Function predict can be used to find site and species scores or
estimates of the response data with new data sets, Function
calibrate estimates values of constraints with new data set.
Functions fitted and residuals return estimates of
response data.
# S3 method for cca
fitted(object, model = c("CCA", "CA", "pCCA"),
type = c("response", "working"), ...)
# S3 method for capscale
fitted(object, model = c("CCA", "CA", "pCCA", "Imaginary"),
type = c("response", "working"), ...)
# S3 method for cca
residuals(object, ...)
# S3 method for cca
predict(object, newdata, type = c("response", "wa", "sp", "lc", "working"),
rank = "full", model = c("CCA", "CA"), scaling = "none",
hill = FALSE, ...)
# S3 method for rda
predict(object, newdata, type = c("response", "wa", "sp", "lc", "working"),
rank = "full", model = c("CCA", "CA"), scaling = "none",
correlation = FALSE, const, ...)
# S3 method for cca
calibrate(object, newdata, rank = "full", ...)
# S3 method for cca
coef(object, norm = FALSE, ...)
# S3 method for decorana
predict(object, newdata, type = c("response", "sites", "species"),
rank = 4, ...)The functions return matrices, vectors or dissimilarities as is appropriate.
A result object from cca,
rda, dbrda, capscale or
decorana.
Show constrained ("CCA"), unconstrained
("CA") or conditioned “partial” ("pCCA")
results. For fitted method of capscale this can
also be "Imaginary" for imaginary components with negative
eigenvalues
New data frame to be used in prediction or in
calibration. Usually this a new community data frame, but with
type = "lc" and for constrained component with type =
"response" and type = "working" it must be a data frame of
constraints. The newdata must have the same number of rows
as the original community data for a cca result with
type = "response" or type = "working". If the
original model had row or column names, then new data must contain
rows or columns with the same names (row names for species scores,
column names for "wa" scores and constraint names of
"lc" scores). In other cases the rows or columns must match
directly.
The type of prediction, fitted values or residuals:
"response" scales results so that the same ordination gives
the same results, and "working" gives the values used
internally, that is after Chi-square standardization in
cca and scaling and centring in
rda. In capscale and
dbrda the "response" gives the
dissimilarities, and "working" the internal data structure
analysed in the ordination. Alternative "wa" gives the site
scores as weighted averages of the community data, "lc" the
site scores as linear combinations of environmental data, and
"sp" the species scores. In predict.decorana the
alternatives are scores for "sites" or "species".
The rank or the number of axes used in the approximation.
The default is to use all axes (full rank) of the "model" or
all available four axes in predict.decorana.
logical, character, or numeric; Scaling or predicted
scores with the same meaning as in cca,
rda, dbrda, and
capscale. See scores.cca for further details
on acceptable values.
logical; correlation-like scores or Hill's
scaling as appropriate for RDA and CCA respectively. See
scores.cca for additional details.
Constant multiplier for RDA scores. This will be used
only when scaling is not FALSE, and the default value
will give similar scaling as in scores.rda.
Coefficients for variables that are centred and scaled to unit norm.
Other parameters to the functions.
Jari Oksanen.
Function fitted gives the approximation of the original data
matrix or dissimilarities from the ordination result either in the
scale of the response or as scaled internally by the function.
Function residuals gives the approximation of the original data
from the unconstrained ordination. With argument type =
"response" the fitted.cca and residuals.cca function
both give the same marginal totals as the original data matrix, and
fitted and residuals do not add up to the original data. Functions
fitted and residuals for dbrda and
capscale give the dissimilarities with type =
"response", but these are not additive. However, the
"working" scores are additive for capscale (but
not for dbrda). The fitted and residuals
for capscale and dbrda will include the
additive constant if that was requested in the function call. All
variants of fitted and residuals 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 or dissimilarities (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 for cca or rda.
The function can be used with new data, and it can be used to add new
species or site scores to existing ordinations. The function returns
(weighted) orthonormal 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. With type = "response" or
type = "working" the new data must contain environmental variables
if constrained component is desired, and community data matrix if
residual or unconstrained component is desired. With these types, the
function uses newdata to find new "lc" (constrained) or
"wa" scores (unconstrained) and then finds the response or
working data from these new row scores and species scores. The
original site (row) and species (column) weights are used for
type = "response" and type = "working" in correspondence
analysis (cca) and therefore the number of rows must
match in the original data and newdata.
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 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 or
dbrda 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).
Greenacre, M. J. (1984). Theory and applications of correspondence analysis. Academic Press, London.
cca, rda, dbrda,
capscale, decorana,
goodness.cca.
data(dune)
data(dune.env)
mod <- cca(dune ~ A1 + Management + Condition(Moisture), data=dune.env)
# Definition of the concepts 'fitted' and 'residuals'
mod
cca(fitted(mod))
cca(residuals(mod))
# Remove rare species (freq==1) from 'cca' and find their scores
# 'passively'.
freq <- specnumber(dune, MARGIN=2)
freq
mod <- cca(dune[, freq>1] ~ A1 + Management + Condition(Moisture), dune.env)
predict(mod, type="sp", newdata=dune[, freq==1], scaling="species")
# New sites
predict(mod, type="lc", new=data.frame(A1 = 3, Management="NM", Moisture="2"), scal=2)
# Calibration and residual plot
mod <- cca(dune ~ A1 + Moisture, dune.env)
pred <- calibrate(mod)
pred
with(dune.env, plot(A1, pred[,"A1"] - A1, ylab="Prediction Error"))
abline(h=0)
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