asclogit to run McFadden's conditional logit model. model doesn't converge

[Jenny Mak]

Hi everyone,

I hope you are good. I am trying to understand college choice for high school seniors. Specifically, I want to know the relationship between school choice and institutional characteristics. I am running McFadden's conditional logit model. Below is an example of my dataset. I have a variable called student_id which indicates a student's id. I have a variable called school_id which indicates a school's id. I have a variable called instnm which is the name of the school. I have four unique schools and the variable school_mode tells you the number of unique schools. I have two institutional characteristic variables with the variable student_services describing the amount of money allocated to student services and the variable academic_support representing the money allocated to academic support.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float student_id long school_id str91 instnm float(school_mode Dest_chosen) long(student_services academic_support)
1 151351 "Indiana University-Bloomington"   1 1 30001999  1822905
1 170976 "University of Michigan-Ann Arbor" 2 0 19154000 32586000
1 240444 "University of Wisconsin-Madison"  3 0 18868514 25590210
1 243780 "Purdue University-Main Campus"    4 0 26458803  5262139
2 151351 "Indiana University-Bloomington"   1 0 30001999  1822905
2 170976 "University of Michigan-Ann Arbor" 2 1 19154000 32586000
2 240444 "University of Wisconsin-Madison"  3 0 18868514 25590210
2 243780 "Purdue University-Main Campus"    4 0 26458803  5262139
3 151351 "Indiana University-Bloomington"   1 0 30001999  1822905
3 170976 "University of Michigan-Ann Arbor" 2 0 19154000 32586000
3 240444 "University of Wisconsin-Madison"  3 1 18868514 25590210
3 243780 "Purdue University-Main Campus"    4 0 26458803  5262139
4 151351 "Indiana University-Bloomington"   1 0 30001999  1822905
4 170976 "University of Michigan-Ann Arbor" 2 0 19154000 32586000
4 240444 "University of Wisconsin-Madison"  3 0 18868514 25590210
4 243780 "Purdue University-Main Campus"    4 1 26458803  5262139
5 151351 "Indiana University-Bloomington"   1 0 30001999  1822905
5 170976 "University of Michigan-Ann Arbor" 2 1 19154000 32586000
5 240444 "University of Wisconsin-Madison"  3 0 18868514 25590210
5 243780 "Purdue University-Main Campus"    4 0 26458803  5262139
6 151351 "Indiana University-Bloomington"   1 0 30001999  1822905
6 170976 "University of Michigan-Ann Arbor" 2 0 19154000 32586000
6 240444 "University of Wisconsin-Madison"  3 1 18868514 25590210
6 243780 "Purdue University-Main Campus"    4 0 26458803  5262139
7 151351 "Indiana University-Bloomington"   1 0 30001999  1822905
7 170976 "University of Michigan-Ann Arbor" 2 0 19154000 32586000
7 240444 "University of Wisconsin-Madison"  3 1 18868514 25590210
7 243780 "Purdue University-Main Campus"    4 0 26458803  5262139
end

I am using Stata 15 and I ran the following line:

asclogit Dest_chosen student_services academic_support, case(student_id) alternative(school_mode)

When I ran the line of code, Stata says "not concave" and "convergence not met". Does anyone know how I fix this? Any suggestion or solutions would be greatly appreciated. I promise to pay it forward.

[Hong Il Yoo]

Each person in your sample faced exactly the same choice set. This means that your alternative-specific constants are perfectly collinear with your alternative-specific attributes. The model that includes all ASCs and the alternative-specific attributes are not identified.

[Jenny Mak]

Thank you Professor Yoo. Your explanation is very clear and I see that my choice sets are exactly the same for everyone. I will attempt a different model. Do you have any recommendations or guidance of possible alternative models? Thank you.

[Hong Il Yoo]

If your research question does not relate to the alternative-specific attributes, you can just estimate a model without the alternative-specific attributes.

Otherwise the best approach, I think, is for you to collect another semester or year of data which will allow you to observe some variation in the alternative-specific attributes within a university over time. Then you can estimate your current model specification using the pooled data across two time periods, under the maintained assumption of temporal stability in preferences. If collecting more data is not an option then you must think of other identifying assumptions. For example, you may create a dummy variable that equals 1 for the two universities located in Indiana and 0 elsewhere, and then use -clogit- to estimate a model that controls for the Indiana-specific constant and the alternative-specific attributes. The identifying assumption is that ASCs for the unviersities in Indiana are the same and ASCs for the non-Indiana universities are the same.

[Jenny Mak]

Hi Professor Yoo. Thank you so much for your suggestion. I love your suggestion to college another year of data. I have students who have to choose to attend a college in 2012, 2013, 2014 and 2015. My ASC, student_services and academic_support vary for each college every year. Thanks for your patience and clear explanation.