Computes a fuzzy set for samples along a specified environmental or
experimental gradient based on
sample similarities and gradient values as weights. The fuzzy set memberships
represent the degree to which a sample is similar to one end of the
gradient while not similar to the other.
Usage
## S3 method for class 'formula'
fso(formula,dis,data,permute=FALSE,...)
## Default S3 method:
fso(x,dis,permute=FALSE,...)
## S3 method for class 'fso'
summary(object,...)
Arguments
formula
a formula in the form of ~x+y+z (no LHS)
dis
a dist object such as that returned by dist,
dsvdis, or vegdist
data
a data frame that holds variables listed in the formula
permute
if FALSE, estimate probabilities from Z distribution for correlation;
if numeric, estimate probabilities from permutation of input
x
a numerical vector, a matrix, or numeric dataframe
object
an object of class ‘fso’
...
generic arguments for future use
Details
The algorithm converts the input to a full symmetric similarity matrix
and bounds [0,1] (if necessary). It then calculates
several fuzzy sets:
where y_{i,j} is the similarity of sample i to sample j.
A separate fuzzy set ordination is calculated for each term in the
formula. If x is a matrix or dataframe a separate fuzzy set ordination is
calculated for each column or field.
If permute is numeric, the permutation is performed permute-1 times,
and the probability is estimated as
(correlations >= observed + 1)/permute.
Value
An object of class ‘fso’ which has the following elements:
mu
the fuzzy membership values for individual plots in the fuzzy
set. If x is a matrix or dataframe then mu is also a matrix of the
same dimension.
data
a copy of data vector or matrix y
r
the correlation between the original vector and the fuzzy
set. If x is a matrix or dataframe then r is a vector with length equal
to the number of columns in the matrix or dataframe.
p
the probability of obtaining a correlation between the data
and fuzzy set as large as observed
d
the correlation of pair-wise distances among each fuzzy set
compared to the dissimilarity matrix from which the fso was constructed
var
the variable name(s) from matrix y
Note
Fuzzy set ordination is a method of multivariate analysis employed in
vegetation analysis.
fso can be run with the first argument either a dataframe or a formula
(with no left hand side). The formula version has distinct advantages:
1) The data= argument allows the user to specify a data frame
containing the variables of interest. In this way variables
need not be local.
2) The formula version handles categorical variables by converting
them to dummy variables. In the default version, all variables
must be quantitative or binary.
3) The formula version is somewhat more graceful about handling
missing values in the data.