# RE: st: Non-linear MLE programming + inequality constraints

 From "Nick Cox" To Subject RE: st: Non-linear MLE programming + inequality constraints Date Thu, 1 Feb 2007 14:37:45 -0000

```I think the objection to that is that it is
dimensionally unbalanced. That is, X2 and
whatever is added to it should have the same units
and the same dimensions. (Perhaps economists don't
care about these things, but my wannabe physicist
persona does.)

That would be achieved by fixing it to

ln(X2 + beta * exp(alpha))

but then we are back where we started, because
unless beta emerges as positive from estimation
without constraint, the logarithm
of the sum is not guaranteed to be determinate
for all X2. And if we are going to do that,
we might as well be working with

ln(X2 + alpha)

as originally mentioned.

Nick
n.j.cox@durham.ac.uk

Rodrigo A. Alfaro

> following Maarten suggestion:
> lnY=B0+B1*lnX1+B2*ln (X2+exp(alpha))+epsilon??
>
> Maarten buis
>
> > There is no command in Stata that enables you to use an inequality
> > constraint. There are tricks you can use. For instance: A
> > variance must
> > be larger then zero, so instead of maximizing the variance you can
> > maximize the ln(variance), a proportion must remain between zero and
> > one, so instead of maximizing the proportion one can maximize
> > the logit
> > of the proportion, a correlation must stay between -1 and 1
> > of maximizing the correlation one can maximize the Fisher Z
> > transformed
> > correlation.
> >
> > However, Nick just explained that you do not need to do that, and I
> > agree. Adding some constant to a variable so that the log doesn't
> > become zero is making an error, maybe or maybe not a necessary error
> > but still an error, why do you expect your data to be able to inform
> > you about an error?
>

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```