Prediction Tools for [Constrained] Ordination (CCA, RDA, DCA, CA, PCA)
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.
residuals return estimates of
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## S3 method for class 'cca' fitted(object, model = c("CCA", "CA", "pCCA"), type = c("response", "working"), ...) ## S3 method for class 'capscale' fitted(object, model = c("CCA", "CA", "pCCA", "Imaginary"), type = c("response", "working"), ...) ## S3 method for class 'cca' residuals(object, ...) ## S3 method for class 'cca' predict(object, newdata, type = c("response", "wa", "sp", "lc", "working"), rank = "full", model = c("CCA", "CA"), scaling = "none", hill = FALSE, ...) ## S3 method for class 'rda' predict(object, newdata, type = c("response", "wa", "sp", "lc", "working"), rank = "full", model = c("CCA", "CA"), scaling = "none", correlation = FALSE, ...) ## S3 method for class 'cca' calibrate(object, newdata, rank = "full", ...) ## S3 method for class 'cca' coef(object, ...) ## S3 method for class 'decorana' predict(object, newdata, type = c("response", "sites", "species"), rank = 4, ...)
A result object from
Show constrained (
New data frame to be used in prediction or in
calibration. Usually this a new community data frame, but with
The type of prediction, fitted values or residuals:
The rank or the number of axes used in the approximation.
The default is to use all axes (full rank) of the
logical, character, or numeric; Scaling or predicted
scores with the same meaning as in
logical; correlation-like scores or Hill's
scaling as appropriate for RDA/
Other parameters to the functions.
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.
residuals gives the approximation of the original
data from the unconstrained ordination. With argument
both give the same marginal totals as the original data matrix, and
fitted and residuals do not add up to the original data. Functions
residuals.capscale give the
type = "response", but these are not
additive, but the
"working" scores are additive. All
residuals are defined so that
mod <- cca(y ~ x),
cca(fitted(mod)) is equal
to constrained ordination, and
cca(residuals(mod)) is equal
to unconstrained part of the ordination.
predict can find the estimate of the original data
matrix or dissimilarities (
type = "response") with any rank.
rank = "full" it is identical to
addition, the function can find the species scores or site scores from
the community data matrix for
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
scaling to add those scores to ordination
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
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
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
cca) and therefore the number of rows must
match in the original data and
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
newdata can be a data frame or matrix, but
extreme care is needed that the columns match in the original and
calibrate.cca finds estimates of constraints from
community ordination or
"wa" scores from
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
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
and it cannot be used with
results. The results may only be interpretable for continuous variables.
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.
predict.decorana is similar to
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
type = "response" has no meaning in detrended
analysis (except with
rank = 1).
The functions return matrices, vectors or dissimilarities as is appropriate.
Greenacre, M. J. (1984). Theory and applications of correspondence analysis. Academic Press, London.
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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=2) # 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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