Hi Aldo, distance-based Moran's eigenvector map analysis (dbMEM) is a spatial eigenfunction method. Basically, dbMEM (also known as principal coordinates of neighbour matrices, PCNM) decomposes the spatial structure of your dataset in a large number of eigenfunctions (number of sites-1). These eigenfunctions can be used as new proxy variables of spatial structure in OLS, GLM or similar methods (in the case of univariate responses) or a redundancy analysis (RDA, in the case of multivariate responses, such as in analyses of species composition). These eigenvalues allow you to test/account the importance of spatial structure per se on a particular phenomenon. One downside is that the number of eigenfunctions to be used needs to be determined manually which can be cumbersome for large datasets. Only eigenvalues with a significant spatial structure (i.e. spatially autocorrelated) are used in further analyses. 

Here is an excellent explanation of the method and its applications:

http://biol09.biol.umontreal.ca/PLcourses/Spatial_eigenfunction_methods.pdf

Both dbMEM (PCNM) and RDA can be run in the package vegan in R (implemented by the group of Pierre Legendre and co-workers).

Take a look of a previous discussion about alternative methods to PCNM (also implemented in R!)

 https://www.researchgate.net/post/Is_Morans_eigenvector_maps_MEM_really_better_than_principal_coordinates_of_neighbour_matrices_PCNM

Good luck with your research.

Marcelo

Hi Aldo, distance-based Moran's eigenvector map analysis (dbMEM) is a spatial eigenfunction method. Basically, dbMEM (also known as principal coordinates of neighbour matrices, PCNM) decomposes the spatial structure of your dataset in a large number of eigenfunctions (number of sites-1). These eigenfunctions can be used as new proxy variables of spatial structure in OLS, GLM or similar methods (in the case of univariate responses) or a redundancy analysis (RDA, in the case of multivariate responses, such as in analyses of species composition). These eigenvalues allow you to test/account the importance of spatial structure per se on a particular phenomenon. One downside is that the number of eigenfunctions to be used needs to be determined manually which can be cumbersome for large datasets. Only eigenvalues with a significant spatial structure (i.e. spatially autocorrelated) are used in further analyses. 

Here is an excellent explanation of the method and its applications:

http://biol09.biol.umontreal.ca/PLcourses/Spatial_eigenfunction_methods.pdf

Both dbMEM (PCNM) and RDA can be run in the package vegan in R (implemented by the group of Pierre Legendre and co-workers).

Take a look of a previous discussion about alternative methods to PCNM (also implemented in R!)

 https://www.researchgate.net/post/Is_Morans_eigenvector_maps_MEM_really_better_than_principal_coordinates_of_neighbour_matrices_PCNM

Good luck with your research.

Marcelo

Thank you very much for this input Marcelo. Very much appreciated, I will have a look into this material. saludo 

Hi Aldo,

there is nothing much left to add to what Marcelo very clearly explained!

thx Marcelo.

I just wanted to share with you a little document I prepared for a group of research when we analyzed Wombat's burrow spatial clustering ( absed on an activity value from 1 (inactive or little evidence) to 3 (very active, hints of recent activity)).

In the second part I breifly explained the group how to read and interpret Hot Spot Analysis (Getis-Ord Gi*) maps, based on prior dbMEM.

Might be helpful as simple applied example.

That is all done within ArcMap, you will find all the geoprocessing tools for doing it.

Obviously it allows less customisation than R, but depending on your programming skills and licensing level, it might be helpful to use ArcMap.

I cannot be sure Qgis has it simply because I have no experience with Qgis (unfortunatly), but I am positive there is a way to use freeGIS for accomplish your task. Mainly becasue open source GIS platforms have a broad community of people that use them, ask questions and answer them, just like R-Cran.

Take a look at the document attached!

Have a nice day,

Nic

thank you very much nic