I read in this paper (page 3) comparing principal component analysis (PCA) to factor analysis (FA) that both methods need a number of observations about 5 times the number of variables. Why? and how would you reduce the number of variables if you have few observations only?

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    $\begingroup$ I checked the link, and the recommendation there is clearly wrong. I have often eared 5 times the number of desired components which makes more sense: for example PCA is often used when there are more variable than observations....though you don't need to take either as gospel: these things can be tested. $\endgroup$ – user603 May 28 '14 at 15:15
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    $\begingroup$ The "5 time" recommendation is for FA only, and is very crude rule of thumb. As the data grows in size, the ratio may safely shrink. For example, with 20 variables I'd prefer 100+ cases, sure. But with 100 variables, 300 cases will suffice. $\endgroup$ – ttnphns May 28 '14 at 15:45
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    $\begingroup$ @user603, I've never heard of FA (not PCA) with n<p. I even doubt such algorithm exist or is needed. $\endgroup$ – ttnphns May 28 '14 at 17:51
  • $\begingroup$ @ttnphns: sorry I miss-read your comment. $\endgroup$ – user603 May 28 '14 at 17:52

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