
 Hi Mujeb,

<<But some statistician questions using such data in PCA. So my questions in
<<on the relevance of using PCA in my study for soil fauna abundance data and
<<interpreting the result. How can interpret the result of PCA here?, The
<<eigen values and % variance explained by first few factors are suffieceinet
<<to explain this?. 

Yes, interpret the first few factors (2-3) which together sum-up >60% of the total variance. They will explain the variation in your data.
Then each factor is independent (i.e. not correlated to another one), therefore they should give you insight into a process in your dataset/species assemblages, etc. 

<<how can I interpret factor loadings and correlations.

Interpret one factor and the associated variables (the ones with highest loadings, see bellow) as in linear regression analysis with fit line.
Consider the highest loading (correlation) of the variable on a factor/PC. E.g.:

         PC1    PC2    PC3
var1   0.1     0.8     -0.4
var2   0.6     0.3     0.5
var3   0.3     0.1     -0.9
var4   0.9     0.7     0.6

In bold are the values with highest loadings on the PC. Interpret var2 and var4 as associated to PC1, var1 to PC2 and var3 to PC3.

Generally correlation var-PC >0.5 are optimal.

Good luck

Dragos



Dragos Zaharescu
Animal Anatomy Laboratory
Faculty of Biological Sciences
Vigo University, apd. 137
36310, Vigo (Pontevedra), SPAIN
zaha_dragos@yahoo.com
zdragos@uvigo.es
http://webs.uvigo.es/zdragos/

~ You should be the change you want to see in the world ~ Ghandi




________________________________
From: "r-sig-ecology-request@r-project.org" <r-sig-ecology-request@r-project.org>
To: r-sig-ecology@r-project.org
Sent: Thursday, August 20, 2009 12:00:02 PM
Subject: R-sig-ecology Digest, Vol 17, Issue 8

Send R-sig-ecology mailing list submissions to
    r-sig-ecology@r-project.org

To subscribe or unsubscribe via the World Wide Web, visit
    https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
or, via email, send a message with subject or body 'help' to
    r-sig-ecology-request@r-project.org

You can reach the person managing the list at
    r-sig-ecology-owner@r-project.org

When replying, please edit your Subject line so it is more specific
than "Re: Contents of R-sig-ecology digest..."


Today's Topics:

  1. Usefulness of PCA (mujeeb rahman)
  2. Re: wascores() for metaMDS? (Jari Oksanen)
  3. Re: wascores() for metaMDS? (Gavin Simpson)
  4. Help with downloading package (Leigh Fall)
  5. Re: Help with downloading package (Peter Solymos)
  6. Re: Help with downloading package (Peter Cowan)
  7. Re: wascores() for metaMDS? (gabriel singer)


----------------------------------------------------------------------

Message: 1
Date: Wed, 19 Aug 2009 15:31:29 +0530
From: mujeeb rahman <mujeebrahmanp@gmail.com>
Subject: [R-sig-eco] Usefulness of PCA
To: r-sig-ecology@r-project.org
Message-ID:
    <ac3840600908190301l1bdc60act7a9f3a039bdaf162@mail.gmail.com>
Content-Type: text/plain

Dear All
Thanks all of you for your valuable suggestions for my previous queries,
which help me to improve my knowledge better.
I greatly appreciate your kind attention in this matter. I am working on
soil fauna biodiversity and my data consist of soil fauna abundance (count
data from unit area) from 15 different landuse systems. To know the spatial
distribution pattern, in many previous studies (for eg: Seasonal and
land-use induced variations of soil macrofauna composition in the Western
Ghats, southern India, *Soil Biology and
Biochemistry*<http://www.sciencedirect.com/science/journal/00380717>
Volume
37, Issue 6<http://www.sciencedirect.com/science?_ob=PublicationURL&_tockey=%23TOC%235163%232005%23999629993%23585703%23FLA%23&_cdi=5163&_pubType=J&view=c&_auth=y&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=6820623f4f32951905c98a204a6d508f>,
June 2005, Pages 1093-1104), PCA on correlation matrix was conducted.

But some statistician questions using such data in PCA. So my questions in
on the relevance of using PCA in my study for soil fauna abundance data and
interpreting the result. How can interpret the result of PCA here?, The
eigen values and % variance explained by first few factors are suffieceinet
to explain this?. how can I interpret factor loadings and correaltions.

I am awaitng for your elaborate result in this matter.

Thanking in advance

Mujeeb Rahman P
KFRI, Peechi, Thrissur
Kerala, India

    [[alternative HTML version deleted]]



------------------------------

Message: 2
Date: Wed, 19 Aug 2009 15:43:21 +0300
From: Jari Oksanen <jari.oksanen@oulu.fi>
Subject: Re: [R-sig-eco] wascores() for metaMDS?
To: gabriel singer <gabriel.singer@univie.ac.at>,
    <r-sig-ecology@r-project.org>
Message-ID: <C6B1CE19.22A3%jari.oksanen@oulu.fi>
Content-Type: text/plain;    charset="US-ASCII"

Gabriel,


On 19/08/09 12:40 PM, "gabriel singer" <gabriel.singer@univie.ac.at> wrote:

> Hi sig-ecology!
> 
> Here comes a probably stupid question... I am looking for smart ways to
> include information about underlying variables in MDS plots. In other
> words, after having computed an ordination with isoMDS or metaMDS from a
> community table, I would like to add something like species
> coefficients/loadings as vectors to the plot of sites. As no species
> coefficients exist in this case, the best I could come up with so far is
> simply vectors calculated from correlation coefficients of the
> individual species with the site scores (on two MDS axes).
> The function metaMDS allows to compute "species scores" using the
> function wascores().... I have now pondered for 2 days how these scores
> are calculated and what their precise meaning would be. Would these
> species scores be appropriate to show as vectors in the MDS?
> Thanks for any answer...
> 
I think these were documented... Please point out the unclear parts of the
documentation so that I can correct those.

The wascores are Weighted Averages Scores and they are calculated like
weighted averages, or similarly as species scores in correspondence
analysis. This means that (with some scaling) they show the centroid
("barycentre") of the species occurrence in the ordination graph. It is not
appropriate to present these as arrows which indicate a linear increase to
the direction of the arrow instead of the centre of abundance. Therefore the
species scores can (and as default in metaMDS, will) be presented as points.
If -- for any reason that is none of my business -- you want to get vectors
of species, you can fit species as vectors. This happens with metaMDS or
isoMDS like this:

library(vegan)
data(dune)
m <- metaMDS(dune)
# or m <- isoMDS(vegdist(dune))
vec <- envfit(m, dune)
plot(m, dis="site")
# or with isoMDS: ordiplot(m)
plot(vec)

I promised that I won't comment on this, but still I must say that I cannot
find a reason to do so.

Please note that you can also use ordisurf to fit nonlinear species
responses if you think that species are not points nor arrows. Vegan
tutorial (from the Web) gives an example.

Cheers, Jari Oksanen



------------------------------

Message: 3
Date: Wed, 19 Aug 2009 13:44:43 +0100
From: Gavin Simpson <gavin.simpson@ucl.ac.uk>
Subject: Re: [R-sig-eco] wascores() for metaMDS?
To: gabriel singer <gabriel.singer@univie.ac.at>
Cc: r-sig-ecology@r-project.org
Message-ID: <1250685883.9938.20.camel@prometheus.geog.ucl.ac.uk>
Content-Type: text/plain

On Wed, 2009-08-19 at 11:40 +0200, gabriel singer wrote:
> Hi sig-ecology!
> 
> Here comes a probably stupid question... I am looking for smart ways to
> include information about underlying variables in MDS plots. In other 
> words, after having computed an ordination with isoMDS or metaMDS from a
> community table, I would like to add something like species 
> coefficients/loadings as vectors to the plot of sites. As no species 
> coefficients exist in this case, the best I could come up with so far is
> simply vectors calculated from correlation coefficients of the 
> individual species with the site scores (on two MDS axes).
> The function metaMDS allows to compute "species scores" using the 
> function wascores().... I have now pondered for 2 days how these scores
> are calculated and what their precise meaning would be.

An individual taxon's "species score" is computed as the weighted
average of the "site scores", weights being the abundance of that taxon
in each site. It is the abundance weighted centroid of all the samples
in which the species occurs. The motivation for this is that in CA,
species scores are weighted averages of site scores that are themselves
weighted averages of species scores and so on in the Two-way algorithm
of Mark Hill - not that vegan computes the CA solution that way in cca()
- so it is an analogous approach to computing species scores for nMDS.

> Would these 
> species scores be appropriate to show as vectors in the MDS?

Not as vectors, as that implies directionality or increasing abundance
and there is no reason to assume that the abundance of a given taxon
will increase linearly or even monotonically in a given direction across
the nMDS plot.

Although I hesitate to call it that, the species score computed as the
weighted average of the site scores, is an optima (of nMDS site scores)
and thus abundance declines as one moves away from the point. So in this
sense, you display the species scores in the same manner as on a CA or
CCA plot, as a point, instead of the vector in PCA/RDA. However, the
decline in CA is uniform in any direction (fitted not actual abundance),
i.e. in 2-D the species score is the point at the top of a 2-D
bell-shaped surface as this is the implied response model in CA. With
nMDS there is no reason to assume this is the case.

For one or two taxa, you could just project a surface of actual
abundances using ordisurf() or you could just use the points as you
would in a CA diagram, more or less. The problem with the surface
approach is that you can only show a couple of species at most on a
single ordination plot.

ordisurf would likely be the best option for most extra data you wish to
impose on to the nMDS plot, again for the reason that the relationship
between nMDS axes and the variable of interest need not be a simple
linear or monotonic surface.

HTH

G

> Thanks for any answer...
> 
> Gabriel Singer
> 
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology@r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
-- 
%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%
Dr. Gavin Simpson            [t] +44 (0)20 7679 0522
ECRC, UCL Geography,          [f] +44 (0)20 7679 0565
Pearson Building,            [e] gavin.simpsonATNOSPAMucl.ac.uk
Gower Street, London          [w] http://www.ucl.ac.uk/~ucfagls/
UK. WC1E 6BT.                [w] http://www.freshwaters.org.uk
%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%



------------------------------

Message: 4
Date: Wed, 19 Aug 2009 16:58:33 -0500
From: Leigh Fall <leigh.fall@gmail.com>
Subject: [R-sig-eco] Help with downloading package
To: R-sig-ecology@r-project.org
Message-ID:
    <e003f4490908191458x43e77350t3376da7bb32fc4e9@mail.gmail.com>
Content-Type: text/plain

Hey all,

I have recently starting using R, so I'm still on the steep-learning curve
of the program.  I have been unable to install Diveristy.R from Dr.
Pelissier's website (http://pelissier.free.fr/Diversity.html).  I have
downloaded the libraries "ade4" and "spdep" (along with all the other
packages needed to run spdep).  I'm running R version 2.9.1 on a MAC OS X
version 10.5.8.  When I click on "Package source (all platforms):
diversity_1.5-9.tar.gz<http://pelissier.free.fr/diversity/R-2.8.1/diversity_1.5-9.tar.gz>"
from the website, a folder labeled "diversity" is downloaded onto my
desktop.  One question I have is where the package/folder/library should be
downloaded.  My other question is how to install it.  I've tried to Package
Installer-Local Binary Package and Local Source Package at the user level
without success.  I also just downloaded the tar.gz file directly to my
desktop and then use the Package Installer, but again without success.  I
tried the install.packages command, but I don't know if I'm using it
correctly.  The solution is probably simple, but with my limited experience
with writing code and programming, I'm not sure what I'm doing wrong.

[[elided Yahoo spam]]

Cheers,
Leigh


-- 
********************************************
Leigh M. Fall
Ph.D. Candidate
Dept. of Geology and Geophysics
Texas A&M University
3115 TAMU
College Station, TX  77843
Phone: (979) 845-3071
E-mail: leigh.fall@gmail.com
http://geoweb.tamu.edu/profile/LFall
********************************************

    [[alternative HTML version deleted]]



------------------------------

Message: 5
Date: Wed, 19 Aug 2009 16:17:38 -0600
From: Peter Solymos <solymos@ualberta.ca>
Subject: Re: [R-sig-eco] Help with downloading package
To: Leigh Fall <leigh.fall@gmail.com>
Cc: R-sig-ecology@r-project.org
Message-ID:
    <34896f090908191517m64679880j8d9f52b91b02207a@mail.gmail.com>
Content-Type: text/plain; charset=UTF-8

Dear Leigh,

You have 2 options:

1. build the MAC OS X package for yourself and install it, in this way
you will be able to use the help files as usual,
2. unpack the .tar.gz and source all files in the /R directory (on how
to do it at once see Example in help(source)).

Cheers,

Peter


On Wed, Aug 19, 2009 at 3:58 PM, Leigh Fall<leigh.fall@gmail.com> wrote:
> Hey all,
>
> I have recently starting using R, so I'm still on the steep-learning curve
> of the program. ?I have been unable to install Diveristy.R from Dr.
> Pelissier's website (http://pelissier.free.fr/Diversity.html). ?I have
> downloaded the libraries "ade4" and "spdep" (along with all the other
> packages needed to run spdep). ?I'm running R version 2.9.1 on a MAC OS X
> version 10.5.8. ?When I click on "Package source (all platforms):
> diversity_1.5-9.tar.gz<http://pelissier.free.fr/diversity/R-2.8.1/diversity_1.5-9.tar.gz>"
> from the website, a folder labeled "diversity" is downloaded onto my
> desktop. ?One question I have is where the package/folder/library should be
> downloaded. ? My other question is how to install it. ?I've tried to Package
> Installer-Local Binary Package and Local Source Package at the user level
> without success. ?I also just downloaded the tar.gz file directly to my
> desktop and then use the Package Installer, but again without success. ?I
> tried the install.packages command, but I don't know if I'm using it
> correctly. ?The solution is probably simple, but with my limited experience
> with writing code and programming, I'm not sure what I'm doing wrong.
>
[[elided Yahoo spam]]
>
> Cheers,
> Leigh
>
>
> --
> ********************************************
> Leigh M. Fall
> Ph.D. Candidate
> Dept. of Geology and Geophysics
> Texas A&M University
> 3115 TAMU
> College Station, TX ?77843
> Phone: (979) 845-3071
> E-mail: leigh.fall@gmail.com
> http://geoweb.tamu.edu/profile/LFall
> ********************************************
>
> ? ? ? ?[[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology@r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>
>



------------------------------

Message: 6
Date: Wed, 19 Aug 2009 18:30:50 -0700
From: Peter Cowan <cowan.pd@gmail.com>
Subject: Re: [R-sig-eco] Help with downloading package
To: Leigh Fall <leigh.fall@gmail.com>
Cc: R-sig-ecology@r-project.org
Message-ID:
    <e1fc21b0908191830t30f698e7o61cdfbfc2afe15e6@mail.gmail.com>
Content-Type: text/plain; charset=ISO-8859-1

On Wed, Aug 19, 2009 at 2:58 PM, Leigh Fall<leigh.fall@gmail.com> wrote:
> Hey all,
>
> I have recently starting using R, so I'm still on the steep-learning curve
> of the program. ?I have been unable to install Diveristy.R from Dr.
> Pelissier's website (http://pelissier.free.fr/Diversity.html). ?I have
> downloaded the libraries "ade4" and "spdep" (along with all the other
> packages needed to run spdep). ?I'm running R version 2.9.1 on a MAC OS X
> version 10.5.8. ?When I click on "Package source (all platforms):
> diversity_1.5-9.tar.gz<http://pelissier.free.fr/diversity/R-2.8.1/diversity_1.5-9.tar.gz>"
> from the website, a folder labeled "diversity" is downloaded onto my
> desktop. ?One question I have is where the package/folder/library should be
> downloaded. ? My other question is how to install it. ?I've tried to Package
> Installer-Local Binary Package and Local Source Package at the user level
> without success. ?I also just downloaded the tar.gz file directly to my
> desktop and then use the Package Installer, but again without success. ?I
> tried the install.packages command, but I don't know if I'm using it
> correctly. ?The solution is probably simple, but with my limited experience
> with writing code and programming, I'm not sure what I'm doing wrong.
>
[[elided Yahoo spam]]

To build packages on Mac OS X you need to have the developer tools
installed.  You can download the developer tools at the Apple website
<http://developer.apple.com/tools/>.  This will install Xcode among
other things and allow you to  compile the C code in the package.
Once you have the developer tools installed you can open the terminal
and run

R CMD INSTALL diversity_1.5-9.tar.gz

Or if you have in intel mac you can download the binary version from
<http://pelissier.free.fr/Diversity.html>

Peter

>
> Cheers,
> Leigh
>
>
> --
> ********************************************
> Leigh M. Fall
> Ph.D. Candidate
> Dept. of Geology and Geophysics
> Texas A&M University
> 3115 TAMU
> College Station, TX ?77843
> Phone: (979) 845-3071
> E-mail: leigh.fall@gmail.com
> http://geoweb.tamu.edu/profile/LFall
> ********************************************
>
> ? ? ? ?[[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology@r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>



------------------------------

Message: 7
Date: Thu, 20 Aug 2009 11:17:37 +0200
From: gabriel singer <gabriel.singer@univie.ac.at>
Subject: Re: [R-sig-eco] wascores() for metaMDS?
To: gavin.simpson@ucl.ac.uk, jari.oksanen@oulu.fi
Cc: r-sig-ecology@r-project.org
Message-ID: <4A8D14B1.3060600@univie.ac.at>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed


Dear Jari and Gavin,

thanks a lot, everything clear... with the connection to CCA I now get 
the meaning of the species scores, almost trivial after all...

gg



Gavin Simpson wrote:
> On Wed, 2009-08-19 at 11:40 +0200, gabriel singer wrote:
>  
>> Hi sig-ecology!
>>
>> Here comes a probably stupid question... I am looking for smart ways to
>> include information about underlying variables in MDS plots. In other 
>> words, after having computed an ordination with isoMDS or metaMDS from a
>> community table, I would like to add something like species 
>> coefficients/loadings as vectors to the plot of sites. As no species 
>> coefficients exist in this case, the best I could come up with so far is
>> simply vectors calculated from correlation coefficients of the 
>> individual species with the site scores (on two MDS axes).
>> The function metaMDS allows to compute "species scores" using the 
>> function wascores().... I have now pondered for 2 days how these scores
>> are calculated and what their precise meaning would be.
>>    
>
> An individual taxon's "species score" is computed as the weighted
> average of the "site scores", weights being the abundance of that taxon
> in each site. It is the abundance weighted centroid of all the samples
> in which the species occurs. The motivation for this is that in CA,
> species scores are weighted averages of site scores that are themselves
> weighted averages of species scores and so on in the Two-way algorithm
> of Mark Hill - not that vegan computes the CA solution that way in cca()
> - so it is an analogous approach to computing species scores for nMDS.
>
>  
>> Would these 
>> species scores be appropriate to show as vectors in the MDS?
>>    
>
> Not as vectors, as that implies directionality or increasing abundance
> and there is no reason to assume that the abundance of a given taxon
> will increase linearly or even monotonically in a given direction across
> the nMDS plot.
>
> Although I hesitate to call it that, the species score computed as the
> weighted average of the site scores, is an optima (of nMDS site scores)
> and thus abundance declines as one moves away from the point. So in this
> sense, you display the species scores in the same manner as on a CA or
> CCA plot, as a point, instead of the vector in PCA/RDA. However, the
> decline in CA is uniform in any direction (fitted not actual abundance),
> i.e. in 2-D the species score is the point at the top of a 2-D
> bell-shaped surface as this is the implied response model in CA. With
> nMDS there is no reason to assume this is the case.
>
> For one or two taxa, you could just project a surface of actual
> abundances using ordisurf() or you could just use the points as you
> would in a CA diagram, more or less. The problem with the surface
> approach is that you can only show a couple of species at most on a
> single ordination plot.
>
> ordisurf would likely be the best option for most extra data you wish to
> impose on to the nMDS plot, again for the reason that the relationship
> between nMDS axes and the variable of interest need not be a simple
> linear or monotonic surface.
>
> HTH
>
> G
>
>  
>> Thanks for any answer...
>>
>> Gabriel Singer
>>
>> _______________________________________________
>> R-sig-ecology mailing list
>> R-sig-ecology@r-project.org
>> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>>    

-- 
Dr. Gabriel Singer
Department of Freshwater Ecology - University of Vienna
and Wassercluster Lunz Biologische Station GmbH
+43-(0)664-1266747
gabriel.singer@univie.ac.at



------------------------------

_______________________________________________
R-sig-ecology mailing list
R-sig-ecology@r-project.org
https://stat.ethz.ch/mailman/listinfo/r-sig-ecology


End of R-sig-ecology Digest, Vol 17, Issue 8
********************************************



      
	[[alternative HTML version deleted]]

