Linked Questions
38 questions linked to/from What are the assumptions of factor analysis?
269
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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 ...
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137
votes
7
answers
30k
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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 ...
- 2,415
146
votes
6
answers
88k
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Should one remove highly correlated variables before doing PCA?
I'm reading a paper where author discards several variables due to high correlation to other variables before doing PCA. The total number of variables is around 20.
Does this give any benefits? It ...
- 1,571
102
votes
1
answer
126k
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What correlation makes a matrix singular and what are implications of singularity or near-singularity?
I am doing some calculations on different matrices (mainly in logistic regression) and I commonly get the error "Matrix is singular", where I have to go back and remove the correlated variables. My ...
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42
votes
2
answers
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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 ...
- 3,653
42
votes
1
answer
45k
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Is there Factor analysis or PCA for ordinal or binary data?
I have completed the principal component analysis (PCA), exploratory factor analysis (EFA), and confirmatory factor analysis (CFA), treating data with likert scale (5-level responses: none, a little, ...
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37
votes
3
answers
59k
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PCA on correlation or covariance: does PCA on correlation ever make sense? [closed]
In principal component analysis (PCA), one can choose either the covariance matrix or the correlation matrix to find the components (from their respective eigenvectors). These give different results (...
- 669
43
votes
1
answer
62k
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Doing principal component analysis or factor analysis on binary data
I have a dataset with a large number of Yes/No responses. Can I use principal components (PCA) or any other data reduction analyses (such as factor analysis) for this type of data? Please advise how I ...
- 431
33
votes
1
answer
47k
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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 ...
- 14.5k
20
votes
3
answers
21k
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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
17
votes
2
answers
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Why does sphericity diagnosed by Bartlett's Test mean a PCA is inappropriate?
I understand that Bartlett's Test is concerned with determining if your samples are from populations with equal variances.
If the samples are from populations with equal variances, then we fail to ...
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14
votes
2
answers
36k
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In Factor Analysis (or in PCA), what does it mean a factor loading greater than 1?
I've just run a FA using a oblique rotation (promax) and an item yielded a factor loading of 1.041 on one factor, (and factor loadings of -.131, -.119 and .065 on the other factors using pattern ...
11
votes
3
answers
24k
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Is it acceptable to have only two (or less) items (variables) loaded by a factor in factor analysis?
I have a set of 20 variables that I have put through factor analysis in SPSS. For purposes of the research, I need to develop 6 factors. SPSS has shown that 8 variables (out of 20) have been loaded ...
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6
votes
3
answers
4k
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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
9
votes
2
answers
10k
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Skewed variables in PCA or factor analysis
I want to do principal component analysis (factor analysis) on SPSS based on 22 variables. However, some of my variables are very skewed (skewness calculated from SPSS ranges from 2–80!).
So ...
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