Utility formula: we need to be more specific about the model and review the math notation (which is currently incorrect).

[TianyuDu]

• Utility formula: we need to be more specific about the model and review the math notation (which is currently incorrect).
  • for details, see page 376 of Athey et al (2021)
  • the model assumes unit demand for each category, independent choices across categories, and error term distributed according to Guembel distribution (logit)
  • there needs to be a discussion on how the outside option is modelled. How does the model choose that the user biuys nothing from a given category? Can we change the value of the outside option in each category or is normalized to 0 for each category?
  • Regarding notation: (i) need to index the variables by _{uis} and (ii) decompose the utility into a deterministic part and the error term: $\mathcal{U}{uis} = U{uis} + \varepsilon_{uis}$ .
    Then $P(i|u,s)$ is a function of $U_{uis}$ instead of $\mathcal{U}_{uis}$
  • I suggest we write the utility function that the package can accommodate in its most general form (ie. sum all the terms that can be included) and then discuss each term one by one

[TianyuDu]

I have added a more complete and self-contain description on the BEMB model here in the ## The BEMB Model section.

I have fixed the math notation as the following: the utility is \mathcal{U}_{uis} = U_{uis} + \varepsilon_{uis} and the model is modelling the determinsitc part U_{uis}.

Could you please review it to check if there's any mistake in it? @kanodiaayush @charlespebereau

This issue should be marked as resolved after Charles or Ayush review the change.