Re: st: clogit for discrete choice experiment with multiple choice sets

[Nick Cox <njcoxstata@gmail.com>]

Thanks on behalf of the list to Klaus for giving full references.

A pedantic correction: Cambridge University is not based in Cambridge,
MA but in Cambridge, UK! Cambridge, MA is the seat of much younger
universities.

Nick

On Mon, Jan 30, 2012 at 9:36 AM, Klaus Pforr <kpforr@googlemail.com> wrote:
> <>
> Dear Hadji,
>
> this seems to be an application for multilevel or panel multinomial logit.
> There is a fixed effects model by Chamberlain (1980). The fixed effects are
> in your case on the person level. Possible random effects solutions are
> discussed in Train (2009). The first model has not been implemented yet (cf.
> Allison 2009, p.44), but I'm am currently working on an ado for this model
> (http://www.stata.com/meeting/germany11/desug11_pforr.pdf). The latter
> models are complicated and can be estimated with GLM.
>
> There is a also back door solution for the fixed effects estimator for small
> samples and short panel/small clusters (in your case the the number of
> experiments). Börsch-Supan applied the Chamberlain model on housing choices
> and rearranged the data in a way so that he could use the implemented clogit
> to estimate the model. The data organisation is the following: In a
> simplified version of your case you would have only 3 experiments (or panel
> time points in the chamberlain lingo) and 3 alternatives.
> Lets say you have the indiv 1 with this selection (this is example is
> purposely simple)
> xp choice
> 1 1
> 2 2
> 3 3
>
> When you look up the equation in the chamberlain model, you find the
> conditional likelihood of the prob to choose the time series that was chosen
> conditional ("i.e. divided by") the prob of all permutations of the chosen
> alternatives.
>
> You look at all combination of choices, which have the same number of 1's,
> 2's and 3's (or in general all of your outcomes) for the specific
> individual. This set of permutation makes your set of alternatives:
>
> Permutaion Was it chosen?
> 123 yes
> 132 no
> 213 no
> 231 no
> 312 no
> 321 no
>
> After this reorganisation you run a clogit on the data with respondent as
> group, and have the multinomial logit with fixed effects. This is very
> cumbersome even your simple application, but it works. You also have to
> think about how to generate you independet variable for this to get the
> coefficents that you want.
>
> Here is the literature:
>
> Börsch-Supan, Axel. 1987. Econometric analysis of discrete choice: With
> applications on the demand for housing in the U.S. and West-Germany. Berlin
> et al.: Springer Verlag.
>
> Börsch-Supan, Axel. 1990. Panel data analysis of housing choices. Regional
> science and urban economics 20: 65–82.
>
> Börsch-Supan, Axel, und Henry O. Pollakowski. 1990. Estimating housing
> consumption adjustments from panel data. Journal of urban economics 27:
> 131–150.
>
> Chamberlain, Gary. 1980. Analysis of Covariance with Qualitative Data.
> Review of Economic Studies 57: 225–238.
>
> Train, Kenneth E. 2009. Discrete choice methods with simulation. 2. ed.
> Cambridge, MA et al.: Cambridge University Press.
>
> I hope this helps
>
> best
>
> Klaus
>
> Am 28.01.2012 08:32, schrieb Hadji Cortez Jalotjot:
>>
>> Hi!
>>
>> I
>> implemented a discrete choice experiment to model vehicle choice.  In my
>> questionnaire, I presented each respondents with 10 choice experiments
>> or choice sets with each choice set having 3 alternatives or choices.
>>
>> The explanatory variables are the characteristics of the vehicles.  With
>> this, I am fitting a conditional logit model.
>>
>> In my data set, dummy variables were used to represent the explanatory
>> variables.  Since each choice experiment has 3 alternative options, each
>> choice experiment corresponds to 3 rows of observations.  So 10 choice
>> experiments per respondent X 3 alternative options per choice
>> experiments = 30 rows of observations per respondent. (sample data below
>> shows only 3 choice experiments with
>> some of the explanatory variables for respondent 1)
>>
>>
>> respno        choice_set    choice    var1a    var1b    var1c  .. . ..
>>   none
>>
>> 1                       1                1            1        0        0
>>                        0
>> 1                       1                0            0        0        1
>>                        0
>> 1                       1               0            0        0       0
>>                      1
>>
>> 1                        2              0            0        1        0
>>                      0
>>
>> 1                        2               1            1        0        0
>>                        0
>>
>> 1                        2               0            0        0        0
>>                        1
>>
>>
>> 1                        3                0            0        0        1
>>                        0
>>
>> 1                        3                0            1        0        0
>>                        0
>>
>> 1                        3                1            0        0        0
>>                        1
>>
>> For clogit to work, I must select a variable that will identify the
>> grouping for which the software will run the analysis.
>>
>> Now, for this kind of data in which respondents answered multiple choice
>> sets (10 in my case), which should I used as a group?
>> Is it the respno or choice_set?
>>
>> I am confused because if I use respno, Stata says multiple positve
>> outcomes in a group.  And the predicted probabilities is computed for
>> the whole 30 alternative options and not only for the 3 alternative
>> options per choice set.
>>
>> But if I use the choice_set as the grouping and I extend the model to
>> include respondent characteristics (e.g. income), I may have problem
>> with fixed effects because for example choice_set 1 and choice_set 2 is
>> from the same respondent and therefore will have exactly the same
>> income.
>>

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