Holly writes,

I am interested in where children live when their parent is incarcerated. It turns out that there is a major gender difference in that when the father is incarcerated the child tends to live with the other parent, but when the mother is incarcerated the child tends to go to other relative or agency care.

In the data set I have, information (albiet limited) is available on up to 11 children of the incarcerated parent. What I think I have here is a two level model where at level 1 the child’s age and gender are predictors (as older children may end up living on their own), and at level 2 the variables are those of the incarcerated parent. My question concerns the two level non-linear (multinomial logit) model. My concern is at level 1. I understand that if a household only has one child, it “borrows strength” from other households with more children to estimate the level 1 model. Is that correct? So if there are two individual level predictors and usually one, two or three children with about 1000 parents, the two level model would be estimable? The outcome variable is polytomous with 5 categories: live with other parent, live with other relatives, live in agency or foster care, other care arrangement, and live on own. All children in this analysis are under age 18.

My response: yes, you should be able to estimate this model with no problems. You should also consider interactions between the level 1 and level 2 predictors.