Linked Questions
52 questions linked to/from Methods to compute factor scores, and what is the "score coefficient" matrix in PCA or factor analysis?
262
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15
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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 ...
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93
votes
7
answers
286k
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What are principal component scores?
What are principal component scores (PC scores, PCA scores)?
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71
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8
answers
58k
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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 ...
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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 ...
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86
votes
4
answers
33k
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How to visualize what canonical correlation analysis does (in comparison to what principal component analysis does)?
Canonical correlation analysis (CCA) is a technique related to principal component analysis (PCA). While it is easy to teach PCA or linear regression using a scatter plot (see a few thousand examples ...
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41
votes
2
answers
21k
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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 ...
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43
votes
1
answer
64k
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What is the intuitive reason behind doing rotations in Factor Analysis/PCA & how to select appropriate rotation?
My Questions
What is the intuitive reason behind doing rotations of factors in factor analysis (or components in PCA)?
My understanding is, if variables are almost equally loaded in the top ...
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45
votes
1
answer
23k
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PCA and Correspondence analysis in their relation to Biplot
Biplot is often used to display results of principal component analysis (and of related techniques). It is a dual or overlay scatterplot showing component loadings and component scores simultaneously. ...
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17
votes
3
answers
63k
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How to compute varimax-rotated principal components in R?
I ran PCA on 25 variables and selected the top 7 PCs using prcomp.
prc <- prcomp(pollutions, center=T, scale=T, retx=T)
I ...
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20
votes
2
answers
20k
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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 ...
- 301
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:
...
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19
votes
2
answers
87k
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How to interpret PCA loadings?
While reading about PCA, I came across the following explanation:
Suppose we have a data set where each data point represents a single student's scores on a math test, a physics test, a reading ...
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19
votes
2
answers
22k
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Creating a single index from several principal components or factors retained from PCA/FA
I am using Principal Component Analysis (PCA) to create an index required for my research. My question is how I should create a single index by using the retained principal components calculated ...
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12
votes
1
answer
58k
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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 ...
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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 ...
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