How many factors to retain in EFA (Exploratory Factor Analysis)? I have multiple measures from a scale and I want to determine the best factorial structure using EFA, in SPSS. I don't understand if I can retain the number of factors that I want to retain because they seem to be the most theoretically valid, or if I must keep the number of factors the program gives me based on Kaiser criterion or a scree plot. 
Say, I want to extract a total of 4 factors, after eliminating cross-loadings and items with small communality scores. Based on these criteria, the program extracts 6 (hypothetical) factors. Can I say I used EFA and retained 4 factors? Is that correct?
If I'm not clear, please state it. 
Any help greatly appreciated!
 A: Welcome to factor analysis, land of dubious decisions backed up by gut feeling, theory and intuition :) 
More seriously, you can retain any number of factors you like, even when the data is clearly telling you something else. The best test for a factor solution (indeed any statistical model) is how it performs on data not seen in the fitting process. 
There are many different decision criteria one can use to decide how many factors to retain, unfortunately they all tend to disagree with one another, which makes things harder.
The eigenvalues greater than one criterion (which SPSS uses by default) tends not to work very well in practice. I like to use parallel analysis or the miniumum average partial criterion (both available in the psych package for R).
However, given that you are using SPSS, my advice is to look at the scree plot, and retain the number of factors where the scree plot levels off.
I personally tend to use multiple criteria (and multiple rotations) to look for a structure that makes sense. If you have enough data (say 400 plus), I would perform EFA on half of the data, and then CFA on the other half so that you can test your model in a better way. 
To summate, I would look for the structure that makes the items fit together the best, and which matches theory as well as is possible (its important to try to prove theories wrong though, that's what science is all about). 
To answer your original question, yes you can say that you retained four factors, but (as with much else) you need to be able to back up your decision.
Hope this helps.
