How many factors to retain in EFA?

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!

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Of possible interest: VSS criterion for the number of factors. –  chl Sep 24 '12 at 21:23

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.

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Are you aware of SPSS, SAS, and MATLAB Programs for Determining the Number of Components and Factors. Using Parallel Analysis and Velicer's MAP Test? EFA on training sample followed by CFA on validation sample is no more than internal cross-validation and proned to overfitting, IMO (individuals were sampled altogether at the same time; better to have a new sample, which is often not available :-). –  chl Sep 24 '12 at 21:20
Thank you for the answer. That cleared some of the confusion. That is what I am looking for - the structure that makes the items fit best and is theoretically sound. I've done a number of rotations, eliminated some items rechecked the variance explained, etc. and in the end, after considering and reconsidering, I've decided to keep this one .. backing it up would be the second step. I could try what you've suggested but I don't have enough data to try two methods.. –  Ander Sep 24 '12 at 21:29
@chl i wasn't aware of those links for SPSS, SAS and MATLAB. I completely agree that the splitting sample approach is prone to overfitting, but it is less prone to overfitting than is prforming EFA and CFA on the whole sample (which happens far too often for my taste) –  richiemorrisroe Sep 25 '12 at 11:53
Sure. No problem with your response (I already +1). BTW, parallel analysis is now available in the latest version (v7) of Mplus. –  chl Sep 25 '12 at 11:56