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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 suest command 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).

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  • $\begingroup$ do you have many discreet design variables with small #of modality smaller than, say, 6? $\endgroup$
    – user603
    Commented Aug 16, 2012 at 12:38
  • $\begingroup$ @user603 sorry, I have no idea what you mean by discreet design variables. There are 5-10 explanatory variables (I try a few different models), 1 or 2 are continuous and the others binary. $\endgroup$
    – Stuart
    Commented Aug 16, 2012 at 12:44
  • $\begingroup$ ok, that answers my question. $\endgroup$
    – user603
    Commented Aug 16, 2012 at 12:49
  • $\begingroup$ I've just checked one of the 2 papers you mention. It happens to be a political sciences master thesis, I'll be rather sceptical in regards of their conclusions as numerical issues with MNP model may explain them. $\endgroup$
    – JDav
    Commented Aug 16, 2012 at 17:01
  • $\begingroup$ @JDav Thanks, I was a bit confused about whether those papers had widespread application or depended on particular data sets or types of data. I came across them while trying to figure out whether violating IIA is always a problem. (I think you edited out an earlier comment which seemed to say something useful about how the data sets examined in both those papers probably have particular characteristics explaining why MNP and MNL give similar results?) $\endgroup$
    – Stuart
    Commented Aug 16, 2012 at 21:49

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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: http://ideas.repec.org/a/tsj/stataj/v6y2006i2p229-245.html THe mixed mlogit approach introduces a random parameter that is common to your three categories, this way dependence across categories can be accounted for.

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  • $\begingroup$ Thanks, this is helpful, I'm looking into using a mixed multinomial model and `gllamm' as mentioned in your link. (Computational time is probably not an issue here.) (Incidentally, redoing the tests properly suggests that the model doesn't violate IIA. However, I don't find this plausible given my strong priors about school types, so want to try different models anyway.) $\endgroup$
    – Stuart
    Commented Aug 16, 2012 at 22:03
  • $\begingroup$ The IIA assumption refers to the correlation between unobservables across categories or conditional correlation. Your priors about school types might be already taken into account within your explanatory variables (observables) i.e. It's possible that IIA holds if your covariates are capturing the correlation between non private schools, this would explain your test result. You can try to estimate the model without covariates and rerun the tests to check for this. $\endgroup$
    – JDav
    Commented Aug 16, 2012 at 22:58

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