# Alternatives to multinomial logistic regression

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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do you have many discreet design variables with small #of modality smaller than, say, 6? –  user603 Aug 16 '12 at 12:38
@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. –  Stuart Aug 16 '12 at 12:44
ok, that answers my question. –  user603 Aug 16 '12 at 12:49
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. –  JDav Aug 16 '12 at 17:01
@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?) –  Stuart Aug 16 '12 at 21:49
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