[R-sig-eco] pca or nmds (with which normalization and distance ) for abundance data ?

[Stephen Sefick]

On Fri 14 Dec 2012 05:08:32 AM CST, Gavin Simpson wrote:
> On Thu, 2012-12-13 at 14:03 -0600, Stephen Sefick wrote:
> <snip />
>>> My aim was to study how the distribution of species is linked with
>>> environmental data.
>>>
>>> Firstly, I did a PCA (with vegan library), using a Hellinger
>>> transformation,
>>> with commands like this :
>>>
>>> acp1<-rda(decostand(myDataSpec[,c(25:62)], "hellinger"))
>>>
>>>
>>
>> Is the Hellinger transform done on relative proportions?
>
> The transformation includes division by by the row sum and hence
> conversion to proportions. As such it can be applied to count data or
> relative abundance data; with the latter the division by row sum will
> have no effect and then the transformation collapses to a simple square
> root transformation of the proportional abundance data.
>
> This is one of the reasons for the apparent contradictions over the
> utility of the chord distance in ecological and palaeoecological
> disciplines. In the latter we commonly use proportional data whilst
> count abundances are common in the former. Directly applying the chord
> distance to count abundances carries with it the baggage of the
> Euclidean distance (squared differences emphasise the big things). But
> chord distance applied to proportional data *is* the Hellinger distance
> and hence palaeoecologists have found the chord distance a useful
> dissimilarity coefficients in their field.
>
> <snip />
>>>
>>> a) Which ordination method would be better for my data : PCA knowing
>>> that the represented inertia is 35.62% or NMDS with a stress value about
>>> 0.22?
>>>
>> My opinion is PCA on hellinger transformed relative proportions "means"
>> more than an NMDS
>
> ?? NMDS with Hellinger distances could optimise a k-D PCA with Hellinger
> transform.

Gavin, maybe I have spoken beyond my knowledge.  My though was that a 
PCA has a unique solution and is therefore "better" (as long as an 
appropriate distance is used that deals with the double zero problem 
effectively).  I am sure that this is too simple for the reality of the 
situation.  I don't know what a k-D PCA is.  Would you mind explaining 
or directing me to some reading material?

>
> Given that NMDS essentially subsumes PCA I'm not sure what you are
> getting at.

I don't understand.  Would you mind explaining this?
many thanks,

Stephen

>
> G
>
>>> b) If NMDS is more adapted which one is the better? with Hellinger
>>> normalization and Bray-Curtis distance, or with the normalization
>>> recommended by Legendre and Legendre and Kulcynski distance ?
>>>
>> I sounds like the normalization you are referring to is relative
>> proportion which is si/sum(s); s is a vector of taxon at a site.
>>
>>> c) Is there other method to apply? I’m going to try co-inertia with
>>> ade4 package
>>>
>>>
>>>
>> I am reading about co-inertia analysis now as it may be useful for some
>> of the things that I am planning on doing.  This method looks promising.
>>
>> You are going to have to decide on what type of ordination to use with
>> COIA...
>>
>> HTH,
>>
>> Stephen
>>
>>> Thanks in advance.
>>>
>>> Cheers.
>>>
>>> Claire Della Vedova
>>>
>>>
>>>
>>>
>>> [[alternative HTML version deleted]]
>>>
>>>
>>>
>>> _______________________________________________
>>> R-sig-ecology mailing list
>>> R-sig-ecology at r-project.org
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>>> -- 
>>> Stephen Sefick
>>> **************************************************
>>> Auburn University
>>> Biological Sciences
>>> 331 Funchess Hall
>>> Auburn, Alabama
>>> 36849
>>> **************************************************
>>> sas0025 at auburn.edu
>>> http://www.auburn.edu/~sas0025
>>> **************************************************
>>>
>>> Let's not spend our time and resources thinking about things that are so little or so large that all they really do for us is puff us up and make us feel like gods.  We are mammals, and have not exhausted the annoying little problems of being mammals.
>>>
>>>                                   -K. Mullis
>>>
>>> "A big computer, a complex algorithm and a long time does not equal science."
>>>
>>>                                 -Robert Gentleman
>>>
>>
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>
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-- 
Stephen Sefick
**************************************************
Auburn University                                         
Biological Sciences                                      
331 Funchess Hall                                       
Auburn, Alabama                                        
36849                                                           
**************************************************
sas0025 at auburn.edu                                  
http://www.auburn.edu/~sas0025                 
**************************************************

Let's not spend our time and resources thinking about things that are 
so little or so large that all they really do for us is puff us up and 
make us feel like gods.  We are mammals, and have not exhausted the 
annoying little problems of being mammals.

                                -K. Mullis

"A big computer, a complex algorithm and a long time does not equal 
science."

                              -Robert Gentleman