Can I flip the sign of PCA loadings?

[Janys Ung]

Hi, I am wondering if I can flip the sign of the Principal Components loadings? I am trying to replicate someone's work on principal component analysis using STATA and got exactly the opposite sign of PCA loadings. The correlation between my component scores and previous researcher's scores is exactly -1. Can anyone please advice?

Your help is much appreciated!

[Lance Erickson]

I would double check how the coding of your variables compares with the work that you are trying to replicate. You can change the sign by reverse coding the items.

[Nick Cox]

Yes, you can. It's a consequence of the symmetry properties of the problem that you can get either sign arbitrarily from different programs. Says he airily: don't ask me to write down the equations off the top of my head.

But if you do, you should state explicitly in any report that you did this. Otherwise you could get into all kinds of difficulties.

Alternatively, just state your results and explain that a change of sign is immaterial. That's what I would do.

I still remember, many years later, my surprise when everything came out the same as somebody else's results except for the sign. That wasn't resolved for some time until I stumbled on an explanation. I don't get the impression that PCA explanations typically make this very clear.

What you can't do is spell "Stata" incorrectly! http://www.statalist.org/forums/help#spelling

[Janys Ung]

Hi, many thanks for both your advice! Nick Cox, thanks for correcting me on the "Stata" spelling! Does the explanation you got related to the sign of PCA? Or it was related to the issue you were studying?

[Nick Cox]

This should help: http://stats.stackexchange.com/quest...g-may-i-revers

It's not where I first read about this, but no matter: I've forgotten where that was.

[Janys Ung]

Nick Cox, many thanks for your link!

[Janys Ung]

Hi Nick Cox, do you have any idea on any book that explain pretty well on the sign of PCA loading? I would greatly appreciate if you could recommend it to me. I'm still struggling to search for an explanation on my case.

[Nick Cox]

Sorry, no. I am not better informed than I was on 31 January, just older. I would explore books on the computational aspects of linear algebra, not those on PCA as such.

[Janys Ung]

Okay, many thanks for your suggestion!