Linked Questions

1
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0answers
149 views

Principal component analysis (PCA) vs. method of principal components for factor analysis (FA) [duplicate]

I have just read in one of the answers here as follows: One of the biggest reasons for the confusion between the two [principal component analysis (PCA) and factor analysis (FA)] has to do with the ...
216
votes
14answers
239k 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 ...
112
votes
6answers
14k views

Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?

For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical ...
73
votes
4answers
120k 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 ...
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 ...
19
votes
2answers
14k 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 ...
11
votes
3answers
13k 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 ...
12
votes
1answer
18k 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: ...
8
votes
2answers
16k views

Whether to use original or reverse coded items in factor analysis?

I am currently analyzing data from a 34-item Likert scale. I already recoded the negatively stated variables in SPSS as different variables. I'm about to do a factor analysis. Should I use the ...
3
votes
2answers
19k views

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 ...
7
votes
2answers
2k views

What is the relation between singular correlation matrix and PCA?

Can anyone kindly give me some information about the statement (last sentence) at the end of below definition. What does it mean by "It can be used when a correlation matrix is singular"? This quote ...
4
votes
1answer
10k 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, ...
5
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1answer
4k views

Estimating specific variance for items in factor analysis - how to achieve the theoretical maximum?

(Remark: this is a "scholastic" question - I'm reviewing my implementation of factor analysis procedures; I'm not looking for good approximations for an actual survey/actual data or the like.) ...
4
votes
1answer
3k views

High KMO but low communality in factor analysis

I'm performing a factor analysis and I have for a variable a Kaiser-Meyer-Olkin (KMO) measurement of .710 and a communality of ...
6
votes
1answer
4k views

Chi Square test in SPSS Exploratory Factor Analysis

I ran an Exploratory Factor Analysis in SPSS recently with ML as the extraction method, and got the following table in my output: I was not used to seeing goodness-of-fit tests in the context of EFA (...

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