My observations are points along a transect, irregularly spaced.
I aim at finding the distance values that maximize the clustering of my observation attribute, in order to use it in the following LISA analysis (Local Moran I).
I iteratively run Global Moran I function with PySAL 2.0, recreating a different distance-based weight matrix (binary, assigning 1 to neighbors and 0 to not neighbors) with a search radius 0.5m longer at every iteration.
At every iteration, I save z_sim,p_sim, I statistics, together with the distance at which these stats have been computed.
From these information, what strategy is best to find distances that potentially show underlying spatial processes that (pseudo)-significantly cluster my point data?
PLEASE NOTE:
- Esri style: ArcMap Incremental Global Moran I tool identify peaks of z-values where p is significant as interesting distances
- Literature: I found many papers that simply choose the distance with the higher absolute significant value of I
CONSIDERATIONS
Because with varying search radius the number of observations considered in the neighborhood change, thus, the weight matrix also change, the I value is not comparable
I would like to say: start with something like average distance between points and increase this this by a value which will make sure that every point might have at least 2 neighbors. The idea here is to start with some value which every point might have at least 1 neighbor, then 2 neighbors, 3 neighbors, etc.
Hi Patrik, thx for your answer.
However, what you suggest is basically to use the k-neighbours method for defining the weight matrix, where k is the number of observations the neighborhood must have. I cannot use this approach because the points are irregularly spaced, iteratively increasing k will not tell me a distance value but a k value. Furthermore, at the end the question remains, what would be k value that best conceptualises neighborhoods that shows maximal clustering??
Thx again,
Nick
dear take the average distance add to that, why you do not try check out the previous work relates to yours
Hi Konstantinos Vlachos ,
thx for your complete answer, I really appreciated your effort.
You are right, my points are elevation points sampled from 1000+ cross-shore transects along the Victorian coastline. I cleaned them by removing vegetation, so interpolation is a viable option (trade-off), often used for cleaning.
Then, having a regular lattice, and increasing the distance band by 2m, I will ensure that a minimum of 200 pts are considered neighbors (at 2m distance radius), then 400 pts (at 4m search) and so on. Statistically, I use a conditional permutation approach to compute a pseudo p-value of 0.001 (with 999 permutations at every Moran-I) run).
So, after I have the result, you suggest to look at the peaks of Moran-I values, right?
So why ESRI ArcMap (I do not use that tool) return peaks of z-values as an indication of interesting distances to study spatial phenomena???
Thx again,
Nick
Nicolas Pucino ArcMap has a tool called incremental autocorrelation, which i would recommend you since it allows run multiple moran I test for a set of specified bandwidth. Normally the first peak of Z value is recommended as the optimal distance to pick. The Z value is part of Moran I index (is a test statistic to show how our distribution is differing from the random pattern) and it is interpreted together with p-value.
NOTE: in other words never interpret only the Moran I coefficient, but look also the Z value showing you how far the distribution is from the expected value and the p-value will tell you if it is statistically significant or not.
I would add the Konstantinos Vlachos suggestions here: " then I would pick the Moran's I that corresponded to the spatial scale that I wanted to analyze". Maybe the proper term here is to distance (not the moran I ) which shows a pick of Z value (the first peak is recommended when we dont have any any about the scale of our phenomenon), however you could peak any other peak which you think is more appropriated for you analysis.
Hope it helps!
Please, see this picture to understand I am talking about:
http://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-statistics-toolbox/GUID-A9FBCE6E-2E45-47F7-A246-29CDB1021E7E-web.png
Thx Patrik Silva for the reply.
I am running exactly the same as the Incremental autocorrelation tool in ArcMap, but with Python with Open Source tools (PySAL).
ArcMap recommend the PEAKS OF Z-VALUES, while in the literature, I found researchers used maximum Moran's Index values (the I value, in the ArcMap tool). The only difference, I cannot look at plots, as I am running it for 6000+ cases.
Having said that, thank you Patrik and Konstantinos Vlachos for your opinions on this, I will select the peaks of Z-values, then if multiple peaks are returned, I will use the maximum Z-values of the peaks, as I do not want to bias my following analysis with my distance decision.
Thx again!
Cheers,
Nick
- Badges
- Science topic
- Similar topics
- Computer Science and Engineering
- Programming Languages
- Python