Multilevel logistic regression with rare events


I've conducted a survey with a binary dependent variable that I assessed twice. My sample is small (n=160) and I got one answer rarely (0=6; 1=154).

I'm wondering which statistical test to use. I know that there is multilevel logistic models to account for the nested data structure and that there is, for example, penalized maximum likelihood for the small sample/rare events. Is there a combination of both?

I'm using Stata14.



Not a robit
Good question. Did 80 people answer it twice or if not what was the outcome proportion at each unique time point?

How man covariates do you have and how are they formatted?

I wasn't precise when asking my question, sorry... 160 people participated in my survey, so I actually have n=320 for my dependent variable. All participants answered twice (no missings). But unfortunately, for both measurements the distribution of 0 and 1 is unequal, biased heavily towards 1.

I have 6 covariates, all continous.

Thanks a lot!