[R] Cummulative Variance in Correspondence Analysis (ADE4)

[Stéphane Dray]

Dear Antonio,
if you have questions on the ade4 package, please  send email to adelist 
(http://listes.univ-lyon1.fr/wws/info/adelist).
The total inertia (variance) of CA is equal to the sum of all eigenvalues :

 > data(rpjdl)
 > rpjdl.coa <- dudi.coa(rpjdl$fau, scannf = FALSE, nf = 4)
 > sum(rpjdl.coa$eig)
[1] 4.468333

This is equal to the chi2 stat divided by the number of individuals:

 > chisq.test(rpjdl$fau)$statistic/sum(rpjdl$fau)
X-squared
 4.468333

One can obtain the inertia associated to i-th axis by dividing the i-th 
eigenvalue by the total inertia. Here are percentages:

 > round(rpjdl.coa$eig/sum(rpjdl.coa$eig)*100,2)
 [1] 16.86  6.56  5.13  4.58  3.52  3.39  3.37  3.12  2.87  2.72  2.63  2.56
[13]  2.49  2.43  2.34  2.21  2.09  2.00  1.86  1.76  1.61  1.48  1.45  1.43
[25]  1.38  1.26  1.23  1.15  1.14  1.08  1.07  1.01  0.94  0.92  0.89  0.83
[37]  0.77  0.71  0.65  0.61  0.59  0.49  0.47  0.46  0.38  0.36  0.35  0.32
[49]  0.29  0.19

The cumulative inertia is obtained by :

 > round(cumsum(rpjdl.coa$eig)/sum(rpjdl.coa$eig)*100,2)
 [1]  16.86  23.41  28.55  33.13  36.65  40.03  43.41  46.53  49.39  52.11
[11]  54.75  57.31  59.79  62.23  64.57  66.78  68.87  70.87  72.73  74.49
[21]  76.10  77.58  79.02  80.45  81.83  83.09  84.32  85.47  86.61  87.69
[31]  88.76  89.77  90.71  91.63  92.53  93.36  94.13  94.84  95.49  96.10
[41]  96.69  97.19  97.66  98.12  98.49  98.85  99.20  99.52  99.81 100.00

Antonio Punzon wrote:
> Hi all:
> How can I calculate the cumulative variance (or variance for each component)
> in correspondence analysis?
> If were possible in ADE4 package
> Thank you
>
>
>
>  -- Antonio Punzón Merino
>  O__---- Instituto Español de Oceanografía
> c/ /'_ --- Centro Oceanográfico de Santander
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-- 
Stéphane DRAY (dray at biomserv.univ-lyon1.fr )
Laboratoire BBE-CNRS-UMR-5558, Univ. C. Bernard - Lyon I
43, Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
Tel: 33 4 72 43 27 57       Fax: 33 4 72 43 13 88
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