Linked Questions

4
votes
1answer
5k views

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 ...
4
votes
0answers
1k views

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 ...
0
votes
0answers
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 ...
1
vote
0answers
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 ...
0
votes
0answers
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.
73
votes
6answers
22k views

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 ...
64
votes
8answers
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 ...
95
votes
4answers
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 ...
122
votes
1answer
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 ...
73
votes
4answers
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 ...
32
votes
3answers
11k views

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 ~...
37
votes
2answers
15k 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 ...
27
votes
4answers
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 ...
31
votes
3answers
38k views

Latent Class Analysis vs. Cluster Analysis - differences in inferences?

What are the differences in inferences that can be made from a latent class analysis (LCA) versus a cluster analysis? Is it correct that a LCA assumes an underlying latent variable that gives rise to ...
29
votes
1answer
31k views

Best factor extraction methods in factor analysis

SPSS offers several methods of factor extraction: Principal components (which isn't factor analysis at all) Unweighted least squares Generalized least squares Maximum Likelihood Principal Axis Alpha ...

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