Learn R Programming

vegan (version 2.0-10)

predict.cca: Prediction Tools for [Constrained] Ordination (CCA, RDA, DCA, CA, PCA)

Description

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.

Usage

## 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 = 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, ...)

Arguments

object
A result object from cca, rda, capscale or decorana.
model
Show constrained ("CCA"), unconstrained ("CA") or conditioned partial ("pCCA") results. For fitted method of capscale this c
newdata
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
type
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 standardizatio
rank
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.
scaling
Scaling or predicted scores with the same meaning as in cca, rda and capscale.
...
Other parameters to the functions.

Value

  • The functions return matrices, vectors or dissimilarities as is appropriate.

Details

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.capscale and residuals.capscale give the dissimilarities with type = "response", but these are not additive, but the "working" scores are additive. 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 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).

References

Greenacre, M. J. (1984). Theory and applications of correspondence analysis. Academic Press, London.

See Also

cca, rda, capscale, decorana, vif, goodness.cca.

Examples

Run this code
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)

Run the code above in your browser using DataLab