st: Multiple imputation with incidental selection

[Lance Erickson <lance_erickson@byu.edu>]

Dear Statalisters,

My question is first conceptual and second about application in Stata.

First, is it reasonable and/or defensible to use multiple imputation for missing data due to incidental selection? 

The particulars: I have a dataset with a module on religion that asks a variety of questions about behaviors (e.g., frequency of church attendance, prayer, etc.). The first question in the module asked about religious affiliation and respondents were skipped out of the module from there if they reported no affiliation. However, just because someone isn't officially affiliated with a religion doesn't mean that they never pray, read sacred texts, etc. So, recoding unaffiliated to "never pray" seems like it would introduce some bias. On the other hand, it seems safe to assume that, on average, the unaffiliated might have lower levels of these religious behaviors than the affiliated. My (perhaps incorrect) understanding of missing data theory is that as long as I include religious affiliation in the imputation model, I can be confident that my results are unbiased. But I have a vague sense that if I impute missing values on these variables for the unaffiliated that I will also i!
 ntroduce bias. Any ideas?

Disclaimer: I've estimated 3 models (dependent variable educational attainment) using different approaches to identify any implications for my results. One model imputes values for religious behaviors (e.g., frequency of prayer) for the unaffiliated. Another model has religious behaviors for the unaffiliated coded to the minimum of the scale (i.e., never). The final model excludes the unaffiliated. I take this as evidence that the results are robust to the approach taken, but I wonder if there is a more general, conceptual approach to the issue that I haven't been able to locate.

Second, other than include religious affiliation in the imputation model, would there be a particular way to program -mi impute- to account for the incidental selection here?

Thanks,
Lance


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