procrustes {vegan} | R Documentation |

Function `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, 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), xlab, ylab, main, ar.col = "blue", len=0.05, ...) ## S3 method for class 'procrustes': points(x, display = c("target", "rotated"), ...) ## S3 method for class 'procrustes': text(x, display = c("target", "rotated"), labels, ...) ## S3 method for class 'procrustes': lines(x, type = c("segments", "arrows"), choices = c(1, 2), ...) ## S3 method for class 'procrustes': residuals(object, ...) ## S3 method for class 'procrustes': fitted(object, truemean = TRUE, ...) protest(X, Y, scores = "sites", permutations = 999, strata, ...)

`X` |
Target matrix |

`Y` |
Matrix to be rotated. |

`scale` |
Allow scaling of axes of `Y` . |

`symmetric` |
Use symmetric Procrustes statistic (the rotation will still be non-symmetric). |

`scores` |
Kind of scores used. This is the `display` argument
used with the corresponding `scores` function: see
`scores` , `scores.cca` and
`scores.cca` for alternatives. |

`x, object` |
An object of class `procrustes` . |

`digits` |
Number of digits in the output. |

`kind` |
For `plot` function, the kind of plot produced:
`kind = 1` plots shifts in two configurations, `kind = 0`
draws a corresponding empty plot, and `kind = 2`
plots an impulse diagram of residuals. |

`choices` |
Axes (dimensions) plotted. |

`xlab, ylab` |
Axis labels, if defaults unacceptable. |

`main` |
Plot title, if default unacceptable. |

`display` |
Show only the `"target"` or `"rotated"`
matrix as points. |

`type` |
Combine `target` and `rotated` points with line
segments or arrows. |

`truemean` |
Use the original range of target matrix instead of centring the fitted values. |

`permutations` |
Number of permutation to assess the significance of the symmetric Procrustes statistic. |

`strata` |
An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata. |

`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. |

`...` |
Other parameters passed to functions. In `procrustes`
and `protest` parameters are passed to `scores` , in
graphical functions to underlying graphical functions. |

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, which may
be either logical or illogical. 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 `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.''

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 `Y` . |

`X` |
Target matrix. |

`ss ` |
Sum of squared differences between `X` and `Yrot` . |

`rotation` |
Orthogonal rotation matrix. |

`translation` |
Translation of the origin. |

`scale` |
Scaling factor. |

`symmetric` |
Type of `ss` statistic. |

`call` |
Function call. |

`t0` |
This and the following items are only in class
`protest` : Procrustes correlation from non-permuted solution. |

`t` |
Procrustes correlations from permutations. |

`signif` |
`Significance' of `t` |

`permutations` |
Number of permutations. |

`strata` |
The name of the stratifying variable. |

`stratum.values` |
Values of the stratifying variable. |

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.

`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 mds.null <- isoMDS(vare.dist, tol=1e-7) mds.alt <- isoMDS(vare.dist, initMDS(vare.dist), maxit=200, tol=1e-7) vare.proc <- procrustes(mds.alt, mds.null) vare.proc summary(vare.proc) plot(vare.proc) plot(vare.proc, kind=2) residuals(vare.proc)

[Package *vegan* version 1.16-32 Index]