[R-sig-eco] how are compuetd the species scores of pca from veganpackage ?

[claire della vedova]

Dear Jari,

You're right I missed the Design decision vignette....sorry for that.
Thanks you so much for your reply.
All the best

Claire Della Vedova


-----Message d'origine-----
De : Jari Oksanen [mailto:jari.oksanen at oulu.fi] 
Envoyé : mardi 27 mai 2014 10:43
À : claire della vedova; r-sig-ecology at r-project.org
Objet : RE: [R-sig-eco] how are compuetd the species scores of pca from
veganpackage ?

Dear Claire Della Vedova,

It seems that you have searched in many places, except in vegan
documentation. Look at the vignette on Design decisions, section "Scaling in
redundancy analysis".

Cheers, Jari Oksanen
________________________________________
From: r-sig-ecology-bounces at r-project.org
<r-sig-ecology-bounces at r-project.org> on behalf of claire della vedova
<claire.della-vedova at magelisgroup.com>
Sent: 27 May 2014 11:17
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] how are compuetd the species scores of pca from
veganpackage ?

Hi everybody,

I'm working on PCA approach, and comparing outputs from ade4 and vegan
packages.
I'm ok with the normalization of the variables coordinates coming from ade4
outputs.
(with $co : coordinates are scaled to eigen values ; with  $c1 : coordinates
are scaled to 1).

But I have difficulties to understand how are computed the Species scores in
vegan's outputs with scaling 1 or 2 options, and what means  the message
concerning scaling, especially about the 'General scaling constant of
scores'.
For example :

'Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions
* General scaling constant of scores:  4.226177 '
'

I've search on the archives of R-sig-ecology , cross validate and
stackoverflow, and found nothing that helped me. If somebody has some
information about it, I would greatly appreciate some help.
All the best.

Claire Della Vedova

Here some parts of my code :


library(ade4)
library(vegan)

doubs.env <- read.csv
('http://www.sci.muni.cz/botany/zeleny/wiki/anadat-r/data
                       -download/DoubsEnv.csv', row.names = 1)

###################### with ade4 ##########################################
pca.ad<-dudi.pca(doubs.env, scale = TRUE, center = TRUE, scann = FALSE,nf=3)

# eigen value of the fisrt eigen vector
pca.ad$eig[1]
[1] 5.968749

#variables coordinates in first eigen vector pca.ad$co[,1] [1]  0.85280863
-0.81918008 -0.45283333  0.75214647 -0.04996375  0.70722171  [7]  0.83048310
0.90260821  0.79011263 -0.76485397  0.76373149


#check the normalization of laodings
sum(pca.ad$co[,1]^2)
[1] 5.968749
#=> coordinatesscaled to eigen values

#variables normed scores in first eigen vector pca.ad$c1[,1] [1]  0.34906791
-0.33530322 -0.18535177  0.30786532 -0.02045094  0.28947691  [7]  0.33992972
0.36945166  0.32340546 -0.31306670  0.31260725


#check the normalization
sum(pca.ad$c1[,1]^2)
[1] 1
#=> coordinates scaled to 1

###################### with vegan ######################################
pca.veg<-rda(doubs.env, scale = TRUE)

# species scores for the fisrt eigen vector, with sacling 1 summary(pca.veg,
scaling=1)
      das        alt        pen        deb         pH        dur        pho
 1.4752228 -1.4170507 -0.7833294  1.3010933 -0.0864293  1.2233806  1.4366031
       nit        amm        oxy        dbo
 1.5613681  1.3667687 -1.3230752  1.3211335

'Scaling 1 for species and site scores
* Sites are scaled proportional to eigenvalues
* Species are unscaled: weighted dispersion equal on all dimensions
* General scaling constant of scores:  4.226177 '



summary(pca.veg, scaling=2)[1][[1]][,1]
das         alt         pen         deb          pH         dur
1.08668311 -1.04383225 -0.57701847  0.95841533 -0.06366582  0.90117039
pho         nit         amm         oxy         dbo
1.05823501  1.15013974  1.00679334 -0.97460773  0.97317743 'Scaling 2 for
species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions
* General scaling constant of scores:  4.226177 '




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