goodness.cca  R Documentation 
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, choices, display = c("species", "sites"),
model = c("CCA", "CA"), summarize = FALSE, addprevious = FALSE, ...)
inertcomp(object, display = c("species", "sites"),
unity = FALSE, proportional = FALSE)
spenvcor(object)
intersetcor(object)
vif.cca(object)
## S3 method for class 'cca'
alias(object, names.only = FALSE, ...)
object 
A result object from 
display 
Display 
choices 
Axes shown. Default is to show all axes of the

model 
Show constrained ( 
summarize 
Show only the accumulated total. 
addprevious 
Add the variation explained by previous components
when 
unity 
Scale inertia components to unit sum (sum of all items is 1). 
proportional 
Give the inertia components as proportional for
the corresponding total of the item (sum of each row is 1). This
option takes precedence over 
names.only 
Return only names of aliased variable(s) instead of defining equations. 
... 
Other parameters to the functions. 
Function goodness
gives cumulative proportion of inertia
accounted by species up to chosen axes. The proportions can be
assessed either by species or by sites depending on the argument
display
, but species are not available in distancebased
dbrda
. The function is not implemented for
capscale
.
Function inertcomp
decomposes the inertia into partial,
constrained and unconstrained components for each site or species.
Legendre & De Cáceres (2012) called these inertia
components as local contributions to betadiversity (LCBD) and
species contributions to betadiversity (SCBD), and they give these
as relative contributions summing up to unity (argument
unity = TRUE
). For this interpretation, appropriate dissimilarity
measures should be used in dbrda
or appropriate
standardization in rda
(Legendre & De
Cáceres 2012). The function is not implemented for
capscale
.
Function spenvcor
finds the socalled “species –
environment correlation” or (weighted) correlation of
weighted average scores and linear combination scores. This is a bad
measure of goodness of ordination, because it is sensitive to extreme
scores (like correlations are), and very sensitive to overfitting or
using too many constraints. Better models often have poorer
correlations. Function ordispider
can show the same
graphically.
Function intersetcor
finds the socalled “interset
correlation” or (weighted) correlation of weighted averages scores
and constraints. The defined contrasts are used for factor
variables. This is a bad measure since it is a correlation. Further,
it focuses on correlations between single contrasts and single axes
instead of looking at the multivariate relationship. Fitted vectors
(envfit
) provide a better alternative. Biplot scores
(see scores.cca
) are a multivariate alternative for
(weighted) correlation between linear combination scores and
constraints.
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, or
only their names with argument names.only = TRUE
.
The functions return matrices or vectors as is appropriate.
Jari Oksanen. The vif.cca
relies heavily on the code by
W. N. Venables. alias.cca
is a simplified version of
alias.lm
.
Greenacre, M. J. (1984). Theory and applications of correspondence analysis. Academic Press, London.
Gross, J. (2003). Variance inflation factors. R News 3(1), 13–15.
Legendre, P. & De Cáceres, M. (2012). Beta diversity as the variance of community data: dissimilarity coefficients and partitioning. Ecology Letters 16, 951–963. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/ele.12141")}
cca
, rda
, dbrda
,
capscale
.
data(dune)
data(dune.env)
mod < cca(dune ~ A1 + Management + Condition(Moisture), data=dune.env)
goodness(mod, addprevious = TRUE)
goodness(mod, addprevious = TRUE, summ = TRUE)
# Inertia components
inertcomp(mod, prop = TRUE)
inertcomp(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))
# The standard correlations (not recommended)
## IGNORE_RDIFF_BEGIN
spenvcor(mod)
intersetcor(mod)
## IGNORE_RDIFF_END
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