[R] prcomp - arbitrary direction of the returned principal components

[Ivan Krylov]

В Wed, 12 Oct 2022 17:18:26 +0530
Ashim Kapoor <ashimkapoor using gmail.com> пишет:

> My problem is that I am building an index based on Principal
> Components Analysis.
> When the index is high it should indicate stress in the market.

Have you considered using supervised methods, like PLS, to predict
stress in the market?

Imagine what happens when you take the points where there's stress in
the market and feed only those to PCA. The first principal direction is
now gone (if there is a variation along this axis, it's much smaller
than it was), so now some other direction occupies its place. Even if
the first direction is preserved, after centering, there are now points
with low values of PC1, despite all points should correspond to stress
in the market.

Apologies if the paragraph above is complete nonsense, a reasonable
researched would always conduct the analysis on a representative sample
of the points, and the whole point of the proposed index is that high
stress is indicated by points on the positive end of the multivariate
sausage that PCA considers the data to be. If that's the case,
post-processing the signs as described by Chris Evans could be the
right solution.

-- 
Best regards,
Ivan