R help - May 2005 - units of a biplot

Hello everybody,
I am afraid this might be a stupid question, but after scanning a little 
bit through the help archive and the internet, I didn't come up with an 
answer myself.
I have done a principle component analysis on a data set, which yields 
the mean response of 14 olfactory neurons to 16 different odors. When 
plotting the result in a biplot, it nicely shows me the odors in 
different positions in the principle component space. Additionally, the 
neurons are shown as vectors within this plot. My question now is: what 
are the units of the axes? When doing the principle component in IDL, 
the relative positions of the odors are the same, but units on the axes 
span a much wider range. Additionally I couldn't figure out what the 
units in the variable space (right and upper border in the biplot) do 
represent.
I really hope somebody can helpme with this,
Mathias Ditzen

First, I think you are talking about the princomp method of biplot, and 
not a general biplot.

There are many different biplots for PCA, some incorrectly implemented. 
The derivation is in MASS4 pp. 310-1, as well as the interpretation.  You 
need to understand what a biplot is to understand the units, which depend 
on the value of 'scale' and 'pc.biplot'.  See the note on the
help page
for biplot.princomp.

On Mon, 9 May 2005, Mathias Ditzen wrote:
> I am afraid this might be a stupid question, but after scanning a little
bit
> through the help archive and the internet, I didn't come up with an
answer
> myself.
> I have done a principle component analysis on a data set, which yields the 
> mean response of 14 olfactory neurons to 16 different odors. When plotting 
> the result in a biplot, it nicely shows me the odors in different positions
> in the principle component space. Additionally, the neurons are shown as 
> vectors within this plot. My question now is: what are the units of the
axes?
> When doing the principle component in IDL, the relative positions of the 
> odors are the same, but units on the axes span a much wider range. 
> Additionally I couldn't figure out what the units in the variable space
> (right and upper border in the biplot) do represent.
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595