st: WTP distribution with LN Cost coefficient

["Heidi Pitts" <hmpitts@salud.unm.edu>]

Hi Stata users,
Can anyone help me with a couple of issues regarding estimating WTP distributions using lognormally distributed coefficients?  I'm trying to estimate WTP distributions for two mixed logit models with two normally distributed and three lognormally distributed coefficients as well as two Cost*Income interaction terms.
 
Model 1
mixlogit choice Notify FreqLen, rand(Reuse Green negLength negFreq negCost) ln(3) group(newid) id(userid2) nrep(500) robust

Model 2:  adds the Cost*Income terms
mixlogit choice Notify FreqLen Cost_IncHi Cost_IncMed, rand(Reuse Green negLength negFreq negCost) ln(3) group(newid) id(userid2) nrep(500) robust

I calculate the mean/median/standard deviation for the lognormally distributed coefficients using Revelt and Train (1998).  The code is 
nlcom (mean_freq: -1*exp([Mean]_b[negFreq]+0.5*[SD]_b[negFreq]^2))(med_freq: -1*exp([Mean]_b[negFreq]))(sd_freq: exp([Mean]_b[negFreq]+0.5*[SD]_b[negFreq]^2)* sqrt(exp([SD]_b[negFreq]^2)-1))
 
So my questions are:
 
1.   How do I transform the lognormal coefficients first and then get the mixlbeta individual-level coefficients for all the parameters?   Because if  I have the individual-level coefficients for each person conditional on their previous choices, I could calculate their WTP, then sort it and take the values at 0.05 and 0.95 as my 90% confidence interval.
 
2.  Or do I transform the three lognormally distributed variables (Length, Freq, Cost) before using the mixlogit command and then just estimate everything normally distributed?
 
3.  If I calculate the mean of Leng, Freq, Cost and then save a matrix (Tmeans) using these means and the other means estimated by the model, how would I create the variance covariance matrix?  Then I could use the following command:  drawnorm b_Notify b_FreqLen b_Reuse b_Green b_negLength b_negFreq b_negCost, means(Tmeans) cov(e(V)) n(1000) seed(12345)
 
I appreciate, in advance, any suggestions.
 
Thank you.
Best,
Heidi Pitts
Ph.D. candidate
Department of Economics
University of New Mexico
  


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