17 votes

Is PCA followed by a rotation (such as varimax) still PCA?

This answer is to present, in a path chart form, things about which @amoeba reasoned in his deep (but slightly complicated) answer on this thread (I'm a kind of agree with it by 95%) and how they ...
ttnphns's user avatar
  • 57.2k
12 votes
Accepted

In Factor Analysis (or in PCA), what does it mean a factor loading greater than 1?

Who told you that factor loadings can't be greater than 1? It can happen. Especially with highly correlated factors. This passage from a report about it by a prominent pioneer of SEM pretty much ...
gammer's user avatar
  • 1,487
11 votes

In Factor Analysis (or in PCA), what does it mean a factor loading greater than 1?

Loading in factor analysis or in PCA (see 1, see 2, see 3) is the regression coefficient, weight in a linear combination predicting variables (items) by standardized (unit-variance) factors/components....
ttnphns's user avatar
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10 votes
Accepted

What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis?

The two citations do not generally contradict each other and both look to me correct. The only underwork is in ...
ttnphns's user avatar
  • 57.2k
9 votes

What is the difference between PCA and PAF method in factor analysis?

Both PCA and PAF can be seen as ways of dimension reduction. In discussing their differences, I'll be relying on Exploratory Factor Analysis by Fabrigar and Wegener (2012). I'm not going to get too ...
Mark White's user avatar
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6 votes
Accepted

How to use principal components as predictors in regression?

Yes. That's exactly what principal component regression is: https://en.wikipedia.org/wiki/Principal_component_regression. No need to rotate. In fact, rotating would not make any difference as far as ...
6 votes
Accepted

Why do the loadings returned by psych::principal() in R change with the number of components?

There are several (at least two) potentially confusing issues cropping up here. Confusing issue #1: psych::principal() uses varimax rotation by default The ...
amoeba's user avatar
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5 votes
Accepted

How does oblimin rotation method affect confirmatory factor analysis in lavaan?

It doesn't make any difference where your model comes from. Lavaan doesn't know that the model comes form an EFA, or that you used oblimin (or any other) rotation. You should always include ...
Jeremy Miles's user avatar
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5 votes
Accepted

Why is factor rotation always recommended, though it obscures general factors?

Do we need factor rotation? Of all the factors? Do the strongest unrotated factor reveal the "general factor"? Books do not urge, "rotate, don't leave your factors unrotated". ...
ttnphns's user avatar
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4 votes
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How to obtain unstandardized scores in factor analysis (FA)?

An overview of methods to compute component and factor scores notices on the so called "standardized" factor scores, The scores computed ... are scaled: they have variances equal to or ...
ttnphns's user avatar
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4 votes
Accepted

Oblique vs. Orthogonal Rotation for EFA

Orthogonal rotations are special cases of oblique rotations, so yes, they can show up. (Can you provide better links to your articles?) Edit: I don't think that the Bandalos and Boehn-Haufman says ...
Jeremy Miles's user avatar
  • 17.5k
3 votes

Very different results of principal component analysis in SPSS and Stata after rotation

The differences between the Stata PCA methods and the conventional methods used in R or SPSS are: 1. Scaling eigenvectors/components Stata rotates eigenvectors. Whereas, R or SPSS PCA-rotation ...
am313's user avatar
  • 76
3 votes
Accepted

Open source code for factor-augmented VAR (FAVAR) model

Here one can find R-language replication of the model described in the paper Bernanke, Boivin and Eliasz (2005). It took me some time to understand PCA in details, cover some basic VAR topics to be ...
Petr Garmider's user avatar
2 votes
Accepted

Reproducing SAS Factor Analysis in R

If appears that fa defaults to iterated principal factors. So, to be somewhat careful in this: If you want a principal factors solution with priors based on Squared multiple correlations (and not ...
Phil Wood's user avatar
2 votes

How to maximize regression coefficient instead of factor loadings in SEM?

As Jeremy mentioned in the comments, if your goal is prediction, then there is no sense in creating an interpretable factor. You can use flexible regression or machine learning methods directly on the ...
Noah's user avatar
  • 32.3k
2 votes

Can one variable load onto different components in (varimax-rotated) PCA?

As answered by Eoin, you are asking about PCA but in your analyses, it seems you are performing an exploratory (?) Factor Analysis (FA); for this reason, I added the ...
utobi's user avatar
  • 11.6k
1 vote

Can one variable load onto different components in (varimax-rotated) PCA?

The output you've shown is for exploratory factor analysis, not PCA. There are many tutorials out there that explain the relationship between PCA and factor analysis. In both PCA and exploratory ...
Eoin's user avatar
  • 8,837
1 vote

What is the contribution of base variables to principal components (PCA) after rotation?

The idea of principal component analysis is to transform your original variables into new uncorrelated or "perpendicular" ones. So if your original variables were already pretty much ...
David's user avatar
  • 2,596
1 vote
Accepted

How do I solve this system of equations?

$U$ is an orthonormal matrix, with columns having norm $1$ and orthogonal to each other. The solution is not unique, so coming up with a solution should suffice for you I guess, if there are no other ...
gunes's user avatar
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1 vote

Calculating variance explained by factors after exploratory factor analysis with oblique rotation in R

I do not know what is usually reported in papers using oblique factor analysis. However, this is what I would do, as in this case at least I know exactly what I am reporting and this makes sense to me....
Aleš Žiberna's user avatar
1 vote

Correlated component scores after PCA with varimax rotation in Stata

Here a relevant excerpt found on page 429 in chapter 12 "Principal component analysis" from the book "Methods of multivariate analysis" by AC Rencher and WF Christensen (3rd ed.): The authors seem to ...
COOLSerdash's user avatar
  • 30.1k
1 vote
Accepted

Interpreting PCA with varimax rotation

The first principal component corresponds to extraversion (loosely speaking) because it has relatively high and positive loadings on all but one of the measures of extraversion. Similarly, the second ...
The Laconic's user avatar
  • 1,584
1 vote
Accepted

How does factanal() function in R calculate correlations between factors?

Its calculated using the following code which can be found here https://github.com/SurajGupta/r-source/blob/master/src/library/stats/R/factanal.R: ...
Taylor Braund's user avatar
1 vote

What is the difference between PCA and PAF method in factor analysis?

I think that there is one large difference between PCA and PFA that is tacitly mentioned in any discussion and is not usually explicated. I make this an answer rather than a comment, because it was a ...
meh's user avatar
  • 2,070
1 vote

How to do a factor analysis with just one component?

Are you doing a PCA or an EFA? You say that you do a factor analysis and use a direct oblimin rotation, but you also note that you are extracting components. PCA and EFA rely on different theoretical ...
Mark White's user avatar
  • 10.2k
1 vote

PCA on a Likert scale data

I think EFA (or CFA) would be a better fit for this analysis. The reason I'm stating this is because you already have a proposed model (two latent constructs, each associated with ten items) and ...
ksfowler's user avatar
1 vote

The number of free parameters in factor analysis after an orthogonal rotation

I found the following references - Rotation in Factor analysis by Darton and this presentation wherein it is stated that because of the rotational indeterminacy, an extra constraint is imposed - ...
honeybadger's user avatar
  • 1,552
1 vote
Accepted

Why does varimax applied to PCA outcome fail to do anything at all?

General remarks: One should not varimax-rotate eigenvectors of PCA but loadings of PCA (i.e. eigenvectors scaled up by respective standard deviations). Also, it does not make sense to rotate all ...
Gottfried Helms's user avatar
1 vote

How to assess similarity of two sets of Principal Component Analysis loadings

Maybe the (modified) RV-coefficient is suitable for your problem. This measure computes the similarity/correlation between two matrices. Also note that a factor rotation is somewhat arbitrary, perhaps ...
Jeffrey Durieux's user avatar
1 vote

Factor rotation methods (varimax, quartimax, oblimin, etc.) - what do the names mean and what do the methods do?

Rotation methods optimise heuristic fuctions with the aim of "simplifying" factor loadings. Simplicity can be defined in many different ways. The most commonly used ones come from Thurnstone [2]: ...
Marco Stamazza's user avatar

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