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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 Wed, 15 Jun 2011 11:14:01 +0200

```Thank you. I will follow your suggestion. I might update the thread
for how it worked.

Kind regards,
Tunga

>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 Kantarci <tungakantarci@gmail.com> wrote:
>>
>> 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 Kantarci <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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