Linked Questions

262 votes
15 answers

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 ...
Brandon Bertelsen's user avatar
164 votes
5 answers

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?
Stephen Turner's user avatar
84 votes
6 answers

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 ...
Carine's user avatar
  • 849
72 votes
8 answers

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 ...
Roman Luštrik's user avatar
108 votes
5 answers

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 ...
user2696565's user avatar
  • 1,379
41 votes
2 answers

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 ...
avocado's user avatar
  • 3,499
34 votes
1 answer

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 ...
Placidia's user avatar
  • 14.1k
17 votes
3 answers

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 ...
Sihem's user avatar
  • 343
24 votes
1 answer

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 ...
Kartikeya Pandey's user avatar
15 votes
1 answer

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: ...
dato datuashvili's user avatar
12 votes
1 answer

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 ...
Katigkou's user avatar
  • 143
4 votes
2 answers

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 ...
Nadav Keyson's user avatar
6 votes
3 answers

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 ...
Old_Mortality's user avatar
8 votes
1 answer

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 "...
user1205901 - Слава Україні's user avatar
8 votes
1 answer

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?
stats's user avatar
  • 83

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