cca.object {vegan} | R Documentation

## Result Object from Constrained Ordination with cca, rda or capscale

### Description

Ordination methods `cca`, `rda` and `capscale` return similar result objects. Function `capscale` `inherits` from `rda` and `rda` inherits from `cca`. This inheritance structure is due to historic reasons: `cca` was the first of these implemented in vegan. Hence the nomenclature in `cca.object` reflects `cca`. This help page describes the internal structure of the `cca` object for programmers.

### Value

A `cca` object has the following elements:

`call` | function call.
`colsum, rowsum` | Column and row sums in `cca`. In `rda`, item `colsum` contains standard deviations of species and `rowsum` is `NA`.
`grand.total` | Grand total of community data in `cca` and `NA` in `rda`.
`inertia` | Text used as the name of inertia.
`method` | Text used as the name of the ordination method.
`terms` | The `terms` component of the `formula`. This is missing if the ordination was not called with `formula`.
`terminfo` | Further information on terms with three subitems: `terms` which is like the `terms` component above, but lists conditions and constrainst similarly; `xlev` which lists the factor levels, and `ordered` which is `TRUE` to ordered factors. This is produced by vegan internal function `ordiTerminfo`, and it is needed in `predict.cca` with `newdata`. This is missing if the ordination was not called with `formula`.
`tot.chi` | Total inertia or the sum of all eigenvalues.
`pCCA, CCA, CA` | Actual ordination results for conditioned (partial), constrained and unconstrained components of the model. Any of these can be `NULL` if there is no corresponding component. Items `pCCA`, `CCA` and `CA` have similar structure, and contain following items: alias The names of the aliased constraints or conditions. Function `alias.cca` does not access this item directly, but it finds the aliased variables and their defining equations from the item `QR`. biplot Biplot scores of constraints. Only in `CCA`. centroids (Weighted) centroids of factor levels of constraints. Only in `CCA`. Missing if the ordination was not called with `formula`. eig Eigenvalues of axes. In `CCA` and `CA`. envcentre (Weighted) means of the original constraining or conditioning variables. In `pCCA` and in `CCA`. Fit The fitted values of standardized data matrix after fitting conditions. Only in `pCCA`. QR The QR decomposition of explanatory variables as produced by `qr`. The constrained ordination algorithm is based on `QR` decomposition of constraints and conditions (environmental data). The environmental data are first centred in `rda` or weighted and centred in `cca`. The QR decomposition is used in many functions that access `cca` results, and it can be used to find many items that are not directly stored in the object. For examples, see `coef.cca`, `coef.rda`, `vif.cca`, `permutest.cca`, `predict.cca`, `predict.rda`, `calibrate.cca`. For possible uses of this component, see `qr`. In `pCCA` and `CCA`. rank The rank of the component. tot.chi Total inertia or the sum of all eigenvalues of the component. u (Weighted) orthonormal site scores. Please note that scaled scores are not stored in the `cca` object, but they are made when the object is accessed with functions like `scores.cca`, `summary.cca` or `plot.cca`, or their `rda` variants. Only in `CCA` and `CA`. In `CCA` component these are the so-called linear combination scores. u.eig `u` scaled by eigenvalues. There is no guarantee that any `.eig` variants of scores will be kept in the future releases. v (Weighted) orthonormal species scores. If missing species were omitted from the analysis, this will contain attribute `na.action` that lists the omitted species. Only in `CCA` and `CA`. v.eig `v` weighted by eigenvalues. wa Site scores found as weighted averages (`cca`) or weighted sums (`rda`) of `v` with weights `Xbar`, but the multiplying effect of eigenvalues removed. These often are known as WA scores in `cca`. Only in `CCA`. wa.eig The direct result of weighted avaraging or weighted summation (matrix multiplication) with the resulting eigenvalue inflation. Xbar The standardized data matrix after previous stages of analysis. In `CCA` this is after possible `pCCA` or after partialling out the effects of conditions, and in `CA` after both `pCCA` and `CCA`. In `cca` the standardization is Chi-square, and in `rda` centring and optional scaling by species standard deviations using function `scale`.

### Author(s)

Jari Oksanen

### References

Legendre, P. and Legendre, L. (1998) Numerical Ecology. 2nd English ed. Elsevier.

### See Also

The description here provides a hacker's interface. For more user friendly acces to the `cca` object see `alias.cca`, `coef.cca`, `deviance.cca`, `predict.cca`, `scores.cca`, `summary.cca`, `vif.cca`, `weights.cca`, `spenvcor` or `rda` variants of these functions. You can use `as.mlm` to cast a `cca.object` into result of multiple response linear model (`lm`) in order to more easily find some statistics (which in principle could be directly found from the `cca.object` as well).

### Examples

    # Some species will be missing in the analysis, because only a subset
    # of sites is used below.
    data(dune)
    data(dune.env)
    mod <- cca(dune[1:15,] ~ ., dune.env[1:15,])
    # Look at the names of missing species
    attr(mod$CCA$v, "na.action")
    # Look at the names of the aliased variables:
    mod$CCA$alias
    # Access directly constrained weighted orthonormal species and site
    # scores, constrained eigenvalues and margin sums.
    spec <- mod$CCA$v
    sites <- mod$CCA$u
    eig <- mod$CCA$eig
    rsum <- mod$rowsum
    csum <- mod$colsum

[Package vegan version 1.8-6 Index]