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ANOSIM in vegan

7 messages · Soumi Ray, Jari Oksanen, Michael Gerisch +1 more

Original
Jari Oksanen
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On 12/11/10 02:23 AM, "Soumi Ray" <soumiray74 at gmail.com> wrote:

            

      
      
      
    

        
Soumi,

I only comment the db-RDA/anosim choice: if you can use one, you can use the
other. They are very similar and have the same limitation and "assumptions".
Both are based on dissimilarity measures, and you can use the same
dissimilarities in both methods. They also handle the dissimilarities very
similarly. Overall tests for db-RDA by terms (as implemented in anova(...,
by = "term") for vegan::capscale) and adonis tests give very similar
results. However, they are not identical. The difference is that for
non-Euclidean dissimilarities you will have some negative eigenvalues. These
are ignored in db-RDA (capscale), but they are taken into account in adonis.
Which method to use depends on your questions, and what else you want to do
with your data than get the test statistics.

Cheers, Jari Oksanen

  
  


  


      

    

    
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7 days later

    

      
      

        


  

        

      Gavin Simpson
    

    

      
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On Mon, 2010-11-15 at 10:09 -0500, Soumi Ray wrote:

            

      
      
      
    

        
The best example I can come up with is that these are coordinates, like
map coordinates, in the ordination space, that is all. They are
certainly not "axis scores" in the sense of PCA et al implying that they
are independent, you need both (in 2D solution, all in k-D solutions)
coordinates to represent the "distances" between your samples in terms
of species composition.

The scores are the "best" mapping of the n-dimensional dissimilarity
matrix (n == number of sites or samples) in a k-dimensional space. Where
"best" means i) subject to convergence to a suitable global minimum in
the algorithm, and ii) the mapping is in regards to the /rank/ ordering
of the dissimilarities not their actual values.

HTH

G

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Michael Gerisch
    

    

      
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Hi Soumi,

it just came into my mind - no idea if i am wrong: For me it sounds like your 
sampling design is not independent, as you sample 400 plots twice and you will 
have high probability that the community of a pair of similar sites is more 
equal just because it is the same site and not because of some environmental 
factors. Call it pseudoreplication or else, but i think large part of the 
"similarity" will be due to this fact. Unless you have something like an 
extreme event between the dates which sort of "reset" your communites...maybe 
then its appropriate.

But i don`t know if anosim has the assumption of independence anyway. Maybe 
there is "reanypeated measure" variant? Or maybe i am  totally wrong...

Sorry, did not want to confuse, but it would also be interesting for me.

cheers
michael

        
On Friday 12 November 2010 01:23:41 Soumi Ray wrote:

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Gavin Simpson
    

    

      
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On Wed, 2010-11-24 at 10:21 +0100, Michael Gerisch wrote:

            

      
      
      
    

        
I don't think ANOSIM has many assumptions at all - we test using
permutations and so long as you can generate an appropriate Null
distribution that respects the dependence structures in the data, we can
provide a test. Generating the appropriate Null requires doing a lot by
hand at the moment if you want anything but random permutations (or
random within blocks).

Think of Soumi's Q the other way round. We want to test if there is a
difference in community composition in sample between times A and B. The
TIME variable would explain all the temporal dependence structure. If
there is no other dependence structure (say spatial, or spatially
correlated environmental dependence - the effect of an env var across
the survey sites), then we could assume a Null distribution for the
permutation via random permutation - the residuals are assumed random in
that case.

The issue to hand (in your email) is dependence in the residuals - in
general in statistical methods. If you model this dependence such that
the residuals meet the assumptions of the method, you are fine. It is
only an issue when you fail to (or can't) model the dependence structure
as part of the statistical method itself. Because then the residuals
will not be independent, identically distributed etc.

HTH

G

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Gavin Simpson
    

    

      
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On Thu, 2010-11-11 at 19:23 -0500, Soumi Ray wrote:

            

      
      
      
    

        
Soumi,

You can't do what you want with these methods. Think about what you are
trying to do? You want to know if the community composition is the same
(or similar enough) at two time points. This is a test of equivalence
and is the exact opposite of what we normally test in classical
statistics. We normally test for a difference in the response due to one
or more covariates. In other words, the one or more covariates can
explain variation in the response. We test whether the amount of
variation explained is large relative to the unexplained variation. If
there is no difference, then there is nothing to explain.

If you were to run your analysis through adonis() or similar, we would
test the amount of variation in the response explained by TIME to see if
it were as larger or larger than some extreme quantiles of a
permutation-derived null distribution of variations explained when there
is no difference between the community composition of the two time
periods. This means we set up the Null of no difference and the
Alternative of some difference. We see if the test statistic is likely
to have arisen under the Null. If it is, we say we have evidence
*against* the Null and reject it in favour of the Alternative. We have
not tested the Alternative.

You are interested in the opposite; that there *isn't* a difference.
But, you can't use the fact that you get an insignificant result from
the above test as evidence in support of the Null as the permutation
p-value (just like any other p-value) tells you nothing about the
probability of the Null hypothesis (the thing you are actually
interested in) being TRUE - it is a uniform random variable in such
circumstances.

In short, you can test for a difference, but not for no difference in
community composition.

Andrew Robinson has a package on CRAN to do equivalence tests:

http://cran.r-project.org/web/packages/equivalence/index.html

but it is not set-up to do the sort of analysis you want with ANOSIM.
Whether you could process your species data in some way so that you
could use his code is another matter, but beyond the scope of an email
list for help.

Please note I have no idea what papers you referred to above and the
comments I make are not comments on their methodology. For all I know,
their Alternative was one of difference and thus they were right to use
normal methods.

HTH

G