The following dynamic plots demonstrate some issues handles in
- PCA as rotation of species
space: the graph shows a species space of three reindeer lichens
(Cladina). The dots show the abundance of each species in
sample plots. The axes are centred so that zero corresponds to the
average cover of each species. The crossed lines show the first
Principal Components. If you rotate the graph so that only first and
second PC are visible, you have performed the PCA.
- CA as rotation of spcies space:
The differences to PCA are
- Data are proportional. Because of this, you only have
independent informatin on two species: you know the proportion of
the third species when you sum together abundances of two other
species. Therefore points lay on a plane (2D) in the 3D space.
- Analysis is weighted: the size of the dot is proportional to
the total abundance of these three lichens. There are only two CA
axes, and they will lay on this plane, and the first axis as as
close as possible to heavy (large) points.
- CA distortion: Correspondence
Analysis of Bryce Canyon data shows marked arcs in 3D. These are
actually more complicated than the standard simple arc. These do not
describe meaningful features in the data and therefore they are
regarded as artefacts.
- DCA distortion: Detrended
Correspondence Analysis attempts to remove CA distortion, but it
brings along its own kind of artefacts. Spinning the graph, you see
that the plot is like a plane twisted in 3D. This is known as lolly
paper effect (in Queen's English) or as a lasagna effect (in US