mixlogit Choice Experiment interpretation of no-choice dummy in terms of WTP

[Paul Arnem]

Dear statalisters,

I ran multiple discrete choice experiments in which I included a no-choice/status quo option. In the analysis, I included a dummy variable for the no-choice option. My question now is how to interpret a no-choice dummy in terms of WTP. Say my model is an unlabeled choice experiment where one chooses between different types of cars. Can I then interpret the (negative) WTP value for the no-choice dummy (either from preference space or a WTP space model) as the mean WTP for any car, independent of the attributes? I cannot think of any other way to interpret it, but I am unsure if I can do that at all.

Another thing that made me wonder about the interpretability of the WTP value of the no-choice dummy is that the WTP value from both preference and WTP space models is much higher than the levels of the cost attributes we included, meaning that the respondents were not even able to express that WTP value...

In the end, what I want is to say what the average WTP for choosing an option (buying) in an unlabelled DCE is, regardless of the attributes.

I am grateful for any help and tips regarding this.

[Hong Il Yoo]

Paul Arnem: Could you provide more clarity regarding your choice experiment and coding scheme? I'm wondering:

(1) whether your experiment asks the respondent to make a choice from Car A vs Car B vs (...) vs status quo;

(2) what the status quo means (e.g., driving whatever car you currently own?)

(3) whether your no-choice dummy is equal to 1 for the status quo and 0 for all other options;

(4) whether you have coded the car attribute variables so that all of them are equal to 0 for the status quo option; and

(5) whether at least one of the car attributes takes a non-zero value for each option other than the status quo (e.g., the price of a non-status quo car is always positive).

[Paul Arnem]

Thank you so much for your response. I didn't clarify more, because it is kind of different for several choice experiments we conducted. But this would be the most fitting:

(1) The choice is between purchasing a good that we know the respondents don't already own vs. not purchasing (empty alternative that just says "I don't want to purchase", i.e. no levels are shown at all.)
(2) The status quo is thus just the option not to purchase.
(3) Yes
(4) Yes
(5) Yes, most of our attributes are always positive for the options other than the status quo, including, for example, a cost attribute.

Thank you so much

[Hong Il Yoo]

Paul Arnem: Thanks for clearing that up. The mean coefficient on your no-choice dummy can be viewed as a parameter that enhances the average decision maker's preference for the opt-out option. However, I'd be cautious about equating it directly with the average WTP for the opt-out option, even if your model is in the WTP space. When switching between any opt-in option and the opt-out option, you're also experiencing the loss of utilities tied to the attributes of the opt-in option. Any WTP assessment for the opt-out option should consider these utility changes alongside the alternative specific constant (ASC) of the opt-out option. The WTP for the opt-out option can't be calculated solely from the ASC. The usual thought experiment behind the WTP formula, which is of changing one attribute-level while holding other attribute-levels unchanged, makes little sense in relation to your no-choice dummy because you cannot change the value of that dummy without changing the values of other attributes.

[Paul Arnem]

Thank you very much for that explanation! So am I correct in assuming that in this case I cannot derive an "average WTP for a car", only for changes in the attribute levels of a car? Would that mean that if I want both, using something like a payment ladder in combination with a choice experiment makes sense?