From Lixian.Qian at xjtlu.edu.cn Thu Dec 20 01:44:29 2018 From: Lixian.Qian at xjtlu.edu.cn (Lixian Qian) Date: Wed, 19 Dec 2018 14:44:29 +0000 Subject: [Limdep Nlogit List] Reference alternative of individual characteristics in the case of variable sized choice sets Message-ID: 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) = ?cost costi,bus + ?time timei,bus + ?bus + ?bus incomei U(train) = ?cost costi,train + ?time timei,train + ?train + ?train incomei U(car) =?cost costi,car + ?time 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 From Lixian.Qian at xjtlu.edu.cn Thu Dec 20 02:04:29 2018 From: Lixian.Qian at xjtlu.edu.cn (Lixian Qian) Date: Wed, 19 Dec 2018 15:04:29 +0000 Subject: [Limdep Nlogit List] Reference alternative of individual characteristics in the case of variable sized choice sets In-Reply-To: References: Message-ID: Sorry for the format issue in the utility functions. They should be as follows: U(bus) = ?_cost * cost(bus) + ?_time *time (bus) + ?_bus + ?_bus * income U(train) = ?_cost * cost(train) + ?_time * time (train) + ?_train + ?_train * income U(car) =?_cost * cost(car) + ?_time * time (car) Best, Lixian -----Original Message----- From: Limdep [mailto:limdep-bounces at mailman.sydney.edu.au] On Behalf Of Lixian Qian Sent: 19 December 2018 22:44 To: limdep at limdep.itls.usyd.edu.au Subject: [Limdep Nlogit List] Reference alternative of individual characteristics in the case of variable sized choice sets 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) = ?cost costi,bus + ?time timei,bus + ?bus + ?bus incomei U(train) = ?cost costi,train + ?time timei,train + ?train + ?train incomei U(car) =?cost costi,car + ?time 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 _______________________________________________ Limdep site list Limdep at mailman.sydney.edu.au http://limdep.itls.usyd.edu.au From Lixian.Qian at xjtlu.edu.cn Thu Dec 20 02:04:29 2018 From: Lixian.Qian at xjtlu.edu.cn (Lixian Qian) Date: Wed, 19 Dec 2018 15:04:29 +0000 Subject: [Limdep Nlogit List] Reference alternative of individual characteristics in the case of variable sized choice sets In-Reply-To: References: Message-ID: Sorry for the format issue in the utility functions. They should be as follows: U(bus) = ?_cost * cost(bus) + ?_time *time (bus) + ?_bus + ?_bus * income U(train) = ?_cost * cost(train) + ?_time * time (train) + ?_train + ?_train * income U(car) =?_cost * cost(car) + ?_time * time (car) Best, Lixian -----Original Message----- From: Limdep [mailto:limdep-bounces at mailman.sydney.edu.au] On Behalf Of Lixian Qian Sent: 19 December 2018 22:44 To: limdep at limdep.itls.usyd.edu.au Subject: [Limdep Nlogit List] Reference alternative of individual characteristics in the case of variable sized choice sets 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) = ?cost costi,bus + ?time timei,bus + ?bus + ?bus incomei U(train) = ?cost costi,train + ?time timei,train + ?train + ?train incomei U(car) =?cost costi,car + ?time 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 _______________________________________________ Limdep site list Limdep at mailman.sydney.edu.au http://limdep.itls.usyd.edu.au From wgreene at stern.nyu.edu Thu Dec 20 02:19:04 2018 From: wgreene at stern.nyu.edu (William Greene) Date: Wed, 19 Dec 2018 10:19:04 -0500 Subject: [Limdep Nlogit List] Reference alternative of individual characteristics in the case of variable sized choice sets In-Reply-To: References: Message-ID: 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 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) = ?cost costi,bus + ?time timei,bus + ?bus + ?bus incomei > U(train) = ?cost costi,train + ?time timei,train + ?train + ?train incomei > U(car) =?cost costi,car + ?time 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 > _______________________________________________ > Limdep site list > Limdep at mailman.sydney.edu.au > http://limdep.itls.usyd.edu.au > -- William Greene Department of Economics Stern School of Business, New York University 44 West 4 St., 7-90 New York, NY, 10012 URL: https://protect-au.mimecast.com/s/UMBJCXLKZoiZ4Ak9s6KF3J?domain=people.stern.nyu.edu Email: wgreene at stern.nyu.edu Ph. +1.212.998.0876 Editor in Chief: Journal of Productivity Analysis Editor in Chief: Foundations and Trends in Econometrics Associate Editor: Economics Letters Associate Editor: Journal of Business and Economic Statistics Associate Editor: Journal of Choice Modeling From Lixian.Qian at xjtlu.edu.cn Thu Dec 20 02:34:07 2018 From: Lixian.Qian at xjtlu.edu.cn (Lixian Qian) Date: Wed, 19 Dec 2018 15:34:07 +0000 Subject: [Limdep Nlogit List] Reference alternative of individual characteristics in the case of variable sized choice sets In-Reply-To: References: Message-ID: 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 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) = ?cost costi,bus + ?time timei,bus + ?bus + ?bus incomei > U(train) = ?cost costi,train + ?time timei,train + ?train + ?train incomei > U(car) =?cost costi,car + ?time 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 > _______________________________________________ > Limdep site list > Limdep at mailman.sydney.edu.au > http://limdep.itls.usyd.edu.au > -- William Greene Department of Economics Stern School of Business, New York University 44 West 4 St., 7-90 New York, NY, 10012 URL: https://protect-au.mimecast.com/s/qYd5CwVLQminv64ZIVX4_q?domain=people.stern.nyu.edu Email: wgreene at stern.nyu.edu Ph. +1.212.998.0876 Editor in Chief: Journal of Productivity Analysis Editor in Chief: Foundations and Trends in Econometrics Associate Editor: Economics Letters Associate Editor: Journal of Business and Economic Statistics Associate Editor: Journal of Choice Modeling _______________________________________________ Limdep site list Limdep at mailman.sydney.edu.au http://limdep.itls.usyd.edu.au