vegan (version 2.0-10)

goodness.cca: Diagnostic Tools for [Constrained] Ordination (CCA, RDA, DCA, CA, PCA)

Description

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').

Usage

## 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)
spenvcor(object)
intersetcor(object)
vif.cca(object)
## S3 method for class 'cca':
alias(object, names.only = FALSE, ...)

Arguments

object

A result object from cca, rda, capscale or decorana.

display

Display "species" or "sites".

choices

Axes shown. Default is to show all axes of the "model".

model

Show constrained ("CCA") or unconstrained ("CA") results.

statistic

Statistic used: "explained" gives the cumulative percentage accounted for, "distance" shows the residual distances. Distances are not available for sites in constrained or partial analyses.

summarize

Show only the accumulated total.

proportional

Give the inertia components as proportional for the corresponding total.

names.only

Return only names of aliased variable(s) instead of defining equations.

...

Other parameters to the functions.

Value

• The functions return matrices or vectors as is appropriate.

Details

Function goodness gives the diagnostic statistics for species or sites. The alternative statistics are the cumulative proportion of inertia accounted for by the axes, and 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 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 correlations. Function ordispider can show the same graphically.

Function 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 (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.

References

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.

See Also

cca, rda, capscale, decorana, vif.

Examples

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")
# 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)