Description Usage Arguments Details Value Note Author(s) References See Also Examples
Function procrustes
rotates a configuration to maximum similarity
with another configuration. Function protest
tests the
non-randomness (‘significance’) between two configurations.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | procrustes(X, Y, scale = TRUE, symmetric = FALSE, scores = "sites", ...)
## S3 method for class 'procrustes'
summary(object, digits = getOption("digits"), ...)
## S3 method for class 'procrustes'
plot(x, kind=1, choices=c(1,2), to.target = TRUE,
type = "p", xlab, ylab, main, ar.col = "blue", len=0.05,
cex = 0.7, ...)
## S3 method for class 'procrustes'
points(x, display = c("target", "rotated"),
choices = c(1,2), truemean = FALSE, ...)
## S3 method for class 'procrustes'
text(x, display = c("target", "rotated"),
choices = c(1,2), labels, truemean = FALSE, ...)
## S3 method for class 'procrustes'
lines(x, type = c("segments", "arrows"),
choices = c(1, 2), truemean = FALSE, ...)
## S3 method for class 'procrustes'
residuals(object, ...)
## S3 method for class 'procrustes'
fitted(object, truemean = TRUE, ...)
## S3 method for class 'procrustes'
predict(object, newdata, truemean = TRUE, ...)
protest(X, Y, scores = "sites", permutations = how(nperm = 999), ...)
|
X |
Target matrix |
Y |
Matrix to be rotated. |
scale |
Allow scaling of axes of |
symmetric |
Use symmetric Procrustes statistic (the rotation will still be non-symmetric). |
scores |
Kind of scores used. This is the |
x, object |
An object of class |
digits |
Number of digits in the output. |
kind |
For |
choices |
Axes (dimensions) plotted. |
xlab, ylab |
Axis labels, if defaults unacceptable. |
main |
Plot title, if default unacceptable. |
display |
Show only the |
to.target |
Draw arrows to point to target. |
type |
The type of plot drawn. In |
truemean |
Use the original range of target matrix instead of
centring the fitted values. Function |
newdata |
Matrix of coordinates to be rotated and translated to the target. |
permutations |
a list of control values for the permutations
as returned by the function |
ar.col |
Arrow colour. |
len |
Width of the arrow head. |
labels |
Character vector of text labels. Rownames of the result object are used as default. |
cex |
Character expansion for points or text. |
... |
Other parameters passed to functions. In |
Procrustes rotation rotates a matrix to maximum similarity with a
target matrix minimizing sum of squared differences. Procrustes
rotation is typically used in comparison of ordination results. It is
particularly useful in comparing alternative solutions in
multidimensional scaling. If scale=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 procrustes
passes extra arguments to
scores
, scores.cca
etc. so that you can
specify arguments such as scaling
.
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 if to.target = TRUE
, and to rotated
configuration if to.target = FALSE
. Target and original
rotated axes are shown as cross hairs in two-dimensional Procrustes
analysis, and with a higher number of dimensions, the rotated axes
are projected onto plot with their scaled and centred
range. Function plot
passes parameters to underlying plotting
functions. For full control of plots, you can draw the axes using
plot
with kind = 0
, and then add items with
points
or lines
. These functions pass all parameters
to the underlying functions so that you can select the plotting
characters, their size, colours etc., or you can select the width,
colour and type of line segments
or arrows, or you can
select the orientation and head width of arrows
.
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 predict
can be used to add new rotated
coordinates to the target. The predict
function will always
translate coordinates to the original non-centred matrix. The
function cannot be used with newdata
for symmetric
analysis.
Function protest
performs symmetric Procrustes analysis
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 also prints the sum of
squares of the symmetric analysis, sometimes called
squared m12. Function protest
has own
print
method, but otherwise uses procrustes
methods. Thus plot
with a protest
object yields a
“Procrustean superimposition plot.”
Function procrustes
returns an object of class
procrustes
with items. Function protest
inherits from
procrustes
, but amends that with some new items:
Yrot |
Rotated matrix |
X |
Target matrix. |
ss |
Sum of squared differences between |
rotation |
Orthogonal rotation matrix. |
translation |
Translation of the origin. |
scale |
Scaling factor. |
xmean |
The centroid of the target. |
symmetric |
Type of |
call |
Function call. |
t0 |
This and the following items are only in class
|
t |
Procrustes correlations from permutations. The distribution
of these correlations can be inspected with |
signif |
‘Significance’ of |
permutations |
Number of permutations. |
control |
A list of control values for the permutations
as returned by the function |
control |
the list passed to argument |
The function protest
follows Peres-Neto & Jackson (2001),
but the implementation is still after Mardia et al.
(1979).
Jari Oksanen
Mardia, K.V., Kent, J.T. and Bibby, J.M. (1979). Multivariate Analysis. Academic Press.
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.
monoMDS
, for obtaining
objects for procrustes
, and mantel
for an
alternative to protest
without need of dimension reduction. See
how
for details on specifying the type of
permutation required.
1 2 3 4 5 6 7 8 9 10 |
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-3
Call:
procrustes(X = mds.alt, Y = mds.null)
Procrustes sum of squares:
8.418
Call:
procrustes(X = mds.alt, Y = mds.null)
Number of objects: 24 Number of dimensions: 2
Procrustes sum of squares:
8.418224
Procrustes root mean squared error:
0.5922494
Quantiles of Procrustes errors:
Min 1Q Median 3Q Max
0.07430277 0.12550990 0.16920764 0.45983040 2.27654275
Rotation matrix:
[,1] [,2]
[1,] -0.99509290 0.09894507
[2,] -0.09894507 -0.99509290
Translation of averages:
[,1] [,2]
[1,] 2.356519e-17 5.837006e-20
Scaling of target:
[1] 0.8057547
18 15 24 27 23 19 22
0.07430277 0.19455883 2.27654275 0.68205548 0.10931717 0.10342982 0.09795846
16 28 13 14 20 25 7
0.09970144 0.52003706 0.16963767 0.26908016 0.13380614 0.64973770 0.15689374
5 6 3 4 2 9 12
0.33486690 0.12129342 0.12691539 0.27457163 1.01227686 0.13508889 0.15190715
10 11 21
0.16877761 0.58503884 0.43976151
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