What do residuals mean in the context of zero-inflated negative binomial regression?
I'm learning zero-inflated negative binomial regression. The data is from a state education system and includes variables about the number of migrant students identified by each school (which is zero-inflated) as well as variables reflecting a number of sociodemographic characteristics (e.g., poverty level, race)
My analyses have two goals:
- Can I predict zero-inflation and the number of migrant students identified at each school by sociodemographic characteristics?
- Can I use the residuals to identify individual schools that are likely under-identifying migrant students?
I still have a soft/incomplete understanding of the dual-component nature of the ZINB regression, meaning the binomial / zero-inflation model combined with the negative binomial / count model. When I ask r for residuals, I get one residual coefficient for each school.
Is the residual for the binomial model? Or is the residual for the count model? Some combination? Am I thinking about this all wrong?