cca.object {vegan}R Documentation

Result Object from Constrained Ordination with cca, rda or capscale

Description

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.

Value

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

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. If constraints or conditions are not given, the corresponding components CCA and pCCA are NULL. If they are specified but have zero rank and zero eigenvalue (e.g., due to aliasing), they have a standard structure like described below, but the result scores have zero columns, but the correct number of rows. The residual component is never NULL, and if there is no residual variation (like in overdefined model), its scores have zero columns. The standard print command does not show NULL components, but it prints zeros for zeroed components. Items pCCA, CCA and CA contain following items:

alias

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

Biplot scores of constraints. Only in CCA.

centroids

(Weighted) centroids of factor levels of constraints. Only in CCA. Missing if the ordination was not called with formula.

eig

Eigenvalues of axes. In CCA and CA.

envcentre

(Weighted) means of the original constraining or conditioning variables. In pCCA and in CCA.

Fit

The fitted values of standardized data matrix after fitting conditions. Only in pCCA. This element will be deprecated in the future. Instead of directly accessing this component, you should use ordiYbar(<result>, "pCCA") which will work both with the current and future releases.

QR

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.

rank

The rank of the ordination component.

qrank

The rank of the constraints which is the difference of the ranks of QR decompositions in pCCA and CCA components. Only in CCA.

tot.chi

Total inertia or the sum of all eigenvalues of the component.

real.tot.chi

If there are negative eigenvalues in capscale, these will be included in tot.chi, and the sum of positive eigenvalues will be given in these items.

imaginary.chi, imaginary.rank, imaginary.u.eig

The sum, rank (number) of negative eigenvalues and scaled site scores for imaginary axes in capscale. Only in CA item and only if negative eigenvalues were found in capscale.

u

(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.

v

(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.

wa

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.

wa.excluded, u.excluded

WA scores for rows removed by na.action = na.exclude in CCA and CA components if these could be calculated.

Xbar

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. This component will be deprecated in the future. Instead of directly accessing these components, you should use commands ordiYbar(<result>, "partial") (for <result>$CCA$Xbar) or ordiYbar(<result>, "CA") (for <result>$CA$Xbar) which will work both in the current and in the future versions of vegan.

NA Action and Subset

If the constraints had missing values or subsets, and na.action was set to na.exclude or na.omit, the result will have some extra items:

subset

subset evaluated as a logical vector (TRUE for included cases).

na.action

The object returned by na.action which is a named vector of indices of removed items. The class of the vector is either "omit" or "exclude" as set by na.action. The na.action is applied after subset so that the indices refer to the subset data.

residuals.zombie

A zombie vector of the length of number of rows in the residual ordination. R versions before 2.13.0 may use this vector to find the number of valid observations, and it is provided for their use although this is useless in R 2.13.0 and in vegan. Currently R uses nobs.cca to find the number of observations.

rowsum.excluded

Row sums of removed observations. Only in cca.

CCA$wa.excluded

The WA scores for sites (found from community data) in constrained ordination if na.action was na.exclude and the scores could be calculated. The scores cannot be found for capscale and in partial ordination.

CA$u.excluded

Row scores for sites in unconstrained ordination with identical conditions as above.

capscale and dbrda

Vegan has two functions for distance-based Redundancy analysis: capscale and dbrda. Function capscale uses rda and returns its result object, but it may add some items depending on its arguments:

real.tot.chi

Sum of positive eigenvalues if there are negative eigenvalues. The item tot.chi gives the total inertia with negative eigenvalues. This item is given for the whole model and for each component pCCA, CCA and CA if there are negative eigenvalues.

metaMDSdist

The data set name if metaMDSdist = TRUE.

sqrt.dist

Logical value, TRUE if squareroots of dissimilarities were used.

ac

Additive constant used if add = TRUE.

add

The adjustment method to find ac, either "lingoes" or "cailliez" (Legendre & Legendre 2012).

adjust

Adjustment of dissimilarities: see capscale, section “Notes”.

G

The working structure of Gower transformed dissimilarities defined as -(D^2 - M)/2, where D are the dissimilarities and M is the centring matrix. This structure is used to asses the total inertia, and it will be used also in permutation tests. This is given for items pCCA and CCA, and for CCA it is the residual G after pCCA.

Function dbrda does not use rda but provides a parallel implementation for dissimilarities. Its result output is very similar to capscale described above with the following differences:

Xbar, v

are NA because they cannot be calculated from dissimilarities.

Fit

of pCCA is from Gower double centred dissimilarities G instead of Xbar (that does not exist).

G

is returned with pCCA, CCA and CA components. It always gives the transformed dissimilarities as they enter the stage of analysis, i.e., before applying conditions or constraints.

eig

lists also negative eigenvalues for CCA and pCCA.

u

or row scores only give real axes with positive eigenvalues. The imaginary scores (if any) are in imaginary.u. The number of columns of real scores (positive eigenvalues) is given in item poseig. There is no imaginary.u.eig.

Note

In old versions of vegan the object also included scores scaled by eigenvalues (u.eig, v.eig and wa.eig), but these were removed in vegan 2.2-0. The scores are scaled when they are accessed with scores function. It is advisable to always use scores in accessing the results instead of directly accessing the elements of the the cca object.

Author(s)

Jari Oksanen

References

Legendre, P. and Legendre, L. (2012) Numerical Ecology. 3rd English ed. Elsevier.

See Also

The description here provides a hacker's interface. User level functions for further analysis and handling of cca objects are described in this section in cca. Also for a hacker interface, it may be better to use following low level functions to access the results: scores.cca (which also scales results), predict.cca (which can also use newdata), fitted.cca, residuals.cca, alias.cca, coef.cca, model.frame.cca, model.matrix.cca, deviance.cca, eigenvals.cca, RsquareAdj.cca, weights.cca, nobs.cca, 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).

This section in cca gives a more complete list of methods to handle the constrained ordination result object.

Examples

# Some species will be missing in the analysis, because only a subset
# of sites is used below.
data(dune)
data(dune.env)
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:
mod$CCA$alias
# 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 2.4-3 Index]