Linked Questions

215
votes
14answers
230k 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 ...
134
votes
5answers
92k 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?
113
votes
6answers
54k views

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 ...
73
votes
6answers
21k views

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 ...
63
votes
8answers
37k views

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 ...
49
votes
4answers
13k views

Why does the correlation coefficient between X and X-Y random variables tend to be 0.7

Taken from Practical Statistics for Medical Research where Douglas Altman writes in page 285: ...for any two quantities X and Y, X will be correlated with X-Y. Indeed, even if X and Y are ...
72
votes
4answers
21k views

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 ...
66
votes
1answer
69k views

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 ...
38
votes
3answers
31k views

Would PCA work for boolean (binary) data types?

I want to reduce the dimensionality of higher order systems and capture most of the covariance on a preferably 2 dimensional or 1 dimensional field. I understand this can be done via principal ...
29
votes
1answer
30k views

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 ...
33
votes
1answer
38k views

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 ...
20
votes
2answers
33k views

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 ...
19
votes
2answers
13k 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 ...
17
votes
1answer
14k views

What is the proper association measure of a variable with a PCA component (on a biplot / loading plot)?

I am using FactoMineR to reduce my data set of measurements to the latent variables. The variable map above is clear for me to interpret, but I am confused when ...
11
votes
3answers
11k 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 ...

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