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st: RE: how to turn off the concavity criterion for -moptimize-

From   "Verkuilen, Jay" <[email protected]>
To   "'[email protected]'" <[email protected]>
Subject   st: RE: how to turn off the concavity criterion for -moptimize-
Date   Fri, 22 Jan 2010 16:00:41 -0500

László Sándor wrote:

>my algorithm needs to invoke -moptimize- multiple times, and I'd like
to make it ignore the concavity criterion (for maximization) in the
early calls. There does not seem to be an option for that. Is there
any other way? My justfication: I expect numerical problems with the numerical
differentiation, and as my algorithm makes some some changes from the
supposed optimum before attempting another maximization, I'm OK with
only the last 'optimum' being in a significantly concave region.<

I'm not sure if any of these make any sense but can you:

(1) Turn off concavity entirely and try to get a sense of what reasonable starting values are for your process? In short, explore more of the likelihood space in the same basic manner as "protect" optimizations do in -factor- (or several other Stata procedures). 

(2) Recast the objective function in a way that imposes some kind of smoothness penalty/prior to make it more regular? For instance, many models have frequent concavity violations but given a very gentle smoothing, everything works out. Classic example: A relatively high dimensional table, which is pretty much guaranteed to be sparse, which creates misfit and lack of concavity due to expected values approaching 0. Even a little flattening goes a long way in this case. 

What's the nature of the concavity violation that you are getting? 

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