# Re: st: Double bounded WTP

 From "Arne Risa Hole" <[email protected]> To [email protected] Subject Re: st: Double bounded WTP Date Tue, 4 Dec 2007 22:25:03 +0000

```Hi Henrik,

Take a look at "Maximum Likelihood Estimation with Stata" by William
Gould, Jeffrey Pitblado and William Sribney
<http://stata-press.com/books/ml.html>. It should be fairly
straightforward to extend the logit example in the book to the
double-bounded CV model you outlined.

Hope this helps.

Arne

On 04/12/2007, Henrik Andersson <[email protected]> wrote:
> 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
>
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>
>
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