predict.cca: Prediction Tools for [Constrained] Ordination (CCA, RDA, DCA,...
In vegan: Community Ecology Package
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
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
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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, ...)
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
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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)
Example output
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-4
Call: cca(formula = dune ~ A1 + Management + Condition(Moisture), data
= dune.env)
Inertia Proportion Rank
Total 2.1153 1.0000
Conditional 0.6283 0.2970 3
Constrained 0.5109 0.2415 4
Unconstrained 0.9761 0.4615 12
Inertia is mean squared contingency coefficient
Eigenvalues for constrained axes:
CCA1 CCA2 CCA3 CCA4
0.24932 0.12090 0.08160 0.05904
Eigenvalues for unconstrained axes:
CA1 CA2 CA3 CA4 CA5 CA6 CA7 CA8 CA9 CA10
0.30637 0.13191 0.11516 0.10947 0.07724 0.07575 0.04871 0.03758 0.03106 0.02102
CA11 CA12
0.01254 0.00928
Call: cca(X = fitted(mod))
Inertia Rank
Total 0.5109
Unconstrained 0.5109 4
Inertia is mean squared contingency coefficient
Eigenvalues for unconstrained axes:
CA1 CA2 CA3 CA4
0.24932 0.12090 0.08160 0.05904
Call: cca(X = residuals(mod))
Inertia Rank
Total 0.9761
Unconstrained 0.9761 12
Inertia is mean squared contingency coefficient
Eigenvalues for unconstrained axes:
CA1 CA2 CA3 CA4 CA5 CA6 CA7 CA8 CA9 CA10
0.30637 0.13191 0.11516 0.10947 0.07724 0.07575 0.04871 0.03758 0.03106 0.02102
CA11 CA12
0.01254 0.00928
Achimill Agrostol Airaprae Alopgeni Anthodor Bellpere Bromhord Chenalbu
7 10 2 8 6 6 5 1
Cirsarve Comapalu Eleopalu Elymrepe Empenigr Hyporadi Juncarti Juncbufo
1 2 5 6 1 3 5 4
Lolipere Planlanc Poaprat Poatriv Ranuflam Rumeacet Sagiproc Salirepe
12 7 14 13 6 5 7 3
Scorautu Trifprat Trifrepe Vicilath Bracruta Callcusp
18 3 16 3 15 3
CCA1 CCA2 CCA3 CCA4
Chenalbu 1.5737337 -0.7842538 0.5503660 0.35108333
Cirsarve 0.5945146 -0.3714228 -0.2862647 0.88373727
Empenigr -1.8771953 -0.9904299 -0.2446222 0.04858656
CCA1 CCA2 CCA3 CCA4
1 -2.38829 -1.230652 -0.2363485 -0.3338258
A1 Moisture.L Moisture.Q Moisture.C
1 2.2630533 -0.62633470 -0.20456759 0.220761764
2 4.0510042 -0.47341146 -0.36986691 0.474939409
3 4.2752294 -0.07214500 -0.60797514 0.303213289
4 4.5398659 0.03192745 -1.12417368 0.932223234
5 5.0409406 -0.84235946 0.43000738 -0.291599200
6 5.1962100 -0.91316862 1.11354235 -0.804453944
7 4.2452549 -0.76452556 0.60464291 -0.484842066
8 5.0208369 0.43886340 0.08169514 0.132995916
9 4.2663219 0.10720486 -0.34067849 -0.675151598
10 4.0411356 -0.65472729 0.02832164 0.558402684
11 2.8280051 -0.45762457 0.63079135 -0.089977975
12 5.1204137 0.36328912 -0.69118581 -0.665622948
13 4.9034218 0.47069541 -0.54378271 -0.118643453
14 11.6455841 0.60920550 0.78341426 0.532852308
15 10.7829689 0.69208513 0.82190786 0.237311062
16 7.9892176 0.96421599 0.46793089 0.373647014
17 0.9218684 -0.15822891 0.14593271 1.189161582
18 3.1680733 -0.41737900 1.03352732 -0.236938282
19 -1.2003506 0.57033354 0.72777285 0.509955590
20 4.7876770 1.00324330 1.49898460 0.009202396
vegan documentation built on May 2, 2019, 5:51 p.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
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 |
model |
Show constrained ( |
newdata |
New data frame to be used in prediction or in
calibration. Usually this a new community data frame, but with
|
type |
The type of prediction, fitted values or residuals:
|
rank |
The rank or the number of axes used in the approximation.
The default is to use all axes (full rank) of the |
scaling |
logical, character, or numeric; Scaling or predicted
scores with the same meaning as in |
correlation, hill |
logical; correlation-like scores or Hill's
scaling as appropriate for RDA/ |
... |
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)
|
Example output
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-4
Call: cca(formula = dune ~ A1 + Management + Condition(Moisture), data
= dune.env)
Inertia Proportion Rank
Total 2.1153 1.0000
Conditional 0.6283 0.2970 3
Constrained 0.5109 0.2415 4
Unconstrained 0.9761 0.4615 12
Inertia is mean squared contingency coefficient
Eigenvalues for constrained axes:
CCA1 CCA2 CCA3 CCA4
0.24932 0.12090 0.08160 0.05904
Eigenvalues for unconstrained axes:
CA1 CA2 CA3 CA4 CA5 CA6 CA7 CA8 CA9 CA10
0.30637 0.13191 0.11516 0.10947 0.07724 0.07575 0.04871 0.03758 0.03106 0.02102
CA11 CA12
0.01254 0.00928
Call: cca(X = fitted(mod))
Inertia Rank
Total 0.5109
Unconstrained 0.5109 4
Inertia is mean squared contingency coefficient
Eigenvalues for unconstrained axes:
CA1 CA2 CA3 CA4
0.24932 0.12090 0.08160 0.05904
Call: cca(X = residuals(mod))
Inertia Rank
Total 0.9761
Unconstrained 0.9761 12
Inertia is mean squared contingency coefficient
Eigenvalues for unconstrained axes:
CA1 CA2 CA3 CA4 CA5 CA6 CA7 CA8 CA9 CA10
0.30637 0.13191 0.11516 0.10947 0.07724 0.07575 0.04871 0.03758 0.03106 0.02102
CA11 CA12
0.01254 0.00928
Achimill Agrostol Airaprae Alopgeni Anthodor Bellpere Bromhord Chenalbu
7 10 2 8 6 6 5 1
Cirsarve Comapalu Eleopalu Elymrepe Empenigr Hyporadi Juncarti Juncbufo
1 2 5 6 1 3 5 4
Lolipere Planlanc Poaprat Poatriv Ranuflam Rumeacet Sagiproc Salirepe
12 7 14 13 6 5 7 3
Scorautu Trifprat Trifrepe Vicilath Bracruta Callcusp
18 3 16 3 15 3
CCA1 CCA2 CCA3 CCA4
Chenalbu 1.5737337 -0.7842538 0.5503660 0.35108333
Cirsarve 0.5945146 -0.3714228 -0.2862647 0.88373727
Empenigr -1.8771953 -0.9904299 -0.2446222 0.04858656
CCA1 CCA2 CCA3 CCA4
1 -2.38829 -1.230652 -0.2363485 -0.3338258
A1 Moisture.L Moisture.Q Moisture.C
1 2.2630533 -0.62633470 -0.20456759 0.220761764
2 4.0510042 -0.47341146 -0.36986691 0.474939409
3 4.2752294 -0.07214500 -0.60797514 0.303213289
4 4.5398659 0.03192745 -1.12417368 0.932223234
5 5.0409406 -0.84235946 0.43000738 -0.291599200
6 5.1962100 -0.91316862 1.11354235 -0.804453944
7 4.2452549 -0.76452556 0.60464291 -0.484842066
8 5.0208369 0.43886340 0.08169514 0.132995916
9 4.2663219 0.10720486 -0.34067849 -0.675151598
10 4.0411356 -0.65472729 0.02832164 0.558402684
11 2.8280051 -0.45762457 0.63079135 -0.089977975
12 5.1204137 0.36328912 -0.69118581 -0.665622948
13 4.9034218 0.47069541 -0.54378271 -0.118643453
14 11.6455841 0.60920550 0.78341426 0.532852308
15 10.7829689 0.69208513 0.82190786 0.237311062
16 7.9892176 0.96421599 0.46793089 0.373647014
17 0.9218684 -0.15822891 0.14593271 1.189161582
18 3.1680733 -0.41737900 1.03352732 -0.236938282
19 -1.2003506 0.57033354 0.72777285 0.509955590
20 4.7876770 1.00324330 1.49898460 0.009202396
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