Re: [Gretl-users] Principal Components
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