Re: st: ml maximize works if ml check is run first but hits a discontinuous region otherwise Poi TSP

["Brian P. Poi" <brian@poiholdings.com>]

On 05/05/2011 11:58 PM, Alex Olssen wrote:
> Dear Statlisters,
>
> I am in the process of reproducing the results from Berndt and Savin's
> 1975 Econometrica estimation of a singular system of equations with
> autoregressive errors in Stata using manual maximum likelihood.
>
> Poi's stata help desk articles have been of invaluable assistance.
>
> I have noticed something odd.
>
> For my estimation of model 7 in table 1
>
> If I run the sequence
>
> ml model d0 ...
> ml check
> ml maximize
>
> everything runs fine and the results are similar to those in Berndt and Savin.
>
> If I run the sequence
>
> ml model d0 ...
> ml maximize
>
> Stata hits a discontinuous region.
>
> Any ideas what is going on here?

-ml- might be making use of random numbers in its search for initial 
values when checking and maximizing your likelihood function.  When you 
run -ml check- before -ml maximize-, the first random number that -ml 
maximize- would therefore be different than when you call -ml maximize- 
without having called -ml check-.

Have you tried using -ml search- before -ml maximize-?  -ml search- does 
a more thorough search for initial values than -ml maximize- does by 
itself.  Also, did -ml check- issue some kind of message indicating it 
was going to call -ml search-?

> Also, for model 8, my maximum likelihood procedure in Stata reproduces
> Berndt and Savin's coefficients to only 2 decimal places - at the 3rd
> decimal place there are often differences.
> Standard errors are reproduced more accurately.
>
> Does anyone have any ideas what is happening here either?  I have seen
> somebody reproduce one part of Berndt and Savin in TSP and their
> results were much closer - the paper was originally done in TSP.
>
> Kind regards,
>
> Alex

Have you tried specifying initial values?  Getting different packages to 
produce the same estimates with difficult problems can itself be a 
difficult problem.  You could try playing with different optimization 
techniques, convergence criteria, etc., though that is no guarantee. 
I've found that sometimes having a small dataset makes matching results 
even more difficult than if the dataset were larger.

One final thought: for estimating a system of nonlinear equations, even 
singular systems, you might try using -nlsur- instead.  It's much faster 
on these problems.  The reference manual entry for -nlsur- shows how to 
fit an AIDS model, and my article from 2008 in the Stata Journal (v. 8 
number 4) shows how to replicate the results in my old helpdesk article 
using -nlsur-.

   -- Brian Poi
   -- brian@poiholdings.com
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