Ignorable and nonignorable missing data

[Bill Smith]

Suppose I have a data set with variables A-Z. Say each A-Y has a small percentage of values MAR, and Z a much larger percentage of missing values, all of which are MNAR, so that two separate imputation models apply. Would it be better to impute A-Y first using standard multiple imputation techniques, then use that data in a model (i.e., Heckman, PMM) to fill in the values in Z, or would one use the non-missing data in A-Z to first impute the values of Z, then impute the values of A-Y? I understand the dangers inherent in the assumptions behind models that underlie imputation of MNAR data.

[Carlo Lazzaro]

Bill:
I would:
- use multiple imputation for MAR first;
- make a set of assumptions concerning MNAR, choose one of them as base case hypothesis for replacing MNAR values and use the remaining assumptions for sensitivity analysis purposes.
You may also want to take a look at: Van Buuren, S. (2012), Flexible Imputation of Missing Data. Chapman & Hall/CRC, Boca Raton, FL. ISBN 97814398