Plot or Extract Results of Constrained Correspondence Analysis or Redundancy Analysis

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).

Usage

# S3 method for class 'cca'
plot(x, choices = c(1, 2), display = c("sp", "wa", "cn"),
     scaling = "species", type, xlim, ylim, const,
     correlation = FALSE, hill = FALSE, cex = 0.7, ...)
# S3 method for class '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 class '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 class 'cca'
scores(x, choices = c(1,2), display = "all",
       scaling = "species", hill = FALSE, tidy = FALSE, droplist = TRUE,
       ...)
# S3 method for class 'rda'
scores(x, choices = c(1,2), display = "all",
       scaling = "species", const, correlation = FALSE, tidy = FALSE,
       droplist = TRUE, ...)
# S3 method for class '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 class 'cca'
labels(object, display, ...)

Arguments

x, object

A cca result object.

choices

Axes shown.

display

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

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.

correlation, hill

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.

tidy

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

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.

xlim, ylim

the x and y limits (min,max) of the plot.

labels

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.

arrow.mul

Factor to expand arrows in the graph. Arrows will be scaled automatically to fit the graph if this is missing.

head.arrow

Default length of arrow heads.

select

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.

const

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.

droplist

Return a matrix instead of a named list when only one kind of scores were requested.

axis.bp

Draw axis for biplot arrows.

axes

Number of axes in summaries.

digits

Number of digits in output.

cex

Character expansion.

...

Parameters passed to other functions.

Details

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 arrow.mul. With display="cn" the centroids of levels of factor variables are displayed. 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).

Value

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.

Author

Jari Oksanen

Note

Up to vegan release 2.6-4 summary printed ordination scores, and function was occasionally used to extract scores. This is now deprecated and you should use scores. This version of vegan still enables extracting scores with summary, but you should change your code to use scores before next vegan release. For instructions, see https://github.com/vegandevs/vegan/discussions/644.

Examples

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)