1 vote
208 views

### Rotation in PCA and Factor Analysis [duplicate]

I want to know what elements are (varimax-)rotated when I rotate after PCA and after Factor Analysis. Let’s assume a standardized data vector $X$ of dimension $N \times q$. In PCA, I have the ...
• 391
492k views

### Relationship between SVD and PCA. How to use SVD to perform PCA?

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix ...
• 105k
295k views

### What are the differences between Factor Analysis and Principal Component Analysis?

It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use ...
• 7,242
225k views

### Loadings vs eigenvectors in PCA: when to use one or another?

In principal component analysis (PCA), we get eigenvectors (unit vectors) and eigenvalues. Now, let us define loadings as $$\text{Loadings} = \text{Eigenvectors} \cdot \sqrt{\text{Eigenvalues}}.$$ I ...
• 1,389
53k views

### Minimum sample size for PCA or FA when the main goal is to estimate only few components?

If I have a dataset with $n$ observations and $p$ variables (dimensions), and generally $n$ is small ($n=12-16$), and $p$ may range from small ($p = 4-10$) to perhaps much larger ($p= 30-50$). I ...
• 1,571
21k views

### How does Factor Analysis explain the covariance while PCA explains the variance?

Here is a quote from Bishop's "Pattern Recognition and Machine Learning" book, section 12.2.4 "Factor analysis": According to the highlighted part, factor analysis captures the covariance between ...
• 3,581
66k 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 ...
• 5,603
65k 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 ...
• 609
54k views

### Methods to compute factor scores, and what is the "score coefficient" matrix in PCA or factor analysis?

As per my understanding, in PCA based on correlations we get factor (= principal component in this instance) loadings which are nothing but the correlations between variables and factors. Now when I ...
20k views

### PCA and exploratory Factor Analysis on the same dataset: differences and similarities; factor model vs PCA

I would like to know if it makes any logical sense to perform principal component analysis (PCA) and exploratory factor analysis (EFA) on the same data set. I have heard professionals expressly ...
• 301
26k views

### Steps done in factor analysis compared to steps done in PCA

I know how to perform PCA (principal component analysis), but I would like to know steps that should be used for factor analysis. To perform PCA, let us consider some matrix $A$, for instance: ...
19k 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 ...
10k 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 ...
• 93
17k 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, ...