Re: [Gretl-users] Principal Components Analysis: "pca" command versus "eigengen" function

On Wed, 23 Aug 2017, Henrique Andrade wrote: > Dear Gretl Community, > > I would like to replicate the "pca" command using "eigengen" function > but I can't replicate the "signs behavior" of the component loadings. > Sorry if this is a very newbie/dummy question, but I really don't > understand the signal inversion in PC1 PC6 and PC7. The "component loadings" are eigenvectors of the relevant matrix (correlation or covariance) and eigenvectors are unique only up to an arbitrary (non-zero) real constant. In this case the loadings for PC1, PC6 and PC7 as produced by "pca" and by your eigengen procedure differ by a factor of -1. It can be shown that when they're multiplied into the component series they produce series that again just differ by a constant. Try this script: <hansl> set verbose off open AWM.gdt --quiet list L = CAN COMPR EEN FDD HICP ITN KSR smpl ok(L) --restrict pca L --save-all --quiet matrix X = {L} matrix E = {} eigengen(mcorr(X), &E) matrix stdX = (X .- meanc(X)) ./ sdc(X,1) list stdL = null loop i=1..cols(X) --quiet stdL += genseries(sprintf("stdx_%d", i), stdX[,i]) endloop list altPCs = null loop i = 1..cols(E) --quiet altPCs += genseries(sprintf("altPC%d", i), lincomb(stdL, E[,i])) endloop ols PC1 0 altPC1 --simple-print ols PC6 0 altPC6 --simple-print ols PC7 0 altPC7 --simple-print </hansl>