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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69
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8answers
47k views

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

I have tried to reproduce some research (using PCA) from SPSS in R. In my experience, principal() function from package psych ...
38
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1answer
49k views

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 ...
15
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3answers
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 ...
15
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1answer
14k views

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 ...
13
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2answers
20k views

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

I've just run a FA using a oblique rotation (promax) and an item yielded a factor loading of 1.041 on one factor, (and factor loadings of -.131, -.119 and .065 on the other factors using pattern ...
12
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2answers
14k views

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 ...
11
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2answers
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 ...
10
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3answers
13k views

On the use of oblique rotation after PCA

Several statistical packages, such as SAS, SPSS, and R, allow you to perform some kind of factor rotation following a PCA. Why is a rotation necessary after a PCA? Why would you apply an oblique ...
10
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3answers
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 ...
8
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1answer
6k views

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 ...
7
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4answers
9k views

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 ...
5
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2answers
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): <...
5
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1answer
2k views

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

I am looking for an open source package (R, Python, Julia) that has an implemented FAVAR (factor-augmented VAR) class for time-series prediction problem. I've already tried to use several solutions ...
5
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1answer
1k views

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 ...
4
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1answer
13k views

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, ...
4
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1answer
561 views

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

Background I'm reading some notes in multivariate data analysis, in particular factor analysis. A data vector $X_{p\times 1}$, with $E(X) = \mu$ A vector $F_{m \times 1} $ of factors, A matrix $L_{...
4
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1answer
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 ...
3
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2answers
27k views

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

What is the difference between principal component analyses (PCA) and principal axis factoring (PAF)? Also, I understand the difference between varimax and oblimin rotations, but is that the same as ...
3
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1answer
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 ...
3
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1answer
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 ...
3
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1answer
156 views

How to obtain unstandardized scores in factor analysis (FA)?

When conducting factor analysis (FA), retained factors are standardised. I want to know if it is possible to obtain the factor scores in the same metric as the untandardized observed variables. This ...
3
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1answer
653 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 ...
3
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0answers
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 ...
2
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1answer
5k views

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 (...
2
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1answer
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 ...
2
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1answer
165 views

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

I have discovered that factor rotation has had detrimental effects in a lot of studies applying factor analysis in cross-cultural studies. I have made a meta-analysis of cultural differences between ...
2
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1answer
404 views

Reproducing SAS Factor Analysis in R

I need to be able to reproduce some SAS results in R, as far as this is possible (note: I'm very familiar with R and barely used SAS). The original SAS code is as follows: ...
2
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1answer
5k views

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

We conducted an exploratory factor analysis using the psych package with oblique rotation and found an acceptable solution with 3 factors. Now a reviewer ask me to provide the proportion of variance ...
2
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0answers
65 views

PCA Questions on the principal() function of psych package

I recently learned PCA and have the following questions on the use of principal() function of psych package: From 20 variables I decided to keep 4 components / factors. I used principal() function ...
2
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1answer
29 views

Poor models from PCA and CFA

For my undergraduate dissertation I'm analysing a 75-item self-report questionnaire filled out by 1140 autistic participants (randomly split into two groups. I have split the sample and am carrying ...
2
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0answers
268 views

Creating scree plot before or after varimax rotation

I am performing a principal components analysis using the psych package in R. I have the results for a PCA with varimax rotation, but I can only figure out how to make a scree plot for the PCA without ...
2
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0answers
127 views

Inconsistent varimax rotated scores from robust PCA output

This great answer shows how to compute varimax-rotated loadings and scores from PCA results using princomp. I am conducting a robust PCA analysis using the pcaHubert function from the rrcov package. ...
2
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0answers
180 views

2D rotation of standardized PCA, how to compute new eigen values, eigen vectors, and loadings ?

I want to apply a 2D rotation of a $\theta$ angle to my two first principal components of a PCA. What I understood from this post is that I have to apply a rotation matrix R : $$ R_\theta = \left( \...
2
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0answers
400 views

PCA rotation and principal component scores [duplicate]

This is my first post so apologies for any incorrect formatting or whether this has been answered elsewhere but I seem to be going around in circles. Basically, I have 12 survey plots and have ...
2
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0answers
4k views

Factor Analysis - Rotation failed to converge in 25 iterations!

I am conducting a Factor Analysis using PCA. I have used Oblique and Orthagonal Rotations and when I am trying to analyse my results I get the message: "Rotation failed to converge in 25 iterations" ...
2
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0answers
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: ...
2
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0answers
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 ...
2
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0answers
444 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 ...
2
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0answers
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 ...
1
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1answer
761 views

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

I am conducting a CFA on a questionnaire with 4 factors. I know that the exploratory factor analysis to obtain theses 4 factors was done using oblimin rotation. I am now wondering, if this affects the ...
1
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1answer
579 views

Oblique vs. Orthogonal Rotation for EFA

Will orthogonal relationships show up when using Oblique rotation? Based on the articles I have read on EFA rotation my understanding is that although oblique rotation procedures might be expected ...
1
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1answer
464 views

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

I'm using SPSS for factor analysis with these options: ...
1
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1answer
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: ...
1
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1answer
53 views

How do I solve this system of equations?

I am doing something that is commmon practice in economics to uniquely identify matrices. After deriving 3 unrotated factors from PCA, I then want to rotate them to be able to interpret them in ...
1
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2answers
258 views

Correlated component scores after PCA with varimax rotation in Stata

I have a dataset with 6 personality traits for 155 individuals that are highly correlated. To get rid of multicollinearity (and potential noise in the original variables) in my regression analysis, I ...
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0answers
15 views

How to use ICA as a specific factor rotation in orthogonal factor model

I am trying to understand the way ICA is used as factor rotation in the traditional orthogonal factor model. The idea of using ICA as a specific factor rotation is often mentioned in the literature (...
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0answers
54 views

Independence of components in PCA

Let's have spatio-temporal dataset ($Y \in \mathbb{R}^{L \times T}$). Where $L$ stands for spatial grid points and $T$ for time. Now let's say that the noise of the system follows a multivatiate ...
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0answers
21 views

Can I obtain original data by multiplying varimax-rotated principal components with varimax-rotated unit length loadings?

I have perform conventional Empirical Orthogonal Function (EOF) analysis to my data set and obtain loadings (eigenvector scaled by square root of eigenvalue) and corresponding principal component. ...
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0answers
15 views

Why protect “general factor”s in factor analysis?

My Multivariate Analysis textbook states that As we have noted, a general factor (that is, one on which all the variables load highly) tends to be "destroyed after rotation." For this reason, ...
1
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0answers
69 views

How does the solve() function produce factor correlation scores in the factanal() function?

Using the factanal() function in R produces factor correlations: ...