stata mlogit IIA under Hausman and Small-Hsiao tests
Dear Statalists,
I am currently using a multinomial logit model, where the dependent variable has four categories, 0, 1, 2, and 3. The base case is category 0. Before running the multinomial logit regressions, I test the independence of irrelevant alternatives (IIA) assumption. I use two different tests: Hausman test and Small-Hsiao test.
The result of Hausman test shows below:
From the above results, I guess the IIA assumption is violated.
Then I use the Small-Hsiao test:
Small-Hsiao shows that IIA is not violated.
In my case, Hausman and Small-Hsiao give different results. Could anyone help with which test I should follow and can I still use multinomial logit regression? Many thanks.
I am currently using a multinomial logit model, where the dependent variable has four categories, 0, 1, 2, and 3. The base case is category 0. Before running the multinomial logit regressions, I test the independence of irrelevant alternatives (IIA) assumption. I use two different tests: Hausman test and Small-Hsiao test.
The result of Hausman test shows below:
Code:
. mlogtest, haus base
**** Hausman tests of IIA assumption (N=3106)
Ho: Odds(Outcome-J vs Outcome-K) are independent of other alternatives.
Omitted | chi2 df P>chi2 evidence
---------+------------------------------------
1 | 257.499 28 0.000 against Ho
2 | 0.000 1 1.000 for Ho
3 | 0.000 1 1.000 for Ho
0 | 0.000 2 1.000 for Ho
----------------------------------------------
.
Then I use the Small-Hsiao test:
Code:
. mlogtest, smhsiao base
**** Small-Hsiao tests of IIA assumption (N=3106)
Ho: Odds(Outcome-J vs Outcome-K) are independent of other alternatives.
Omitted | lnL(full) lnL(omit) chi2 df P>chi2 evidence
---------+---------------------------------------------------------
1 | -488.683 -476.399 24.568 30 0.746 for Ho
2 | -1213.261 -1197.199 32.123 30 0.362 for Ho
3 | -1051.023 -1032.170 37.705 30 0.157 for Ho
0 | -376.918 -355.686 42.464 30 0.065 for Ho
-------------------------------------------------------------------
.
In my case, Hausman and Small-Hsiao give different results. Could anyone help with which test I should follow and can I still use multinomial logit regression? Many thanks.
