cca.object {vegan}R Documentation

Result Object from Constrained Ordination with cca, rda or capscale


Ordination methods cca, rda and capscale return similar result objects. Function capscale inherits from rda and rda inherits from cca. This inheritance structure is due to historic reasons: cca was the first of these implemented in vegan. Hence the nomenclature in cca.object reflects cca. This help page describes the internal structure of the cca object for programmers.


A cca object has the following elements:

call the function call.
colsum, rowsum, rowsum.excluded Column and row sums in cca. In rda, item colsum contains standard deviations of species and rowsum is NA. If some data were removed in na.action, the row sums of excluded observations are in item rowsum.excluded in cca (but not in rda). The rowsum.excluded add to the total (one) of rowsum. Grand total of community data in cca and NA in rda.
inertia Text used as the name of inertia.
method Text used as the name of the ordination method.
terms The terms component of the formula. This is missing if the ordination was not called with formula.
terminfo Further information on terms with three subitems: terms which is like the terms component above, but lists conditions and constraints similarly; xlev which lists the factor levels, and ordered which is TRUE to ordered factors. This is produced by vegan internal function ordiTerminfo, and it is needed in predict.cca with newdata. This is missing if the ordination was not called with formula.
tot.chi Total inertia or the sum of all eigenvalues.
na.action The result of na.action if missing values in constraints were handled by na.omit or na.exclude (or NULL if there were no missing values). This is a vector of indices of missing value rows in the original data and a class of the action, usually either "omit" or "exclude".
pCCA, CCA, CA Actual ordination results for conditioned (partial), constrained and unconstrained components of the model. Any of these can be NULL if there is no corresponding component. Items pCCA, CCA and CA have similar structure, and contain following items:
The names of the aliased constraints or conditions. Function alias.cca does not access this item directly, but it finds the aliased variables and their defining equations from the QR item.
Biplot scores of constraints. Only in CCA.
(Weighted) centroids of factor levels of constraints. Only in CCA. Missing if the ordination was not called with formula.
Eigenvalues of axes. In CCA and CA.
(Weighted) means of the original constraining or conditioning variables. In pCCA and in CCA.
The fitted values of standardized data matrix after fitting conditions. Only in pCCA.
The QR decomposition of explanatory variables as produced by qr. The constrained ordination algorithm is based on QR decomposition of constraints and conditions (environmental data). The environmental data are first centred in rda or weighted and centred in cca. The QR decomposition is used in many functions that access cca results, and it can be used to find many items that are not directly stored in the object. For examples, see coef.cca, coef.rda, vif.cca, permutest.cca, predict.cca, predict.rda, calibrate.cca. For possible uses of this component, see qr. In pCCA and CCA.
The rank of the ordination component.
The rank of the constraints which is the difference of the ranks of QR decompositions in pCCA and CCA components. Only in CCA.
Total inertia or the sum of all eigenvalues of the component.
imaginary.chi, imaginary.rank
The sum and rank (number) of negative eigenvalues in capscale. Only in CA and only if negative eigenvalues were found in capscale.
(Weighted) orthonormal site scores. Please note that scaled scores are not stored in the cca object, but they are made when the object is accessed with functions like scores.cca, summary.cca or plot.cca, or their rda variants. Only in CCA and CA. In the CCA component these are the so-called linear combination scores.
u scaled by eigenvalues. There is no guarantee that any .eig variants of scores will be kept in the future releases.
(Weighted) orthonormal species scores. If missing species were omitted from the analysis, this will contain attribute na.action that lists the omitted species. Only in CCA and CA.
v weighted by eigenvalues.
Site scores found as weighted averages (cca) or weighted sums (rda) of v with weights Xbar, but the multiplying effect of eigenvalues removed. These often are known as WA scores in cca. Only in CCA.
The direct result of weighted averaging or weighted summation (matrix multiplication) with the resulting eigenvalue inflation.
wa.excluded, u.excluded
WA scores for rows removed by na.action = na.exclude in CCA and CA components if these could be calculated.
The standardized data matrix after previous stages of analysis. In CCA this is after possible pCCA or after partialling out the effects of conditions, and in CA after both pCCA and CCA. In cca the standardization is Chi-square, and in rda centring and optional scaling by species standard deviations using function scale.


Jari Oksanen


Legendre, P. and Legendre, L. (1998) Numerical Ecology. 2nd English ed. Elsevier.

See Also

The description here provides a hacker's interface. For more user friendly access to the cca object see alias.cca, coef.cca, deviance.cca, predict.cca, scores.cca, summary.cca, vif.cca, weights.cca, spenvcor or rda variants of these functions. You can use as.mlm to cast a cca.object into result of multiple response linear model (lm) in order to more easily find some statistics (which in principle could be directly found from the cca.object as well).


# Some species will be missing in the analysis, because only a subset
# of sites is used below.
mod <- cca(dune[1:15,] ~ ., dune.env[1:15,])
# Look at the names of missing species
attr(mod$CCA$v, "na.action")
# Look at the names of the aliased variables:
# Access directly constrained weighted orthonormal species and site
# scores, constrained eigenvalues and margin sums.
spec <- mod$CCA$v
sites <- mod$CCA$u
eig <- mod$CCA$eig
rsum <- mod$rowsum
csum <- mod$colsum

[Package vegan version 1.16-32 Index]