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# Re: st: Mixed logit estimation with mixlogit

 From Arne Risa Hole To statalist@hsphsun2.harvard.edu Subject Re: st: Mixed logit estimation with mixlogit Date Wed, 15 Jun 2011 09:27:51 +0100

```Tunga

This is the sort of specification I had in mind. In response to your questions:

Q1: Yes, X should be specified to have a random coefficient and the
X*Y interaction a fixed coefficient

Q2: Gamma is estimated (as the mean parameter) along with n (the SD
parameter) when you specify X to be random.

I hope this helps.

Arne

On 14 June 2011 16:03, Tunga Kantarcı <tungakantarci@gmail.com> wrote:
> 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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