8:33 p.m.
Dear Gretl community,
I want to create a *index* using five variables using gretl's principal
components analysis and I would like to know if I'm doing it properly. I'll
describe my steps:
Step 1: Compute principal components (Main window, View -> Principal
components);
Step 2: Save all components (PC1, ..., PC5);
Step 3: *index* = PC1 + ... + PC5.
I know this is a silly little question, but I have no background in this
kind of stuff :(
Best,
Henrique
Enviado de meu iPhone
10:26 p.m.
Hi,
I did some test, since I am learning too :). It seems that is not
possible to save the PC vars from GUI. But from command we have
options: --save and --save-all. Just do a help pca ;).
Here is my test:
<script>
open /usr/local/share/gretl/data/greene/greene14_1.gdt
pca Q PF LF C --save-all
index = PC1 + PC2 + PC3 + PC4
print index
gnuplot index --with-lines --time-series
</script>
Bye,
Hélio
On Fri, Jan 22, 2010 at 8:33 PM, Henrique <henrique.coelho(a)gmail.com> wrote:
Dear Gretl community,
I want to create a index using five variables using gretl's principal
components analysis and I would like to know if I'm doing it properly. I'll
describe my steps:
Step 1: Compute principal components (Main window, View -> Principal
components);
Step 2: Save all components (PC1, ..., PC5);
Step 3: index = PC1 + ... + PC5.
I know this is a silly little question, but I have no background in this
kind of stuff :(
Best,
Henrique
Enviado de meu iPhone
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10:45 p.m.
On Fri, 22 Jan 2010, Hélio Guilherme wrote:
I did some test, since I am learning too :). It seems that is not
possible to save the PC vars from GUI.
Yes, you can: use the "+" icon (with tooltip "Add to dataset") on
the tollbar at the top of the PCA output window.
But from command we have
options: --save and --save-all. Just do a help pca ;).
Here is my test:
<script>
open /usr/local/share/gretl/data/greene/greene14_1.gdt
pca Q PF LF C --save-all
index = PC1 + PC2 + PC3 + PC4
print index
gnuplot index --with-lines --time-series
</script>
You can also do this via matrix functions:
matrix X = {Q, PF, LF, C}
matrix idx = sumr(princomp(X, 4))
matrix G = idx~seq(1,$nobs)'
gnuplot 1 2 --matrix=G --suppress
Allin
11:01 p.m.
On Fri, 22 Jan 2010, Henrique wrote:
Dear Gretl community,
I want to create a index using five variables using gretl's principal components
analysis and I would like to know if I'm doing it properly. I'll describe my
steps:
Step 1: Compute principal components (Main window, View -> Principal components);
Step 2: Save all components (PC1, ..., PC5);
Step 3: index = PC1 + ... + PC5.
Sorry, Henrique, maybe I'm missing the point, but what are you trying to
do? Principal components are useful exactly because they are orthogonal
(incorrelated if you prefer) to each other, so they carry non-overlapping
information. If you want an index that contains the maximum possible
amount of information that one single variable can contain, take the first
PC (the one associated with the highest eigenvalue) and you're ok. If you
take their sum you end up with a variable that contains LESS information,
not more.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
11:40 p.m.
On Sat, 23 Jan 2010, Riccardo (Jack) Lucchetti wrote:
On Fri, 22 Jan 2010, Henrique wrote:
> Dear Gretl community,
>
> I want to create a index using five variables using gretl's principal
components
> analysis and I would like to know if I'm doing it properly. I'll describe my
steps:
>
> Step 1: Compute principal components (Main window, View -> Principal
components);
> Step 2: Save all components (PC1, ..., PC5);
> Step 3: index = PC1 + ... + PC5.
Sorry, Henrique, maybe I'm missing the point, but what are you trying to
do? Principal components are useful exactly because they are orthogonal
(incorrelated if you prefer) to each other, so they carry non-overlapping
information. If you want an index that contains the maximum possible
amount of information that one single variable can contain, take the first
PC (the one associated with the highest eigenvalue) and you're ok. If you
take their sum you end up with a variable that contains LESS information,
not more.
I gather via google that's there's a literature out there on
constructing index variables of one sort or another on the basis
of PCA. I suppose if you add up all the components you get some
sort of weighted sum of the original series, which might perhaps
be useful in certain contexts (supposing that you _want_ to lose
information relative to the original set of data).
This untutored example doesn't prove anything at all but I found
it moderately interesting:
<script>
open data7-12
pca wbase length width height weight --save-all
series idx = PC1 + PC2 + PC3 + PC4 + PC5
series xsum = wbase + length + width + height + weight
ols price 0 idx
ols price 0 xsum
ols price 0 PC1
ols price 0 weight
</script>
The sum of PCs of cars' characteristics predicts price better than
the sum of characteristics (which is hardly meaningful), and a bit
better than PC1 alone, but it doesn't do nearly as well as the
most relevant of the original variables, namely the weight of the
car.
Allin.
6:46 p.m.
At first I would like to thank you, Hélio, Allin, and Riccardo for your help.
Em 22 de janeiro de 2010 Riccardo escreveu:
On Fri, 22 Jan 2010, Henrique wrote:
> Dear Gretl community,
>
> I want to create a index using five variables using gretl's
> principal components analysis and I would like to know
> if I'm doing it properly. I'll describe my steps:
>
> Step 1: Compute principal components (Main window, View -> Principal
> components);
> Step 2: Save all components (PC1, ..., PC5);
> Step 3: index = PC1 + ... + PC5.
Sorry, Henrique, maybe I'm missing the point, but what are you trying to do?
I'm trying to rebuild the Financial Stress Index (Balakrishnan,
Danninger, Elekdag & Tytell (2009) The Transmission of Financial
Stress. IMF Working Paper) using a different technique. In this paper
the authors use a variance-equal weighting, something live this:
Index = (X1 - E(X1))/sd(X1) + ... + (X5 - E(X5))/sd(X5)
Where:
E(X1) -> mean of X1
sd(X1) -> standard deviation of X1
I would like to use principal components to determine the weights of
each variable in the index.
Em 22 de janeiro de 2010, Hélio escreveu:
<script>
open /usr/local/share/gretl/data/greene/greene14_1.gdt
pca Q PF LF C --save-all
index = PC1 + PC2 + PC3 + PC4
print index
gnuplot index --with-lines --time-series
</script>
Em 22 de janeiro de 2010 Allin escreveu:
On Fri, 22 Jan 2010, Hélio Guilherme wrote:
> <script>
> open /usr/local/share/gretl/data/greene/greene14_1.gdt
> pca Q PF LF C --save-all
> index = PC1 + PC2 + PC3 + PC4
> print index
> gnuplot index --with-lines --time-series
> </script>
You can also do this via matrix functions:
matrix X = {Q, PF, LF, C}
matrix idx = sumr(princomp(X, 4))
matrix G = idx~seq(1,$nobs)'
gnuplot 1 2 --matrix=G --suppress
I think we have a new problem here: when I put this instructions into
a script, Gretl doesn't plot any graph. To get the plots I need to
enter the lines "gnuplot index --with-lines --time-series"or "gnuplot
1 2 --matrix=G --suppress" on Gretl console. I'm using Gretl 1.8.6 CVS
(build 2010-01-21) for Mac.
Best regards,
Henrique C. de Andrade
Doutorando em Economia Aplicada
Universidade Federal do Rio Grande do Sul
www.ufrgs.br/ppge
--
Henrique C. de Andrade
Doutorando em Economia Aplicada
Universidade Federal do Rio Grande do Sul
www.ufrgs.br/ppge
7:15 p.m.
On Sat, 23 Jan 2010, Henrique wrote:
Em 22 de janeiro de 2010 Allin escreveu:
> You can also do this via matrix functions:
>
> matrix X = {Q, PF, LF, C}
> matrix idx = sumr(princomp(X, 4))
> matrix G = idx~seq(1,$nobs)'
> gnuplot 1 2 --matrix=G --suppress
I think we have a new problem here: when I put this instructions
into a script, Gretl doesn't plot any graph...
It won't do a real-time plot if the graph command is in a script.
You should see something like
wrote /path/to/gpttmp01.plt
where gpttmp01.plt contains the gnuplot commands to create the
plot.
Allin.
8:15 p.m.
Henrique a écrit :
I'm trying to rebuild the Financial Stress Index (Balakrishnan,
Danninger, Elekdag & Tytell (2009) The Transmission of Financial
Stress. IMF Working Paper) using a different technique. In this paper
the authors use a variance-equal weighting, something live this:
Index = (X1 - E(X1))/sd(X1) + ... + (X5 - E(X5))/sd(X5)
Where:
E(X1) -> mean of X1
sd(X1) -> standard deviation of X1
I would like to use principal components to determine the weights of
each variable in the index.
In such a case, as Riccardo pointed out all you have to do is to take
the 1st principal component which is supposed to provide the best mix of
information from the X(i)s variables. Indeed, a PC is by construct, a
linear combination of X(i)s that are most correlated with it. Depending
on the software you are using (( I never tried to do a PCA with gretl
:-[ ) you should obtain something like "factor loadings" or "factor
coordinates" which represent the correlation between the 1st (or other)
PC with each of X(i) variables? These help you interpreting or naming -
the PC.
For more useful details on PCA see
http://www.statsoft.com/textbook/principal-components-factor-analysis/?bu...
That's a wonderful resource.
Best,
Artur
9:10 p.m.
Em 25 de janeiro de 2010 artur bala <artur.bala(a)laposte.net> escreveu:
For more useful details on PCA see
http://www.statsoft.com/textbook/principal-components-factor-analysis/?bu...
That's a wonderful resource.
I agree! It's really good. Thank you for this suggestion.
Best,
Henrique C. de Andrade
Doutorando em Economia Aplicada
Universidade Federal do Rio Grande do Sul
www.ufrgs.br/ppge
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8 comments
5 participants
participants (5)
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Allin Cottrell -
artur bala -
Henrique -
Hélio Guilherme -
Riccardo (Jack) Lucchetti