Multinomial Logit - Heteroscedasticity& Logistic Distribution Tests

[Igor Pavlok]

Hello all,

I'm currently writing a seminar paper and I'm using data of the National Institue of Health to indicate the impact of problem drinking on the employment status.

So far I could estimate the multinomial logitmodel and test for the IIA assumption. Everything was straight forward.
To answer your questions in advance: YES, I do have to use a logitmodel, I cannot fall back on a probitmodel.

Now, I'm already looking for about a week for how to test my multinomial logit for heteroscedasticity and the underlying logistic distribution.
I know that if my errors are heteroscedastic this will lead to a inconsistent ML-estimator and this will compound the interpretation of the coefficients.
Same is for the logistic distribution.

I'm totally desperate and do not know how to continue, without beeing able to check for these two assumptions. (And I guess it is quite to test for omitted variables as well. Haven't figured this out yet as well....)

I already tried to get some theoretical information from Greene (2002), Cameron/Trivedi (2005) and Agresti (2007), but for some reason, these authors only give detailed information for linear models, but not for discrete choice models.

Further I checked the "oglm" command, that someone mentioned in this forum, but as I figured out, this Stata command is only applicable to ordered choice models, not for multinomial models.

Additionally, the "hetprob" command is only useful for a probitmodel (as far as I know).

I hope some of you can help me with my issue. I am really thankful for every single hint!

Thank you in advance!

Best regards

-Igor

[Richard Williams]

Why are yu so determined to do this? I could be wrong, but (rightly or wrongly) I don't think most people worry about this.

I don't think there is anything built in to stata, but you might check out

http://www.stata-journal.com/article...article=st0104

https://www.sheffield.ac.uk/polopoly...e/mixlogit.pdf

[Igor Pavlok]

Why are yu so determined to do this? I could be wrong, but (rightly or wrongly) I don't think most people worry about this.

I don't think there is anything built in to stata, but you might check out

http://www.stata-journal.com/article...article=st0104

https://www.sheffield.ac.uk/polopoly...e/mixlogit.pdf

Thank you for your quick reply!

My professor urges me do to these tests, because they check/verify the model assumptions.
So the assumption that Var [u | X] = sigma² * I , i.e. all errors are homoskedastic, has to be checked, in his opinion.

Do you have any source, which says that it is not necessary to do so? Or more important, do you have any source that tells me what can happen if the error term is not homoskedastic and NOT logistic distributed? As I already said, I checked Greene, Cameron/Trivedi, Ronning and Agresti, but no one says anything about the consequences of missing or false model assumptions.

Thanks again very much for any advice.

Best regards
-Igor

[Richard Williams]

Do you have any source, which says that it is not necessary to do so? Or more important, do you have any source that tells me what can happen if the error term is not homoskedastic and NOT logistic distributed? As I already said, I checked Greene, Cameron/Trivedi, Ronning and Agresti, but no one says anything about the consequences of missing or false model assumptions.

I wouldn't say it is unnecessary. It may be a good idea. But as your own list of very prominent sources indicates, it is not something that is widely done.

[John Mullahy]

Igor: I agree with Richard: "…it is not something that is widely done." That said, these powerpoint slides from Bill Greene might be helpful. http://pages.stern.nyu.edu/~wgreene/...asticity.pptx.