# Re: MCOA

Date: Tue Mar 08 2005 - 01:58:51 MET

• Next message: Bernard Palagos: "AFM"

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
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 :

?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.

Hope this help,

Regards,

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 :-)))
>
>
>
>

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