MRS/WTP estimation with effects-coded mixlogit

[Xinyi Ng]

Hi, does anyone have advice on using effects-coded model for MRS/WTP estimation in DCE.

Assuming I have a continuous price variable (price) and a categorical car model variable with 3 categories (car1, car2 , car3 )

In a dummy coded mixlogit model (with X3 being the reference), I would use the nlcom command "nlcom (_b[car2])/(_b[lprice])" to estimate the MRS for car2 compared to car3.

However, if I have to run an effects coded model, how can i estimate the MRS of car 1 vs car3? Say car 3 is the omitted variable whose coefficient from the mixlogit is derived from the negative sum of car1 and car2.

Would the command then be "nlcom (_b[car1]-(-(_b[car1]+_b[car2])))/(_b[lprice])"?

Thanks!

[Clyde Schechter]

No, if car 3 is the omitted variable, it's coefficient is, by definition, 0. So you don't need -nlcom-; you don't even need to do the regression: _b[car3]/_b[lprice] is automatically 0.

So the question naturally arises why you are even calculating these expressions. Because car1 car2 and car3 are three levels of a categorical variable, indicator variables for them are necessarily colinear with the constant term, which also means that their coefficients are unidentifiable parameters of your model: the coefficients you appear to get are artifacts of which one you pick to be the omitted variable. (Try running the model once with car2 omitted and again with car 3 omitted--you will see that you get a different result for car 1 each time. Which one is "correct?" Neither one: the parameter is simply unidentifiable.) And the same will be true of other expressions calculated from them (except for certain lucky combinations of them which will turn out not to depend on the particular parametrization.)

Perhaps you should explain your problem better for more specific advice. I know you started out with an explanation of your problem. But this is a multi-disciplinary international forum. Abbreviations should only be used if any college educated person anywhere in the world could be expected to recognize them. I am probably not the only Forum member who has no idea what MRS/WTP and DCE stand for. And I might not understand the full expressions either. So when posting here, it is best to avoid discipline-specific jargon and explain things in language understandable by any college-educated person.

[Xinyi Ng]

Hi, Apologies if I did not explain the problem better. Attempting to do so with more details as follow:

I am looking at using effects-coded mixlogit models for marginal rate of substitution (MRS)/willingness-to-pay (WTP) estimates from a discrete choice experiment (DCE).

So I'm looking at the ratio of change in preference weights (estimates from the mixlogit) from switching between car 1 to car2 that can be offset by the change in price.
Assuming I have a continuous price variable (price) and a categorical car model variable with 3 categories (car1, car2 , car3 ).

In a dummy-coded model, I can derive the willingness-to-pay estimates using the nlcom command but I'm wondering how to adapt that to an effects-coded model.

In a dummy coded mixlogit model (with car3 being the reference), I would use the nlcom command "nlcom (_b[car2])/(_b[lprice])" to estimate the willingness-to-pay for car2 compared to car3.

If I ran an effects-coded mode, and want to estimate willingness-to-pay of car1 vs car3 (with car3 being the omitted variable), would the command then be "nlcom (_b[car1]-(-(_b[car1]+_b[car2])))/(_b[lprice])"?

[Clyde Schechter]

OK, I see what you're getting at.

I think that if you are interested in contrasting one car with another, then it does not make sense to use effects coding: that just complicates your life. Use dummy coding for that. Then if car 3 is the omitted category, the difference between car1 and car3 is just _b[car1], and if you want to contrast car1 with car2, that's _b[car1] - _b[car2]. There are situations where effects coding makes life simpler than dummy coding, but this is definitely not one of them!

[Xinyi Ng]

Thanks!