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# Re: st: Regression analysis with a minimum function on the RHS

 From sjsamuels@gmail.com To statalist@hsphsun2.harvard.edu Subject Re: st: Regression analysis with a minimum function on the RHS Date Fri, 5 Mar 2010 14:42:52 -0500

```How about this approach?
1. run -sureg- to fit the regressions separately on x1 and x2.  Apply
-constraint- first to get equal intercepts.
2. Use b0 + b1*X1  where   b1*x1 < b2*x2;  otherwise use b2*x2.

Steve

On Fri, Mar 5, 2010 at 2:14 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> Sebastian van Baal <s.vanbaal@arcor.de> :
> This seems likely to be problematic no matter what you do--typically
> the objective function should be differentiable in the parameters in
> these kinds of problems.  What is the theory that drives this
> specification?  Is there an alternative parameterization that is
> differentiable?
>
> On Fri, Mar 5, 2010 at 10:51 AM, Sebastian van Baal <s.vanbaal@arcor.de> wrote:
>> Dear Stata Users:
>>
>> I attempt to fit a regression model that has a minimum function on the
>> right-hand side. My current working solution is to use nonlinear least
>> squares:
>>
>> . nl ( y = {b0} + min({b1}*x1 , {b2}*x2) )
>>
>> Being admittedly unexperienced with nonlinear least squares, I am unsure if
>> this is correct. I have not seen an application of nonlinear least squares
>> (or any other form of regression analysis) involving a minimum function.
>> Would you say that is the correct way to proceed?
>>
>> Advance thanks for any hints you can give me.
>>
>> Sebastian van Baal
>> Cologne, Germany
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--
Steven Samuels
sjsamuels@gmail.com
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```