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

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. Please take a look at my code: <hansl> set echo off set messages off open AWM.gdt --quiet list L = CAN COMPR EEN FDD HICP ITN KSR printf "\n########## Gretl's native PCA ##########\n\n" pca L printf "\n########## Alternative PCA (using 'eigengen' function) ##########\n\n" matrix X = {L} matrix C = mcorr(X) matrix Eigenvector = {} matrix Eigenvalue = eigengen(C, &Eigenvector) matrix Proportion = zeros(rows(Eigenvalue), 1) matrix Cumulative = zeros(rows(Eigenvalue), 1) loop i = 1..rows(Eigenvalue) --quiet Proportion[i, 1] = Eigenvalue[i, 1]/sumc(Eigenvalue) Cumulative[i, 1] = sumc(Proportion[1:i]) endloop matrix Eigenvalue = Eigenvalue ~ Proportion ~ Cumulative rownames(Eigenvalue, "1 2 3 4 5 6 7") colnames(Eigenvalue, "Eigenvalue Proportion Cumulative") rownames(Eigenvector, "CAN COMPR EEN FDD HICP ITN KSR") colnames(Eigenvector, "PC1 PC2 PC3 PC4 PC5 PC6 PC7") printf "Principal Components Analysis\nn = %d\n\n", rows(X) printf "Eigenanalysis of the Correlation Matrix\n\n" printf "%15.4f\n", Eigenvalue printf "Eigenvectors (component loadings)\n\n" printf "%10.3f\n", Eigenvector </hansl> Best regards, Henrique Andrade