Skip to main content

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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
18 views

Variance after factor analysis in Stata [duplicate]

I run a factor analysis in Stata (-factor- command) and get the eigenvalues for each factor. Then, I do a rotation, and the table presents not the eigenvalues, but the variance. I have two questions: ...
Eran's user avatar
  • 185
0 votes
0 answers
18 views

Specifics of varimax criterion

The varimax criterion maximises high and low value factor loadings and minimises mid-value factor loadings, in order to achieve the maximum value for its objective function. How does doing this ensure ...
python noob's user avatar
3 votes
1 answer
99 views

How does varimax work

I have some questions regarding how varimax works. I read that given an n by k matrix A, the k by k orthogonal matrix B maximises the varimax criterion, which measures the difference of these 2 terms: ...
python noob's user avatar
0 votes
0 answers
52 views

Predict score based on rotated PCA

I have done a varimax rotated PCA on my "test" dataset. I would like to use this PCA (i.e. the varimax rotated PCA) on a new dataset and predict the scores. This function ...
user390578's user avatar
1 vote
1 answer
114 views

Extrapolate Principal Components Factors with other variables in the components

Hi StackExchange Community, I am performing a Principal Components Analyses (PCA). I would like to know how to extrapolate some PCA components with other variables that were not considered in the PCA ...
ronald's user avatar
  • 57
2 votes
2 answers
269 views

Can one variable load onto different components in (varimax-rotated) PCA?

I performed PCA on 33 items with 133 observations. Considering the criteria to take components with eigenvalues >1, 4 factors can be extracted. I then did varimax rotation of those. However, I ...
Benu P Dahal's user avatar
4 votes
0 answers
169 views

{R Psych Package} Factor Rotation Appears to Lower Proportion of Variance Explained?

This issue arose using R's psych package, specifically the fa function, but the problem is a ...
Daniel O'Loan's user avatar
1 vote
0 answers
36 views

Why the correlation between factors are penalized when weight is large negative in Oblimin rotation?

I'm facing difficulties in interpreting the criterion for the Oblimin rotation. In my knowledge, the following criterion shall be minimized in oblimin rotation. $$\sum_{ij} (\sum_{v}{l_i}^2{l_j}^2 - \...
No Ru's user avatar
  • 143
1 vote
0 answers
92 views

Does Quartimax rotation really maximize the variance of rows in the loading matrix?

The textbook I'm currently reading says that the quartimax rotation in the factor analysis maximizes the rows' variance in the loading matrix. In order to do that, it says, the quartimax rotation ...
No Ru's user avatar
  • 143
0 votes
0 answers
55 views

Why aren't varimax-rotated loadings orthogonal?

Start with a $n \times p$ data matrix $X$. To simplify the notation, suppose it's already centered and standardized. Use SVD to get the rank-$k$ principal component approximation $X \approx (U_k)(...
Dan Hicks's user avatar
  • 802
0 votes
0 answers
100 views

How to mathematically interpret orthogonal rotation in principal components analysis for more than 2 factors

When performing orthogonal rotations for a loading matrix in principal components analysis, the mathematical interpretation is relatively simple - rotate the two axes while keeping them perpendicular. ...
ZombiePlan37's user avatar
0 votes
1 answer
89 views

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 ...
js_Dudley's user avatar
1 vote
0 answers
104 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 (...
monsterhaij's user avatar
0 votes
0 answers
72 views

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 ...
Bálint L. Tóth's user avatar
0 votes
1 answer
493 views

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, ...
kix's user avatar
  • 1
4 votes
1 answer
1k 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 ...
iditbela's user avatar
  • 127
2 votes
1 answer
873 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 ...
A Fog's user avatar
  • 133
0 votes
0 answers
560 views

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 ...
Dicky's user avatar
  • 31
3 votes
1 answer
642 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 ...
Dicky's user avatar
  • 31
2 votes
1 answer
62 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 ...
T August's user avatar
1 vote
0 answers
114 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 ...
Xbel's user avatar
  • 123
1 vote
1 answer
81 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 ...
Rollo99's user avatar
  • 157
0 votes
1 answer
142 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 ...
Mike's user avatar
  • 1
1 vote
0 answers
26 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. ...
jack7989's user avatar
1 vote
0 answers
42 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, ...
nalzok's user avatar
  • 1,797
5 votes
1 answer
4k 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 ...
Petr Garmider's user avatar
1 vote
2 answers
590 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 ...
martins's user avatar
  • 111
0 votes
1 answer
651 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". ...
FancyFrancy's user avatar
0 votes
0 answers
255 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 ...
Mofongo's user avatar
1 vote
0 answers
107 views

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

Using the factanal() function in R produces factor correlations: ...
Taylor Braund's user avatar
0 votes
1 answer
779 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. ...
Taylor Braund's user avatar
1 vote
0 answers
29 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 ...
Houtin's user avatar
  • 33
1 vote
0 answers
550 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 ...
sequoia's user avatar
  • 143
0 votes
1 answer
137 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 ...
Maksim's user avatar
  • 61
1 vote
0 answers
109 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 "...
Zizi's user avatar
  • 11
1 vote
0 answers
277 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 ...
ruboin's user avatar
  • 11
2 votes
0 answers
389 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 ...
melbez's user avatar
  • 165
0 votes
0 answers
278 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 ...
hatmatrix's user avatar
  • 869
3 votes
1 answer
9k 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 ...
sophar's user avatar
  • 161
2 votes
1 answer
614 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: ...
Spätzle's user avatar
  • 4,032
0 votes
0 answers
122 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 %)...
Dhaif's user avatar
  • 1
2 votes
0 answers
173 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. ...
AliMM's user avatar
  • 21
1 vote
1 answer
739 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 ...
Dementedpenguin's user avatar
1 vote
0 answers
52 views

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,...
Frank's user avatar
  • 118
2 votes
0 answers
268 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( \...
Cucus's user avatar
  • 21
1 vote
0 answers
456 views

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

What are the differences between varimax and promax rotations in PCA?
BeatTheStar's user avatar
0 votes
0 answers
95 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 ...
DomB's user avatar
  • 541
2 votes
0 answers
462 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 ...
Rich_b's user avatar
  • 21
0 votes
0 answers
73 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 ...
FranHartung's user avatar
6 votes
2 answers
44k 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 ...
Nadav Keyson's user avatar