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

[claire della vedova]

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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