be used to assess the goodness of fit for individual sites or
alias.cca can be used to
analyse linear dependencies among constraints and conditions. In
addition, there are some other diagnostic tools (see 'Details').
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## S3 method for class 'cca' goodness(object, display = c("species", "sites"), choices, model = c("CCA", "CA"), statistic = c("explained", "distance"), summarize = FALSE, addprevious = FALSE, ...) inertcomp(object, display = c("species", "sites"), statistic = c("explained", "distance"), proportional = FALSE) spenvcor(object) intersetcor(object) vif.cca(object) ## S3 method for class 'cca' alias(object, names.only = FALSE, ...)
A result object from
Axes shown. Default is to show all axes of the
Show constrained (
Show only the accumulated total.
Add the variation explained by previous components
Give the inertia components as proportional for the corresponding total.
Return only names of aliased variable(s) instead of defining equations.
Other parameters to the functions.
goodness gives the diagnostic statistics for species
or sites. The alternative statistics are the cumulative proportion of
inertia accounted for up to the axes, and the residual distance left
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.
spenvcor finds the so-called “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
ordispider can show the same
intersetcor finds the so-called “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
scores.cca) are a multivariate alternative for
(weighted) correlation between linear combination scores and
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
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.
It is a common practise to use
goodness statistics to remove
species from ordination plots, but this may not be a good idea, as the
total inertia is not a meaningful concept in
cca, in particular
for rare species.
Jari Oksanen. The
vif.cca relies heavily on the code by
W. N. Venables.
alias.cca is a simplified version of
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.
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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, stat="d") # 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) spenvcor(mod) intersetcor(mod)
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