Functions to plot or extract results of constrained correspondence analysis
(cca), redundancy analysis (rda), distance-based
redundancy analysis (dbrda) or
constrained analysis of principal coordinates (capscale).
# S3 method for cca
plot(x, choices = c(1, 2), display = c("sp", "wa", "cn"),
scaling = "species", type, xlim, ylim, const,
correlation = FALSE, hill = FALSE, ...)
# S3 method for cca
text(x, display = "sites", labels, choices = c(1, 2),
scaling = "species", arrow.mul, head.arrow = 0.05, select, const,
axis.bp = FALSE, correlation = FALSE, hill = FALSE, ...)
# S3 method for cca
points(x, display = "sites", choices = c(1, 2),
scaling = "species", arrow.mul, head.arrow = 0.05, select, const,
axis.bp = FALSE, correlation = FALSE, hill = FALSE, ...)
# S3 method for cca
scores(x, choices = c(1,2), display = "all",
scaling = "species", hill = FALSE, tidy = FALSE, droplist = TRUE,
...)
# S3 method for rda
scores(x, choices = c(1,2), display = "all",
scaling = "species", const, correlation = FALSE, tidy = FALSE,
droplist = TRUE, ...)
# S3 method for cca
summary(object, scaling = "species", axes = 6,
display=c("sp","wa","lc","bp","cn"),
digits = max(3, getOption("digits") - 3),
correlation = FALSE, hill = FALSE, ...)
# S3 method for cca
labels(object, display, ...)The plot function returns
invisibly a plotting structure which can be used by function
identify.ordiplot to identify the points or other
functions in the ordiplot family.
A cca result object.
Axes shown.
Scores shown. These must include some of the
alternatives "species" or "sp" for species scores,
sites or "wa" for site scores, "lc" for linear
constraints or LC scores, or "bp" for biplot arrows or
"cn" for centroids of factor constraints instead of an arrow,
and "reg" for regression coefficients (a.k.a. canonical
coefficients). The alternative "all" selects all available
scores.
Scaling for species and site scores. Either species
(2) or site (1) scores are scaled by eigenvalues, and
the other set of scores is left unscaled, or with 3 both are
scaled symmetrically by square root of eigenvalues. Corresponding
negative values can be used in cca to additionally multiply
results with \(\sqrt(1/(1-\lambda))\). This scaling is know as Hill
scaling (although it has nothing to do with Hill's rescaling of
decorana). With corresponding negative values
in rda, species scores are divided by standard deviation of each
species and multiplied with an equalizing constant. Unscaled raw
scores stored in the result can be accessed with scaling = 0.
The type of scores can also be specified as one of "none",
"sites", "species", or "symmetric", which
correspond to the values 0, 1, 2, and 3
respectively. Arguments correlation and hill in
scores.rda and scores.cca respectively can be used in
combination with these character descriptions to get the
corresponding negative value.
logical; if scaling is a character
description of the scaling type, correlation or hill
are used to select the corresponding negative scaling type; either
correlation-like scores or Hill's scaling for PCA/RDA and CA/CCA
respectively. See argument scaling for details.
Return scores that are compatible with
ggplot2: all scores are in a single data.frame,
score type is identified by factor variable score, the
names by variable label, and weights (in CCA) are in
variable weight. The possible values of score are
species, sites (for WA scores), constraints
(LC scores for sites calculated directly from the constraining
variables), biplot (for biplot arrows), centroids
(for levels of factor variables), factorbiplot (biplot
arrows that model centroids), regression (for regression
coefficients to find LC scores from constraints). These scores
cannot be used with conventional plot, but they are
directly suitable to be used with the ggplot2 package.
Type of plot: partial match to text
for text labels, points for points, and none for
setting frames only. If omitted, text is selected for
smaller data sets, and points for larger.
the x and y limits (min,max) of the plot.
Optional text to be used instead of row names. If you
use this, it is good to check the default labels and their order
using labels command.
Factor to expand arrows in the graph. Arrows will be scaled automatically to fit the graph if this is missing.
Default length of arrow heads.
Items to be displayed. This can either be a logical
vector which is TRUE for displayed items or a vector of indices
of displayed items.
General scaling constant to rda scores. The
default is to use a constant that gives biplot scores, that is,
scores that approximate original data (see vignette
on ‘Design Decisions’ with browseVignettes("vegan")
for details and discussion). If const is a vector of two
items, the first is used for species, and the second item for site
scores.
Return a matrix instead of a named list when only one kind of scores were requested.
Draw axis for biplot arrows.
Number of axes in summaries.
Number of digits in output.
Parameters passed to other functions.
Jari Oksanen
Same plot function will be used for cca and
rda. This produces a quick, standard plot with current
scaling.
The plot function sets colours (col), plotting
characters (pch) and character sizes (cex) to
certain standard values. For a fuller control of produced plot, it is
best to call plot with type="none" first, and then add
each plotting item separately using text.cca or
points.cca functions. These use the default settings of standard
text and points functions and accept all
their parameters, allowing a full user control of produced plots.
Environmental variables receive a special treatment. With
display="bp", arrows will be drawn. These are labelled with
text and unlabelled with points. The arrows have
basically unit scaling, but if sites were scaled (scaling
"sites" or "symmetric"), the scores of requested axes
are adjusted relative to the axis with highest eigenvalue. With
scaling = "species" or scaling = "none", the arrows will
be consistent with vectors fitted to linear combination scores
(display = "lc" in function envfit), but with
other scaling alternatives they will differ. The basic plot
function uses a simple heuristics for adjusting the unit-length arrows
to the current plot area, but the user can give the expansion factor
in mul.arrow. With display="cn" the centroids of levels
of factor variables are displayed (these are available
only if there were factors and a formula interface was used in
cca or rda). With this option continuous
variables still are presented as arrows and ordered factors as arrows
and centroids. With display = "reg" arrows will be drawn for
regression coefficients (a.k.a. canonical coefficients) of constraints
and conditions. Biplot arrows can be interpreted individually, but
regression coefficients must be interpreted all together: the LC score
for each site is the sum of regressions displayed by arrows. The
partialled out conditions are zero and not shown in biplot arrows, but
they are shown for regressions, and show the effect that must be
partialled out to get the LC scores. The biplot arrows are more
standard and more easily interpreted, and regression arrows should be
used only if you know that you need them.
If you want to have a better control of plots, it is best to
construct the plot text and points commands which
accept graphical parameters. It is important to remember to use the
same scaling, correlation and hill arguments
in all calls. The plot.cca command returns invisibly an
ordiplot result object, and this will have consistent
scaling for all its elements. The easiest way for full control of
graphics is to first set up the plot frame using plot with
type = "n" and all needed scores in display and save
this result. The points and text commands for
ordiplot will allow full graphical control (see
section Examples). Utility function labels returns the default
labels in the order they are applied in text.
Palmer (1993) suggested using linear constraints (“LC scores”)
in ordination diagrams, because these gave better results in
simulations and site scores (“WA scores”) are a step from
constrained to unconstrained analysis. However, McCune (1997) showed
that noisy environmental variables (and all environmental measurements
are noisy) destroy “LC scores” whereas “WA scores” were
little affected. Therefore the plot function uses site scores
(“WA scores”) as the default. This is consistent with the usage
in statistics and other functions in R (lda,
cancor).
data(dune)
data(dune.env)
mod <- cca(dune ~ A1 + Moisture + Management, dune.env)
## better control -- remember to set scaling etc identically
plot(mod, type="n", scaling="sites")
text(mod, dis="cn", scaling="sites")
points(mod, pch=21, col="red", bg="yellow", cex=1.2, scaling="sites")
text(mod, "species", col="blue", cex=0.8, scaling="sites")
## catch the invisible result and use ordiplot support - the example
## will make a biplot with arrows for species and correlation scaling
pca <- rda(dune)
pl <- plot(pca, type="n", scaling="sites", correlation=TRUE)
with(dune.env, points(pl, "site", pch=21, col=1, bg=Management))
text(pl, "sp", arrow=TRUE, length=0.05, col=4, cex=0.6, xpd=TRUE)
with(dune.env, legend("bottomleft", levels(Management), pch=21, pt.bg=1:4, bty="n"))
## Scaling can be numeric or more user-friendly names
## e.g. Hill's scaling for (C)CA
scrs <- scores(mod, scaling = "sites", hill = TRUE)
## or correlation-based scores in PCA/RDA
scrs <- scores(rda(dune ~ A1 + Moisture + Management, dune.env),
scaling = "sites", correlation = TRUE)
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