Factor analysis with more variables than observations

[shkingdom]

Dear all,

I have a plan to conduct a factor analysis to identify a smaller number of underlying components. The problem is that I have more variables than observations (i.e., 30 variables with 20 observations).
Are there any methods that can deal with this problem?

Thanks.

[Joseph Coveney]

I cannot offer anything other than the obvious two, which you've undoubtedly already considered. Someone else on the list might announce the availability of some kind of penalized or regularized factor analysis method, perhaps along the lines of LASSO and elastic net, that will work its magic and come to your rescue.

But I'm curious in that with factor analysis--exploratory or confirmatory--my impression is that you'd typically know what it is you're getting into; you'd have a good idea of at least how many factors you're seeking (and a general idea of their conceptual nature), and so you can plan your data gathering accordingly. How'd you get yourself into such a pickle?

[shkingdom]

Thanks for your reply.
No, I have not heard any of them. Are there any Stata commands for that? Additionally, I have never faced and thought about this situation. However, I heard that this kind of situation is common in some discplines (e.g., biology), and I think that it is also possible to deal with this issue in any other discplines if one has to deal with the fixed number of observations (e.g., administrative areas). Thanks.