Hausman test of IIA - Interpretation

[Jill Adona]

Dear all,

I tested my 2011 data for IIA and got this result:

qui mlogit outcomes $xlist [pw=pfwgtpop], baseoutcome(0) vce(cluster hh_id) allbaselevels
estimates store all
qui mlogit outcomes $xlist if outcomes<3 [pw=pfwgtpop], baseoutcome(0) vce(cluster hh_id) allbaselevels
estimates store no3
hauman all no3, alleqs force

Result:
chi2(50) = -44.07
chi2<0 ==> model fitted on these data fails to meet the asymptotic assumptions of the Hausman test

Doing the same for 2013, I get:
chi2(50) = 65.97
Prob>chi2 = 0.0645

And for 2014:
chi2(50) = 19.33
Prob>chi2 = 1.000

First, can anyone help me interpret this? From what I've read, a negative chi2 quite basically means that IIA is not violated. But what do positive chi2 results mean, and their P-values? Why didn't I get a P-value when I got a negative chi2? Do my 2013 and 2014 data also not violate the IIA assumption?

Second, this is the Hausman test for only one instance where I remove the 3rd outcome. Do I need to conduct it removing all the outcomes one at a time? Do I switch the base outcomes as well?

Thanks for your help!

[Carlo Lazzaro]

Jill:
Example 2 under -hausman- entry in Stata .pdf manual (pages 938-41) covers what you're interested in.

[Joao Santos Silva]

Dear Jill,

A couple of points here:

a) If you are testing the IIA, you should not be using clustered (or robust) standard errors. That will have an impact on the outcome of the test.

b) I would not say that a negative Hausman statistic can be interpreted as supporting the null; quite on the contrary.

Finally, there are much better ways to test the IIA assumption.

Best regards,

Joao

[Jill Adona]

Dear Joao, yes, thanks, I realized that I shouldn't be using vce(cluster)!

Carlo, I read up on that and it helped a lot, thank you!

[Scott Rick]

Joao Santos Silva and Carlo Lazzaro To establish IIA for a multinomial logistic regression model which has three a category dependent variable called DV (1 = no college, 2 = immediate enrollment in college, and 3 = on-time enrollment in college; base category is 2) do I need to do the hausman on all combinations? So, allcats+no3 and allcats+no1? Or can I just do it on allcats+no3 and establish IIA?

[Joao Santos Silva]

Dear Scott Rick,

You can use just one but, as I said above, there are better ways to test the IIA.

Best wishes,

Joao

[Scott Rick]

Thank you Joao Santos Silva

[Hugo Castro Silva]

Joao Santos Silva, you previously mentioned there are better ways to test the IIA other than the Hausman test. Can you recommend other ways to test?

Thank you!

[Joao Santos Silva]

Dear Hugo Castro Silva,

In my experience, this works much better and it is easy to implement.

Best wishes,

Joao

[Hugo Castro Silva]

Dear Hugo Castro Silva,

In my experience, this works much better and it is easy to implement.

Best wishes,

Joao

Thank you! I will have a look.