ade4 (version 1.2-2)

procuste: Simple Procruste Rotation between two sets of points

Description

performs a simple procruste rotation between two sets of points.

Usage

procuste(df1, df2, scale = TRUE, nf = 4, tol = 1e-07) 
plot.procuste (x, xax = 1, yax = 2, ...)
print.procuste (x, ...)

Arguments

df1, df2

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

an objet of class procuste

xax

the column number for the x-axis

yax

the column number for the y-axis

...

further arguments passed to or from other methods

Value

• returns a list of 9 components of the class procuste
• d
  a numeric vector of the singular values
• rank
  an integer indicating the rank of the crossed matrix
• nfact
  an integer indicating the number of kept axes
• tab1
  a data frame with the array 1, possibly scaled
• tab2
  a data frame with the array 2, possibly scaled
• rot1
  a data frame with the result of the rotation from array 1 to array 2
• rot2
  a data frame with the result of the rotation from array 2 to array 1
• load1
  a data frame with the loadings of array 1
• load2
  a data frame with the loadings of array 2
• scor1
  a data frame with the scores of array 1
• scor2
  a data frame with the scores of array 2
• call
  a call order of the analysis

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. Sch�nemann, P.H. (1968) On two-sided Procustes problems. Psychometrika, 33, 19--34. Torre, F. and Chessel, D. (1994) Co-structure de deux tableaux totalement appari�s. Revue de Statistique Appliqu�e, 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)
par(mfrow = c(2,2))
pro1 <- procuste(macaca$xy1, macaca$xy2, scal = FALSE)
s.match(pro1$tab1, pro1$rot2, clab = 0.7)
s.match(pro1$tab2, pro1$rot1, clab = 0.7)
pro2 <- procuste(macaca$xy1, macaca$xy2)
s.match(pro2$tab1, pro2$rot2, clab = 0.7)
s.match(pro2$tab2, pro2$rot1, clab = 0.7)
par(mfrow = c(1,1))

data(doubs)
pca1 <- dudi.pca(doubs$mil, scal = TRUE, scann = FALSE)
pca2 <- dudi.pca(doubs$poi, scal = FALSE, scann = FALSE)
pro3 <- procuste(pca1$tab, pca2$tab, nf = 2)
par(mfrow = c(2,2))
s.traject(pro3$scor1, clab = 0)
s.label(pro3$scor1, clab = 0.8, add.p = TRUE)
s.traject(pro3$scor2, clab = 0)
s.label(pro3$scor2, clab = 0.8, add.p = TRUE)
s.arrow(pro3$load1, clab = 0.75)
s.arrow(pro3$load2, clab = 0.75)
plot(pro3)
par(mfrow = c(1,1))

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