envfit {vegan} | R Documentation

## Fits an Environmental Vector or Factor onto an Ordination

### Description

The function fits environmental vectors or factors onto an ordination. The projections of points onto vectors have maximum correlation with corresponding environmental variables, and the factors show the averages of factor levels.

### Usage

    ## Default S3 method:
    envfit(X, P, permutations = 0, strata, choices=c(1,2), ...)
    ## S3 method for class 'formula':
    envfit(formula, data, ...)
    ## S3 method for class 'envfit':
    plot(x, choices = c(1,2), arrow.mul, at = c(0,0), axis = FALSE,
        p.max = NULL, col = "blue", add = TRUE, ...)
    ## S3 method for class 'envfit':
    scores(x, display, choices, ...)
    vectorfit(X, P, permutations = 0, strata, choices=c(1,2),
          display = c("sites", "lc"), w = weights(X), ...)
    factorfit(X, P, permutations = 0, strata, choices=c(1,2),
          display = c("sites", "lc"), w = weights(X), ...)

### Arguments

`X` | Ordination configuration.
`P` | Matrix or vector of environmental variable(s).
`permutations` | Number of permutations for assessing significance of vectors or factors.
`formula, data` | Model `formula` and data.
`x` | A result object from `envfit`.
`choices` | Axes to plotted.
`arrow.mul` | Multiplier for vector lengths. The arrows are automatically scaled similarly as in `plot.cca` if this is not given and `add = TRUE`.
`at` | The origin of fitted arrows in the plot. If you plot arrows in other places then origin, you probably have to specify `arrrow.mul`.
`axis` | Plot axis showing the scaling of fitted arrows.
`p.max` | Maximum estimated P value for displayed variables. You must calculate P values with setting `permutations` to use this option.
`col` | Colour in plotting.
`add` | Results added to an existing ordination plot.
`strata` | An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata.
`display` | In fitting functions these are ordinary site scores or linear combination scores (`"lc"`) in constrained ordination (`cca`, `rda`, `capscale`). In `scores` function they are either `"vectors"` or `"factors"` (with synonyms `"bp"` or `"cn"`, resp.).
`w` | Weights used in fitting (concerns mainly `cca` and `decorana` results which have nonconstant weights).
`...` | Parameters passed to `scores`.

### Details

Function `envfit` finds vectors or factor averages of environmental variables. Function `plot.envfit` adds these in an ordination diagram. If `X` is a `data.frame`, `envfit` uses `factorfit` for `factor` variables and `vectorfit` for other variables. If `X` is a matrix or a vector, `envfit` uses only `vectorfit`. Alternatively, the model can be defined a simplified model `formula`, where the left hand side must be an ordination result object or a matrix of ordination scores, and right hand side lists the environmental variables. The formula interface can be used for easier selection and/or transformation of environmental variables. Only the main effects will be analysed even if interaction terms were defined in the formula.

Functions `vectorfit` and `factorfit` can be called directly. Function `vectorfit` finds directions in the ordination space towards which the environmental vectors change most rapidly and to which they have maximal correlations with the ordination configuration. Function `factorfit` finds averages of ordination scores for factor levels. Function `factorfit` treats ordered and unordered factors similarly.

If `permutations` > 0, the `significance' of fitted vectors or factors is assessed using permutation of environmental variables. The goodness of fit statistic is squared correlation coefficient (r^2). For factors this is defined as r^2 = 1 - ss_w/ss_t, where ss_w and ss_t are within-group and total sums of squares.

User can supply a vector of prior weights `w`. If the ordination object has weights, these will be used. In practise this means that the row totals are used as weights with `cca` or `decorana` results. If you do not like this, but want to give equal weights to all sites, you should set `w = NULL`. The weighted fitting gives similar results to biplot arrows and class centroids in `cca`. For complete similarity between fitted vectors and biplot arrows, you should set `display = "lc"` (and possibly `scaling = 2`).

The results can be accessed with `scores.envfit` function which returns either the fitted vectors scaled by correlation coefficient or the centroids of the fitted environmental variables.

### Value

Functions `vectorfit` and `factorfit` return lists of classes `vectorfit` and `factorfit` which have a `print` method. The result object have the following items:

`arrows` | Arrow endpoints from `vectorfit`. The arrows are scaled to unit length.
`centroids` | Class centroids from `factorfit`.
`r` | Goodness of fit statistic: Squared correlation coefficient
`permutations` | Number of permutations.
`pvals` | Empirical P-values for each variable.

Function `envfit` returns a list of class `envfit` with results of `vectorfit` and `envfit` as items.
Function `plot.envfit` scales the vectors by correlation.

### Note

Fitted vectors have become the method of choice in displaying environmental variables in ordination. Indeed, they are the optimal way of presenting environmental variables in Constrained Correspondence Analysis `cca`, since there they are the linear constraints. In unconstrained ordination the relation between external variables and ordination configuration may be less linear, and therefore other methods than arrows may be more useful. The simplest is to adjust the plotting symbol sizes (`cex`, `symbols`) by environmental variables. Fancier methods involve smoothing and regression methods that abound in R, and `ordisurf` provides a wrapper for some.

### Author(s)

Jari Oksanen. The permutation test derives from the code suggested by Michael Scroggie.

### See Also

A better alternative to vectors may be `ordisurf`.

### Examples

    data(varespec)
    data(varechem)
    library(MASS)
    ord <- metaMDS(varespec)
    (fit <- envfit(ord, varechem, perm = 1000))
    scores(fit, "vectors")
    plot(ord)
    plot(fit)
    plot(fit, p.max = 0.05, col = "red")
    ## Adding fitted arrows to CCA. We use "lc" scores, and hope
    ## that arrows are scaled similarly in cca and envfit plots
    ord <- cca(varespec ~ Al + P + K, varechem)
    plot(ord, type="p")
    fit <- envfit(ord, varechem, perm = 1000, display = "lc")
    plot(fit, p.max = 0.05, col = "red")
    ## Class variables, formula interface, and displaying the
    ## inter-class variability with `ordispider'
    data(dune)
    data(dune.env)
    attach(dune.env)
    ord <- cca(dune)
    fit <- envfit(ord ~ Moisture + A1, dune.env)
    plot(ord, type = "n")
    ordispider(ord, Moisture, col="skyblue")
    points(ord, display = "sites", col = as.numeric(Moisture), pch=16)
    plot(fit, cex=1.2, axis=TRUE)

[Package vegan version 1.8-6 Index]