I have a large public dataset describing traffic crashes. I am interested in events occurring in a certain type of street intersection only. The dataset has a lot of missing values, and I plan to use multiple imputation (I'm using SAS).
My plan has been to use the full dataset to do the MI, then select the cases I want to analyze, then do the analysis.
Three variables provide information for selecting the cases in which I am interested. But here is the problem: two of these variables have missing values, so there will likely be uncertainty as to whether these cases belong in my analysis.
I have looked and looked for a description or example of this online but found nothing. I'm not sure at this point if I'm making some kind of naive student error (my first time doing MI), or whether people don't really talk about this.
It's easy to think of ad hoc ways of proceeding (e.g., impute only from cases that are complete on the selection variables--which seems almost as bad as just analyzing only complete cases--or selecting cases in which some threshold proportion of imputed values for a case meet the selection criterion). However, I'd like to do this "by the book," to the degree there is a book.
Does anyone have thoughts about how I should select cases for analysis?
(A few details: Most of the variables are categorical, and the missing pattern is decidedly nonmonotonic. I have been planning to convert the categorical variables into dummy binaries and use MCMC for the imputation. There is a monotonic-ish missing pattern among the case selection variables, so I could do MI in two steps, using the discriminant analysis method, which at least gives discrete values within a dataset, for the selection variables, but this still does not solve the likely problem of variability of values across MI datasets in the selection variables. As you can see, without a case selection method in mind ahead of time, I'm just grasping for things that make the problem seem simpler.)