I've actually already done a lot of work on imputing eligibility. For my dissertation, I used the fraction of missing information as a measure of data quality. I applied the measure to survey data collections. In order to use this measure, I had to impute for item and unit nonresponse (including the eligibility of cases that are not yet screened for eligibility). The surveys that I used both had low eligibility rates (one was an area probability sample with an eligibility rate of about 0.59 and the other was an RDD survey with many nonsample cases). As a result, I had to impute eligibility for this work. An article on this subject has been accepted by POQ and is forthcoming.
The chart shown below uses data from the area probability survey. It shows the distribution of eligibility rates that incorporate imputations for the missing values. The eligiblility rate for the observed cases is the red line.
The imputed estimates appear to be generally higher than the observed value. This makes sense if the nonsample cases are mostly removed from the sample, and the remaining unobserved cases are more likely to be households than in the observed part of the sample.
The chart shown below uses data from the area probability survey. It shows the distribution of eligibility rates that incorporate imputations for the missing values. The eligiblility rate for the observed cases is the red line.
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