R: Projections of Supplementary Rows for a Partial Triadic...

suprow.pta {ade4} | R Documentation

## Projections of Supplementary Rows for a Partial Triadic Analysis of K-tables

### Description

This function performs a projection of supplementary rows (i.e. supplementary individuals) for a Partial Triadic Analysis (`pta`) of K-tables. Computations are valid ONLY if the `pta` has been done on a K-Tables obtained by the `withinpca` function, followed by calls to the `ktab.within` and `t` functions.

### Usage

    ## S3 method for class 'pta'
    suprow(x, Xsup, facSup, ...)

### Arguments

`x` | an object of class `pta`
`Xsup` | a table with the supplementary rows
`facSup` | a factor partitioning the rows of `Xsup`
`...` | further arguments passed to or from other methods

### Details

This function computes the coordinates of the supplementary rows for a K-tables. The table of supplementary rows is standardized according to the 'Bouroche' standardization used in the Within Analysis of the original `pta`. In a first step, the table of supplementary rows is standardized (centred and normed) with the mean and variance of the original table of active individuals (i.e. the K-tables used in `pta`). Then, according to the `withinpca` procedure, a second transformation is applied.

For "partial", supplementary rows are standardized in each sub-table (corresponding to each level of the factor) by the mean and variance of each corresponding sub-sample in the table of active individuals. Hence, supplementary rows have null mean and unit variance in each sub-table.

For "total", supplementary rows are centred in each sub-table with the mean of each coresponding sub-sample in the table of active individuals and then normed with the global variance ot the table of active individuals. Hence, supplementary rows have a null mean in each sub-table and a global variance equal to one.

### Value

Returns a list with the transformed table `Xsup` in `tabsup` and the coordinates of the supplementary rows in `lisup`.

### Author(s)

Benjamin Alric benjamin.alric@irstea.fr
Jean Thioulouse jean.thioulouse@univ-lyon1.fr

### References

Bouroche, J. M. (1975) Analyse des données ternaires: la double analyse en composantes principales. Thèse de 3ème cycle, Université de Paris VI.

### Examples

    data(meau)
    # Active rows
    actenv <- meau$env[meau$design$site != "S6", -c(5)]
    actfac <- meau$design$season[meau$design$site != "S6"]
    # Suplementary rows
    supenv <- meau$env[meau$design$site == "S6", -c(5)]
    supfac <- meau$design$season[meau$design$site == "S6"]
    # Total = active + suplementary rows
    totenv <- meau$env[, -c(5)]
    totfac <- meau$design$season
    # PTA with 6 sampling sites
    wittot <- withinpca(df = totenv, fac = totfac, scannf = FALSE, scaling = "partial")
    kta1tot <- ktab.within(wittot, colnames = rep(c("S1", "S2", "S3", "S4", "S5", "S6"), 4))
    kta2tot <- t(kta1tot)
    pta1tot <- pta(kta2tot, scann = FALSE)
    # PTA with 5 sampling sites and site 6 added as supplementary element
    wit1 <- withinpca(df = actenv, fac = actfac, scannf = FALSE, scaling = "partial")
    kta1 <- ktab.within(wit1, colnames = rep(c("S1", "S2", "S3", "S4", "S5"), 4))
    kta2 <- t(kta1)
    pta1 <- pta(kta2, scann = FALSE)
    supenv.pta <- suprow(x = pta1, Xsup = supenv, facSup = supfac)
    if (adegraphicsLoaded()) {
    # g1t = active + suplementary rows
    	g1t <- s.label(pta1tot$Tli, labels = rownames(totenv),
    	  plabels = list(box = list(draw = FALSE), optim = TRUE), xlim = c(-6, 5), ylim = c(-5, 5),
    	  psub = list(text="Total", position="topleft"), plot = FALSE)
    # g1 = Active rows
    	g1 <- s.label(pta1$Tli, labels = rownames(actenv),
    	  plabels = list(box = list(draw = FALSE), optim =TRUE), xlim = c(-6, 5), ylim = c(-5, 5),
    	  psub = list(text="Active", position="topleft"), pgrid = list(text=list(cex = 0)),
    	  plot = FALSE)
    # g2 = Supplementary rows
    	g2 <- s.label(supenv.pta$lisup, plabels = list(box = list(draw = FALSE), optim = TRUE),
    	  ppoints = list(col = "red"), psub = list(text="Supplementary", position="topright"),
    	  pgrid = list(text=list(cex = 0)), plot = FALSE)
    # g3 = superposition of active and suplementary rows
    	g3 <- g1 + g2
    # Comparison of the total analysis and the analysis with supplementary rows
    	ADEgS(list(g1t,g3))
    } else {
    	par(mfrow=c(2,2))
    # g1t = active + suplementary rows
    	g1t <- s.label(pta1tot$Tli, label = rownames(totenv), xlim = c(-6, 5), ylim = c(-5, 5),
    	  sub="Total")
    # g1 = Active rows
    	g1 <- s.label(pta1$Tli, label = rownames(actenv), clabel = 1, xlim = c(-6, 5),
    	  ylim = c(-5, 5), sub="Active+Supplementary")
    # g2 = Supplementary rows
    	g2 <- s.label(supenv.pta$lisup, clabel = 1.5, xlim = c(-6, 5), ylim = c(-5, 5),
    	  add.plot = TRUE)
    }

[Package ade4 version 1.7-16 Index]