How to write the nonlinear least squares syntax when the equation involves taking minimum?

[Ting Jiang]

Dear all,

My data set contains variables Y and X1, X2, X3, and I would like to estimate the following model:

Y= a + b * min {c1 * X1, c2 * X2, c3 * X3} + epsilon

where a, b, and c1, c2, c3 are parameters to be estimated, and epsilon is the error term.

I'm wondering how this can be done in Stata? How shall I write the -nl- syntax?

Thanks!

[Nick Cox]

At a guess

 
nl (Y = {a} + {b} * min({c1}*X1, {c2}*X2, {c3}*X3))

The Laws of nl:

1. Nonlinear models are difficult to fit.
2. Nonlinear models are difficult to fit, even if you know Law 1.
3. ...

[Ting Jiang]

It worked. Thanks a lot, Nick. Now I'm regretting I should have tried it before posting the question since the answer is so straightforward...

[Nick Cox]

It never stops. All my mistakes and bugs are trivial too once I work out what they are.