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I am building a model for predicting whether my users would recommend my wine. In the final model, the dependent variable, $Y_{ni}$ is whether user $n$ recommends wine variant $i$. However, in some cases, the income level of $n$, $Z_n$, is missing, and NOT at random (that is, a larger proportion of younger users have missing income level).

Now I really like the income variable, and do not want to exclude it in my final model. Therefore, I set out to impute this categorical variable $Z_n$ for where it is missing, using a simple multinomial logit model. My question is, should I involve $Y_{ni}$ in the imputation of $Z_n$? Why or why not, what is the best way to think about this? Does the answer depend on the final model family where $Y_{ni}$ is the dependent variable?

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    $\begingroup$ Paul Allison, in his 2001 book Missing Data, clearly states that using the DV when imputing missing information for predictors is not only viable, it's recommended. $\endgroup$ – Mike Hunter Mar 11 at 13:41
  • $\begingroup$ @MikeHunter Does that not create problems with overfitting? $\endgroup$ – sebhofer Mar 11 at 14:04
  • $\begingroup$ @MikeHunter Thanks for the reference! Do you have a quick intuition as to why this was recommended? $\endgroup$ – J Li Mar 12 at 16:03

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