[Limdep Nlogit List] Reference alternative of individual characteristics in the case of variable sized choice sets

[Lixian Qian]

Dear Bill,

Thanks a lot for your reply.

Maybe I used the wrong term of "reference alternative".

Please let me rephrase the problem.

When everyone has the same choice set, we normally interpret the income coefficient as "compared to those choosing the reference alternative of car", people with high income are more/less likely to choose bus/train.
As you can see, in the utility functions, we don't have the income part for the alternative of "car", which indicate the comparison reference is the income for "car" alternative.

It is unclear to me when the choice set varies, for example when "car" is unavailable for some people. 
For these people who don't have "car" in their choice set, which alternative is compared against when interpreting the income effect for other alternatives (e.g. bus/train)?


Best,
Lixian


-----Original Message-----
From: Limdep [mailto:limdep-bounces at mailman.sydney.edu.au] On Behalf Of William Greene via Limdep
Sent: 19 December 2018 23:19
To: Limdep and Nlogit Mailing List
Cc: William Greene
Subject: Re: [Limdep Nlogit List] Reference alternative of individual characteristics in the case of variable sized choice sets

Lixian.  There is no "reference" alternative.  The probability is computed
as
exp(V_j) / Sum[j=1,...,J] exp(V_j).
All alternatives have the same precedence.  When you have only a subset of
the alternatives
in the choice set, the probabilities are computed conditionally on the
specific choices in that
choice set.

On Wed, Dec 19, 2018 at 9:59 AM Lixian Qian <Lixian.Qian at xjtlu.edu.cn>
wrote:

> Dear all,
>
> I am running a discrete choice model with variable sized choice sets for
> two groups of people.
> Say there are three alternatives, bus, train and car, where car is only
> available for some people. Each alternative has two attributes of cost and
> time, and each people has individual characteristic of income.
>
> Then, I have following utility functions:
>
> U(bus) = βcost costi,bus + βtime timei,bus + αbus + γbus incomei
> U(train) = βcost costi,train + βtime timei,train + αtrain + γtrain incomei
> U(car) =βcost costi,car + βtime timei,car
>
> My puzzle is that for the people without car in their choice set, what is
> the reference alternative when estimating and interpreting the coefficients
> of income.
>
> Appreciate your time to answer my question.
> Thank you.
>
>
> Best,
> Lixian
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> Limdep at mailman.sydney.edu.au
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>


-- 
William Greene
Department of Economics
Stern School of Business, New York University
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