procuste: Simple Procruste Rotation between two sets of points

In ade4: Analysis of Ecological Data: Exploratory and Euclidean Methods in Environmental Sciences

Simple Procruste Rotation between two sets of points

Description

performs a simple procruste rotation between two sets of points.

Usage

procuste(dfX, dfY, scale = TRUE, nf = 4, tol = 1e-07) 
## S3 method for class 'procuste'
plot(x, xax = 1, yax = 2, ...)
## S3 method for class 'procuste'
print(x, ...)
## S3 method for class 'procuste'
randtest(xtest, nrepet = 999, ...)

Arguments

dfX, dfY	two data frames with the same rows
scale	a logical value indicating whether a transformation by the Gower's scaling (1971) should be applied
nf	an integer indicating the number of kept axes
tol	a tolerance threshold to test whether the distance matrix is Euclidean : an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue.

x, xtest	an objet of class procuste
xax	the column number for the x-axis
yax	the column number for the y-axis
nrepet	the number of repetitions to perform the randomization test
...	further arguments passed to or from other methods

Value

returns a list of the class procuste with 9 components

d	a numeric vector of the singular values
rank	an integer indicating the rank of the crossed matrix
nf	an integer indicating the number of kept axes
tabX	a data frame with the array X, possibly scaled
tabY	a data frame with the array Y, possibly scaled
rotX	a data frame with the result of the rotation from array X to array Y
rotY	a data frame with the result of the rotation from array Y to array X
loadX	a data frame with the loadings of array X
loadY	a data frame with the loadings of array Y
scorX	a data frame with the scores of array X
scorY	a data frame with the scores of array Y
call	a call order of the analysis

Author(s)

Daniel Chessel
Anne-Béatrice Dufour [e-mail]

References

Digby, P. G. N. and Kempton, R. A. (1987) Multivariate Analysis of Ecological Communities. Population and Community Biology Series, Chapman and Hall, London.

Gower, J.C. (1971) Statistical methods of comparing different multivariate analyses of the same data. In Mathematics in the archaeological and historical sciences, Hodson, F.R, Kendall, D.G. & Tautu, P. (Eds.) University Press, Edinburgh, 138–149.

Schönemann, P.H. (1968) On two-sided Procustes problems. Psychometrika, 33, 19–34.

Torre, F. and Chessel, D. (1994) Co-structure de deux tableaux totalement appariés. Revue de Statistique Appliquée, 43, 109–121.

Dray, S., Chessel, D. and Thioulouse, J. (2003) Procustean co-inertia analysis for the linking of multivariate datasets. Ecoscience, 10, 1, 110-119.

Examples

data(macaca)
pro1 <- procuste(macaca$xy1, macaca$xy2, scal = FALSE)
pro2 <- procuste(macaca$xy1, macaca$xy2)
if(adegraphicsLoaded()) {
  g1 <- s.match(pro1$tabX, pro1$rotY, plab.cex = 0.7, plot = FALSE)
  g2 <- s.match(pro1$tabY, pro1$rotX, plab.cex = 0.7, plot = FALSE)
  g3 <- s.match(pro2$tabX, pro2$rotY, plab.cex = 0.7, plot = FALSE)
  g4 <- s.match(pro2$tabY, pro2$rotX, plab.cex = 0.7, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
} else {
  par(mfrow = c(2, 2))
  s.match(pro1$tabX, pro1$rotY, clab = 0.7)
  s.match(pro1$tabY, pro1$rotX, clab = 0.7)
  s.match(pro2$tabX, pro2$rotY, clab = 0.7)
  s.match(pro2$tabY, pro2$rotX, clab = 0.7)
  par(mfrow = c(1,1))
}

data(doubs)
pca1 <- dudi.pca(doubs$env, scal = TRUE, scann = FALSE)
pca2 <- dudi.pca(doubs$fish, scal = FALSE, scann = FALSE)
pro3 <- procuste(pca1$tab, pca2$tab, nf = 2)
if(adegraphicsLoaded()) {
  g11 <- s.traject(pro3$scorX, plab.cex = 0, plot = FALSE)
  g12 <- s.label(pro3$scorX, plab.cex = 0.8, plot = FALSE)
  g1 <- superpose(g11, g12)
  g21 <- s.traject(pro3$scorY, plab.cex = 0, plot = FALSE)
  g22 <- s.label(pro3$scorY, plab.cex = 0.8, plot = FALSE)
  g2 <- superpose(g21, g22)
  g3 <- s.arrow(pro3$loadX, plab.cex = 0.75, plot = FALSE)
  g4 <- s.arrow(pro3$loadY, plab.cex = 0.75, plot = FALSE)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

} else {
  par(mfrow = c(2, 2))
  s.traject(pro3$scorX, clab = 0)
  s.label(pro3$scorX, clab = 0.8, add.p = TRUE)
  s.traject(pro3$scorY, clab = 0)
  s.label(pro3$scorY, clab = 0.8, add.p = TRUE)
  s.arrow(pro3$loadX, clab = 0.75)
  s.arrow(pro3$loadY, clab = 0.75)
  par(mfrow = c(1, 1))
}

plot(pro3)
randtest(pro3)

data(fruits)
plot(procuste(scalewt(fruits$jug), scalewt(fruits$var)))

ade4 documentation built on Feb. 16, 2023, 7:58 p.m.