No-choice dummy WTP interpretation

[tomschuette]

Greetings,

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 through their choices...

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 using Stata 17 with the mixlogit command for my models.

I am grateful for any help and tips regarding this.

[Michiel Bliemer]

The opt-out alternative either has a utility of zero or a constant. It is easiest to interpret if it is set to zero.

U(A) = b0 + b1*X1 + ... + bc*Cost
U(B) = b0 + b1*X1 + ... + bc*Cost
U(optout) = 0

Perhaps you are referring to the alternative-specific constant because an opt-out alternative cannot have a dummy variable because it has no attributes.

b0 represents the preference of purchasing a car, versus not purchasing a car, ALL ELSE BEING EQUAL (so X1=0, X2=0, Cost=0). I am not sure whether it is meaningful to use b0 as a WTP to purchase a car because it assumes that the car costs nothing. WTP is usually only computed for attributes, not for constants, I would not use constants to interpret WTP.

In simple experiments one sometimes checks the so-called boundary WTP values to ensure that the ranges and trade-offs in the choice experiment allow a wide range of WTP in the population, i.e. ensuring that cost levels are wide enough. For example, in transport they sometimes look at Boundary Value of Travel Time (BVTT), see for example https://link.springer.com/article/10.1007/s11116-020-10139-3.

Michiel

[dtobin02]

Hello,
I have a question that is similar to this one. I have an unlabeled choice experiment with two alternatives and a "take none" opt out option. We can imagine that this is an experiment to purchase a car (though my experiment is about whether or not a farmer would be willing to plant certain types of trees). My question is how to interpret the value of b0 given that this constant appears to change depending on the reference levels I leave out in my attributes.

I think I can write my utility function one of two ways (which are equivalent except for the sign given to b0):

U(A) = b0 + b1*X1 + ... + bc*Cost
U(B) = b0 + b1*X1 + ... + bc*Cost
U(optout) = 0

U(A) = b1*X1 + ... + bc*Cost
U(B) = b1*X1 + ... + bc*Cost
U(optout) = b0

I want to know, holding all else constant, how much does a person want / not want to purchase a car (or plant a tree). As you noted in the comment, b0 for a car might not be appropriate, but in my case, the trees are given by an NGO and are free, yet some farmers still reject them (based on each farmer's opportunity cost -- I would like the average opportunity cost or average value a farmer assigns to planting a tree). The WTP for b0 changes depending on whether for my categorical variable "tree type", I leave out the level "all timber trees" versus the level "all fruit trees". This makes it more challenging to interpret how much a farmer values / finds costly planting a tree of "any type". I would appreciate any thoughts here.

Thanks,
Danny

[Michiel Bliemer]

I am not sure whether it is appropriate to interpret a constant in terms of WTP. WTP is the trade-off, within an alternative, between an increase in cost and an improvement in an attribute. The constant merely reflects the probability of not choosing A and B, dependent on what levels are used for the attributes in A and B. If the attributes in A and B do not all contain 0 as a level then constant b0 will become dependent on the minimum utility achievable with the available levels. In other words, b0 has no meaning, it merely corrects the choice probabilities.

You could decide to dummy code all attributes in A and B, which allows the minimum utilities to be zero independent of the attributes and levels chosen in the utility function.

Michiel