# Questions tagged [factor-rotation]

Linear transformation of factors in a factor analysis (or PCA) solution, usually done to improve interpretability. Factor rotation methods include varimax, promax, oblimin, etc.

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### PCA and varimax on linear dependent variables

I am currently trying to use a PCA in combination with a varimax rotation on some measurements to extract underlying factors. However, some of the variables are related, in the sense that they ...
302 views

### How to use varimax rotated PCA to produce raster layers?

I have a raster stack of 19 layers called "raster_bio". The code to do PCA analysis is: ...
650 views

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

I am trying to perform PCA with varimax rotation on a set of data with 2 variables, in order to orthogonalise them (not for dimension reduction). I used prcomp() to ...
218 views

### Can I rotate a (classical) MDS result with varimax etc.?

I have a matrix of (scaled) co-occurence counts which I would like to summarise using (classical, i.e. PCA-related) Multi-Dimensional Scaling (MDS), and then rotate (with ...
466 views

### Interpretation of negative factor correlations?

How would you interpret negative correlations between factors in factor analysis, and should they ever be negative? I did FA with oblique rotation (Oblimin) on 30 variables which were intended to ...
245 views

### Exploratory factor analysis using oblique and bifactor rotation : different pattern loadings

When I try to compare oblique rotated factor analysis (promax, ML) with bifactor rotated analysis (ML), I get different pattern loadings. I don't know which solution should be retained; I am planning ...
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### Why do the loadings returned by psych::principal() in R change with the number of components?

I have been using the principal() function of the psych package in R and setting the number of components after a scree plot analysis (...
2k views

### PCA on a Likert scale data

I am trying to conduct a small experiment based on Likert style data. I have a total of 20 questions, 10 are referring to a latent construct of happiness, and the other 10 to a latent construct of ...
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### What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis?

On the one hand I read in a comment here that: You can't speak of "eigenvalues" after rotation, even orthogonal rotation. Perhaps you mean sum of squared loadings for a principal component, ...
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### How to compute explained variances in PCA with varimax rotation?

I've done a PCA and varimax-rotated the EOF loadings (i.e. eigenvectors of the covariance matrix scaled by the square roots of the respective eigenvalues) and calculated the rotated PCs by multiplying ...
4k views

### How to use principal components as predictors in regression?

I have a couple of questions involving doing a regression (logistic or linear) after principal component analysis. If I find principal components using Principal component analysis, can I use these ...
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### How to assess similarity of two sets of Principal Component Analysis loadings

A predictive model that I currently use relies on PCA with varimax rotation to reduce the dimensionality of the data (whether this is appropriate is a separate question). The dataset consists of ...
441 views

### Rotation as conceptualization: what would be an intuitive illustration of varimax vs quartimax?

I am trying to find an intuitive illustration -- particular of varimaxand quartimax -- to inform the choice of rotation (in the ...
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### Factor rotation methods (varimax, oblimin, etc.) - what do the names mean and what do the methods do?

Factor analysis has several rotation methods, such as varimax, quartimax, equamax, promax, oblimin, etc. I am unable to find any information that relates their names to their actual mathematical or ...
464 views

### Same rotated component matrix in Factor Analysis despite using different data normalizations

I'm using SPSS for factor analysis with these options: ...
260 views

### Rotation in (Univariate) Partial Least Squares Regression

according to a not so recent paper (http://www.sciencedirect.com/science/article/pii/S0167947303003049), it is a good idea to Varimax-rotate the factors that have emerged by Partial Least Squares. ...
3k views

### Rotate PCA components to equalize the variance in each component

I'm trying to reduce the dimensionality and noise of a dataset by performing PCA on the dataset and throwing away the last few PCs. After that, I want to use some machine learning algorithms on the ...
2k views

### How to obtain the same varimax-rotated PCA results in MATLAB and SPSS?

I'm trying to perform a PCA Extraction + Varimax Rotation in MATLAB and obtain the same results as in SPSS. My data is the following matrix A: ...
1k views

### Should I reorder principal components after rotation?

I recently noticed that psych::principal reorders principal components on (automatic) rotation, according to their Eigenvalues (from highest to lowest). (Recall ...
1k views

### Calculating Absolute Principal Component Scores from varimax-rotated principal components scores

In many receptor-modeling studies, after performing the PCA analysis, they often "rescale" their varimax-rotated PC scores (which are standardized with mean zero and standard deviaiton of 1) to ...
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### What are “rotated” and “unrotated” principal components, given that PCA always rotates the coordinates axes?

As far as I understand, principal components are obtained by rotating the coordinate axes to align them with the directions of maximum variance. Nevertheless, I keep reading about "unrotated ...
3k views

### Strange results of varimax rotation of principal component analysis in Stata: rotated components are all zeros and ones

This is my initial output of Principal Component Analysis (PCA) using Stata and correlation matrix (because different scales and measurement units of inputs): <...
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### Very different results of principal component analysis in SPSS and Stata after rotation

For my PhD thesis I have to do a Principal Component Analysis (PCA). I didn't find it too difficult in Stata and was happy interpreting the results (I know there is a difference between factor and ...
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### What is the intuitive reason behind doing rotations in Factor Analysis/PCA & how to select appropriate rotation?

My Questions What is the intuitive reason behind doing rotations of factors in factor analysis (or components in PCA)? My understanding is, if variables are almost equally loaded in the top ...
11k views

### What does “varimax” mean in factor analysis?

In the rotation options of SPSS Factor Analysis, there is a rotation method named "Varimax". If I choose this option, does it mean the orthogonal rotation technique of Principal Component Analysis ...
3k views

### Is there a reason to leave an exploratory factor analysis solution unrotated?

Are there any reasons to not rotate an exploratory factor analysis solution? It's easy to find discussions comparing orthogonal solutions with oblique solutions, and I think I completely understand ...
50k views

### How to compute varimax-rotated principal components in R?

I ran PCA on 25 variables and selected the top 7 PCs using prcomp. prc <- prcomp(pollutions, center=T, scale=T, retx=T) I ...
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### Using varimax-rotated PCA components as predictors in linear regression

After doing PCA, the first component describes the largest part of variability. This is important e.g. in study of body measurements where it is commonly known (Jolliffe, 2002) that PC1 axis captures ...
570 views

### How is the proof that the Quartimax/Varimax-rotation converges?

Empirically the quartimax-/varimax-rotation has proven useful and it was always converging in my applications. But from my readings years ago (most prominent S.Mulaik and K.Überla monographies on ...