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st: Double bounded WTP


From   "Henrik Andersson" <henrik.andersson@vti.se>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Double bounded WTP
Date   Tue, 4 Dec 2007 22:31:28 +0100

Hi,

I would to maximize the likelihood function for interval data from a dichotomous stated preference study. In this kind of study respondents are first asked if they are accepting to pay a certain bid (bid0). Depending on their answer they are then asked whether they accept a second higher bid (bid1) if they answered yes to the first question and a second lower bid if they answered no (bid 2).

My log likelihood is made up of four parts and is given by

LL=-{
YY*ln(1+exp(-($a+$c*bid1+`Xb')))
+NN*ln(exp(-($a+$c*bid2+`Xb')))/(1+exp(-($a+$c*bid2+`Xb')))
+YN*ln((exp(-($a+$c*bid1+`Xb')))/(1+exp(-($a+$c*bid1+`Xb')))-(exp(-($a+$c*bid0+`Xb')))/(1+exp(-($a+$c*bid0+`Xb'))))
+NY*ln((exp(-($a+$c*bid0+`Xb')))/(1+exp(-($a+$c*bid0+`Xb')))-(exp(-($a+$c*bid2+`Xb')))/(1+exp(-($a+$c*bid2+`Xb'))))}

where

YY = variable that defines respondent who has answered yes to initial and follow-up bid
NN = variable that defines respondent who has answered no to initial and follow-up bid
YN = variable that defines respondent who has answered yes to initial but no follow-up bid
NY = variable that defines respondent who has answered no to initial but yes follow-up bid

bid0=initial bid level
bid1= follow-up bid (2*bid0)
bid2= follow-up bid (bid0/2)

X = other covariates
a, b, and c = parameters

The variables YY, NN, YN, and NY can be defined as both dummies or a continuous variable. The intervals for the bid levels may overlap since the initial bid level is varied among respondents.

My experience from programming in Stata is very limited (close to nonexisting) so I don't know if what I want to do is trivial to solve, or if it is not possible to do. I would be very grateful for any help.

Thank you 

Henrik

Corresponding address Sep 2007 until May 2008:
Henrik Andersson 
Program in Health Decision Science
Harvard School of Public Health
718 Huntington Avenue, 2nd Floor
Boston, MA  02115-5924
phone +1-617-432-0394
fax: +1-617-432-0190
email: handerss@hsph.harvard.edu	
www.healthdecisionscience.hsph.harvard.edu	

Permanent address:
vti
Henrik Andersson 
Researcher, PhD
Dept. of Transport Economics
Post: VTI / P.O. Box 55685 / SE-102 15 Stockholm / Sweden 
Visit: Lindstedtsvägen 24 / KTH Campus Vallhallavägen
Tel: +46-13-20 40 00 
Direct: +46-8-555 770 27 
Fax: +46-8-28 50 43
E-mail: henrik.andersson@vti.se / www.vti.se/henrik	
www.vti.se	



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