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CRTRIPLOT procedure

Plots ordination biplots or triplots after CCA or RDA (A.I. Glaser).


DIMENSIONS = scalars Which dimensions of the ordinations to display; default 1,2
PLOT = string token What to plot (sitescores, speciesscores, xvariables); default spec, site, xvar
DGROUPS = string token Features to plot for the XGROUPS variate (ellipse, hull, lines, spider); default * i.e. none
DBINARY = string token What to plot for binary variables (biplot, centroid); default bipl
MULTIPLIER = scalar Value to multiply species and environmental variables scores by when plotting RDA; default *, i.e. none chosen
WINDOW = scalar Which graphical window to use; default 1
SAVE = pointer Supplies results from an ordination analysis by CCA or RDA; default uses the most recent analysis


LMXVARIABLES = string tokens How to label the x-variables (identifiers, labels, none, numbers); default labe if LXVARIABLES is set, otherwise iden
LMSPECIES = string tokens How to label the species scores (identifiers, labels, none, numbers); default labe if LSPECIES is set, otherwise numb
LMSITES = string tokens How to label the site scores (labels, none, numbers); default labe if LSITES is set, otherwise numb
LXVARIABLES = texts Labels for variables
LSPECIES = texts Labels for species scores
LSITES = texts Labels for site scores
XGROUPS = variates, factors or scalars X-variate to generate grouping information to appear on the plot (see the DGROUPS option)


CRTRIPLOT plots ordination biplots or triplots following an analysis from either the CCA or RDA procedures. By default it uses the results from the most recent RDA or CCA, but you can display results from an earlier analysis by saving the information about the analysis with the SAVE parameter of CCA or RDA, and then providing this to CRTRIPLOT using its own SAVE option.

An ordination biplot displays the site scores, species scores and biplot scores of environmental variables in a two or three dimensional plot. The site scores are plotted as crosses, the species scores are plotted as dashed arrows. The biplot scores of non-binary variables are represented as full lines. The DBINARY option controls how any binary variables are plotted: they can be represented either by triangles plotted at the centroid of the site scores associated with the value ‘1’, or as arrows showing the biplot scores.

The DIMENSIONS option lists the dimensions of the ordination that you want to use. You can list either two or three of these. The default is a two dimensional plot of dimensions 1 and 2. The PLOT option allows you to control what results are plotted, using the following settings:

    sitescores sites scores,
    speciesscores species scores,
    xvariables biplot scores of the environmental variables.

However, if any of the specified DIMENSIONS is higher than the number of canonical axes, the biplot scores of the environmental variables will not be plotted.

In RDA plots, the species scores and biplot scores of environmental variables are usually much smaller than the site scores. So their values are multiplied by a scalar to make them easier to read. The value is set by the procedure and displayed in the output, but you can set your own multiplier by using the MULTIPLIER option.

You can display additional information for one of the explanatory variables by setting the XGROUPS option either to the identifier of the relevant variate or factor, or to a scalar containing its position in the X pointer (see the X parameter of CCA and RDA). The information that appears is controlled by the DGROUPS option, with settings:

    ellipse draws an ellipse showing an approximate 95% confidence interval for the group centroid (2-dimensional plots only),
    hull draws an enclosing convex hull around the species scores by XGROUPS (2-dimensional plots only),
    lines links the species scores by XGROUPS, and
    spider draws lines from the group centroid to each site score.

The group centroid is the (weighted) group mean of the site scores.

The labels for the species scores, site scores and x-variable(s) can be set using the LMSPECIES, LMSITES and LMXVARIABLES parameters respectively, by selecting one of the following settings:

    identifiers uses the identifiers of the X and Y variates,
    labels expects labels to be supplied (in a text) using the LSPECIES, LSITES or LXVARIABLES parameter,
    none gives no labels, and
    numbers uses the column numbers of X and Y.

The defaults are LMSPECIES=numbers, LMSITES=numbers and LMXVARIABLES=identifiers, unless LSPECIES, LSITES or LXVARIABLES is set when the corresponding default becomes labels.




CCA and RDA are explained in Chapter 11 of Legendre & Legendre (1998).


Legendre, P. & Legendre, L. (1998). Numerical Ecology, Second English Edition. Elsevier, Amsterdam.

See also

Procedures: CCA, RDA, CRBIPLOT.

Commands for: Multivariate and cluster analysis, Graphics.


CAPTION   'CRTRIPLOT example','Example from Legendre & Legendre (1998)';\
" The data for this example come from Table 11.3 on page 590 of Legendre &
  Legendre. The data simulate fish observations at 10 sites from a beach at
  different water depths and substrates."
POINTER   [VALUES=Depth_m,Coral,Sand,Other] X
VARIATE   [NVALUES=10] Species[1...9],X[]; VALUES=\
          !(1, 0, 0, 11, 11, 9, 9, 7, 7, 5),\
          !(0, 0, 1, 4, 5, 6, 7, 8, 9, 10),\
          !(0, 0, 0, 0, 17, 0, 13, 0, 10, 0),\
          !(0, 0, 0, 0, 7, 0, 10, 0, 13, 0),\
          !(0, 0, 0, 8, 0, 6, 0, 4, 0, 2),\
          !(0, 0, 0, 1, 0, 2, 0, 3, 0, 4),\
          !(2, 5, 0, 6, 6, 10, 4, 6, 6, 0),\
          !(4, 6, 2, 2, 6, 1, 5, 6, 2, 1),\
          !(4, 1, 3, 0, 2, 4, 4, 4, 0, 3),\
          !(1, 2, 3, 4, 5, 6, 7, 8, 9, 10),\
          !(0, 0, 0, 0, 1, 0, 1, 0, 1, 0),\
          !(1, 1, 1, 0, 0, 0, 0, 0, 0, 0),\
          !(0, 0, 0, 1, 0, 1, 0, 1, 0, 1)
CCA       Species; X
Updated on June 20, 2019

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