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I get a negative value for the Hausman test for the independence of irrelevant alternatives (IIA) assumption. Now I find contradicting conclusions in the literature: some people say that I should take the absolute value, others say that the value should be rounded to $0$. What should I do?

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From Long's Regression models for categorical and limited dependent variables (pg. 184):

a negative $H_{\text{IIA}}$ is evidence that IIA holds.

They cite Hausman and McFadden (1984, p. 1226) as the source. Rounding to zero should make no difference in the $\chi^2$ test, as that is not the tail of the distribution you are looking at (so you would always fail to reject the null in that case). Hausman and McFadden (1984) do propose an alternative estimator to force the covariance matrix to be positive definite.

I'm confused how taking the absolute value could ever be justified in this circumstance, but I would not claim expertise in this area.


Citations

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