I have some response data that has the 5 following categories:
- strongly agree
- somewhat agree
- somewhat disagree
- strongly disagree
- don't know
I want a two component model that uses a logistic regression for the probability of a "don't know" response, and a separate ordinal model for the ordered categories conditional on response in one of those categories.
My question: is it possible to construct a likelihood function to fit the two components simultaneously, and if so, how would you do that?