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I have a data set with 18% of AGE variable missing which is an important variable for analysis.

  1. Should I try regression imputation or should I drop those observations?

  2. Does even regression imputation make sense in this case (for age)??

  3. I also have income variable but the correlation between age and income is negative and strength is .1

What should I do?

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In any missing data situation the first thing to ask is why the data are missing. There are three types;

Missing completely at random (MCAR) - this means that the missing data are a totally random set of the data. This rarely happens unless there is some sort of mechanical glitch

Missing at random (MAR) - this means that the missing data could be a non-random subset of the data, but that the non-randomness can be completely explained by variables that are in the data.

Not missing at random aka nonignorable non-response (NMAR) - neither of the first two.

If it's MCAR, then the only thing lost by deleting the data is statistical power. If MAR, then the usual approach is multiple imputation, to account for the variance in single imputation regression imputation

If the data are NMAR then, technically, nothing will really work. However, multiple imputation may still be a good choice. Joe Schafer said (informally; he gave a talk at my old workplace and this was in the Q and A) that MI works well unless the data are "really NMAR".

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Peter's response highlights the main issues with missing values. If you are looking for a thorough non-technical discussion, could I point you towards the chapter in Gelman and Hill (pdf).

I assume you are working from survey data, in which case you could have quite a few variables with which you can perform imputation.

If you are doing your analysis in R, you may want to check out random forest missing values imputation, or rfImpute in the randomForest package. This approach has the advantage that it deals well with both categorical and continuous data, and the underlying model is quite flexible. In a paper last year (it's not a great paper!) I give a little description of how it works (see section 4 of this paper).

All the best

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