# Factor analysis on multiply imputed data

I have a data set with approximately 500 observations on eight key variables. There are a lot of missing data; only about 1/12 of the observations are complete. I am using PROC MI and MIANALYZE in SAS to run various regressions on multiply imputed data, and this is working well. (There are about 200 variables in total, and there are high correlations among them which helps multiple imputation.)

However, I would also like to do factor analysis on the imputed data. This does not appear to be easily done in SAS, and it poses some interesting challenges:

1. The signs of the factors are arbitrary, so different imputations could yield opposite signs;
2. What was factor 1 in one imputation could be factor 2 in another imputation (although in this case, with so few key variables, it is likely that one factor is enough),

and probably other issues as well.

I could do exploratory factor analysis on each imputed data set, of course, and I could then average them on a sort of ad-hoc basis, but this seems very sloppy.

Some Googling did not reveal any solutions, but ... well, Google doesn't always find everything.

Any help, ideas, references appreciated. I have access to SAS and to R.

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@Stef's advise is right. Use procrustes rotation to identify which factor in one sample corresponds (similar) to which in the other. The rotation leaves you orthogonal rotation matrix which you can use to "translate" one loading matrix into the other if they proved to be in accordance. –  ttnphns Dec 27 '12 at 10:55
If you were doing a confirmatory FA using SEM, I think you could deal with the missing data under the same MAR assumption with expectation-maximization/ML (e.g. palgrave-journals.com/jt/journal/v11/n1/abs/5740069a.html). However, I'm not sure how to take advantage of the all of the auxiliary information you have, or how this might apply to exploratory FA. Just a thought. –  D L Dahly Dec 27 '12 at 14:07