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### What is the difference between Exploratory Factor Analysis and Principal Components Analysis (PCA)? [duplicate]

I know what you're thinking, this is a duplicate of "What are the differences between Factor Analysis and Principal Component Analysis", but it isn't really. That other question deals with ...
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### What is the difference between scores in Princomp vs. factanal? [duplicate]

In R the princomp()and the factanal() are somewhat similar. At least their output looks pretty similar. I learned that this is ...
815 views

### Difference between FA and PCA [duplicate]

Possible Duplicate: What are the differences between Factor Analysis and Principal Component Analysis I am trying to understand the difference between PCA and FA. Through google research, I have ...
295 views

### PCA vs. Factor Analysis [duplicate]

When should we use PCA over factor analysis? Aren't they essentially the same thing except that factor analysis is modeling observed variables as linear combinations of unobserved factors? Whereas PCA ...
71 views

### What are the main differences between principal component analysis PCA and factor analysis [duplicate]

I have used PCA in my thesis and would like to argue (in best way) during viva the choice in addition to the fact that PCA analyses the variance of the observed items whereas FA analyses covariance.
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### Is there any good reason to use PCA instead of EFA? Also, can PCA be a substitute for factor analysis?

In some disciplines, PCA (principal component analysis) is systematically used without any justification, and PCA and EFA (exploratory factor analysis) are considered as synonyms. I therefore ...
39k 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 ...
122k views

### PCA and proportion of variance explained

In general, what is meant by saying that the fraction $x$ of the variance in an analysis like PCA is explained by the first principal component? Can someone explain this intuitively but also give a ...
91k views

### How to reverse PCA and reconstruct original variables from several principal components?

Principal component analysis (PCA) can be used for dimensionality reduction. After such dimensionality reduction is performed, how can one approximately reconstruct the original variables/features ...
121k 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 ...
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### Visualizing a million, PCA edition

Is it possible to visualize the output of Principal Component Analysis in ways that give more insight than just summary tables? Is it possible to do it when the number of observations is large, say ~...
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### 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 ...
31k 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 ...