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# Re: st: Mixed logit estimation with mixlogit

 From Tunga Kantarcı To statalist@hsphsun2.harvard.edu Subject Re: st: Mixed logit estimation with mixlogit Date Tue, 14 Jun 2011 17:03:59 +0200

```Please let me express what I understand from your suggestion.

U = alfa + beta X + e is the random utility model where beta is a
random coefficient and I assume e is normally distributed.

beta = gamma + lambda Y + n where Y is observed and n is unobserved
and assumed to be normally distributed with mean of zero and variance
to be estimated.

I plug beta in the first equation to get

U = alfa + gamma X + lambda Y X + n X + e is the new random utility
model where n is unobserved.

Question 1: Would I indicate X as the variable with a random
coefficient, which is e, in rand(varlist)?
Question 2: I guess I should get rid of the gamma then?

Tunga

PS. Thanks for the quick reply... and how lucky one can be to get a
reply from the author of mixlogit.

> Tunga
>
> If I understood your question correctly it seems to me that you can
> handle this by interacting X with the observed characteristics driving
> the heterogeneity in beta.

> Arne (author of -mixlogit-)

>> On 14 June 2011 14:27, Tunga Kantarcı <tungakantarci@gmail.com> wrote:
>> Hello,
>>
>> I have a random utility model where the coefficients are treated
>> random. That is, U = alfa + beta * X + U is a random utility model
>> where alfa and beta are treated as "random" coefficients which depend
>> on "observed" and "unobserved" characteristics. This leads to a mixed
>> logit model that needs to be estimated using maximum simulated
>> likelihood. I have read Arne Risa Hole's "Fitting mixed logit models
>> using maximum simulated likelihood" in The Stata Journal, 2007, 7 (3),
>> 388-401. It seemed to me that the mixlogit package can handle my
>> estimation. However, a first question I have is the following: In the
>> article, the random coefficient is treated "unobserved". In my model,
>> the random coefficient (beta above) depends on observed as well as
>> unobserved characteristics. It looks like I cannot specify that the
>> random coefficient depends on observed characteristics in the mixlogit
>> syntax.
>>
>> Would it be possible to specify that my random coefficients depend on
>> observed and unobserved characteristics prior and still make use of
>> the mixlogit procedure?
>>
>> Thanks,
>> Tunga

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