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

From: Kim Milferstedt <milferst_at_uiuc.edu>
Date: Tue 16 May 2006 - 07:54:46 EST


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 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
phone: (001) 217 333-9663
fax: (001) 217 333-6968
email: milferst@uiuc.edu

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