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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Quartimax rotation in Python [closed]

I am trying to use the statsmodels package to do a quartimax rotation on the first two PCs of a dataset. The result is that all but one of the loadings are zero for each of the factors. This seems at ...
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How to perform an oblique rotation on a structure matrix?

I am trying to code an exploratory factor analysis (principal axes factoring) from scratch, on a set of questionnaire items. After determining the appropriate number of factors, I was able to ...
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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, ...
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How to decide if a rotation is necessary in a factor anaysis?

I have a (self-report) scale with 18 items. The scale as a whole is very reliable ($\alpha = .92$); however, the original authors report two sub-scales. Here is the interesting thing that I don't ...
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Percentage of variance explained by rotated factors (PCA, Stata)

I am carrying out an exercise in Principal Component Analysis in Stata. I have created my own rotated factors after carrying out the PCA, and am looking to check the percentage of variance that is ...
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2answers
101 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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1answer
52 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". ...
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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: ...
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1answer
154 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. ...
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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 ...
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37 views

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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44 views

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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131 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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178 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 ...
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105 views

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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2k 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 ...
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1answer
168 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: ...
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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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1answer
421 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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234 views

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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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 ...
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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 ...
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16k 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 ...
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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" ...
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10k 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 ...
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246 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 ...
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1answer
416 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 ...
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154 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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52 views

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 ...
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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_{...
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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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99 views

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 ...
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219 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: ...
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1answer
372 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 ...
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173 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 ...
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384 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 ...
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204 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 (...
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1answer
1k 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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1answer
8k 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, ...
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964 views

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 ...
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2k 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 ...