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RE: Re: st: After non-convergence with xtmixed

From   "Verkuilen, Jay" <[email protected]>
To   <[email protected]>
Subject   RE: Re: st: After non-convergence with xtmixed
Date   Thu, 3 Jan 2008 09:42:30 -0500

>>Thanks to Bobby Gutierrez for suggesting using the emiterate() 
option.  It's working out rather well.  It took a very large number 
of EM iterations to get the log likelihood-ratio into the 
neighborhood where NR bogs down--but they do run very fast and the 
total time to get there is far lower.  And, at least for the problem 
that prompted my original post, the new results do confirm that I'm 
trying to estimate a variance component that is very close to 
zero--something I could not tell from the earlier output.<<

NR is a fantastic algorithm when you are very close to the solution because it converges quadratically, but NR steps far from the solution are dubious. 

You can ask for more information during iteration---I highly recommend it. You can also ask for the model to be fit by EM only. Another thing to check is to ask for the Hessian. Since the Hessian is what NR is using to compute its updates, if the Hessian seems strange, that can be a sign of problems. See Max Options. You may want to take a look a the box in Stata's window interface, as it lays out all the options. 

That said, at least in my experience the most common likely problem when fitting a variance component model that requires many iterations is that you have a variance component near 0. This seems to mess up every estimation method. Simulation methods like MCMC end up having huge autocorrelation even, numerical methods take forever and often iterate to a singular Hessian, etc.... All sign of the same basic problem: You don't know much about a very small random effect. Informative priors and other penalty/smoothing methods help a little, but are usually just a bandaid. 



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