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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
## 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, ...)

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 can also be "Imaginary" for imaginary components with negative eigenvalues.

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 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.

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 standardization in cca and scaling and centring in rda. In capscale the "response" gives the dissimilarities, and "working" the scaled scores that produce the dissimilarities as Euclidean distances. 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".

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

logical, character, or numeric; Scaling or predicted scores with the same meaning as in cca, rda and capscale. See scores.cca for further details on acceptable values.

correlation, hill

logical; correlation-like scores or Hill's scaling as appropriate for RDA/capscale and CCA respectively. See scores.cca for additional details.

...

Other parameters to the functions.

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).

Value

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

Author(s)

Jari Oksanen.

References

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

See Also

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

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
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)

Want to suggest features or report bugs for rdrr.io? Use the GitHub issue tracker.