# Data imputation for statistical analysis

Here is the situation: I have an individual level data set $X$ where each row is a person $i$ and each column denote characteristics of $i$. The problem is that my data is missing an important variable, lets call this $z_{i}$.

To resolve this situation I am considering using data imputation. Note, I have not done this before so I am: (a) a bit unsure of how it actually works in practice, (b) when it can be considered a valid thing to do (and when it is not appropriate). Information pertaining to each of these, or both would therefore be valuable.

My perception of the approach, and proposed way of proceeding is the following (please let me know if this is wrong): I do not have data on $z$ in my dataset, but I have access to other data from which I could devise a empirical CDF $F(z)$. Next I would simply draw from this distribution and crudely impute these data into a new column in my dataset $X$. Is this the general approach taken?

I understand that a more appropriate approach would be to devise the conditional empirical cdf $G(z|X’)$ and to sample form this. I can actually do that because I have a separate sample where a proxy for $z$ is available--call it $z'$, so I could probably use this to get $G(z'|X)$. Would I next simply draw from these conditional distributions in order to construct the new imputed variable in the old dataset $X$?

I understand that these questions are rather naive, and I understand that any procedure of this kind must come with its own set of assumptions that will restrict when it is and is not appropriate, but the suggestions above are simply my take on the "intuition" behind the approach, and I firstly want to make sure that this is correct. Second, any information pertaining to the assumptions required on the data would be much appreciated too.

• Are values of z missing for all individuals, or only for some? Also, do your "other data" contain values of the variables in your main data set?
– EdM
Commented Sep 2, 2014 at 16:53
• @EdM, z is missing for all individuals, and Yes--the "other data" contains the all the values of the variables in the main data.
– Seb
Commented Sep 2, 2014 at 18:23
• This depends on what you want to do with the imputed data set, which the question doesn't specify. Commented Nov 17, 2023 at 14:14