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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218 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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65 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 ...
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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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266 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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127 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. ...
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180 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( \...
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4k 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" ...
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302 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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245 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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441 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 ...
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1k 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 ...
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15 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 (...
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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 ...
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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. ...
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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, ...
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69 views

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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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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166 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 ...
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99 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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181 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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46 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,...
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563 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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60 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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466 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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1k 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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1answer
63 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 ...
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16 views

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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17 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 ...
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1answer
34 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, ...
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10 views

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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126 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 ...
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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 ...
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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 ...
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188 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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59 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 %)...
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80 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 ...
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44 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 ...
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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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105 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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260 views

Rotation in (Univariate) Partial Least Squares Regression

according to a not so recent paper (http://www.sciencedirect.com/science/article/pii/S0167947303003049), it is a good idea to Varimax-rotate the factors that have emerged by Partial Least Squares. ...
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1answer
2k 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 ...