Re: MCOA

From: Pierre BADY (pierre.bady@univ-lyon1.fr)
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
    # 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
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    MEL : pierre.bady@univ-lyon1.fr
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