RE: MCOA

From: Aedin (Aedin.Culhane@ucd.ie)
Date: Tue Mar 08 2005 - 12:03:44 MET


Thanks a million. Merci.
Aedin

-----Original Message-----
From: owner-adelist@biomserv.univ-lyon1.fr
[mailto:owner-adelist@biomserv.univ-lyon1.fr] On Behalf Of Pierre BADY
Sent: 08 March 2005 00:59
To: Aedin
Cc: adelist@biomserv.univ-lyon1.fr
Subject: Re: MCOA

hi all,

1-function mcoa :

$cos2 (squared cosines): correlation between the scores of individual
tables and the synthetic variable of the same rank (1st, 2nd, etc .).

$cov2: squared covariance between the scores of individual tables and
the synthetic variable of the same rank.

$lambda : eigenvalues of the separate analyses of individual tables
weighted by "inertia", "lambda1", etc.

2- RV:
the RV coefficient between the representations of individual table
($Tl1) with the table of synthetic variables (reference, $SynVar).

you can use this function :

RV.mcoa <- function(m,...){
# see RV.rtest
# require(ade4)
    if (!inherits(m, "mcoa"))
        stop("non convenient data")
    blo <- sort(unique(m$TL[, 1]))
    nblo <- length(blo)
    res <- NULL
    for(i in 1:nblo){
        X <- scale(m$SynVar, scale = FALSE)
        Y <- scale(m$Tl1[m$TL[,1]==i,], scale = FALSE)
        X <- X/(sum(svd(X)$d^4)^0.25)
        Y <- Y/(sum(svd(Y)$d^4)^0.25)
        X <- as.matrix(X)
        Y <- as.matrix(Y)
        w <- sum(svd(t(X) %*% Y)$d^2)
        res <- c(res,w)
        }
    names(res)<- row.names(m$cov2)
    return(res)
}

3-summary.mcoa:

Iner: inertia of individual tables for a rank given
Iner+: cumulative inertia of individual tables

Var: inertia of individual tables projected for a rank given
Var+: cumulative inertia projected

Cos2: correlation between the scores of individual tables and the
synthetic variable

Cov2: squared covariance between the scores of individual tables and the
synthetic variable.

4-Example :
require(ade4)

?mcoa

data(friday87)
w1 <- data.frame(scale(friday87$fau, scal = FALSE))
w2 <- ktab.data.frame(w1, friday87$fau.blo, tabnames =
friday87$tab.names)

# individual tables were weighted by the first eigenvalues
# of the separates analyses
mcoa1 <- mcoa(w2, "lambda1", scan = FALSE)
mcoa1
mcoa1$lambda
summary(mcoa1)
plot(mcoa1)
RV.mcoa(mcoa1)

# individual tables were weighted by the total inertia
mcoa2 <- mcoa(w2, "inertia", scan = FALSE)
mcoa2
mcoa2$lambda
summary(mcoa2)
plot(mcoa2)
RV.mcoa(mcoa2)

5-references:

Chessel D. & Hanafi M. (1996) Analyses de la co-inertie de K nuages de
points. Revue de Statistique Appliquée, 44, 35-60.

Bady P., Doledec S., Dumont B. & Fruget J.-F. (2004) Multiple co-inertia
analysis: a tool for assessing synchrony in the temporal variability of
aquatic communities. Comptes Rendus Biologies, 327, 29-36.

English documentation of ADE-4:
ftp://pbil.univ-lyon1.fr/pub/mac/ADE/ADE4/DocModPDFUS/KTA-MFA.pdf

French documentation : http://pbil.univ-lyon1.fr/R/stage/stage6.pdf
http://pbil.univ-lyon1.fr/R/fichestd/tdr68.pdf

Hope this help,

Regards,

P.BADY

PS : I agree with you ... I think that "the Greens" are stronger ... ;"(

En réponse à Aedin <Aedin.Culhane@ucd.ie>:

> Bonjour
>
> Can I get $RV values from an MCOA? Is there a document (en français
> ou si possible en anglais??) which explains the interpretation of
> $cov2, $lambda and summary.mcoa?
>
> Merci,
>
> Aedin
>
> PS: Allez les verts dans le rugby Samedi :-)))
>
>
>
>

---------------------------------------------------------
Pierre BADY <°)))><
Université Claude Bernard Lyon 1
UMR CNRS 5023, LEHF
bat Alphonse Forel
43 boulevard du 11 novembre 1918
F-69622 VILLEURBANNE CEDEX
FRANCE
TEL : +33 (0)4 72 44 62 34
FAX : +33 (0)4 72 43 28 92
MEL : pierre.bady@univ-lyon1.fr
http://limnologie.univ-lyon1.fr
http://pierre.bady.free.fr/ (in construction)



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