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My dependent variable is Choice, 0 for non-issuers, 1 for seasoned equity issuers, 2 for convertible issuers and 3 for bond issuers. I use the following command to run a multinomial logit regression:

mlogit Choice CR $ConVar, base(0)

To test for IIA assumption, I use the following command:

mlogtest, haus

The output is below:

enter image description here

Does this result indicate that IIA is violated?

Then I test the IIA assumption for another multinomial logit regression, in which the dependent variable is Security (0 for seasoned equity issuers, 1 for convertible issuers, and 2 for bond issuers).
The Stata commands are below:

mlogit Security CR $ConVar, base(0)
mlogtest, haus

Output of IIA test is shown below:

enter image description here

Again, does this mean that the IIA assumption is violated?

Could anyone interpret these two results for me? And I am not sure why some categories of dependent variables have negative chi2.

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1 Answer 1

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Significant values of chi2 indicate that the IIA assumption has been violated. You can look at the p-values in the 4th column to gauge that.

Some of your test statistics are negative, which is fairly common. Hausman and McFadden (1984, p. 1226) argue that a negative result is evidence that IIA has not been violated.

This logic would suggest that the first one passes, and the second fails.

A good, accessible book with lots of Stata examples and much intuition on this is Long & Freese's Regression Models for Categorical Dependent Variables Using Stata.

The (partially gated) paper mentioned above is: Hausman, Jerry, and Daniel McFadden. "Specification Tests for the Multinomial Logit Model." Econometrica 52, no. 5 (1984): 1219-240.

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