predict can be used to find site and species scores
with new data sets. Functions goodness and inertcomp can
be used to assess the goodness of fit for individual sites or
species. Function vif.cca and alias.cca can be used to
analyse linear dependencies among constraints and conditions. In
addition, there are some other diagnostic tools (see 'Details').## S3 method for class 'cca':
goodness(object, display = c("species", "sites"), choices,
model = c("CCA", "CA"), statistic = c("explained", "distance"),
summarize = FALSE, ...)
inertcomp(object, display = c("species", "sites"),
statistic = c("explained", "distance"), proportional = FALSE)
vif.cca(object)
## S3 method for class 'cca':
alias(object, ...)
## S3 method for class 'cca':
fitted(object, model = c("CCA", "CA"), ...)
## S3 method for class 'cca':
predict(object, newdata, type = c("response", "wa", "sp", "lc"),
rank = "full", model = c("CCA", "CA"), scaling = FALSE, ...)
## S3 method for class 'cca':
coef(object, ...)"species" or "sites"."model"."CCA") or unconstrained
("CA") results."explained" gives the cumulative
percentage accounted for, "distance" shows the residual
distances.type = "wa" and
type = "sp" this must be the community data, for type =
"lc" a data frame of environmental data (constraints and
"response"
gives an approximation of the original data matrix, "wa" the
site scores as weighted averages of the community data, "lc"
the site scores as linear combinations of envi"model".goodness gives the diagnostic statistics for species
or sites. The alternative statistics are the cumulative proportion of
inertia accounted for by the axes, or the residual distance left
unaccounted for. The conditional (``partialled out'') constraints are
always regarded as explained and included in the statistics. Function inertcomp decomposes the inertia into partial,
constrained and unconstrained components for each site or
species. Instead of inertia, the function can give the total
dispersion or distances from the centroid for each component.
Function vif.cca gives the variance inflation factors for each
constraint or contrast in factor constraints. In partial ordination,
conditioning variables are analysed together with constraints. Variance
inflation is a diagnostic tool to identify useless constraints. A
common rule is that values over 10 indicate redundant
constraints. If later constraints are complete linear combinations of
conditions or previous constraints, they will be completely removed
from the estimation, and no biplot scores or centroids are calculated
for these aliased constraints. A note will be printed with default
output if there are aliased constraints. Function alias will
give the linear coefficients defining the aliased constraints.
Function fitted gives the approximation of the original data
matrix from the ordination result. Function residuals gives
the approximation of the original data from the unconstrained
ordination.
The fitted.cca and
residuals.cca function
both have the same marginal totals as the original data matrix, and
their entries do not add up to the original data. They 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 (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. The function can be used with new data, and it can be used to
add new species or site sccores to existing ordinations. The function
returns (weighted) orthornormal 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. 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.
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.
Gross, J. (2003). Variance inflation factors. R News 3(1), 13--15.
cca, rda, capscale, vif.data(dune)
data(dune.env)
mod <- cca(dune ~ A1 + Management + Condition(Moisture), data=dune.env)
goodness(mod)
goodness(mod, summ = TRUE)
# Inertia components
inertcomp(mod, prop = TRUE)
inertcomp(mod, stat="d")
# Definition of the concepts 'fitted' and 'residuals'
mod
cca(fitted(mod))
cca(residuals(mod))
# vif.cca
vif.cca(mod)
# Aliased constraints
mod <- cca(dune ~ ., dune.env)
mod
vif.cca(mod)
alias(mod)
with(dune.env, table(Management, Manure))
# 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)Run the code above in your browser using DataLab