two time periods I get results that seem counter-intuitive. When I compare the variable over the two maps by just doing a visual look polygons that should be low-high are high-high. The variable was low in the past and in the future the variable was high which to me should be low-high since there was a change in value through time. Why is it presented as high-high when the variable was low in the past and high in the future?

If I wish to compare let's say 2010 to 2000 which should be the first variable selected in the dialogue box?

 

Is there an article or book chapter which explains differential Moran's I and local different Moran's I? I have not found anything yet that I can follow in the geode documentation sight.

 

Am I interpreting the results correctly in the past and now? Have I been interpreting bivariate Moran's I and local bivariate Moran's I in the past corrently?

 

John

 

[Julia Koschinsky]

Hi John,

Sorry for the late response. 

You can find some initial documentation about the differential Moran's I here: https://s3.amazonaws.com/geoda/software/docs/geoda_1.8_2.pdf

We're working on supplementing this with an updated manual.

Re. the bivariate and differential Moran's I interpretation: For the case you mentioned, let's assume you have e.g. crime for 2000 and for 2010. In the bivariate Moran's I, you were comparing crime at a given location i in 2000 (Xi) to the average of its neighbors in 2010 (Xj or Y or spatial lag). So a high-high cluster meant above-average values of crime in 2000 in a given area, surrounded by above-average values of crime in 2010. I.e. it's high values in the cluster core in 2000 vs high values in the cluster neighbors in 2010 -- but it's not high values in 2000 vs. 2010 in the same area (which sounds like was your interpretation). Many people thought it was the latter interpretation, too, which is why we replaced the bivariate Moran's I with the differential one.

What the differential Moran's I does is the following (using the same example):

• it deducts crime in 2000 from crime in 2010 (so you have a new variable, let's say Crime2010-2000)
• it then runs the Moran's I test on this new variable (same result as first computing Crime2010-2000 in GeoDa and then running the univariate Moran's I on it)

You can use the global or local differential Moran's I test to find out if a variable's change over time in a given location is statistically related to that of its neighbors. In other words, it addresses the question whether there are clusters of changes in crime between 2000-2010. A high-high cluster would be one with above-average 2000-10 changes in an area and its neighbors. Low-low would be below-average changes and low-high would be small changes in the core vs. high changes in the neighbors.

The old bivariate low-high cluster interpretation would have been low in Xi (2000) vs. high in Xj (2010). In your case this probably now shows up as a high-high cluster because the difference between crime in 2000 and 2010 is larger than average at both i and j (in your high-high example, it's a hotspot of increasing crime, i.e. the increase in crime between 2000 and 2010 in a given area is significantly correlated with that of its neighbors). So the focus here is on the magnitude of change in the core vs neighbors. 

Hope this helps,

Julia

--
You received this message because you are subscribed to the Google Groups "Openspace List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to openspace-list+unsubscribe@googlegroups.com.
To post to this group, send email to openspa...@googlegroups.com.
Visit this group at https://groups.google.com/group/openspace-list.
For more options, visit https://groups.google.com/d/optout.