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

[Klaus Pforr <kpforr@googlemail.com>]

<>

Dear Hadji,

I forgot to mention this: As you speak of choice experiments, you 
probably randomized the respondents on the "choice sets". This means 
that don't need fixed effects for the individuals, as you can safely 
assume that the covariates and the individual heterogenity are 
independent. This means that you should be able to use the more 
efficient random effects models described in Train. I don't have much 
experience on how these models are estimated, but you come very far with 
GLM. A good read on this with Stata might be Rabe-Hesketh 
(http://www.stata.com/bookstore/mlmus2.html). You could also start with 
a pooled mlogit, with robust or bootstrapped standard errors to correct 
for the correlation within inidividuals.

And to finally give you a short answer on the original question: I dont 
see how you can use clogit on your data without some major 
modifications. Its not simply a choice of the grouping variables.

best

Klaus

Am 30.01.2012 10:36, schrieb Klaus Pforr:
> <>
> 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
> >
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/help.cgi?search
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/


--
__________________________________

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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