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st: Re: xtnbreg - same results after convergence at 9,000 iterations or limiting to 100 iterations


From   Gordon Hughes <G.A.Hughes@ed.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: xtnbreg - same results after convergence at 9,000 iterations or limiting to 100 iterations
Date   Sat, 08 Jun 2013 09:31:57 +0100

A somewhat belated response since no-one has picked this up.

I am not familiar with the programming details of -xtnbreg- but the strategy is obvious. It is common to generate good starting values for difficult ML procedures by estimating a restricted version of the model, whose parameters can be used a starting values for maximising the more general likelihood function. This is what -xtnbreg- is doing. The problem for you is that the restricted model, usually assumed to be easy to maximise, is in fact degenerate or very nearly degenerate. Hence the initial maximisation stage is taking a very long time to find a maximum, which may not even exist. However, once you feed any plausible set of starting values to the full maximisation, the procedure converges rapidly. The -xtnbreg- procedure appears to be unusual because it goes through the process of generating starting values in two steps. The degeneracy that is causing problems is in the first step and disappears at the second step, which produces good starting values for the final stage of full maximisation.

The lesson to draw is that it is rarely, if ever, worth allowing the first stage of a multi-stage maximisation to run for a lot of iterations, unless you happen to be interested in the results of the first stage. You should consider the possibility that your model is not well-defined because failure or close to failure in estimating a simple version of the model may be a warning that the results from a more complex version are merely the by-product of assumptions that you have imposed rather than the information in your sample.

Gordon Hughes
g.a.hughes@ed.ac.uk
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