Hi there, I'm puzzled about the axis scaling in the PCA biplot.
Here's an example. library(pdfCluster) # package cepp seems to have the same data set. data(oliveoil) # 572 observations 10 variables olive <- oliveoil[,3:10] # numerical variables prolive <- princomp(olive) summary(prolive) # Importance of components: # Comp.1 Comp.2 Comp.3 Comp.4 # Standard deviation 479.7299024 150.82827868 45.394449751 27.522646558 # Proportion of Variance 0.8970072 0.08866821 0.008031707 0.002952451 # Cumulative Proportion 0.8970072 0.98567544 0.993707152 0.996659603 # Comp.5 Comp.6 Comp.7 Comp.8 # Standard deviation 24.78169442 1.196956e+01 7.1390744088 6.9756965249 # Proportion of Variance 0.00239367 5.584168e-04 0.0001986489 0.0001896608 # Cumulative Proportion 0.99905327 9.996117e-01 0.9998103392 1.0000000000 plot(prolive$scores) # Scaling of this plot reproduces the variances of the components given in the summary, # as does cov(prolive$scores). This seems all fine, however... biplot(prolive) I have no idea what the numbers on the axes of the biplot are, at least not the larger ones. Chances are the smaller ones indicate the loadings. The larger ones are neither the same as in the first plot, nor are they standardised to one, but they seem to be standardised somehow, as the range on x- and y-axis looks the same, which it shouldn't be if variances represented the PCA eigenvalues. Can anyone explain this to me? Actually the help page of biplot.princomp says something on this, but I don't get my head around it: "scale The variables are scaled by |lambda ^ scale| and the observations are scaled by |lambda ^ (1-scale)| where |lambda| are the singular values as computed by |princomp <https://www.rdocumentation.org/link/princomp?package=stats&version=3.6.2>|. Normally |0 <= scale <= 1|, and a warning will be issued if the specified |scale| is outside this range." The default value of scale seems to be 1, but then (1-scale) is zero so I'd assume data to be unscaled, but that should have reproduced the "plot" scale, shouldn't it? Thanks, Christian -- Christian Hennig Dipartimento di Scienze Statistiche "Paolo Fortunati", Universita di Bologna, phone +39 05120 98163 christian.hen...@unibo.it [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.