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Is PCA and Factor Analysis same? Both are used for Data dimension reduction but theoretically I am not able to find the difference between them?

I did FA in SPSS to reduce number of variables in my data set. I think the same think can be done using PCA as well. Never did PCA so wanted to know exact difference between two techniques.

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  • $\begingroup$ If you look at Wikipedia you will immediately see that the two are different. $\endgroup$ Sep 20, 2018 at 10:43
  • $\begingroup$ Could you please explain with an example so that I get an clear idea $\endgroup$ Sep 20, 2018 at 10:47
  • $\begingroup$ The Wikipedia page actually has a dedicated section on this comparison with its references. Definitely worth exploring deeper... $\endgroup$
    – mapto
    Sep 20, 2018 at 11:38

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Principal components don't have to make sense, they are just artificial numbers, summarized data if you will, used e.g. for visualizations

With factor analysis you try to find a latent variable (an underlying mechanism) that explains the data. Factor analysis is often used in psychology, eg the personality trait extraversion (the factor) explains certain behaviours (eg certain behaviours reported in a questionnaire)

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PCA explains the whole variability (as it reveals latent state-space due to dimensionality reduction). Factor analysys explains only that part of variability that is common for all units.

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