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12 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. ...
0
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0answers
12 views

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 ...
0
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0answers
22 views

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 ...
1
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2answers
104 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 ...
0
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1answer
55 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". ...
0
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0answers
57 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 ...
1
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0answers
90 views

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 ...
1
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0answers
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 "...
1
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0answers
184 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 ...
0
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0answers
108 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 ...
0
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0answers
49 views

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 %)...
2
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0answers
89 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. ...
1
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1answer
426 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 ...
2
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0answers
85 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( \...
1
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0answers
244 views

What are the differences between (varimax and promax) rotations in PCA? [duplicate]

What are the differences between varimax and promax rotations in PCA?
0
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0answers
57 views

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 ...
2
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0answers
137 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 ...
0
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0answers
42 views

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 ...
2
votes
2answers
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 ...
0
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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 ...
2
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0answers
2k 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" ...
9
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2answers
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 ...
1
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0answers
248 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 ...
0
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0answers
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 ...
0
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1answer
1k views

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 ...
0
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0answers
100 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 ...
2
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0answers
222 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: ...
3
votes
1answer
386 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
174 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
votes
1answer
3k 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 (...
0
votes
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 ...
4
votes
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, ...
1
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0answers
975 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 ...
3
votes
1answer
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 ...
4
votes
1answer
610 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 ...
2
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0answers
292 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 ...
9
votes
3answers
2k 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 ...
1
vote
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: ...
3
votes
1answer
892 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 ...
2
votes
0answers
986 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 ...
13
votes
1answer
9k 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 ...
4
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2answers
2k 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): <...
7
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4answers
7k 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 ...
32
votes
1answer
35k 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 ...
2
votes
1answer
10k 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 ...
13
votes
2answers
34k 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 ...
8
votes
1answer
4k 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 ...
9
votes
3answers
12k 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 ...
63
votes
8answers
36k 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 ...