# 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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### 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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### How is correlation done between identified PCA components?

I am very new to statistics on this level (PCA, Correlations etc.). I am currently writing a paper and following the methodology from another journal paper. In the journal paper a PCA is done on a set ...
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### Variance explained by factors in oblique model

The variance explained by the factors in an oblique (exploratory) factor model is obviously computed as: diag(Phi * L' * L) where Phi is the factor correlation matrix and L is the factor loading/...
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### 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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### 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 ...
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### Orthogonality and rotation/factor score method

I am struggling with understanding the relationship (or rather, the interaction) between different factor rotation algorithms and score extraction methods in Exploratory Factor Analysis. As far as I ...
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### What is the contribution of base variables to principal components (PCA) after rotation?

I've run a PCA with PCAmixdata using R. My dataset consists of about 1'600 individuals and 600 variables. After trying several options, I've chosen to retain the 6 first PC (elbow plot, eigenvalue, ...
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### varimax rotatin in PCA with non-standardized scores

I am working with a PCA. I am thinking about varimax rotating the loadings but I have some reservations about it after reading about it in the past few days. First, can I get out the varimax rotated ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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### PCA with oblimin rotation: should I interpret component matrix, pattern matrix or structure matrix?

I conducted a principal component analysis (PCA) with direct oblimin factor rotation in SPSS. Because by that time I didn't know any better, I used the COMPONENT MATRIX for interpretation. I added ...
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### PCA with principal(): no rotation, varimax rotation, and oblimin rotation all give same results

I ran PCA with the principal() function of the psych package on some data with 2 variables and 15 observations . I ran PCA thrice, first with no rotation, then with the varimax rotation, and lastly ...
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### 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 ...
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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 $L_{... 1answer 29 views ### Poor models from PCA and CFA For my undergraduate dissertation I'm analysing a 75-item self-report questionnaire filled out by 1140 autistic participants (randomly split into two groups. I have split the sample and am carrying ... 0answers 54 views ### Independence of components in PCA Let's have spatio-temporal dataset ($Y \in \mathbb{R}^{L \times T}$). Where$L$stands for spatial grid points and$T$for time. Now let's say that the noise of the system follows a multivatiate ... 1answer 53 views ### How do I solve this system of equations? I am doing something that is commmon practice in economics to uniquely identify matrices. After deriving 3 unrotated factors from PCA, I then want to rotate them to be able to interpret them in ... 1answer 40 views ### PCA, highly explained component with no value above 0.3 I was analyzing PCA output, and when I reached "pca$xlist, comp($ncomp) blanks(.3)" to name variables, I found out that component 1. which explains more than 50% didn't have any variable above 3, yet ... 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 ... 1answer 755 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 ... 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. ... 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, ... 2answers 251 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 ... 1answer 134 views ### Interpreting PCA with varimax rotation I have problems understanding the Factor Component Analysis of the paper: "Measuring thirty facets of the Five Factor Model with a 120-item public domain inventory: Development of the IPIP-NEO-120". ... 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 ... 0answers 133 views ### Using varimax – rotated PCA for clustering via Gaussian Mixture Model? After extracting the Principle Components of my data, I apply Gaussian Mixture Models for clustering. I used a subset of the orthogonal basis of the Principle Components and projected my data onto ... 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: ... 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: ... 1answer 307 views ### How does factanal() function in R calculate correlations between factors? When using the factanal() function from the stats package in R using the promax rotation, you are given factor correlations. ... 0answers 24 views ### Uniqueness on bayesian factor model's loading matrix I'm doing uniqueness on factor loading matrix in a factor model.$ y = \Lambda f + \epsilon$where$ f \sim N(0,\Sigma)$,$\epsilon \sim N(0,\Omega) $and$\epsilon \perp f\$. It's well known that ...
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My PCA with prcomp in R results in very low "loadings" (i.e. eigenvectors, see figure below). I've tried a rotation with ...
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### 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: ...
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### 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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### 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 ...
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I wonder if there is a method that allows finding factor loadings so that the factor would predict the distal outcome the best? The ordinary SEM model would estimate factor loadings and regression ...
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### Using weighted or unweighted wPCA scores in Logistic regression model-SAS

Im working on data that I should weight the data using a weight variable that I have and I want to evaluate the association of dietary pattern and obesity. So first I run Proc factor and use the "...
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### Computing factor scores for factors when the PAF is based on tetrachoric correlations

I want to create factors from various binary items. Using the polycor package (Fox, 2006) and R-Essentials I created a tetrachoric correlation matrix in SPSS. The items are all exploratory, so I ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Is there rotational ambiguity in PLS?

There are linearly overlapped components typically in curve resolution or factor analysis techniques [1] [2]. Also for PCA, it is common that it is easy to change the sign of the loadings or scores ...
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### 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 ...
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### PCA: Should I work with rotated score or originals score?

I am currently trying to find the meaning of principal components of my data. I find the raw loading very hard to interpret, because the first components drags a large part of the total variance (50 %)...
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### 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. ...
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### 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 ...