Ordination methods cca, rda,
dbrda and capscale return similar result
objects. All these methods use the same internal function
ordConstrained. They differ only in (1) initial
transformation of the data and in defining inertia, (2) weighting,
and (3) the use of rectangular rows \(\times\) columns data or
symmetric rows \(\times\) rows dissimilarities:
rda initializes data to give variance or correlations
as inertia, cca is based on double-standardized data
to give Chi-square inertia and uses row and column weights,
capscale maps the real part of dissimilarities to
rectangular data and performs RDA, and dbrda performs
an RDA-like analysis directly on symmetric dissimilarities.
Function ordConstrained returns the same result components
for all these methods, and the calling function may add some more
components to the final result. However, you should not access these
result components directly (using $): the internal structure
is not regarded as stable application interface (API), but it can
change at any release. If you access the results components
directly, you take a risk of breakage at any vegan release.
The vegan provides a wide set of accessor functions to those
components, and these functions are updated when the result object
changes. This documentation gives an overview of accessor functions
to the cca result object.
ordiYbar(x, model = c("CCA", "CA", "pCCA", "partial", "initial"))
# S3 method for cca
model.frame(formula, ...)
# S3 method for cca
model.matrix(object, ...)
# S3 method for cca
weights(object, display = "sites", ...)
A result object from cca,
rda, dbrda, or
capscale.
Show constrained ("CCA"), unconstrained
("CA") or conditioned “partial” ("pCCA")
results. In ordiYbar the value can also be "initial"
for the internal working input data, and "partial" for the
internal working input data after removing the partial effects.
Display either "sites" or "species".
Other arguments passed to the the function.
Jari Oksanen
The internal (“working”) form of the dependent (community)
data can be accessed with function ordiYbar. The form depends
on the ordination method: for instance, in cca the
data are weighted and Chi-square transformed, and in
dbrda they are Gower-centred dissimilarities. The
input data in the original (“response”) form can be accessed
with fitted.cca and residuals.cca.
Function predict.cca can return either working or
response data, and also their lower-rank approximations.
The model matrix of independent data (“Constraints” and
“Conditions”) can be extracted with model.matrix. In
partial analysis, the function returns a list of design matrices
called Conditions and Constraints. If either component
was missing, a single matrix is returned. The redundant (aliased)
terms do not appear in the model matrix. These terms can be found
with alias.cca. Function model.frame tries to
reconstruct the data frame from which the model matrices were
derived. This is only possible if the original model was fitted with
formula and data arguments, and still fails if the
data are unavailable.
The number of observations can be accessed with
nobs.cca, and the residual degrees of freedom with
df.residual.cca. The information on observations with
missing values can be accessed with na.action. The
terms and formula of the fitted model can be accessed with
formula and terms.
The weights used in cca can be accessed with
weights. In unweighted methods (rda) all
weights are equal.
The ordination results are saved in separate components for partial terms, constraints and residual unconstrained ordination. There is no guarantee that these components will have the same internal names as currently, and you should be cautious when developing scripts and functions that directly access these components.
The constrained ordination algorithm is based on QR decomposition of
constraints and conditions (environmental data), and the QR
component is saved separately for partial and constrained
components. The QR decomposition of constraints can be accessed
with qr.cca. This will also include the residual
effects of partial terms (Conditions), and it should be used
together with ordiYbar(x, "partial"). 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. See qr for other possible
uses of this component. For instance, the rank of the constraints
can be found from the QR decomposition.
The eigenvalues of the solution can be accessed with
eigenvals.cca. Eigenvalues are not evaluated for
partial component, and they will only be available for constrained
and residual components.
The ordination scores are internally stored as (weighted)
orthonormal scores matrices. These results can be accessed with
scores.cca and scores.rda functions. The
ordination scores are scaled when accessed with scores
functions, but internal (weighted) orthonormal scores can be
accessed by setting scaling = FALSE. Unconstrained residual
component has species and site scores, and constrained component has
also fitted site scores or linear combination scores for sites and
biplot scores and centroids for constraint variables. The biplot
scores correspond to the model.matrix, and centroids
are calculated for factor variables when they were used. The scores
can be selected by defining the axes, and there is no direct way of
accessing all scores of a certain component. The number of dimensions
can be assessed from eigenvals. In addition, some
other types can be derived from the results although not saved in
the results. For instance, regression scores and model coefficients
can be accessed with scores and coef
functions. Partial component will have no scores.
Distance-based methods (dbrda, capscale)
can have negative eigenvalues and associated imaginary axis scores. In
addition, species scores are initially missing in dbrda
and they are accessory and found after analysis in
capscale (and may be misleading). Function
sppscores can be used to add species scores or replace
them with more meaningful ones.
Legendre, P. and Legendre, L. (2012) Numerical Ecology. 3rd English ed. Elsevier.
The core function is ordConstrained which is called by
cca, rda, dbrda and
capscale. The basic class is "cca" for all
methods, and the following functions are defined for this class:
require(vegan, quietly=TRUE);
paste0("\\code{\\link{", methods(class="cca"), "}}", collapse=", ").
Other functions handling "cca" objects include inertcomp,
intersetcor, mso, ordiresids,
ordistep and ordiR2step.