apt | R Documentation |
Compute the additive planar transform of a (dataset of) compositions or its inverse.
apt( x ,...)
aptInv( z ,..., orig=gsi.orig(z))
x |
a composition or a matrix of compositions, not necessarily closed |
z |
the apt-transform of a composition or a matrix of alr-transforms of compositions |
... |
generic arguments, not used. |
orig |
a compositional object which should be mimicked by the inverse transformation. It is especially used to reconstruct the names of the parts. |
The apt-transform maps a composition in the D-part real-simplex
linearly to a D-1 dimensional euclidian vector. Although the
transformation does not reach the whole R^{D-1}
, resulting covariance
matrices are typically of full rank.
The data can then
be analysed in this transformation by all classical multivariate
analysis tools not relying on distances. See
cpt
and ipt
for alternatives. The
interpretation of the results is easy since the relation to the first
D-1 original variables is preserved.
The additive planar transform is given by
apt(x)_i := clo(x)_i, i=1,\ldots,D-1
apt
gives the centered planar transform,
aptInv
gives closed compositions with the given apt-transforms
K.Gerald v.d. Boogaart http://www.stat.boogaart.de
van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.cageo.2006.11.017")}.
alr
,cpt
,ipt
(tmp <- apt(c(1,2,3)))
aptInv(tmp)
aptInv(tmp) - clo(c(1,2,3)) # 0
data(Hydrochem)
cdata <- Hydrochem[,6:19]
pairs(apt(cdata),pch=".")
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.