posvectord | R Documentation |
Position Vector Ordination (PVO) finds ordination axes that go through sample points in species space and maximize the projections of other points onto them. These are similar to Principal Components. Species Vector Ordination (SVO) finds a set of species that maximize the projections of other species on species axes. This also can be similar to Principal Components and can be used to select a subset of species that cover most of the variance in the data.
posvectord(x, scale = FALSE)
spvectord(x, scale = FALSE)
## S3 method for class 'posvectord'
plot(x, ...)
x |
Input data. |
scale |
Scale variables to unit variance. |
... |
Other arguments (passed to |
Position Vector Ordination (PVO, function posvectord
) is a
simple educational method that resembles Principal Component
Analysis, PCA (Orlóci 1966, 1973a). Function posvectord
positions vectors from the data centroid (origin) to sample points
in species space and evaluates the projections of other sample
vectors on these positioned axes, and selects the one with highest
total projection as the ordination axis. Then the effects of that
selected axis are removed from the covariance matrix, zeroing the
row and column of selected sampling unit, and the process is
repeated. Principal Components maximize this projection, but PVO
axes can be close to the Principal Component, in particular in the
large data sets with many observations. The method was proposed as
a computationally light approximation to PCA suitable for the
computers of 1960s (Orlóci 1966). Now it can only be regarded as
historically interesting, and also as an educational tool in
introducing PCA.
Species Vector Ordination (SVO; function spvectord
) is
similar, but it picks the species vector that maximizes the species
projected onto that vector (Orlóci 1973b). The method picks the
species or variable that explains largest proportion of variance
and uses the centred values of this variable as the axis. Then it
orthogonalizes all species or variables to that selected axis and
repeats the selection process. PCA finds a linear combination of
species or variables that minimizes the residual variance, but in
SVO only one species or variable is used. The axes are named by the
species or variables, and the axis scores are the centred
(residual) observed values. The resulting plot has orthogonalized
set of species as axes. SVO can be similar to PCA, in particular
when some few species contribute most of the the total
variance. The method only has educational use in explaining PCA in
species space. Orlóci (1973b) suggesed SVO as a method of selecting
a subset of species or variables that contributes most of the
variance in the data. The current spvectord
function can
also be used for this purpose, although it is mainly geared for
ordination. dave package has function orank
specifically written for variable or species selection using the
same algorithm.
posvectord
returns an object of class
"posvectord"
, and spvectord
returns an object of
class "spvectord"
that inherits from
"posvectord"
. Both result objects have the following
elements:
points
: The ordination scores. In SVO, these are
named by the species (variable) the axes is based on, the
numerical scores are the centred (residual) values of
observed data. In PVO, they are called as PVO, and they are
scaled similarly as in PCA and can reconstitute
(a low-rank approximation of) covariances.
totvar
: The total variance in the input data.
eig
: Eigenvalues of axes.
Orlóci, L. (1966) Geometric models in ecology. I. The theory and application of some ordination methods. J. Ecol. 54: 193–215.
Orlóci, L. (1973a) Ordination by resemblance matrices. In: R. H. Whittaker (ed.) Ordination and Classification of Communities. Handbook of Vegetation Science 5: 249–286.
Orlóci, L. (1973b) Ranking characters by dispersion criterion. Nature 244: 371–373.
polarord
(Polar Ordination) is a similar
educational tool to approximate Principal Coordinates Analysis
(PCoA).
data(spurn)
spvectord(spurn)
m <- posvectord(spurn)
m
plot(m)
if (require(vegan, quietly = TRUE)) {
plot(procrustes(rda(spurn), m, choices=1:2))
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.