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Questions tagged [rotation]

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43 questions
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The difference between varimax and oblimin rotations in factor analysis

What is the difference between varimax rotation and oblimin rotation in factor analysis? Also, I am confused about the relationship between principal component analysis, varimax rotation and exploratory factor analysis, both in theory and in SPSS.…
xiongmao
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How to generate uniformly random orthogonal matrices of positive determinant?

I've got probably a silly question about which, I must confess, I'm confused. Imagine repeated generating of uniformly distributed random orthogonal (orthonormal) matrix of some size $p$. Sometimes the generated matrix has determinant $1$ and…
ttnphns
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Which matrix should be interpreted in factor analysis: pattern matrix or structure matrix?

When doing a factor analysis (by principal axis factoring, for example) or a principal component analysis as factor analysis, and having performed an oblique rotation of the loadings, - which matrix do you use then in order to understand which items…
Katigkou
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Is Mahalanobis distance equivalent to the Euclidean one on the PCA-rotated data?

I've been led to believe (see here and here) that Mahalanobis distance is the same as the Euclidean distance on the PCA-rotated data. In other words, taking multivariate normal data $X$, the Mahalanobis distance of all of the $x$'s from any given…
generic_user
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Find the rotation between set of points

I have two sets (sourc and target) of points (x,y) that I would like to align. What I did so far is: find the centroid of each set of points use the difference between the centroids translations the point in x and y What I would like is to find…
Wiliam
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Can I somehow compute variance explained by PC after Oblique rotation in PCA?

Let´s say that my PCA analysis extracted 2 components, which explain 80% of the variance before rotation. The components were then rotated using oblique (Direct Oblimin) rotation, so SPSS cannot compute how much percentage of variance each component…
Noro
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What is the Rotation Matrix in PCA?

I'm trying to implement th Local Coordinate System (LCS) of this paper. It's all clear to me about how it works, but the only thing that I' dont understand is the "rotation" mechanism. Quoting the paper (sect 4.2): This processing actually…
user6321
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2 answers

Rotation matrices and prior invariance for arbitrary dimensions

I have a question about a rotation matrix, which can be represented in 2 dimensions as: $$R_{2}(\theta)=\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$$ For some arbitrary angle $\theta$. This can be extended to…
probabilityislogic
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Is it acceptable to rotate factors with PCA for binary data?

What issues, if any, might there be in rotating factors in order to obtain factor/component loadings of binary data? Is it acceptable to rotate the factors when doing a traditional PCA? (Assuming I’m using a polychoric correlation matrix.) I am not…
Deryl H.
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Why does my loading matrix following PCA with a varimax rotation contain only ones and zeros?

I'm running a PCA using the R function prcomp. This is the function: d2.pca <- prcomp(sel.d2, center=TRUE, scale.=TRUE) So variables are scaled an centered. (This always has to be done, right?) This is my original loadings matrix: …
Flø
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Multiple linear regression through orthogonal matrices

An example of linear regression could look like: $min \sum_{i=0}^{m}||x_i A - y_i||_2^{2}$, where ${x_i, y_i} \in \mathbb{R}^n$ and $A \in \mathbb{R}^{n\times n}$. I am interested in knowing how do I solve such problem with an of the following extra…
aboSamoor
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3
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Detecting reflection in non-orthogonal rotation

I've known that, in orthogonal rotation, if the rotation matrix has determinant of -1 then reflection is present. Otherwise the determinant is +1 and we have pure rotation. May I extend this "sign-of-determinant" rule for non-orthogonal rotations?…
ttnphns
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3
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A textbook error w.r.t structure and pattern loadings

I have this picture in Lattin representing structure and pattern loadings in factor analysis. If $Z$ (an observed variable) $=w_1 F_1+w_2 F_2$ (according to factor model), then the pattern loadings of $Z$ on $F_1$ and $F_2$ must be $w_1$ and $w_2$…
Bravo
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3
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Exploratory factor analysis - promax & factor cross-loadings

I have a question regarding the best practice for dealing with cross-loadings on factors after conducting an exploratory factor analysis using a promax rotation. Just to give a bit of background information, I am trying to determine the factor…
Madeline
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$\mathbf{Cov}(x,y)$ under rotation of axes

If $\mathbf{Cov}=0$ let $u=x \cdot cos(\theta)+y \cdot sin(\theta)$ and $v =y \cdot cos(\theta)-x \cdot sin(\theta)$. What will be $\mathbf{Cov}(u,v)$? Will it be $0$?
Sumedha ghosh
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