I am using CFA (confirmatory factor analysis) to create a measurement model of social capital that is to be used in a Cox regression. Because of missing data I first impute the incomplete data by MICE in R before I use CFA to make the measurement model. Afterwards, I extract the factor scores from the CFA which I will use in a Cox regression. So far so good.
However, I have several interactions between the computed factor scores for social capital and different variables e.g. gender that I would like to analyze as well.
Now here is my dilemma: One of the ground rules in multiple imputation is that ALL the variables that are in the statistical model HAVE to be in the imputation model including interaction terms. Otherwise the results can be biased towards 0.
Since I don't have the factor scores from the CFA until after the first imputation I can't create the interaction terms to be included in the first imputation.
Since this could significantly bias my results I have chosen to extract the factor scores for my social capital measure and place it in my incomplete (unimputed) dataset where I now can create my interaction terms and impute the data again. I then impute the data based on the same seed, number of datasets and iterations as before. The variables are also the same except of course for my factor score for social capital and the different interaction terms.
My question is as follows. Is this the correct way to handle the dilemma that I don't have my factor scores until after the imputation and therefore can't include the interactions that is to be used in the Cox regression?