Setting constraints based on maximum number of occurrence

[stellamulia]

Hi Ignacio,

I have encountered situations, in which to ensure a balanced dataset (in terms of choices by all respondents), I need to limit the occurrence of maximum levels across all criteria within a set of scenarios. For example:

• Let's say there are five criteria (A, B, C, D, E), with 2, 3, 4, 5, 6 levels respectively.
• The possible choices are X and Y.
• When a scenario contains at least any three criteria at maximum value (e.g. A2, B3, C1, D5, E2), the choice will always be X. In other words:
  • this type of scenarios does not provide much information regarding the tradeoffs anymore, and
  • too many of these scenarios will lead to imbalanced dataset (where most choices will be X).

In practice, this might concern not only maximum levels, but could also be other levels, for example minimum levels, non-maximum levels, specific levels, or a combination of those.

Do you think it is a good to limit the maximum number of occurrence of certain levels of a criterium in relation to the occurrence of certain levels of other criteria? Of course, this would imply some correlation between the constrained criteria.

If so, would it be valuable to add this functionality to the ChoiceDesign package? Currently, defining constrants is already possible, however this type of constraint (which involves more than two criteria) would result in a huge number of 2-criteria-constraints.

Cheers,
Stella

[ighdez]

Hi Stella,

Thanks for your question! I think we also need to consider what are the prior parameters associated to each criterion from A to E. In efficient design theory, decision-makers choose the alternative that reports them with the highest utility. Hence, the criteria and their levels alone are not enough to decide which alternative will be chosen.

Looking forward for your thoughts!

Ignacio

[stellamulia]

Thanks for your response Ignacio!

In this case, I suppose that the prior parameters of the concerned levels (e.g. the maximum levels) are very large. The joint occurrence of such levels would lead to dominant alternatives. Would you say that B-efficient design is more suitable in this situation?

[ighdez]

Hi Stella,

Indeed. If the prior parameters are too large, there is a risk of having dominant alternatives when such attribute levels are involved. In such a case, a B-efficient design could mitigate the risk of having dominant alternatives, but at the cost of not performing a D-efficient design. In addition, ChoiceDesign does not consider (yet) B-efficient designs. I am currently working on that.

Alternatively, what you can do is to do a D-efficient design, but with smaller prior parameters. In fact, the sign of the prior parameters is much more important than the value itself (I remember a paper that tests that, but I need to find it).