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Re: st: Maximising likelihoods that do not meet the linear-form restrictions


From   jpitblado@stata.com (Jeff Pitblado, StataCorp LP)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Maximising likelihoods that do not meet the linear-form restrictions
Date   Fri, 04 Aug 2006 21:03:26 -0500

Arne Risa Hole <arnehole@gmail.com> has a question/suggestion
regarding the quasi Newton techniques in the -ml- command: 

> I was wondering if anyone knows whether StataCorp has considered
> extending the functionality of the -ml- command to allow the
> alternative optimisation algorithms (BHHH etc) to be used to maximise
> likelihoods that do not meet the linear-form restrictions.

> My understanding is that at the moment the only way these algorithms
> can be used is to pass the equation scores to -ml- as g1, g2 etc. and
> that this only works if each observation contains a score.

I believe Arne is referring to BHHH, BFGS, and DFP.  Of which, only BHHH
requires equation-level scores from the 'd1' and 'd2' likelihood evaluators
(BHHH works automatically with 'lf' evaluators, and not at all for 'd0'
evaluators).

BFGS and DFP do not require equation-level scores; they work directly with the
gradient vector to build up their own version of a Hessian-type matrix.

> One useful extension would be to allow the possibility of passing the
> values of the likelihood differentiated with respect to the
> coefficients (instead of the equations/ index functions) directly to
> -ml-. Then the observations containing the scores for the groups of
> observations could be identified using "if==`last'", or something
> similar.

> I have used this approach along with matrix accum to create the outer
> product of gradient matrix. Setting `negH' equal to this matrix
> produces a "homemade" BHHH procedure which seems to work fine, but it
> would be nice to also be able to use the other algorithms.

Arne has devised a way around -ml-'s above restriction on BHHH by making the
likelihood evaluator produce the OPG.

--Jeff
jpitblado@stata.com
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