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Factor Analysis - kick out 1 of the 2 remaining factors?

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Hey guys,
I have a question concerning factor analysis in Stata. It's not really about the implementation but about how to interpret results/ work with them.

if after a FA (and rotation of factors) I have 2 factors left explaining my concept, can I kick out one of them, preferably the one with the lower Cronbach's Alpha? (i.e. I had 7 items asking for political opinions, after FA two factors where identified, each consisting of 3 items (one was droped for high uniqueness values). now i tested for cronbach's alpha and the first factor has a CA of 0.6 and the second of 0.5. can i just continue doing my regressions on "political opinion" with the first factor as dependent variable and simply drop the second (as it has to low explanatory power for the concept of political opinion)?

thanks for helping out!

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