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Re: st: Is it possible that Stata converges to a local maximum in maximum likelihood related procedures?


From   Nick Cox <njcoxstata@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Is it possible that Stata converges to a local maximum in maximum likelihood related procedures?
Date   Mon, 10 Jun 2013 11:24:13 +0100

Short answer: Yes, it's possible, but much of the machinery of -ml- is
designed to make it unlikely. But the more complicated your model, and
the more it is a strain for your data, the more likely that models are
difficult to fit. Some people regard it as a folk theorem that a valid
model is easy to fit.

GAM: much is a matter of taste, but whereas this looked like an
up-and-coming thing in 1990, I think statistics has not moved much in
that direction since then. The Stata philosophy is to support splines
and fractional polynomials.

Nick
njcoxstata@gmail.com


On 10 June 2013 11:04, tshmak <tshmak@hku.hk> wrote:
> Hi list,
>
> Apologies that this may not be so much a Stata question as a general statistics one. However, given that multilevel models appear to be a huge part of the new development in Stata 13, I think this question may be of interest to many users of Stata. In particular, my concern is that if I run a maximum likelihood related procedure in Stata and find converged results, is it possible that the estimates are in fact from a local maximum?
>
> Prior to this post, I did a simple search on Google, and found the following paper:
>
> http://www.jstor.org/stable/2335080
>
> which showed that the likelihood function for GLM using certain commonly used link function is concave, and therefore in these cases, we can be pretty certain that any local maximum found must be a global one also. However, beyond this, I have not been able to identify literature giving proofs for more complicated models, such as mixed effects models, zero-inflated models, and quasi-likelihood models. Yet, in practice, it does not appear that multiple local maxima is a frequently encountered problem. (I haven't encountered any papers reporting such problems using these standard techniques, at least.) And no one seems to ever mention the need to re-run estimation from different initial values.
>
> Perhaps these results are fairly well known and the problem is simply my ignorance in ml, and if so, your help in illuminating me would be most appreciated. On a related note, I have wondered why GAM has never been part of official Stata and whether it might be related to convergence issues such as these.
>
> Thanks for your help.
>
>
> Timothy Mak
> School of Public Health
> The University of Hong Kong
>
> Tel 852 2819 9914
> Fax 852 2855 9528
>
>
>
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