# Should I involve the dependent variable when imputing missing values for an independent variable?

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?

• 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. – Mike Hunter Mar 11 at 13:41
• @MikeHunter Does that not create problems with overfitting? – sebhofer Mar 11 at 14:04
• @MikeHunter Thanks for the reference! Do you have a quick intuition as to why this was recommended? – J Li Mar 12 at 16:03