How to impute or predict a characteristic when one of the IVs in the prediction is other household members having that same characteristic?

Question

In some data set A, we have: household id, person id, age, sex, and then a simple binary likes donuts / does not like donuts variable. In some other data set B, we have just household id, person id, age, and sex.

We have set up a regression in data set A with independent variables: age, sex, and does anyone in the household like donuts? in order to predict who likes donuts in data set B. People living in households where anyone likes donuts are more likely to like donuts themselves, so we don't want to throw out that intra-household probability when imputing donut likeage.

However, I'm unclear how to implement something computationally that maintains these within-household donut affinities when we're imputing do you like donuts in data set B? Do we impute at the household-level first, and then impute a subset of the people within sampled households? I feel like I should take a page out of the cluster sampling playbook, but I'm not really sure where to start looking.

Answer 1

It looks like you need to model sex and age predicting donut liking using a multi-level logistic regression where you have additional random effects and intercept nested within household. e.g.

lmer(donutLiking ~ sex * age + (sex * age | household), data = A)

From that you can get parameters that allow you to make probabilistic statements about the donut liking in data set B both taking into account cross household variability and random and fixed effects of sex and age