Function fitted gives the approximation of the original data
matrix from the ordination result. Function residuals gives
the approximation of the original data from the unconstrained
ordination. The fitted.cca and residuals.cca function
both have the same marginal totals as the original data matrix, and
their entries do not add up to the original data. They are defined so
that for model mod <- cca(y ~ x), cca(fitted(mod)) is equal
to constrained ordination, and cca(residuals(mod)) is equal to
unconstrained part of the ordination. Function predict can find the estimate of the original data
matrix (type = "response") with any rank. With rank =
"full" it is identical to fitted. In addition, the function
can find the species scores or site scores from the community data
matrix. The function can be used with new data, and it can be used to
add new species or site sccores to existing ordinations. The function
returns (weighted) orthornormal scores by default, and you must
specify explicit scaling to
add those scores to ordination diagrams. With
type = "wa" the function finds the site scores from species
scores. In that case, the new data can contain new sites, but species
must match in the original and new data. With type = "sp" the
function finds species scores from site constraints (linear
combination scores). In that case the new data can contain new
species, but sites must match in the original and new
data. With type = "lc" the function finds the linear
combination scores for sites from environmental data. In that case the
new data frame must contain all constraining and conditioning environmental
variables of the model formula. If a completely new data frame is created,
extreme care is needed defining variables similarly as in the original
model, in particular with (ordered) factors. If ordination was
performed with the formula interface, the newdata also can be a
data frame or matrix, but extreme care is needed that the columns
match in the original and newdata.
Function calibrate.cca finds estimates of constraints from
community ordination or "wa" scores from cca,
rda and capscale. This is often known as
calibration, bioindication or environmental reconstruction.
Basically, the method is similar to projecting site scores onto biplot
arrows, but it uses regression coefficients. The function can be called
with newdata so that cross-validation is possible. The
newdata may contain new sites, but species must match in the
original and new data The function
does not work with partial models with Condition term,
and it cannot be used with newdata for capscale
results. The results may only be interpretable for continuous variables.
Function coef will give the regression coefficients from centred
environmental variables (constraints and conditions) to linear
combination scores. The coefficients are for unstandardized environmental
variables. The coefficients will be NA for aliased effects.
Function predict.decorana is similar to predict.cca.
However, type = "species" is not available in detrended
correspondence analysis (DCA), because detrending destroys the mutual
reciprocal averaging (except for the first axis when rescaling is not
used). Detrended CA does not attempt to approximate the original data
matrix, so type = "response" has no meaning in detrended
analysis (except with rank = 1).