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

From   tshmak <>
To   "" <>
Subject   st: Is it possible that Stata converges to a local maximum in maximum likelihood related procedures?
Date   Mon, 10 Jun 2013 18:04:00 +0800

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: 

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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