8:07 p.m.
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
8:58 p.m.
New subject: Principal Components Analysis: "pca" command versus "eigengen" function
Dear Gretl users,
please could anybody help me how to do VECM /Errot correction model/.
I dont know what should I fill and then how can I distinguish between short-term and
long-term relationships...
Or please if there is any manual how to do it.
Thank you for your answer
Jan Cernohorsky
Sent from my Windows Phone
________________________________
From: Henrique Andrade<mailto:henrique.coelho@gmail.com>
Sent: 23/08/2017 22:21
To: Gretl Discussion List (users)<mailto:gretl-users@lists.wfu.edu>
Subject: [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
_______________________________________________
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Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
1:09 a.m.
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>
5:52 p.m.
Dear Allin, Sven, and Yiannis,
At first I would like to thank you all :-)
Em 23 de agosto de 2017, Allin escreveu:
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>
Dear Allin, I got your point, thanks! But one (big) question remains
on my mind: How "pca" command knows that it "has to" multiply the
loadings by -1?
Best,
Henrique Andrade
2708
days inactive
2709
days old
3 comments
3 participants
participants (3)
-
Allin Cottrell -
Cernohorsky Jan -
Henrique Andrade