PCA - which rotation to use?

[Daniela Rozzi]

I'm processing a PCA and my original variables are people's responses to different items in a questionnaire.
I have to decide which kind of rotation to use but I have not understood how to choose among varimax, oblimin and promax.
Someone could help me?

Thanks!

[Nick Cox]

Seriously, if you don't have a preference, why choose any?

The only exception is if this is an assignment and you're being instructed to choose a rotation, in which case presumably either (a) you've been taught something about rotations and are expected to draw on your teaching or (b) you're expected to find out about rotations and choose one. Either way, if it's an assignment, I stop here.

Others might have a better answer with an opinion based on experience of what works well with your kind of data, but I can't help there.

[Daniela Rozzi]

This is not an assignment but I need to rotate because my original variables are people's responses to different items in a questionnaire and as explained in this post (What is the difference between using the PCA method with and without the rotate command ? - Statalist) rotated components are usually better than the unrotated results of PCA.

Given that it is the first time I use PCA I was asking if, to choose which kind of rotation, I have to take into account some particular condition or it depends only to the better results I obtain.

[Nick Cox]

I don't disagree with anything that Clyde Schechter says in that link but I think his post allows a more nuanced summary.

The results that often make most sense for PCA in my experience are the correlations between PCs and variables and the pattern of loadings. The challenge is then to report that in ways that don't even mention the PCs....

[Scott Millis]

You write: "...my original variables are people's responses to different items in a questionnaire." If the items are binary or ordinal, you should probably use a polychoric/tetrachoric correlation matrix in your PCA before you concern yourself with rotations.

[Daniela Rozzi]

I'm analysing a survey of 50 questions and answers are on a scale from 1 to 4 (1 a lot, 2 enough, 3 a little, 4 not at all) for each question.
Given that I haven't used a polychoric/tetrachoric correlation matrix, I' going to describe what I did.
First of all I computed the correlation matrix of the variables and I have excluded the variables that correlate with others with values less than .3 (pearson and spearman give me tha same list of variables to exclude).
Then I processed the pca command and I choose the number of components on the basis of eigenvalues (>1) and I processed again the pca considering only the number of component I choose.
Then I tried tha varimax rotation and the promax rotation and items in the components remain the same (it changes in part the order of the components).
So, I'm now asking if I wrong something.
In addition, how can I obtain in STATA the correlation matrix of components?
Thanks a lot!

[Nick Cox]

I won't willingly comment further on what is wrong (or right) here. There are references arguing that PCA is wrong, period, as a waste of time and papers and books arguing what is right and wrong within PCA, so enough on that. More importantly, we can't give a judgment at a distance on what is a good choice for your data and your goals.

But I wouldn't ignore variables that don't correlate well with others. What's the point of gathering such information? It could tell you something extra.

Peeling off the last question on how to get those correlations in Stata(*):

If you have rotated components then after rotation you can issue predict to put the components in new variables. Once they are in variables you can run correlate.

(*) https://www.statalist.org/forums/help#spelling

[Daniela Rozzi]

Ok, thanks.