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vegan (version 2.6-8)

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 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 cca
alias(object, names.only = FALSE, ...)

Value

The functions return matrices or vectors as is appropriate.

Arguments

object

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

display

Display "species" or "sites". Species are not available in dbrda and capscale.

choices

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

model

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

summarize

Show only the accumulated total.

addprevious

Add the variation explained by previous components when statistic="explained". For model = "CCA" add conditioned (partialled out) variation, and for model = "CA" add both conditioned and constrained variation. This will give cumulative explanation with previous components.

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 unity.

names.only

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

...

Other parameters to the functions.

Author

Jari Oksanen. The vif.cca relies heavily on the code by W. N. Venables. alias.cca is a simplified version of alias.lm.

Details

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 distance-based 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 beta-diversity (LCBD) and species contributions to beta-diversity (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 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.

Legendre, P. & De Cáceres, M. (2012). Beta diversity as the variance of community data: dissimilarity coefficients and partitioning. Ecology Letters 16, 951--963. tools:::Rd_expr_doi("10.1111/ele.12141")

See Also

cca, rda, dbrda, capscale.

Examples

Run this code
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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