3:12 p.m.
Dear all,
many thanks for accepting me in this thread.
I have been a student user of Grelt and now trying to grab it again for PCA modelling in
my current work.
I tried to replicate the score calculation as provided by Gretl (PC1, PC2 etc vectors that
you can store and save after running the PCA command) but i cannot seem to derive those as
simply:
PC Factors = Eigenvectors * standardized original variables (x - mean).
Where am i making a mistake?
Thanks for all your wonderful contribution,
Best
Francesco
3:26 p.m.
Am 06.12.2021 16:12 schrieb francesco.delledonne(a)unicredit.eu:
Dear all,
many thanks for accepting me in this thread.
I have been a student user of Grelt and now trying to grab it again
for PCA modelling in my current work.
I tried to replicate the score calculation as provided by Gretl (PC1,
PC2 etc vectors that you can store and save after running the PCA
command) but i cannot seem to derive those as simply:
PC Factors = Eigenvectors * standardized original variables (x - mean).
Where am i making a mistake?
Thanks for all your wonderful contribution,
Best
Francesco
Hi Francesco,
it would be helpful if you could provide your sample script.
Thanks,
Artur
3:33 p.m.
Am 06.12.2021 16:12 schrieb francesco.delledonne(a)unicredit.eu:
Hi Francesco,
it would be helpful if you could provide your sample script.
Thanks,
Artur
hi Artur,
thanks for your reply.
I am not using the script but simply using the GUI commands.
Working from the outputs of the GUI i receive the below:
Principal Components Analysis
Eigenanalysis of the Covariance Matrix
Component Eigenvalue Proportion Cumulative
1 0.0331 0.8665 0.8665
2 0.0051 0.1325 0.9990
3 0.0000 0.0009 1.0000
4 0.0000 0.0000 1.0000
Eigenvectors (component loadings)
PC1 PC2 PC3 PC4
EUSA2_ICPL_Curncy 0.087 -0.883 0.461 0.017
EUSA5_ICPL_Curncy 0.379 -0.344 -0.714 -0.477
EUSA7_ICPL_Curncy 0.553 -0.045 -0.220 0.802
EUSA10_ICPL_Curncy 0.737 0.315 0.479 -0.358
In order to calculate myself the PC1 i would have assumed to derive it in the following
way:
PC1(i) = 0.087*[EUSA2(i) - mean(EUSA2)] + 0.379*[EUSA5(i) - mean(EUSA5)] + 0.553*[EUSA7(i)
- mean(EUSA7)] + 0.737*[EUSA10(i) - mean(EUSA10)]
But i guess i am wrong as the PCs calculated by Gretl are much different.
Hope i have been clear enough,
Many thanks
Francesco
3:42 p.m.
On Mon, 6 Dec 2021, francesco.delledonne(a)unicredit.eu wrote:
> Am 06.12.2021 16:12 schrieb francesco.delledonne(a)unicredit.eu:
>
> Hi Francesco,
>
> it would be helpful if you could provide your sample script.
>
>
> Thanks,
> Artur
hi Artur,
thanks for your reply.
I am not using the script but simply using the GUI commands.
Working from the outputs of the GUI i receive the below:
Does this help?
<hansl>
open data4-1.gdt
list X = price sqft bedrms baths
# native
pca X --save=2
# by hand
matrix Z = cdemean({X}, -1)
matrix evec = {}
lambda = eigensym(Z'Z, &evec)
series fac1 = Z * evec[,4]
series fac2 = Z * evec[,3]
print PC1 PC2 fac1 fac2 --byobs
</hansl>
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
3:51 p.m.
Thanks Riccardo,
I can nevertheless see that the "byhand" calculation is consistent with theory.
By running your script i get the following:
PC1 PC2 fac1 fac2
1 -2.709256 0.285568 -854.063 -0.26550
2 -2.066726 0.463805 -662.994 -2.01606
3 -1.980962 0.517025 -616.468 -2.60151
4 -0.078544 -0.938229 -335.217 -13.89559
5 -1.666011 0.657474 -318.786 34.83377
6 -0.451584 -0.754696 -162.769 2.05259
7 0.432158 -0.885727 -114.351 16.87650
8 0.087436 -0.349262 -33.981 -52.69935
9 0.327963 -0.744697 20.738 25.60055
10 -0.276806 -0.689980 32.923 32.34589
11 1.754006 -0.244259 349.105 -19.51842
12 1.454298 2.304822 708.354 -90.62917
13 2.519187 0.173682 895.401 16.20702
14 2.654839 0.204476 1092.108 53.70929
Quite different
3:57 p.m.
Am 06.12.2021 um 16:51 schrieb francesco.delledonne(a)unicredit.eu:
Thanks Riccardo,
I can nevertheless see that the "byhand" calculation is consistent with
theory.
By running your script i get the following:
PC1 PC2 fac1 fac2
1 -2.709256 0.285568 -854.063 -0.26550
2 -2.066726 0.463805 -662.994 -2.01606
3 -1.980962 0.517025 -616.468 -2.60151
4 -0.078544 -0.938229 -335.217 -13.89559
5 -1.666011 0.657474 -318.786 34.83377
6 -0.451584 -0.754696 -162.769 2.05259
7 0.432158 -0.885727 -114.351 16.87650
8 0.087436 -0.349262 -33.981 -52.69935
9 0.327963 -0.744697 20.738 25.60055
10 -0.276806 -0.689980 32.923 32.34589
11 1.754006 -0.244259 349.105 -19.51842
12 1.454298 2.304822 708.354 -90.62917
13 2.519187 0.173682 895.401 16.20702
14 2.654839 0.204476 1092.108 53.70929
Quite different
Are you sure you're running the exact script unchanged? If you are, then
please tell us your setup, because you're getting weird stuff.
thanks
sven
2:59 a.m.
On Mon, 6 Dec 2021, francesco.delledonne(a)unicredit.eu wrote:
Thanks Riccardo,
I can nevertheless see that the "byhand" calculation is consistent with
theory.
By running your script i get the following:
PC1 PC2 fac1 fac2
1 -2.709256 0.285568 -854.063 -0.26550
2 -2.066726 0.463805 -662.994 -2.01606
3 -1.980962 0.517025 -616.468 -2.60151
[...]
It's possible your gretl version desn't have the latest behavior for
cdemean(). You could try this variant:
open data4-1.gdt
list X = price sqft bedrms baths
# native
pca X --save=2
# by hand
list SX = stdize(X)
matrix Z = {SX}
matrix evec = {}
lambda = eigensym(Z'Z, &evec)
series fac1 = Z * evec[,4]
series fac2 = Z * evec[,3]
print PC1 PC2 fac1 fac2 --byobs
fac1 and fac2 should be identical to PC1 and PC2.
Allin Cottrell
10:27 a.m.
Am 07.12.2021 um 03:59 schrieb Allin Cottrell:
It's possible your gretl version desn't have the latest behavior for
cdemean().
Hi Allin, what exactly do you mean by that? The optional second argument
was introduced already in version 2018d. Francesco didn't mention the
version he was using, but I assume it's more recent.
I was also wondering why Jack was using -1 as the argument, and then I
had some kind of déjà vu, as if we introduced a special meaning for
negative arguments. But if that's true, it's not in the function
reference (of the latest snapshot).
thanks
sven
4:13 p.m.
just an observation. You show mean adjusted variables. Standardised would
divide by stdevn.
Perhaps thar might account for the difference ?
But then, it's been sometime since I worked on PCA!
regards
Brian
Brian J Revell
Professor Emeritus
Agricultural and Food Economics
Harper Adams University
Newport
Shropshire
TF10 8NB
Tel 01952815237.
Sent from my Galaxy S8+
On Mon, 6 Dec 2021, 15:12 , <francesco.delledonne(a)unicredit.eu> wrote:
Dear all,
many thanks for accepting me in this thread.
I have been a student user of Grelt and now trying to grab it again for
PCA modelling in my current work.
I tried to replicate the score calculation as provided by Gretl (PC1, PC2
etc vectors that you can store and save after running the PCA command) but
i cannot seem to derive those as simply:
PC Factors = Eigenvectors * standardized original variables (x - mean).
Where am i making a mistake?
Thanks for all your wonderful contribution,
Best
Francesco
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877
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8 comments
6 participants
participants (6)
-
Allin Cottrell -
atecon -
Brian Revell -
francesco.delledonne＠unicredit.eu -
Riccardo (Jack) Lucchetti -
Sven Schreiber