procuste function

Simple Procruste Rotation between two sets of points

performs a simple procruste rotation between two sets of points.

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

Returns

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 anne-beatrice.dufour@univ-lyon1.fr

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)))