ade4 (version 1.7-19)

suprow.pta: 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 pta
suprow(x, Xsup, facSup, ...)

Value

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

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

Author

Benjamin Alric
Jean Thioulouse

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.

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)  
}