# 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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### 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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### 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 ...
1answer
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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 ...
1answer
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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 ...
1answer
151 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 ...
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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 ...
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 ...
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### 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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### 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
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### 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 ...
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### 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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### 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, ...
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 ...
2answers
242 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
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### 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". ...
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### 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 ...
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### How does the solve() function produce factor correlation scores in the factanal() function?

Using the factanal() function in R produces factor correlations: ...
1answer
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### 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. ...
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### 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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### How to interpret low loadings all over PC 1?

My PCA with prcomp in R results in very low "loadings" (i.e. eigenvectors, see figure below). I've tried a rotation with ...
1answer
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### How to maximize regression coefficient instead of factor loadings in SEM?

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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174 views

### 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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### 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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182 views

### Is there rotational ambiguity in PLS?

There are linearly overlapped components typically in curve resolution or factor analysis techniques  . Also for PCA, it is common that it is easy to change the sign of the loadings or scores ...
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 ...
1answer
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### 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: ...
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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. ...
1answer
577 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 ...
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### How to implement an alternative rotation in a factor analysis?

I have an application of factor analysis, where the theoretical model specifies that certain loadings within each factor should ideally share a same sign for the sake of interpretability. For example,...
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### 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( \...
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### What are the differences between (varimax and promax) rotations in PCA? [duplicate]

What are the differences between varimax and promax rotations in PCA?
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### Principal component analysis when original variables hardly correlate

I am fairly familiar with the practical application of principal component analysis (PCA). PCA tries to find the first PC, for example, by minimization of the sum of squared perpendicular distances of ...
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389 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 ...
0answers
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### Is my data eligible for PCA?

I have a data set in which each subject answered a subset of questions in response to visual stimuli (picture rating). At the beginning of the experiment, every subject got assigned 2 out of 16 ...
2answers
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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 ...
2answers
2k views

### How to do a factor analysis with just one component?

I have done a questionnaire with six questions to measure engagement. This is the only component I measure. To make sure they measure just one component, I tried to run a Factor analysis with Direct ...
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### 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" ...
2answers
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### 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 ...
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552 views

### Explained variance of principal components analysis followed by varimax rotation (in R)

Using the pcaMethods package in R I have run PCA on a data set of ~500 subjects with ~300 variables each. There are some missing values so I am employing the ...
1answer
734 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
181 views

### Can Thurstone simple structure criteria be applied to PCA loadings?

I have just read about the usual mistake in Principal Components Analysis of confusing between principal directions and component loadings following the explanation and links here: Relationship ...
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### Minimize shared variance of columns between factors in Correspondence Analysis

I am using correspondence analysis (CA) to analyze a contingency table. In the columns I have statements about some brands (characteristics) and in the rows I have the brands. My aim is to obtain in ...
1answer
551 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_{...
1answer
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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 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 ...