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# Re: st: Estimating a mixed logit model with mixlogit

 From Arne Risa Hole To statalist@hsphsun2.harvard.edu Subject Re: st: Estimating a mixed logit model with mixlogit Date Sat, 25 Jun 2011 13:00:31 +0100

```Tunga

You are right: you would have to write your own program to do this as
the utility function U_is is non-linear in the parameters. Note that
this was not the case in the model you outlined in your earlier
question.

Arne

On 24 June 2011 19:54, Tunga Kantarcı <tungakantarci@gmail.com> wrote:
> Hello,
>
> I would like to sketch a discrete response model and ask if I can make
> use of the mixlogit package. Actually I asked in a previous thread a
> similar question and Arne Hole replied my question but I now realize
> that I should elaborate more on my model because it is still not clear
> to me if I can estimate my model with mixlogit, or with any other
> Stata package I am not aware of. The model is as follows.
>
> In an online survey, I provide three retirement scenarios (early,
> normal and delayed retirement) where each scenario describes the labor
> force and work and retirement income trajectory of a hypothetical
> person at each age from 60  to 80. For example, from age 60 to 65, a
> hypothetical person is working full-time and from 66 onward he is
> fully retired. At each age the corresponding hypothetical work and
> retirement income is indicated. I ask the respondent to choose among
> the "three" retirement scenarios the one he likes the best. I want to
> model the choice as follows.
>
> V_is = U_is + E_is
>
> is a random utility model where E_is is assumed to be iid normal.
>
> U_is = sum operator_{t=60}^{80} rho^(t-60) * U_its
>
> is the total life cycle utility from retirement scenario s where s =
> {1,2,3}. rho is the discount rate to be estimated.
>
> U_its = alfa_i^0 + alfa_it^lf * L_its^f + alfa_it^lyf * L_its^f * Y_its^f
>
> is the within period utility: I assume that total utility is
>
> L_its^f is a dummy variable which indicates if respondent i, at age t,
> in scenario s, is working full time.
> Y_its^f indicates a replacement rate, to indicate retirement income,
> which takes a random value among the six predetermined values (I
> randomize over sub-samples in the sample). The base category is
> working full time and hence omitted.
>
> Alfa coefficients represent preference parameters and they are assumed
> to be random and depend on observed and unobserved individual
> characteristics in the following way.
>
> alfa_i^0 = beta^0x * X_i + e_i^0
> alfa_it^lf = beta^lfx * X_i + beta^lft * t + e_i^lf
> alfa_it^lyf = beta^lyfx * X_i + beta^lyft * t + e_i^lyf
>
> Unobserved  e terms are assumed to be iid normal. X_i is a vector of
> observed characteristics such as gender, education etc. t is age in
> the scenario described to the respondent (takes values from 60 to 80
> as defined in U_is).
>
> A respondent will choose, for example, scenario 1 if U_i1 + Ei1 > U_i2
> + Ei2 and if U_i1 + Ei1 > U_i3 + Ei3.
> Hence, probability of choosing first scenario is given by
> P(S=1|L,Y,X,t,e) = P(E_i2 - E_i1 < U_i1 - U_i2, E_i3 - E_i1 < U_i1 -
> U_i3).
>
> Then I write the likelihood function and then that function needs to
> be integrated over all possible values of e_i^0, e_i^lf, and e_i^lyf.
> This is a three dimensional integral which does not have a closed form
> solution and hence needs to be simulated.
>
> My question is the following. I wanted to write a Matlab code to
> estimate this model but I have a time constraint and hence wondering
> if I can estimate this model with mixlogit. It obviously does not seem
> feasible to run the mixlogit syntax right away. I could plug in the
> alfa coefficients in U_its and indicate the variables as having random
> coefficients in the syntax of mixlogit. However, I am not considering
> U_its but U_is. So it looks like I first need to instruct Stata about
> U_is. But U_is is a long expression where U_its at each age t is
> multiplied by the discount factor rho.
>
> Is there a relatively easy way of estimating this model in Stata, for
> example with mixlogit, or shall I give up and program it myself in
> Matlab?
> In particular, would it be feasible to estimate this model in Stata if
> I figure out how to instruct Stata about my utility function U_is?
>
> Thanks,
> Tunga
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>

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```