I know that alternative-specific designs should be favoured, and that's what I tested at first.
However (in ACBC Test Design), the conditional level of the primary attribution seems to be undersampled compared to the other levels of that primary attribute. The number of choice tasks is sufficient such that level frequencies are sufficient, but its undersampling means that it's not shown in enough combinations with another key attribute.
e.g., Say 'a' is the conditional level for the PrimaryAttribute. I would want 'a' to be seen enough times with AttributeB's levels of 'b1', 'b2', 'b3', 'b4.'
In tallying how often concepts occur during manual run-throughs of 24 choice tasks, I would see 'a' being shown far fewer times than other PrimaryAttribute levels; further, combinations that appear tend to be 'a/b1', and no other combinations. I suspect that there could be an interaction between PrimaryAttribute and AttributeB, so I don't think the lack of variety in combinations would give me good data. Please correct me if I am wrong!
So, I'm considering using Prohibitions. I know they should be used sparingly. Wondering if there are any guidelines for their use when considering the number of attributes and levels. The concept in mind for me is that prohibitions are bad because it reduces orthogonality (I think? or introduces correlated redundancies into the design).
Is there a guideline for prohibitions in asymmetric designs? By asymmetric, I mean imbalance in levels among attributes involves in the prohibitions.
Suppose that my design is 4 attributes (7 x 7 x 4 x 2). Suppose that "AttributeA" has 7 levels and "AttributeB" has 2. If I set level 'a1' of "AttributeA" to be prohibited with level 'b1' of "AttributeB", can one guess the "danger level" of the prohibition based on number of levels?
If AttributeB has 2 levels, then the 2 levels will be sufficiently seen in many combinations with the other attributes. While a product with 'a1' will be 100% associated with the appearance of 'b1', a product with 'b1' doesn't always associate with the appearance of 'a1'. Is that a valid way of thinking about it, or no?
That's the specific example that I have in mind so far. Any other heuristics or guidelines regarding setting prohibitions in an informed manner would be most appreciated (or other thoughts on my alt-specific issue)!
Side-note: This is an ACBC with no BYO and no screener for substantive reasons; it's essentially a CBC with constructed listed designed in ACBC module.