Thanks for the response. The first method you propose for exploration could be very useful. I guess I didn't think of it in thee terms and I probably should have.

The second approach is very similar to what I was thinking of doing if all else fails. I would have imputed the expected values and just use that for EFA. (I would do this either through imputing a large number of times and averaging the imputed values, or just use the EM algorithm probably through SPSS MVA.) I guess this does the same thing that you approach proposes.

The problem with this approach is that it underestimates the uncertainty of the unknown values. For most analysis rubin's rules can be used to combine all point estimates as long as they have a standard error. Mplus will now give you standard errors for the loadings so that is very useful. But the decision on the number of factors to extract is problematic. (Even without any missing data it is problematic.) Lets say I establish a rule on the number of factors to extract. I impute m times. Analyze the m datasets and I get 3 factors for a 1/3*m datasets, 4 for 1/3*m and 5 for 1/3*m. How many to extract then? Go with the median? Why? Why not?

Of course, one solution is not to bother. Just do it and consider the problem when (if) it arises. I can totally imagine that all imputations would give me the same results. Problem solved then.

There also might be something else I am missing. It is not entirely clear what the advantage of any of the above is to listwise deletion. etc.

Thanks for your quick input.

On Dec 7, 2009, at 5:58 PM, Tomáš Kubiš wrote:

Hi Levente,
if I understood your issue right, you have MI data and want to conduct fa on this data. I faced the same problem and came up with two ways how to conduct such an analysis.

First, you can use imputations separately, conduct the fa on each one of them and observe if there are significant differences in the loadings of factors in comparisson to an unimputed dataset. Moreover you can observe if imputaions differ among themselves. For pure exploration, this will help you to identify dimensions and you can generalize the result in that you build an average of loadings for each factor and thus get one set of factors.

Second, you can take the covariance or correlation matrices of the imputed datasets and build an average of them. Then you can conduct the fa on this average cor or cov matrix. You have one matrix and thus get again one set of factors.

As you said, it is difficult to find literature and I didn't find support for any of these two methods. I would be inclined to use the second one and make an average of cor matrices because it is the input into the factor analysis.

Good luck with your analysis and I hope that you will get some more scientific help.

Regards,

Tomas

2009/12/7 Levente Littvay <levi@littvay.com>

Dear Amelia List

Does anyone know of a good and accessible way to analyze multiply imputed data using exploratory factor analysis? (Possibly, would Zelig know how to do this?) Anything else? SPSS won't do it. Mplus won't do it (as far as I can see). I found very little by way of published work on the topic. I could use a bit of guidance.

Thanks

Cheers

Levente Littvay
Assistant Professor
Department of Political Science
Central European University
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