ApolloChoiceModelling forum

Dear prof. dr. Hess and dr. Palma,

I've got a question about the modelling of the unforced choice data in a dual-response DCE with status quo (respondents first choose between A and B, and afterwards between the chosen option and the status quo). In case of separate analysis of the forced and unforced choice data, the analysis of the first stage (the forced choice) is straightforward. The analysis of the second stage (the unforced choice) is less clear to me, though, and it seems different approaches are taken in the literature:

• 1. In some studies, like for this DCE, this DCE, or this DCE, the unforced choice data are modelled as if there was a choice between A, B, or the opt-out/status quo. But I'm doubting whether that is correct, because respondents did not actually have the choice between those options: there was only a choice between the previously chosen option and the status quo.

• 2. Other studies do the same as #1, but then using a nested logit (in which A and B are nested together against the opt-out/status quo).

• 3. Yet others model the unforced choice data using a MNL model as the choice between two alternatives: the previously chosen option and the status quo/opt-out. So

• 4. Then there are studies estimating a heteroskedastic extreme value model, like for this DCE and this DCE, in which the error variance is allowed to vary between alternatives.

• 5. And finally, I came across studies that estimated a rank-ordered logit model (like in the appendix of this DCE) - but I'm doubting whether that's correct in this context, given that you don't always get a full preference ordering (if respondents choose the same option in both the first and second stage), unlike in a best-best DCE or best-worst DCE/BWS Case 3.

I'm curious what you think is the preferred approach here.

Kind regards,
Sander

If the second choice is truly only between the first pref and the opt-out, then it's indeed a sequence of two binary choices. let's say someone chooses A over B, then SQ over A. It would then be P(A|A,B)*P(SQ|B,SQ). You need to model them jointly in this way. If you only model the choice for the second stage, you would need to definitely consider endogeneity concerns given that the choice set depends on the first round choice