I have a study where I'd like the design to depend on the class of respondent (derived before entering the CBC part).
Part of the sample will see tasks from one design, and the rest will see tasks from another design.
Each task's layout is the almost same for both groups of respondents, the same applies to the designs: the only difference between the two designs is that one of them will include an extra binary attribute.
My question is whether I could benefit from combining the two designs at analysis phase and estimate the utilities in one model with covariates, or is it better to estimate them as two separate models and combine the utilities afterwards in the simulator?
I am talking HB estimation here.
In the former case, I could add the missing attribute to the first design, and code each task as partial-profile, keeping in mind that I should zero-out the utilities of the missing attribute for the first group after estimation.
In the latter case, I would just put zeros for the missing attribute levels for Group 1 respondents in the simulator.
Two-model approach seems to be better, but what if I don't collect that many respondents in Group 1 for stable estimates of the other attributes?
Would the combined approach help in this case or would it lead to biased estimates and/or divergence in HB?