procrustes rotates a configuration to maximum similarity
with another configuration. Function protest tests the
non-randomness (`significance') between two configurations.procrustes(X, Y, scale = TRUE, symmetric = FALSE)
## S3 method for class 'procrustes':
summary(object, ...)
## S3 method for class 'procrustes':
plot(x, kind=1, choices=c(1,2), xlab, ylab, main,
ar.col = "blue", len=0.05, ...)
## S3 method for class 'procrustes':
residuals(object, ...)
## S3 method for class 'procrustes':
fitted(object, truemean = TRUE, ...)
protest(X, Y, permutations = 1000, strata)Y.procrustes.kind=1 plots shifts in
two configurations and kind=2 plots an impulse diagram of
residuals.procrustes returns an object of class
procrustes with items. Function protest inherits from
procrustes, but amends that with some new items:Y.X and Yrot.ss statistic.protest: Procrustes correlation from non-permuted solution.tscale=FALSE, the function only
rotates matrix Y. If scale=TRUE, it scales linearly
configuration Y for maximum similarity. Since Y is scaled
to fit X, the scaling is non-symmetric. However, with
symmetric=TRUE, the configurations are scaled to equal
dispersions and a symmetric version of the Procrustes statistic
is computed. Instead of matrix, X and Y can be results from an
ordination from which scores can extract results.
Function plot plots a procrustes
object and returns invisibly an ordiplot object so that
function identify.ordiplot can be used for identifying
points. The items in the ordiplot object are called
heads and points with kind=1 (ordination diagram)
and sites with kind=2 (residuals). In ordination
diagrams, the arrow heads point to the target configuration, which may
be either logical or illogical. Function plot passes
parameters to underlying plotting functions.
Function residuals returns the pointwise
residuals, and fitted the fitted values, either centred to zero
mean (if truemean=FALSE) or with the original scale (these
hardly make sense if symmetric = TRUE). In
addition, there are summary and print methods.
If matrix X has a lower number of columns than matrix
Y, then matrix X will be filled with zero columns to
match dimensions. This means that the function can be used to rotate
an ordination configuration to an environmental variable (most
practically extracting the result with the fitted function).
Function protest calls procrustes(..., symmetric = TRUE)
repeatedly to estimate the `significance' of the Procrustes
statistic. Function protest uses a correlation-like statistic
derived from the symmetric Procrustes sum of squares $ss$ as
$r =\sqrt{(1-ss)}$, and sometimes called $m_{12}$. Function
protest has own print method, but otherwise uses
procrustes methods. Thus plot with a protest object
yields a ``Procrustean superimposition plot.''
Peres-Neto, P.R. and Jackson, D.A. (2001). How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test. Oecologia 129: 169-178.
isoMDS, initMDS for obtaining
objects for procrustes, and mantel for an
alternative to protest without need of dimension reduction.data(varespec)
vare.dist <- vegdist(wisconsin(varespec))
library(MASS) ## isoMDS
library(mva) ## cmdscale to start isoMDS
mds.null <- isoMDS(vare.dist, tol=1e-7)
## This was a good seed for me: your rng may vary.
set.seed(237)
mds.alt <- isoMDS(vare.dist, initMDS(vare.dist), maxit=200, tol=1e-7)
vare.proc <- procrustes(mds.alt$points, mds.null$points)
vare.proc
summary(vare.proc)
plot(vare.proc)
plot(vare.proc, kind=2)
residuals(vare.proc)
## Reset rng:
rm(.Random.seed)Run the code above in your browser using DataLab