varipart {ade4} | R Documentation

## Partition of the variation of a response multivariate table by 2 explanatory tables

### Description

The function partitions the variation of a response table (usually community data) with respect to two explanatory tables. The function performs the variation partitioning based on redundancy analysis (RDA, if `dudiY` is obtained by `dudi.pca`) or canonical correspondance analysis (CCA, if `dudiY` is obtained by `dudi.coa`) and computes unadjusted and adjusted R-squared. The significance of R-squared are evaluated by a randomization procedure where the rows of the explanatory tables are permuted.

### Usage

    varipart(Y, X, W = NULL, nrepet = 999, type = c("simulated", "parametric"),
    scale = FALSE, ...)
    ## S3 method for class 'varipart'
    print(x, ...)

### Arguments

`Y` | a vector, matrix or data frame or an object of class `dudi`. If not a `dudi` object, the data are trated by a principal component analysis (`dudi.pca`).
`X, W` | dataframes or matrices of explanatory (co)variables (numeric and/or factor variables). By default, no covariables are considered (`W` is `NULL`) and this case corresponds to simple caonical ordination.
`nrepet` | an integer indicating the number of permutations .
`type` | a character specifying the algorithm which should be used to adjust R-squared (either `"simulated"` or \ code"parametric").
`scale` | If `Y` is not a dudi, a `logical` indicating if variables should be scaled
`...` | further arguments passed to `as.krandtest` or `as.randtest` (if no covariables are considered) for function `varipart`.
`x` | an object of class `varipart`

### Details

Two types of algorithm are provided to adjust R-squared. The "simulated" procedure estimates the unadjusted R-squared expected under the null hypothesis H0 and uses it to adjust the observed R-squared as follows: R2.adj = 1 - (1 - R2) / (1 - E(R2|H0)) with R2.adj the adjusted R-squared and R2 the unadjusted R-squared. The "parametric" procedure performs the Ezequiel's adjustement on the unadjusted R-squared as: R2.adj = 1 - (1 - R2) / (1 - p / (n - 1)) where n is the number of sites, and p the number of predictors.

### Value

It returns an object of class `varipart`. It is a `list` with:

`test`

  the significance test of fractions [ab], [bc], and [abc] based on randomization procedure. An object of class `krandtest`

`R2`

  unadjusted estimations of fractions [a], [b], [c], and [d]

`R2.adj`

  adjusted estimations of fractions [a], [b], [c], and [d]

`call`

  the matched call

### Author(s)

Stephane Dray stephane.dray@univ-lyon1.fr and Sylvie Clappe sylvie.clappe@univ-lyon1.fr

### References

Borcard, D., P. Legendre, and P. Drapeau. 1992. Partialling out the spatial component of ecological variation. Ecology 73:1045.

Peres-Neto, P. R., P. Legendre, S. Dray, and D. Borcard. 2006. Variation partitioning of species data matrices: estimation and comparison of fractions. Ecology 87:2614–2625.

### See Also

`pcaiv`

### Examples

    data(mafragh)

    # PCA on response table Y
    Y <- mafragh$flo
    dudiY <- dudi.pca(Y, scannf = FALSE, scale = FALSE)

    # Variation partitioning based on RDA
    # without covariables
    vprda <- varipart(dudiY,  mafragh$env)
    vprda
    # Variation partitioning based on RDA
    # with covariables and parametric estimation
    vprda <- varipart(dudiY,  mafragh$env, mafragh$xy, type = "parametric")
    vprda
    names(vprda)

[Package ade4 version 1.7-13 Index]