# Missing data due to absent parent

I am using the following regression:

$$\text{Test score} = \beta_0+\beta_1\text{Mother's employment}+\beta_2\text{Mother's education}$$

where "Mother's employment" is a set of dummy variables indicating whether the mother works more than 35 hours a week, is unemployed or is absent, and "Mother's education" is also a set of dummy variables indicating if the mother has a high school diploma, a college degree or a PhD.

If the mother is absent, then "Mother's education" is not applicable, i.e. there is no answer. How do I deal with this in Stata? Mean imputation? How do I do that with dummy variables?

In Stata you can perform multiple imputation. You can either check out Patrick Royston's package ice, which performs multiple imputations using chained equaltions (MICE) by typing (in Stata) net describe ice, from("http://www.homepages.ucl.ac.uk/~ucakjpr/stata/") .

Or you want to use the more recent versions (v11 forward) of Stata's mi impute (which I think is based on Royston's ice package), by typing help mi impute.

If I recall correctly (I may not) there may be some extra arcana in ice that's not in Stata's mi impute.

• Is multiple imputation really appropriate for a situation like this where the data is not missing at random (MAR)? If it is, how do I use multiple imputation given that I'm using multiple dummy variables? May 9 '14 at 14:02
• MI does not necessarily address missing not at random (although if you have data on the kind and causes of missingness that can help), though it does address mar and mcar. It addresses dummy variables by letting you create an appropriate binomial model (e.g logit, probit, complimentary log-log) for such variables. Same is true for other kinds of variables (e,g count, normal, ordered logit, etc.) May 9 '14 at 14:38
• So if multiple imputation isn't appropriate for MNAR, then what should I use instead? May 10 '14 at 16:14
• If you do not have identifiable measures on the causal path to observations being MNAR, you can't really do anything. That is, as I understand it, MI is your best alternative, but does not guarantee unbiased inference. May 11 '14 at 14:49
• What do you mean by causal paths to observations being MNAR? The reason the data on mom's education missing/not available is because the mother simply does not exist. Does this help in deciding what to do? May 11 '14 at 15:42

Mean imputation doesn't fully show the variation that would be in the data if it weren't missing.

Multiple imputation is generally regarded as superior. This is possible with categorical variables. In fact, "education" is ordinal. This article compares SAS and SUDAAN. For more general information see Little & Rubin. As to how to do this in STATA, perhaps someone else here will know, but that might be better asked on a Stata list.