Which econometric model I can use if my choice variables are not mutally exclusive?

[Rimita Hom Chaudhury]

Hello,
We know discrete choice models describe decision-makers’ choices among alternatives and one important characteristic of these models that the alternatives must be mutually exclusive. If this is so we use mlogit/clogit etc. to conclude our study. But if our alternatives are not mutually exclusive i.e., one can choose either A or B or both then which model we can choose to proceed with our study.
Thank you

[Hong Il Yoo]

Hi Rimita,

Suppose that choosing none of the available alternatives is a possibility. That is, continuing with your two-alternative example, you are willing to allow for four possible outcomes, {A, B}, {not A, B}, {A, not B}, and {not A, not B}. In such cases, you can use -biprobit- and -mvprobit- where the latter is a community-contributed software.

Suppose that the individual must choose at least one of the available alternatives. Then you can consider an extension of -biprobit- and -mvprobit- that accounts for truncation, in a similar manner as equation (10) in the following paper:

Weiss, Andrew A. “A Bivariate Ordered Probit Model with Truncation: Helmet Use and Motorcycle Injuries.” Journal of the Royal Statistical Society. Series C (Applied Statistics), vol. 42, no. 3, 1993, pp. 487–499. https://www.jstor.org/stable/2986327

I am not aware of any existing Stata command that allows you to estimate multivariate probit models with truncation, but I must admit that I have not invested any time in looking for one. What I can suggest, though, is that you may take the trivariate probit code template in the following paper as a basis:

Cappellari, Lorenzo, and Stephen P. Jenkins. "Calculation of multivariate normal probabilities by simulation, with applications to maximum simulated likelihood estimation." The Stata Journal, vol 6 no. 2, 2006, pp. 156-189. https://www.stata-journal.com/sjpdf....iclenum=st0101

and write your own code which does the job.

[Rimita Hom Chaudhury]

Hi Hong,
Thank you for your help.