What does the id option in mixlogitwtp do?

[John Bovay]

Hello, I am trying to estimate a mixed logit model in WTP space using mixlogitwtp by Arne Risa Hole. The documentation says that I should use the option id(varname) only when each individual performs several choices; i.e., the dataset is a panel.

What does the id option do? If I have a panel dataset, and I include id, does this mean that I'm including individual-specific random effects? If I have a panel dataset, and I exclude id, is this equivalent to assuming individuals have homogeneous preferences? Or is excluding id equivalent to assuming preferences are heterogeneous across individuals AND that each individual performs only one choice?

To be concrete, we can use the Train (2003) dataset:

use http://fmwww.bc.edu/repec/bocode/t/traindata.dta
mixlogitwtp y, group(gid) price(price) rand(contract local wknown seasonal)
mixlogitwtp y, group(gid) id(pid) price(price) rand(contract local wknown seasonal)

What is the difference between the two models? And what is the proper way to describe them? (I think that they can both be described as mixed logit with error components?) Thanks very much.

[John Bovay]

Arne Risa Hole I just realized that I could tag you, as the author of this command. Thanks for any clarification you can provide.

[Hong Il Yoo]

In both cases, you're estimating the mixed logit model in the WTP space.

In the first case, you're assuming that the WTP for -contract local wknown seasonal- randomly vary between individuals, as well as within an individual across choice tasks. That is, all observations that have the same -gid- value are associated with the same value of WTP. In the context of Train and Hess's [2011; https://doi.org/10.1016/j.trb.2011.05.002] taxonomy, you're estimating the mixed logit model in the WTP space with intrapersonal heterogeneity and no interpersonal heterogeneity.

In the second case, you're assuming that the WTP for -contract local wknown seasonal- randomly vary between individuals, but remain constant within an individual across choice tasks. That is, all observations that have the same -pid- value are associated with the same value of WTP regardless of whether -gid- values vary across those observations or not. You're estimating the mixed logit model in the WTP space with interpersonal heterogeneity and no intrapersonal heterogeneity.

When each person completes only one choice task, the distinction between -gid- and -pid- does not exist, and the two types of approaches become observationally equivalent.

[John Bovay]

Hong Il Yoo Thanks so much!