Coding for stated preference choice experiment marginal willingness to pay

[Nicole Nimlos]

Hi everyone,

I am trying to calculate the marginal WTP for a choice experiment I conducted. I have already ran my random parameters model and gotten my coefficients. I want to calculate the marginal mean WTP with confidence intervals for each of my attributes (quail_rec, tort_rec, water_med, water_high, scenic_med, scenic_high). I have a continuous payment variable called "Tax" and the choice they selected is a binary variable called "Select." I've seen a lot on here but haven't been able to make any of it work.

Does anyone know the coding in STATA to find mean WTP with confidence intervals? Is there a way to do this manually?

Thanks for any help.

[Andrew Musau]

You do not show the command that you ran or provide a sample of your data, thereby making it difficult to provide specific suggestions. If you install mixlogitwtp and look at its documentation, you will find an example of how your data should be set up and how to estimate a mixed logit model in willingness to pay space.

ssc install mixlogitwtp, replace
help mixlogitwtp

[Nicole Nimlos]

Sorry, my coding was: mixlogitwtp Select quail_rec, price(Tax) id(Respondent) group(groupid) krinsky reps (1000)

But it would only run when I included 1 attribute at a time, not all of them together. The results gave me a mean coefficient of 32.06, so is that the mean WTP, $32? It also gave 95% confidence intervals. How do I interpret the model to find mean WTP?

[Andrew Musau]

But it would only run when I included 1 attribute at a time, not all of them together.

What does this mean? The model does not converge?

mixlogitwtp Select quail_rec, price(Tax) id(Respondent) group(groupid) krinsky reps (1000)

Usually, as stated in the documentation, the price variable is assumed to follow a lognormal distribution (the distribution is always positive). Therefore, I assume this applies to you variable "Tax", in which case, you need to take the negative of this variable and then transform the resulting coefficients using nlcom.

price(varname) is required and specifies the price variable, or more generally the variable whose coefficient is the denominator in the WTP expression. The
coefficient on the price variable is assumed to be lognormally distributed. Since this implies that the price coefficient is positive, the price variable must
be multiplied by -1 before entering the model (see the examples below). Train and Weeks (2005) show that the price coefficient in WTP space models incorporates
any differences in scale across respondents.

See how this is done in the example that uses Train's data. As far as interpretations are concerned, yes, the estimated coefficients are mean WTP values.

[Nicole Nimlos]

I got the marginal WTP and the confidence intervals when I ran the mixologitwtp command with 1 attribute at a time - aka I ran the command 6 different times with each of my 6 different attributes. When I ran them all together, I got very high WTP that don't make sense in my case. Also I didn't convert the tax to a negative, and it worked, so I'm not sure if that makes a difference.
It worked for 4 of the 6, however, when I run 2 of the attributes the iterations just keep going (they are all not concave) and I don't up ever getting any results. I looked into the nlcom coding but I'm not sure how to use it in this case. Any help with this? Thanks.

[Andrew Musau]

Also I didn't convert the tax to a negative, and it worked, so I'm not sure if that makes a difference.

It's not a question of it working. Check the distribution of the tax variable. Are negative taxes possible?

sum Tax

I looked into the nlcom coding but I'm not sure how to use it in this case. Any help with this? Thanks.

Resolve the above point first, then attempt the estimation and once you have the estimates, you can move to this. The nlcom transformation is necessary only if you assumed that the tax variable follows a lognormal distribution.

[Nicole Nimlos]

The distribution of taxes is positive, from 0 to 100, so negative taxes aren't possible. When I run all the attributes in the mixlogitwtp command, it doesn't converge. But when I ran the attributes individually in that command, I was able to get results for 4 out of the 6 attributes. However, 2 of the attributes iterations just keep going (they are all not concave) and I don't up ever getting any results. This is what I need help with. Mixlogitwtp command worked for 4 of 6 attributes when I ran them separately.

[Andrew Musau]

So clearly you cannot assume that the tax variable follows a normal distribution as its values are non-negative. The correct implementation should be to use negative tax.

g mtax= -Tax

Then try with "mtax" as the price variable. Beyond that, if you are still experiencing convergence problems, it is difficult to help as we do not have access to your data and cannot tell what is causing problems. You will need to consult with someone who has access to your data and has knowledge of estimation of such models. However, this thread remains open and there may be others who may still be helpful given the information that you have provided.

[Nicole Nimlos]

UPDATE: I was able to get it with this coding:

mixlogitwtp Select, group(groupid) price(Tax) rand(optout quail_rec tort_rec water_med water_high scenic_med scenic_high) id(Respondent)

where "Tax" is the tax payment multiple by -1