envfit  R Documentation 
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. For continuous varaibles
this is equal to fitting a linear trend surface (plane in 2D) for a
variable (see ordisurf
); this trend surface can be
presented by showing its gradient (direction of steepest increase)
using an arrow. The environmental variables are the dependent
variables that are explained by the ordination scores, and each
dependent variable is analysed separately.
## Default S3 method:
envfit(ord, env, permutations = 999, strata = NULL,
choices=c(1,2), display = "sites", w = weights(ord, display),
na.rm = FALSE, ...)
## S3 method for class 'formula'
envfit(formula, data, ...)
## S3 method for class 'envfit'
plot(x, choices = c(1,2), labels, arrow.mul, at = c(0,0),
axis = FALSE, p.max = NULL, col = "blue", bg, add = TRUE, ...)
## S3 method for class 'envfit'
scores(x, display, choices, arrow.mul=1, tidy = FALSE, ...)
vectorfit(X, P, permutations = 0, strata = NULL, w, ...)
factorfit(X, P, permutations = 0, strata = NULL, w, ...)
ord 
An ordination object or other structure from which the
ordination 
env 
Data frame, matrix or vector of environmental variables. The variables can be of mixed type (factors, continuous variables) in data frames. 
X 
Matrix or data frame of ordination scores. 
P 
Data frame, matrix or vector of environmental
variable(s). These must be continuous for 
permutations 
a list of control values for the permutations
as returned by the function 
formula , data 
Model 
na.rm 
Remove points with missing values in ordination scores
or environmental variables. The operation is casewise: the whole
row of data is removed if there is a missing value and

x 
A result object from 
choices 
Axes to plotted. 
tidy 
Return scores that are compatible with ggplot2:
all scores are in a single 
labels 
Change plotting labels. The argument should be a list
with elements 
arrow.mul 
Multiplier for vector lengths. The arrows are
automatically scaled similarly as in 
at 
The origin of fitted arrows in the plot. If you plot arrows
in other places then origin, you probably have to specify

axis 
Plot axis showing the scaling of fitted arrows. 
p.max 
Maximum estimated 
col 
Colour in plotting. 
bg 
Background colour for labels. If 
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
( 
w 
Weights used in fitting (concerns mainly 
... 
Parameters passed to 
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.
The ordination results are extracted with scores
and
all extra arguments are passed to the scores
. The fitted
models only apply to the results defined when extracting the scores
when using envfit
. For instance, scaling
in
constrained ordination (see scores.rda
,
scores.cca
) must be set in the same way in
envfit
and in the plot
or the ordination results (see
Examples).
The printed output of continuous variables (vectors) gives the
direction cosines which are the coordinates of the heads of unit
length vectors. In plot
these are scaled by their
correlation (square root of the column r2
) so that
“weak” predictors have shorter arrows than “strong”
predictors. You can see the scaled relative lengths using command
scores
. The plot
ted (and scaled) arrows are further
adjusted to the current graph using a constant multiplier: this will
keep the relative r2
scaled lengths of the arrows but tries
to fill the current plot. You can see the multiplier using
ordiArrowMul(result_of_envfit)
, and set it with the
argument arrow.mul
.
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 withingroup and total sums of
squares. See permutations
for additional details on
permutation tests in Vegan.
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
fitted vectors are similar to biplot arrows in constrained ordination
only when fitted to LC scores (display = "lc"
) and you set
scaling = "species"
(see scores.cca
). The
weighted fitting gives similar results to biplot arrows and class
centroids in cca
.
The lengths of arrows for fitted vectors are automatically adjusted
for the physical size of the plot, and the arrow lengths cannot be
compared across plots. For similar scaling of arrows, you must
explicitly set the arrow.mul
argument in the plot
command; see ordiArrowMul
and
ordiArrowTextXY
.
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, or a named list
of both.
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 
centroids 
Class centroids from 
r 
Goodness of fit statistic: Squared correlation coefficient 
permutations 
Number of permutations. 
control 
A list of control values for the permutations
as returned by the function 
pvals 
Empirical Pvalues 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.
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.
Jari Oksanen. The permutation test derives from the code suggested by Michael Scroggie.
A better alternative to vectors may be ordisurf
.
data(varespec, varechem)
library(MASS)
ord < metaMDS(varespec)
(fit < envfit(ord, varechem, perm = 999))
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 = 999, display = "lc")
plot(fit, p.max = 0.05, col = "red")
## 'scaling' must be set similarly in envfit and in ordination plot
plot(ord, type = "p", scaling = "sites")
fit < envfit(ord, varechem, perm = 0, display = "lc", scaling = "sites")
plot(fit, col = "red")
## Class variables, formula interface, and displaying the
## interclass variability with ordispider, and semitransparent
## white background for labels (semitransparent colours are not
## supported by all graphics devices)
data(dune)
data(dune.env)
ord < cca(dune)
fit < envfit(ord ~ Moisture + A1, dune.env, perm = 0)
plot(ord, type = "n")
with(dune.env, ordispider(ord, Moisture, col="skyblue"))
with(dune.env, points(ord, display = "sites", col = as.numeric(Moisture),
pch=16))
plot(fit, cex=1.2, axis=TRUE, bg = rgb(1, 1, 1, 0.5))
## Use shorter labels for factor centroids
labels(fit)
plot(ord)
plot(fit, labels=list(factors = paste("M", c(1,2,4,5), sep = "")),
bg = rgb(1,1,0,0.5))
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