I have been using a multinomial logistic regression to examine the correlates of school choice. There are three possibilities for the dependent variable: government school, private school, and NGO (non-government organization, i.e. non-profit) school. However, I’m pretty sure the problem violates the independence of irrelevant alternatives (IIA) assumption – both on intuitive grounds (e.g. removing the NGO option would increase the probability of going to government vis-a-vis private school) and using the
suestcommand in Stata to conduct a Hausman test (not 100% sure I did this correctly, but that’s another issue).
Anyway the question is, if multinomial logit isn’t the best model to use then what else can I try? Since there are only three options, can I simply use two separate logits (e.g. NGO vs. other and private vs. other) or is that not appropriate? As I understand it, other multinomial methods bring their own problems, such as the Invariant Proportion of Substitution property (as explained here (pdf)). For what it’s worth, multinomial probit produces similar results to mlogit.
Is it possible to argue that the mlogit results are reasonably accurate (perhaps, to argue that it is imperfect but the best available model) despite violating IIA, and if so what evidence would support or refute that claim? (These two papers argue that multinomial logit is at least as accurate as multinomial probit, in the field of voter choice).
If your IIA test refuses the IIA , then you should estimate an alternative model like a nested probit or a mixed multinomial logit. As you mention, you may split you problem in two nested dichotomies: private or not, and Ngo or government. The nested approach is already available in stata whereas the mixed multinomial one can be found here:
THe mixed mlogit approach introduces a random parameter that is common to your three categories, this way dependence across categories can be accounted for.