Moran's i vs Incremental Spatial Autocorrelation

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02-22-2012 07:39 AM
LaurenSmith
New Contributor II
Hi,

I am running the hot spot analysis to identify clusters of high and low areas of respiratory diseases. I have watched several esri videos about the topic and in an earlier video it talks about running moran's i autocorrelation to select a suitable distance band, in a more recent video I have watched it talks about calculate distance band and incremental spatial autocorrelation (ISA). I realise they both produce Moran's i z scores but I have run both and get different results so I am not sure which one is better to use. The results from ISA seem to be suggesting higher distance bands (peaking at higher distance values) which means by data is showing large hot spots (more like trends), where as the running Moran's i I see peaks in lower values which produces smaller hot spots.

Would it be acceptable to use the calculate distance band and just use the maximum value in Moran's i as this produces a peak in the z score at a smaller distance. For example, the maximum distance is 2.09736dd, and the average is 0.368413dd. Results in ISA peak at 5.04dd and Moran's peaks at the 2.09dd value. Also, the conceptualisation of spatial relationships is to be the same as I am using in the hot spot analysis, yes?

Thank you.
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3 Replies
DavidBirkigt
New Contributor III
Hi,

I too had challenges with the ISA tool. If I remember right ISA works by calculating Moran I with increasing neighbourhood sizes. Meaning Moran is calculated at each of the increments you set ex 10km 20km 30km etc. This means that each band is calculated with a different number of neighbours. My first band could have 3 neighbours and my last band could have 500 neighbours, this produced very spikey results in near bands and better results as the number of neighours increased, so you need to consider this in interpreting your results. I ended up ignoring all my moran values until a couple distance bands away from the origin.

Depending on the parameters you used to perform the single Moran the value should be the same at the same distance band in the ISA tool. Ie if you set the distance band in the moran tool to 100 and the ISA had the same band value the moran values should be the same.

Also, I see that you quoted your distance in dd. As Moran I is supposed to be calculated in flat space (cartesian) x and Y I would suggest projecting your data to projected coordinate system.

David
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LaurenSmith
New Contributor II
Thanks David.

My data is made up of a base map (Amazon Basin) and an excel document joined to it which shows incidence rates per municipality. The base map has a coordinate system and I've tried to project map once the join has happened but I am still ending up with decimal degrees. I've checked the data source to see which coordinate system the base map has and its the GCS_South_American_1969 (please see below). Is there a way around this so I can use Moran's as I would like to be able to back up my choice of distance? Could I just use the data from the 'Calculate Distance Band' tool which gives a maximum distance so every location has one neighbour? Thanks.

Geometry Type: Polygon

Geographic Coordinate System: GCS_South_American_1969
Datum:  D_South_American_1969
Prime Meridian:  Greenwich
Angular Unit:  Degree
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DavidBirkigt
New Contributor III
Hi,

To address your projection issue I can not give you a straight answer as I know nothing about picking a projection for big areas of the amazon, but this is essentially your problem. Your data is in a Geographic Coordinate System this system essentially describes the location of a place on a sphere in degrees (latitude longitude) and it just does not make sense to do any analysis on this as the degrees are not a uniform measurement (1 deg at the equator covers more distance then one deg at the north pole).

That is where projections come in they are a mathematical way to transform the GCS onto a flat surface. But just like peeling an orange you cannot do this without distorting measurements, including distance, shape, area and angles. That is why there are so many different projections, they are useful for different things. I usually work in a single UTM zone, but you are working on the whole amazon which spans many UTM zones ao that is not the answer. I think in the end you will just need to do some research and find a projection that distorts the variable of concern (distance) the least for your study area, but whatever the solution is I doubt it will be perfect.

You can check out this book, some parts are pretty technical but other parts are not, I think it is good, Datums and map projections for remote sensing, GIS, and surveying  By Jonathan Iliffe

For as to why your data does not change projections when you try, you might want to read up on on the fly projecting in arcgis. What I usually do is go; view data frame properties and set the projection I want. Then export a copy of my files in this projection, open a new map (clears the projection) then add my projected data. There are a lot of ways to achieve this though ex project tool.

As for the second part of your question. There is also no definite answer and it depends on what you want to know. If all of your features have a neighbour within 20km except one that is 500km away then you could miss some important trends. What I would do (if using arcGIS 10) the ISA outputs messages to the geoprocessing results thing, in there it reports the number of features that did not have a neighbour. Using this you can come up with a logical choice that is defendible.

David
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