Generating a categorical variable from an imputed variable

I am using multiple imputation to impute a continuous variable ($X$) with $\approx30\%$ missing values. I have a question regarding the generation of a new categorical variable ($Y$), starting from this imputed variable.

I want to use $Y$ as an independent variable in a logistic regression model instead of $X$ (I understand I'm losing information by doing this).

This is an example of how the categories in $Y$ would work:
$$Y = \begin{cases} 0 &{\rm if}\ \ \quad\quad\quad\! X < 100 \\ 1 &{\rm if}\ \ 100\le X < 200 \\ 2 &{\rm if}\ \ 200\le X < 300 \\ 3 &{\rm if}\ \ 300 < X \end{cases}$$

As imputed values vary between each set, I end up with a (not that much) different number of cases in each category of $Y$ on each imputed set.

Is this an appropriate approach if $X$ was imputed?

• Is there a reason you can't just use the imputed X as the variable? I don't see any advantage in this. – gung Mar 18 '14 at 14:10
• Thanks for the edit! The idea is to allow for easy interpretation and comparison with other studies by using standard reference points found in the literature. – user42148 Mar 18 '14 at 17:37