[R] meaning of "iner" etc. relating to cca(ade4)

[Stephane Dray]

Hi Dominique,
please, if you have some questions about a particular package, do not send 
to R-Help. There is a list about ade4, see details at:

http://pbil.univ-lyon1.fr/ADE-4/adelist.html

cca is a correspondence analysis with constraint imposed by external 
information. Redundancy analysis (available in ade4 by the function pcaiv) 
is PCA with constraint.

Here is an example using pcaiv:

data(rhone)
pca1 <- dudi.pca(rhone$tab, scan = FALSE, nf = 3)
iv1 <- pcaiv(pca1, rhone$disch, scan = FALSE)
iv1$param

  iner inercum inerC inercumC ratio R2    lambda
  6.27 6.27    5.52  5.52     0.879 0.671 3.7
  4.14 10.4    4.74  10.3     0.984 0.747 3.54

iner represent eigenvalues of the unconstrained analysis:
 > pca1$eig[1:2]
[1] 6.274265 4.140947

inercum is equivalent to
cumsum(pca1$eig)

prediction of sites scores by environmental variables produce a new set 
score (often named LC scores), inerC represent variance of this scores:

diag(t(iv1$ls)%*%diag(iv1$lw)%*%as.matrix(iv1$ls))
    Axis1    Axis2
5.515241 4.736362

inercumC is the cumsum.

ratio is simply inercum/inerCcum

Finally note that CCA or RDA find a site score that maximizes the variance 
explained by environmental variables. This is a product of variance by a R2:
  0.671*5.52  # lambda = R2*inerC
[1] 3.70392


At 10:11 14/01/2005, Dominique Grüter wrote:
>Does someone know the meaning of the following values relating to the 
>"cca"-command?
>
>  iner, inercum, inerC, inercumC
>
>Thanks!
>DOMI
>
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Stéphane DRAY
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