How to obtain individual factor scores after PCAs on multple imputed datsets???
I really hope, someone here can help me, I've searched the internet for hours and could not get any clue on how to solve my problem.
I want to do a principal component analysis on my dataset to combine my variables into a few components. The main analysis is, however, not the PCA, but a logistic regression with the different PCA factors as predictors. This means, I need to compute all the individual factor scores before I can proceed with the logistic regression. The problem is, that there are a lot of missings in my dataset and because of that, I cannot simply use listwise deletion because this would reduce my N too much. Therefore, I have to use an imputation method for handling my missing data. My method of choice would be a Multiple imputation method, and I've already generated 5 imputed data sets. BUT WHAT NOW??? In the literature on MI methods, it is usually recommended to combine the results of the main analysis, so I could do 5 PCAs on my five imputed datasets, but then I need to calculate individual factor scores to continue my analysis and do the logistic regression. And here's my dilemma: How can I do that with multiple imputed datasets?! I would have to combine the estimated missings from the 5 datasets directly, but this is not the usual way to analyse imputed datasets. The idea to model the uncertainty would get lost somehow, but I really do not know what to do or how to combine the individual estimates of missing values cases if I would try it - should I just calculate the means of each individual case out of the 5 different values which I obtained after the multiple imputation?!
If it were possible to create one single dataset out of the 5 imputed ones I could - theoretically - do all the analysis including the PCA just on that one data set...
Have you any, ANY ideas how to solve this problems?!