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Rotations for PCoA?

4 messages · Jan Hanspach, Sarah Goslee

Original
Jan Hanspach
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Dear all,
I have a bunch of plant species and their traits (life span, pollination
type, strategy type, association to human disturbance... overall 5
categorical and two interval scaled variables). I want to know how the
traits are interrelated, e.g. are annual plants predominantly ruderals
that grow in habitats strongly disturbed by humans.

Therefore I calculated a Gower dissimilarity matrix on the species
traits (species=rows, traits=columns; using daisy(), which seems to be
appropriate for mixed variable types). With the dissimilartiy matrix I
calculate a PCoA using cmdscale and that works fine (beside some
negative Eigenvalues).

Now, I want to know if  it is possible to get rotations for my traits,
like it is calculated for a PCA? So that I can plot my traits within the
ordinations space (or give the values in a table).
Thanks!
Jan
Sarah Goslee
# 
It isn't "just like a PCA" but you can use a permutation procedure to fit
the traits to a 2-dimensional ordination configuration using vf() in the
ecodist package.

Sarah
On Mon, Oct 19, 2009 at 7:44 AM, Jan Hanspach <jan.hanspach at ufz.de> wrote:

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Jan Hanspach
    

    

      
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Dear Sarah,
that sounds good to me, thanks!

Still, I have two more questions:

The variable fitting with vf() does only work when I "dummy-transform" 
my categorical variables. Are the derived correlations then still 
comparable to the Gower distance - PCoA scores where my categorical 
variables where defined as such?

Is it reasonable to do more than the correlations with two axes with 
vf(), i.e. after calculating the correlation for the first and the 
second axis doing the same for the third and the forth? I guess this is 
a very naive question, but shouldn't this work for the p-Values since 
they are calculated with a permutation procedure?

Best
Jan

        
Sarah Goslee wrote:

            

      
      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Sarah Goslee
    

    

      
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On Mon, Oct 19, 2009 at 10:12 AM, Jan Hanspach <jan.hanspach at ufz.de> wrote:

            

      
      
      
    

        
I think it only makes sense with quantitative variables. There's no "direction"
to categorical variables, so how could you fit one? Usually with categorical
variables I plot the ordination with different symbols to denote the class of
the categorical variables, and look at pattern that way.

            

      
      
      
    

        
You're fitting the variables to that ordination diagram. It's entirely possible
 that the best fit for dimensions 3 and 4 of a four-dimensional fit are not the
same as the best fit of axis 3 and 4 by themselves. So it depends on your
question.

Alternatively, I think the vegan package has a more sophisticated vector-
fitting function.

Sarah