Linked Questions
34 questions linked to/from PCA and exploratory Factor Analysis on the same dataset: differences and similarities; factor model vs PCA
262
votes
15
answers
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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 ...
- 6,992
164
votes
5
answers
143k
views
What's the difference between principal component analysis and multidimensional scaling?
How are PCA and classical MDS different? How about MDS versus nonmetric MDS? Is there a time when you would prefer one over the other? How do the interpretations differ?
- 4,273
84
votes
6
answers
33k
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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 ...
- 849
72
votes
8
answers
59k
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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 ...
- 3,478
108
votes
5
answers
218k
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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 ...
- 1,379
41
votes
2
answers
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 ...
- 3,499
34
votes
1
answer
45k
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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 ...
- 14.1k
17
votes
3
answers
29k
views
What are the assumptions of factor analysis?
I want to check if I really understood [classic, linear] factor analysis (FA), especially assumptions that are made before (and possibly after) FA.
Some of the data should be initially correlated and ...
- 343
24
votes
1
answer
53k
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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 ...
- 453
15
votes
1
answer
25k
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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:
...
- 775
12
votes
1
answer
58k
views
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 ...
- 143
4
votes
2
answers
41k
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What is the difference between PCA and PAF method in factor analysis?
What is the difference between principal component analyses (PCA) and principal axis factoring (PAF)?
Also, I understand the difference between varimax and oblimin rotations, but is that the same as ...
- 49
6
votes
3
answers
4k
views
What does it mean if I have high Cronbach alpha, but poor results in Exploratory Factor Analysis
I have been given a survey to analyse. There are 50 questions, and about 400 respondents.
I have calculated Cronbach alpha for the entire thing, and I get about 0.9.
When I do factor analysis, I do ...
- 359
8
votes
1
answer
9k
views
What's the relationship between covariance, shared variance, and common variance?
I've generally assumed that shared variance and common variance were the same thing. However, here it is written that "Common variance is the realm of total collinearity. On the other hand, the term "...
8
votes
1
answer
2k
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Under which conditions do PCA and FA yield similar results?
Under which conditions can principal components analysis (PCA) and factor analysis (FA) be expected to yield similar results?
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