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

[Klaus Pforr <kpforr@googlemail.com>]

<>
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.
>
> Any advice is appreciated.
>
> Hadji
>
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--
__________________________________

Klaus Pforr
MZES AB - A
Universität Mannheim
D - 68131 Mannheim
Tel:  +49-621-181 2797
fax:  +49-621-181 2803
URL:  http://www.mzes.uni-mannheim.de

Besucheranschrift: A5, Raum A309
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