# RE: st: nonlinear constraints

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject RE: st: nonlinear constraints Date Wed, 14 Feb 2007 12:57:33 +0000 (GMT)

```--- Nick Cox <n.j.cox@durham.ac.uk> wrote:
> Just looking at this, I see scope for some simplifications:
> In the line
>
>           quietly replace `lnf' = ln(exp(`theta')/(1+exp(`theta')))
> if \$ML_y1==1
>
> the log of a ratio is the difference of the logs
>
> 	= ln(exp(`theta')) - ln(1 + exp(`theta')) if \$ML_y1 == 1
>
> but then the first term simplifies too:
>
> 	= `theta' - ln(1 + exp(`theta')) if \$ML_y1 == 1
>
> A similar story below:
>
>           quietly replace `lnf' = ln(1/(1+exp(`theta'))) if \$ML_y1==0
>
> 	= ln(1) - ln(1+exp(`theta')) if \$ML_y1==0
> 	= - ln(1+exp(`theta')) if \$ML_y1==0
>

In my tweak of this program I replaced the lines:
quietly replace `lnf' = ln(exp(`theta')/(1+exp(`theta'))) if \$ML_y1==1
quietly replace `lnf' = ln(1/(1+exp(`theta'))) if \$ML_y1==0

with:
quietly replace `lnf' = ln(invlogit( `theta')) if \$ML_y1==1
quietly replace `lnf' = ln(invlogit(-`theta')) if \$ML_y1==0

I've done this for two reasons:
1) It is less typing so less chance of a typo
2) I tend to trust the numerical properties of Stata functions more
then my own renderings of those functions.

However my experience mirrors that of Richard's in that replacing
gen `theta' = ...
by
gen double `theta' = ...
has a much bigger effect on the speed of convergence.

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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