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Re: st: Convergence with Mata -optimize()-, bfgs
Glenn Goldsmith <[email protected]> asks whether he can trust
convergence using -optimize()- in mata when the final iteration issues a
"backed up" message.
> Occasionally, when fitting a model using Mata's -optimize()- routine
> (and the bfgs technique), the algorithm reaches convergence, but
> issues a "backed up" message at the final iteration. Can I trust the
> results of convergence in this case, or should I be concerned that
> the algorithm may just have backed up to a numerically identical
> point (as per http://www.stata.com/support/faqs/stat/ml.html)?
The short answer is yes, Glenn can trust the results.
The FAQ that Glenn mentions is kept on our website for historical reasons.
The first line of the FAQ is important.
"Note: This FAQ is for users of releases prior to Stata 6. It is not
relevant for more recent versions."
Given the increasingly difficult optimizations that we and others were doing,
we introduced a true convergence criterion in Stata 7. This criterion
supplements the more traditional stopping methods that test whether the
optimization criterion or the parameters are changing from iteration to
iteration. This criterion is used by both -ml- and Mata's -optimize()-.
For Stata to declare convergence, the Hessian must be positive definite and the
gradient vector must be effectively zero when scaled by the shape of the
likelihood (or other convergence criterion) in the neighborhood of the current
solution. Collectively, these two conditions define a maximum or minimum.
See "optimize_init_conv_ptol()" in -help mf_optimize" or in [M-5] optimize for
more details.
The "backed up" message is most useful during intermediate steps in the
optimization. If "backed up" is reported on most of your steps then your
likelihood is difficult and perhaps your model is not identified. At a
minimum, it indicates the the method of taking steps is consistently fooled by
the shape of the likelihood. If backed up occurs at the final step, it just
means that you were very close to convergence before the final step was
attempted.
-- Vince
[email protected]
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