Query on Interpreting Reference Level in a Constrained DCE Design

[MACA]

Dear all,
We are finalizing the design for an unlabelled Discrete Choice Experiment and would appreciate your expert opinion on interpreting the results due to a design constraint.
Attributes and Levels
Our design includes two key attributes:
• Transparency Seal:
o Level 0: No Seal (Reference Level)
o Level 1: Yellow Seal
o Level 2: Green Seal
• External Endorsement:
o Level 0: No Endorsement (Reference Level)
o Level 1: Public Body
o Level 2: Private Certifying Company
o Level 3: NGO
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The Design Constraint
The attributes are logically dependent: an endorsement can only exist if a seal is present.
• If Transparency Seal is Level 0 (No Seal), then External Endorsement must also be Level 0, as an endorsement is "not applicable."
• If Transparency Seal is Level 1 or 2 (Yellow or Green), then External Endorsement can be Level 0 (meaning the seal is present but has "no endorsement") or Levels 1, 2, or 3.
________________________________________
Our Question
Our question relates to the correct interpretation of the parameter estimates for the External Endorsement levels.
The reference level for this attribute (Level 0) carries a dual meaning:
1. It means "Not Applicable" when no seal is present.
2. It means "No Endorsement is Present" when a seal is present.
When we estimate the model using dummy coding, how should we interpret the parameters for the other endorsement levels (Public, Private, NGO)? For example, will the parameter for "Public Body" represent the marginal utility of adding a public endorsement to a seal, compared to a seal with "no endorsement"? Or is this interpretation complicated by the "not applicable" meaning also being part of the reference level?

We'd like to double-check our understanding of this before launching the survey to ensure we interpret the results correctly.
Thank you for your time and help.
Best regards,

[Michiel Bliemer]

The short answer is: the interpretation is compared to "no endorsement".

The "not applicable" part needs to be dealt with via an interaction effect in the utility function so that the attribute "External endorsement" simply drops out. For example, in model estimation you would essentially estimate something like the following:

V = b_yellow * (Seal==1) + b_green * (Seal==2) + (Seal>0) * (b_public * (Endorsement==1) + b_PCC * (Endorsement==2) + b_NGO * (Endorsement==3))

In other words, the last part simply drops out due to the interaction with (Seal>0), which equals one if Seal is 1 or 2 and zero otherwise. By letting it drop out of the utility function, parameters b_public, p_PCC and P_BGO then become purely compared to "no endorsement". Of course this is cosmetic because simply setting Endorsement=0 when the seal is not available yields exactly the same result, but it merely demonstrates that you can interpret the parameters compared to "no endorsement" UNDER THE CONDITION THAT THERE IS A SEAL.

You could also reformulate the attributes as follows, whereby you estimate a parameter for having a seal separately from the colour:
- Seal: Yes, No
- Colour: Yellow, Green (interaction with Seal so that it only applies when Seal=Yes)
- Endorsement: None, public body, PCC, NGO (interaction with Seal so that it only applies when Seal=Yes)

Michiel