[R] Interpretation of PC loadings

[Laura Quinn]

Hello,

Following on from a paper by Ludwig, Horel and Whiteman in 2004, I have
been using PCA to identify surface wind patterns. In the paper they
approach the problem using the "real vector approach", that is, they
create paired (u,v) vectors for the wind data, in effect artificially
doubling the number of variables, then perform the pca, subsequently repairing the
output and plotting the paired site loadings onto a geographical map and
interpreting the plotted vectors as dominant wind flow patterns.

I have followed their approach, using prcomp() in R, using retx=FALSE and
plotting the pairings from the pca$rotation output. When I replot these
vectors onto a map it seems that a spurious angle has been introduced into
the data (ie the data seem to be angled at approx 45 degrees from where I
would expect them to lie).

Due to this I've also tried switching retx=TRUE and plotting pca$x though
the output seems quite different. I have looked at the help section for
prcomp but it doesn't seem very explicit in it's explanation (ie does $x
take the same form as $rotation - will it be analagous to plot them in the
same fashion for instance?)

Could someone advise me which method will be more reliable in terms of
revealing underlying flow direction when remapping onto the original (x,y)
map?

Any advice most welcome!

Thank you,

Laura Quinn
Institute of Atmospheric Science
School of Earth and Environment
University of Leeds
Leeds
LS2 9JT

tel: +44 113 343 1596
fax: +44 113 343 6716
mail: laura at env.leeds.ac.uk