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

 From Klaus Pforr To statalist@hsphsun2.harvard.edu Subject Re: st: clogit for discrete choice experiment with multiple choice sets Date Mon, 30 Jan 2012 11:13:57 +0100

```Wow! Thanks very much for this one.

Klaus

Am 30.01.2012 10:49, schrieb Nick Cox:
```
```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:
```
```<>

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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```

--
__________________________________

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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