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Re: st: After non-convergence with xtmixed

From   [email protected] (Roberto G. Gutierrez, StataCorp)
To   [email protected]
Subject   Re: st: After non-convergence with xtmixed
Date   Wed, 02 Jan 2008 16:29:09 -0600

In response to Maarten Buis <[email protected]>, Clyde Schechter
follows up on his original question:

> I wasn't actually thinking about using the results of an uncompleted attempt
> at estimation as a final result to report in a paper.  It was precisely for
> the purpose of diagnosing what is wrong with the model that I thought the
> results corresponding to the final state of the gradient-based estimation
> might be more helpful than the final EM-iteration results.

> In particular, in addition to the kinds of modeling problems Maarten pointed
> out, xtmixed can fail to converge because of a boundary problem when one of
> the random effects being estimated is close to zero.  In some of my models
> this might be the case.  But the final EM results may be fairly far from the
> correct values and could fail to display this problem, could they not?

> Of course, it is simple enough to re-estimate the model leaving out the
> suspected offending random effect.  But the fact that the reduced model
> converges isn't really evidence that the omitted component is close to zero,
> is it?  So I'm left not really knowing if the reduced model is adequate.

> That's why I thought that seeing the estimates based on the incomplete
> gradient-estimation would be more helpful, because typically the log
> likelihood ratio is much bigger and I would imagine that the corresponding
> random effect estimate would be a better way to judge if I'm up against a
> boundary problem.

While it is true that in well-conditioned problems Newton-Raphson iterations
converge faster to the optimum, in cases where you have problem likelihoods
resulting in many "non-concave" or otherwise unproductive iterations the
benefits of Newton-Raphson pretty much go out the window.  When this occurs, a
Newton-Raphson (NR) iteration is not necessarily any better than one using EM
and, in fact, since NR depends on an inverse Hessian for stepping it may be
even worse if the Hessian is near singular.

The fact that you regularly get a greater log-likelhood with NR may be because
NR benefits from using the terminal EM iteration as a starting point.  By
default, -xtmixed- EM iterations stop at 20 even if convergence has not been
achieved, but you can increase the number of EM iterations with option
-emiterate()-.  Since EM iterations are much faster, using more of them comes
at little computational cost, with the benefit that you can achieve a higher
log-likelihood by iterating more.  Then you can have estimates that better
help you diagnose the problem with the model.

[email protected]
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