[R-sig-Geo] [R-sig-eco] Question about Mantel Test

[Sarah Goslee]

Hi,

Please don't cross-post.

A Mantel test is most suited to problems that must be expressed in
terms of distances, as Legendre states, although there is a
mathematical relationship between correlation between distances and
correlation between raw data.

If your main concern is statistical testing, you can use a permutation
test for significance of correlations without converting them to
distances first, thus avoiding the parametric assumptions.

If you want to use a Mantel approach to investigate *linear* spatial
autocorrelation, then "distance apart" is relevant, and this does
become a distance problem. You could then obtain the correlation
between difference in variable X and difference in variable Y given
their distance apart.

Are you sure there's significant spatial autocorrelation? Have you
tested for it in your data? If there is, is it meaningful in the
context of your question?

There are many approaches to dealing with spatial autocorrelation, and
you might be best served to do some reading on your own and to consult
a statistician, if you have access to one who is familiar with
ecological data.

Sarah

On Thu, May 10, 2012 at 4:45 PM, Jaime Burbano Girón
<jaimebg27 at gmail.com> wrote:
> Hi every body.
>
> I have some questions about Mantel Test. I expect that with experience in
> spatial analysis of people in this list I can resolve them. Your
> explanations and suggestions will help me so much, so, thanks in advance.
>
> For contextualizing. I want to explore the association between some
> environmental variables: precipitation, temperature, bio-climatic
> indicators (construction of "bio variables" proposed in WorlClim), EVI
> (Enhanced Vegetation Index from MODIS-NDVI), NPP (Net Primary Product from
> MODIS), and VCF (Vegetation Continues Fields for trees from MODIS).
>
> *1. *At first instance, I thought to calculate Pearson´s correlation
> coefficient from Mantel Test approach, however, I have some doubts about
> what I am actually doing with this.
>
> I think that I can obtain a more accurate correlation coefficient with out
> the problem of spatial auto-correlation, due to permutation implicit in
> Mantel Test, using as matrices for calculate it  two grids of the set of
> environmental variables.
>
> My real questions comes from the definition of matrices used in Mantel
> Test, because they are proposed from literature to represent a relationship
> between points included in them (often distances), but the grids do not
> represent this, they are the raw values of environmental variables. In
> fact, Legendre recommends that Mantel tests should not be used to test
> hypotheses about the relationships of the original data tables.
>
> So am I correct in try to perform a correlation coefficient with out the
> problem of spatial auto-correlation between any two grids using the Mantel
> Test?
>
> *2. *An other option that I have thought for involving distances is to
> perform the Mantel Test using a distance matrix between the two grids (this
> distance measure could be the correlation coefficient) and the geographic
> distance between grid points (Euclidean distance), since this is a way to
> explore if a variable is spatially autocorrelated, even this is less used
> than Moran Index or Correlogram.
>
> However, I am not sure if with this option I would test the spatial
> correlation of the distance measure used, or I would obtain a correlation
> index of the association of the two grids (distance measure used) with out
> the problem of spatial auto-correlation due to permutation. Or both?
>
> *3.* How else can you recommend me to measure the relationship between two
> environmental grids trying to minimize the effect of spatial
> auto-correlation?
>
> Regards to all and thanks in advance for your help.
>

-- 
Sarah Goslee
http://www.functionaldiversity.org