[R] reproducing scaling used in biplot(pc.biplot=TRUE)

[Kim Milferstedt]

Hello,

I'd like to reproduce the standard biplot with pc.biplot=TRUE using 
xyplot in lattice in order to assign different symbols to groupings 
of observations (similar to the example in fig. 11.2 on page 285 in 
DAAG). In order to reproduce the biplots I need to know how to scale 
the observations and variables. In ?biplot.princomp I found that the 
variables are scaled by 'lambda ^ scale' and the observations by 
'lambda ^ (1-scale)' where lambda are the singular values. Are the 
singular values in princomp the square of the sdev of the components? 
What value for 'scale' does R select when I don't specify 'scale' as 
an argument? And how do I extract the value for 'scale'?

In addition the help file says when pc.biplot=TRUE, 'lambda equals 
1', and observations are scaled up by sqrt(n) and variables are 
scaled down by sqrt(n). I'm having trouble understanding the meaning 
of "scaling up" and "scaling down". Does this mean "multiply the 
score of the observations by sqrt(n)" and "divide the loadings of the 
principal components by sqrt(n)"? Is 'scale' meaningless for 
pc.biplot=TRUE as now the scaling is based on lambda =1 and sqrt(n) 
only? What happens when pc.biplot=FALSE

In Details, ?pc.biplot it says "Gabriel and Odoroff (1990) use the 
same definitions, but their plots actually correspond to 'pc.biplot = 
TRUE'." A little earlier in the help file, it is stated that 
pc.biplot=TRUE corresponds to the Gabriel 1971. Are biplots in 
Gabriel (1971) and in Gabriel and Odoroff (1990) used identical?

It would help me very much if somebody had an piece of example code 
where a biplot is constructed "from the scratch" according to Gabriel 1971.

Thanks a lot,

Kim

__________________________________________

Kim Milferstedt
University of Illinois at Urbana-Champaign
Department of Civil and Environmental Engineering
4125 Newmark Civil Engineering Building
205 North Mathews Avenue MC 250
Urbana, IL 61801
USA
phone: (001) 217 333-9663
fax: (001) 217 333-6968
email: milferst at uiuc.edu
http://cee.uiuc.edu/research/morgenroth