In Factor Analysis, How Do We Decide Whether to Have Rotated or Unrotated Factors?

by Karen Grace-Martin

I recently gave a free webinar on Principal Component Analysis. We had almost 300 researchers attend and didn’t get through all the questions. This is part of a series of answers to those questions.

If you missed it, you can get the webinar recording here.

Question: How do we decide whether to have rotated or unrotated factors?


Great question. Of course, the answer depends on your situation.

When you retain only one factor in a solution, then rotation is irrelevant. In fact, most software won’t even print out rotated coefficients and they’re pretty meaningless in that situation.

But if you retain two or more factors, you need to rotate.

Unrotated factors are pretty difficult to interpret in that situation.

It’s because the variables tend to load on both axes and it’s impossible to see the patterns. All rotation does is change the reference axes, which are themselves arbitrary.

So it’s not changing patterns, it’s just making them more obvious so you can see them.

Rotation is a weird concept and there are many different ways to do it. It would take a few dozen pages of writing to really explain it, but it’s a topic we talk about extensively in my PCA and EFA workshop.

Best practices today are different than when I first learned them 25 years ago.

Principal Component Analysis
Summarize common variation in many variables... into just a few. Learn the 5 steps to conduct a Principal Component Analysis and the ways it differs from Factor Analysis.

{ 1 comment… read it below or add one }


how do i rotate principal axes (varimax rotated PCA)
Can you please explain me with simple matrix. As i want to do it on images.


Leave a Comment

Please note that, due to the large number of comments submitted, any comments on problems related to a personal study/project will not be answered. We suggest joining Statistically Speaking, where you have access to a private forum and more resources 24/7.

Previous post:

Next post: