R help - Oct 2022 - prcomp - arbitrary direction of the returned principal components

Dear R experts,
>From ?prcomp,
---- snip -----
Note:

     The signs of the columns of the rotation matrix are arbitrary, and
     so may differ between different programs for PCA, and even between
     different builds of R.
---- snip ------

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. Due to
the arbitrary sign sometimes I get an index which is HIGH when there
is stress and sometimes I get  the OPPOSITE - an index which is LOW
when there is stress.
This program is shared with other people who may have a different build of R.

I can forcefully use a NEGATIVE sign to FLIP the index when it is LOW.
That works.

Now my query is : Just like we do set.seed(1234) and force the pattern
of generation of random number and make it REPRODUCIBLE, can I do
something like :

set.direction.for.vector.in.pca(1234)

Now each time I do prcomp it should choose the SAME ( high or low )
direction of the principle component on ANY computer having ANY
version of R installed.

That's what I want. I don't want the the returned principal component
to be HIGH(LOW) on my computer and LOW(HIGH) on someone else's
computer.
That would confuse the people the code is shared with.

Is this possible ? How do people deal with this ?

Many thanks,
Ashim

Use absolute value

Tim

-----Original Message-----
From: R-help <r-help-bounces at r-project.org> On Behalf Of Ashim Kapoor
Sent: Wednesday, October 12, 2022 7:48 AM
To: R Help <r-help at r-project.org>
Subject: [R] prcomp - arbitrary direction of the returned principal components

[External Email]

Dear R experts,
>From ?prcomp,
---- snip -----
Note:

     The signs of the columns of the rotation matrix are arbitrary, and
     so may differ between different programs for PCA, and even between
     different builds of R.
---- snip ------

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. Due to the
arbitrary sign sometimes I get an index which is HIGH when there is stress and
sometimes I get  the OPPOSITE - an index which is LOW when there is stress.
This program is shared with other people who may have a different build of R.

I can forcefully use a NEGATIVE sign to FLIP the index when it is LOW.
That works.

Now my query is : Just like we do set.seed(1234) and force the pattern of
generation of random number and make it REPRODUCIBLE, can I do something like :

set.direction.for.vector.in.pca(1234)

Now each time I do prcomp it should choose the SAME ( high or low ) direction of
the principle component on ANY computer having ANY version of R installed.

That's what I want. I don't want the the returned principal component to
be HIGH(LOW) on my computer and LOW(HIGH) on someone else's computer.
That would confuse the people the code is shared with.

Is this possible ? How do people deal with this ?

Many thanks,
Ashim

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? Wed, 12 Oct 2022 17:18:26 +0530
Ashim Kapoor <ashimkapoor at gmail.com> ?????:
> 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